move geometry to geometry2d and add new geometry module (3d)
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# Sphinx build info version 1
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# Sphinx build info version 1
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# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
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config: aaf67f6f94ce2e6ce3750a4b226f6461
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tags: 645f666f9bcd5a90fca523b33c5a78b7
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tags: 645f666f9bcd5a90fca523b33c5a78b7
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<!DOCTYPE html>
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<html xmlns="http://www.w3.org/1999/xhtml">
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<head>
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<meta charset="utf-8" />
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<title>data — pylib 2019.5.19 documentation</title>
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<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
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<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
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<meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
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</head><body>
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<div class="document">
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<div class="documentwrapper">
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<div class="body" role="main">
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<h1>Source code for data</h1><div class="highlight"><pre>
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<span></span><span class="ch">#!/usr/bin/env python</span>
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<span class="c1"># -*- coding: utf-8 -*-</span>
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<span class="sd">"""Read and write data to or from file and manipulate data structures.</span>
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<span class="sd">:Date: 2019-10-11</span>
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<span class="sd">.. module:: data</span>
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<span class="sd"> :platform: *nix, Windows</span>
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<span class="sd"> :synopsis: Handle data files and structures.</span>
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<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
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<span class="sd">"""</span>
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<span class="kn">import</span> <span class="nn">math</span>
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<span class="kn">import</span> <span class="nn">pickle</span>
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<div class="viewcode-block" id="read"><a class="viewcode-back" href="../data.html#data.read">[docs]</a><span class="k">def</span> <span class="nf">read</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">x_column</span><span class="p">,</span> <span class="n">y_column</span><span class="p">,</span> <span class="n">default</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
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<span class="sd">"""Read ascii data file.</span>
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<span class="sd"> :param filename: file to read</span>
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<span class="sd"> :type filename: str</span>
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<span class="sd"> :param x_column: column index for the x data (first column is 0)</span>
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<span class="sd"> :type x_column: int</span>
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<span class="sd"> :param y_column: column index for the y data (first column is 0)</span>
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<span class="sd"> :type y_column: int</span>
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<span class="sd"> :param default: return object if data loading fails</span>
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||||||
<span class="sd"> :type default: object</span>
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||||||
<span class="sd"> :param verbose: verbose information (default = False)</span>
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<span class="sd"> :type verbose: bool</span>
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||||||
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<span class="sd"> :returns: x and y</span>
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<span class="sd"> :rtype: tuple(list, list)</span>
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<span class="sd"> """</span>
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<span class="kn">import</span> <span class="nn">re</span>
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<span class="n">x</span> <span class="o">=</span> <span class="n">default</span>
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<span class="n">y</span> <span class="o">=</span> <span class="n">default</span>
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<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
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<span class="nb">print</span><span class="p">(</span><span class="s1">'check if data is available'</span><span class="p">)</span>
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<span class="k">try</span><span class="p">:</span>
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<span class="n">file</span> <span class="o">=</span> <span class="nb">open</span><span class="p">(</span><span class="n">file_name</span><span class="p">)</span>
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<span class="n">x</span> <span class="o">=</span> <span class="p">[]</span>
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<span class="n">y</span> <span class="o">=</span> <span class="p">[]</span>
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<span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">file</span><span class="p">:</span>
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<span class="n">fields</span> <span class="o">=</span> <span class="n">re</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="sa">r</span><span class="s1">'\s+'</span><span class="p">,</span> <span class="n">row</span><span class="o">.</span><span class="n">strip</span><span class="p">())</span>
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<span class="n">x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">fields</span><span class="p">[</span><span class="n">x_column</span><span class="p">]))</span>
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<span class="n">y</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">fields</span><span class="p">[</span><span class="n">y_column</span><span class="p">]))</span>
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<span class="n">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
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<span class="k">except</span> <span class="ne">IOError</span><span class="p">:</span>
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<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
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<span class="nb">print</span><span class="p">(</span><span class="s1">'data file not found'</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></div>
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<div class="viewcode-block" id="write"><a class="viewcode-back" href="../data.html#data.write">[docs]</a><span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">data</span><span class="p">):</span>
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<span class="sd">"""Write ascii file.</span>
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<span class="sd"> :param file_name: file to write</span>
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<span class="sd"> :type file_name: str</span>
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<span class="sd"> :param data: data to write</span>
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<span class="sd"> :type data: str</span>
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<span class="sd"> """</span>
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<span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="s1">'w'</span><span class="p">)</span> <span class="k">as</span> <span class="n">file</span><span class="p">:</span>
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<span class="n">file</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="n">data</span><span class="p">)</span></div>
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<div class="viewcode-block" id="load"><a class="viewcode-back" href="../data.html#data.load">[docs]</a><span class="k">def</span> <span class="nf">load</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">default</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
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<span class="sd">"""Load stored program objects from binary file.</span>
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||||||
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<span class="sd"> :param file_name: file to load</span>
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||||||
<span class="sd"> :type file_name: str</span>
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||||||
<span class="sd"> :param default: return object if data loading fails</span>
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||||||
<span class="sd"> :type default: object</span>
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||||||
<span class="sd"> :param verbose: verbose information (default = False)</span>
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||||||
<span class="sd"> :type verbose: bool</span>
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||||||
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||||||
<span class="sd"> :returns: loaded data</span>
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||||||
<span class="sd"> :rtype: object</span>
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||||||
<span class="sd"> """</span>
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||||||
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
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||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'check if data is available'</span><span class="p">)</span>
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||||||
<span class="k">try</span><span class="p">:</span>
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||||||
<span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="s1">'rb'</span><span class="p">)</span> <span class="k">as</span> <span class="nb">input</span><span class="p">:</span>
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||||||
<span class="c1"># one load for every dump is needed to load all the data</span>
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||||||
<span class="n">object_data</span> <span class="o">=</span> <span class="n">pickle</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
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<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
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||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'found:'</span><span class="p">)</span>
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||||||
<span class="nb">print</span><span class="p">(</span><span class="n">object_data</span><span class="p">)</span>
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<span class="k">except</span> <span class="ne">IOError</span><span class="p">:</span>
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||||||
<span class="n">object_data</span> <span class="o">=</span> <span class="n">default</span>
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<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
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<span class="nb">print</span><span class="p">(</span><span class="s1">'no saved datas found'</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">object_data</span></div>
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<div class="viewcode-block" id="store"><a class="viewcode-back" href="../data.html#data.store">[docs]</a><span class="k">def</span> <span class="nf">store</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">object_data</span><span class="p">):</span>
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||||||
<span class="sd">"""Store program objects to binary file.</span>
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||||||
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||||||
<span class="sd"> :param file_name: file to store</span>
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||||||
<span class="sd"> :type file_name: str</span>
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||||||
<span class="sd"> :param object_data: data to store</span>
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||||||
<span class="sd"> :type object_data: object</span>
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||||||
<span class="sd"> """</span>
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||||||
<span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="s1">'wb'</span><span class="p">)</span> <span class="k">as</span> <span class="n">output</span><span class="p">:</span>
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||||||
<span class="c1"># every dump needs a load</span>
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||||||
<span class="n">pickle</span><span class="o">.</span><span class="n">dump</span><span class="p">(</span><span class="n">object_data</span><span class="p">,</span> <span class="n">output</span><span class="p">,</span> <span class="n">pickle</span><span class="o">.</span><span class="n">HIGHEST_PROTOCOL</span><span class="p">)</span></div>
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||||||
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<div class="viewcode-block" id="fold_list"><a class="viewcode-back" href="../data.html#data.fold_list">[docs]</a><span class="k">def</span> <span class="nf">fold_list</span><span class="p">(</span><span class="n">lst</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
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<span class="sd">"""Convert one-dimensional kx1 array (list) to two-dimensional mxn</span>
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||||||
<span class="sd"> array. m = k / n</span>
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||||||
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<span class="sd"> :param lst: list to convert</span>
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||||||
<span class="sd"> :type lst: list</span>
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||||||
<span class="sd"> :param n: length of the second dimenson</span>
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<span class="sd"> :type n: int</span>
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||||||
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||||||
<span class="sd"> :returns: two-dimensional array (list of lists)</span>
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<span class="sd"> :rtype: list</span>
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<span class="sd"> """</span>
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<span class="n">k</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">lst</span><span class="p">)</span>
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||||||
<span class="k">if</span> <span class="n">k</span> <span class="o">%</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
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<span class="n">length</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">k</span><span class="o">/</span><span class="n">n</span><span class="p">)</span>
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<span class="k">return</span> <span class="p">[</span><span class="n">lst</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">n</span><span class="p">:</span><span class="n">i</span><span class="o">*</span><span class="n">n</span><span class="o">+</span><span class="n">n</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">length</span><span class="p">)]</span></div>
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<div class="viewcode-block" id="seq"><a class="viewcode-back" href="../data.html#data.seq">[docs]</a><span class="k">def</span> <span class="nf">seq</span><span class="p">(</span><span class="n">start</span><span class="p">,</span> <span class="n">stop</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">step</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Create an arithmetic bounded sequence.</span>
|
|
||||||
|
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||||||
<span class="sd"> The sequence is one of the following;</span>
|
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||||||
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|
||||||
<span class="sd"> - empty :math:`\{\}=\emptyset`, if start and stop are the same</span>
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||||||
<span class="sd"> - degenerate :math:`\{a\}`, if the sequence has only one element.</span>
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||||||
<span class="sd"> - left-close and right-open :math:`[a, b)`</span>
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|
||||||
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|
||||||
<span class="sd"> :param start: start of the sequence, the lower bound. If only start</span>
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||||||
<span class="sd"> is given than it is interpreted as stop and start will be 0.</span>
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|
||||||
<span class="sd"> :type start: int or float</span>
|
|
||||||
<span class="sd"> :param stop: stop of sequence, the upper bound.</span>
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|
||||||
<span class="sd"> :type stop: int or float</span>
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|
||||||
<span class="sd"> :param step: step size, the common difference (constant difference</span>
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|
||||||
<span class="sd"> between consecutive terms).</span>
|
|
||||||
<span class="sd"> :type step: int or float</span>
|
|
||||||
<span class="sd"> :returns: arithmetic bounded sequence</span>
|
|
||||||
<span class="sd"> :rtype: list</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="c1"># example of seq(4, 0, -0.4)</span>
|
|
||||||
<span class="c1"># without round:</span>
|
|
||||||
<span class="c1"># [4.0, 3.6, 3.2, 2.8, 2.4, 2.0, 1.5999999999999996,</span>
|
|
||||||
<span class="c1"># 1.1999999999999997, 0.7999999999999998, 0.3999999999999999]</span>
|
|
||||||
<span class="c1"># with round:</span>
|
|
||||||
<span class="c1"># [4.0, 3.6, 3.2, 2.8, 2.4, 2.0, 1.6, 1.2, 0.8, 0.4]</span>
|
|
||||||
<span class="c1"># example of seq(4, 0, -0.41)</span>
|
|
||||||
<span class="c1"># without round:</span>
|
|
||||||
<span class="c1"># [4.0, 3.59, 3.18, 2.77, 2.3600000000000003,</span>
|
|
||||||
<span class="c1"># 1.9500000000000002, 1.54, 1.1300000000000003,</span>
|
|
||||||
<span class="c1"># 0.7200000000000002, 0.31000000000000005]</span>
|
|
||||||
<span class="c1"># with round:</span>
|
|
||||||
<span class="c1"># [4.0, 3.59, 3.18, 2.77, 2.36, 1.95, 1.54, 1.13, 0.72, 0.31]</span>
|
|
||||||
<span class="k">if</span> <span class="n">stop</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
|
||||||
<span class="k">return</span> <span class="n">seq</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">start</span><span class="p">,</span> <span class="n">step</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">start_str</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="n">start</span><span class="p">)</span>
|
|
||||||
<span class="n">start_exp</span> <span class="o">=</span> <span class="mi">0</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'.'</span> <span class="ow">in</span> <span class="n">start_str</span><span class="p">:</span>
|
|
||||||
<span class="n">start_exp</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">start_str</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s1">'.'</span><span class="p">)[</span><span class="mi">1</span><span class="p">])</span>
|
|
||||||
|
|
||||||
<span class="n">step_str</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="n">step</span><span class="p">)</span>
|
|
||||||
<span class="n">step_exp</span> <span class="o">=</span> <span class="mi">0</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'.'</span> <span class="ow">in</span> <span class="n">step_str</span><span class="p">:</span>
|
|
||||||
<span class="n">step_exp</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">step_str</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s1">'.'</span><span class="p">)[</span><span class="mi">1</span><span class="p">])</span>
|
|
||||||
|
|
||||||
<span class="n">exponent</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">start_exp</span><span class="p">,</span> <span class="n">step_exp</span><span class="p">)</span> <span class="c1"># no stop because it is an open bound</span>
|
|
||||||
|
|
||||||
<span class="n">n</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">ceil</span><span class="p">((</span><span class="n">stop</span> <span class="o">-</span> <span class="n">start</span><span class="p">)</span><span class="o">/</span><span class="nb">float</span><span class="p">(</span><span class="n">step</span><span class="p">)))</span>
|
|
||||||
<span class="n">lst</span> <span class="o">=</span> <span class="p">[]</span>
|
|
||||||
<span class="k">if</span> <span class="n">n</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
|
|
||||||
<span class="n">lst</span> <span class="o">=</span> <span class="p">[</span><span class="nb">round</span><span class="p">(</span><span class="n">start</span> <span class="o">+</span> <span class="n">step</span><span class="o">*</span><span class="n">i</span><span class="p">,</span> <span class="n">exponent</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
|
|
||||||
<span class="k">return</span> <span class="n">lst</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="unique_ending"><a class="viewcode-back" href="../data.html#data.unique_ending">[docs]</a><span class="k">def</span> <span class="nf">unique_ending</span><span class="p">(</span><span class="n">ids</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""From id list get list with unique ending.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param ids: ids</span>
|
|
||||||
<span class="sd"> :type ids: list</span>
|
|
||||||
<span class="sd"> :param n: minumum chars or ints</span>
|
|
||||||
<span class="sd"> :type n: int</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: unique ending of ids</span>
|
|
||||||
<span class="sd"> :rtype: list</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">if</span> <span class="n">ids</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="n">idi</span><span class="p">[</span><span class="o">-</span><span class="n">n</span><span class="p">:]</span> <span class="k">for</span> <span class="n">idi</span> <span class="ow">in</span> <span class="n">ids</span><span class="p">]</span>
|
|
||||||
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">></span> <span class="nb">len</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">x</span><span class="p">)):</span>
|
|
||||||
<span class="k">return</span> <span class="n">unique_ending</span><span class="p">(</span><span class="n">ids</span><span class="p">,</span> <span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="k">else</span><span class="p">:</span>
|
|
||||||
<span class="k">return</span> <span class="n">x</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="get_id"><a class="viewcode-back" href="../data.html#data.get_id">[docs]</a><span class="k">def</span> <span class="nf">get_id</span><span class="p">(</span><span class="n">ids</span><span class="p">,</span> <span class="n">uide</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Get full id from unique id ending.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param ids: ids</span>
|
|
||||||
<span class="sd"> :type ids: list</span>
|
|
||||||
<span class="sd"> :param uide: unique id ending</span>
|
|
||||||
<span class="sd"> :type uide: str</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: full id</span>
|
|
||||||
<span class="sd"> :rtype: str or int</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="c1"># take first element, because we know it is a unique ending</span>
|
|
||||||
<span class="k">return</span> <span class="p">[</span><span class="n">idi</span> <span class="k">for</span> <span class="n">idi</span> <span class="ow">in</span> <span class="n">ids</span> <span class="k">if</span> <span class="n">idi</span><span class="o">.</span><span class="n">endswith</span><span class="p">(</span><span class="n">uide</span><span class="p">)][</span><span class="mi">0</span><span class="p">]</span></div>
|
|
||||||
</pre></div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
|
||||||
<div class="sphinxsidebarwrapper">
|
|
||||||
<h1 class="logo"><a href="../index.html">pylib</a></h1>
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
|
||||||
|
|
||||||
<div class="relations">
|
|
||||||
<h3>Related Topics</h3>
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|
||||||
<ul>
|
|
||||||
<li><a href="../index.html">Documentation overview</a><ul>
|
|
||||||
<li><a href="index.html">Module code</a><ul>
|
|
||||||
</ul></li>
|
|
||||||
</ul></li>
|
|
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</ul>
|
|
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</div>
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|
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<div id="searchbox" style="display: none" role="search">
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|
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<h3 id="searchlabel">Quick search</h3>
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<div class="searchformwrapper">
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<form class="search" action="../search.html" method="get">
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<input type="text" name="q" aria-labelledby="searchlabel" />
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<input type="submit" value="Go" />
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|
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<script type="text/javascript">$('#searchbox').show(0);</script>
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|
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|
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|
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|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
</div>
|
|
||||||
</div>
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|
||||||
<div class="clearer"></div>
|
|
||||||
</div>
|
|
||||||
<div class="footer">
|
|
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©2019, Daniel Weschke.
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|
||||||
|
|
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||||||
Powered by <a href="http://sphinx-doc.org/">Sphinx 2.2.1</a>
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|
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|
|
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|
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|
||||||
|
|
||||||
|
|
||||||
</body>
|
|
||||||
</html>
|
|
||||||
221
docs/build/html/_modules/date.html
vendored
221
docs/build/html/_modules/date.html
vendored
@@ -1,221 +0,0 @@
|
|||||||
|
|
||||||
<!DOCTYPE html>
|
|
||||||
|
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
|
||||||
<head>
|
|
||||||
<meta charset="utf-8" />
|
|
||||||
<title>date — pylib 2019.5.19 documentation</title>
|
|
||||||
<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
|
|
||||||
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
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<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
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<script type="text/javascript" id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script>
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<script type="text/javascript" src="../_static/jquery.js"></script>
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<script type="text/javascript" src="../_static/underscore.js"></script>
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<script type="text/javascript" src="../_static/language_data.js"></script>
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<script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
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<link rel="index" title="Index" href="../genindex.html" />
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<link rel="search" title="Search" href="../search.html" />
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|
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|
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<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
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||||||
|
|
||||||
|
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
|
|
||||||
|
|
||||||
</head><body>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="document">
|
|
||||||
<div class="documentwrapper">
|
|
||||||
<div class="bodywrapper">
|
|
||||||
|
|
||||||
|
|
||||||
<div class="body" role="main">
|
|
||||||
|
|
||||||
<h1>Source code for date</h1><div class="highlight"><pre>
|
|
||||||
<span></span><span class="ch">#!/usr/bin/env python</span>
|
|
||||||
<span class="c1"># -*- coding: utf-8 -*-</span>
|
|
||||||
<span class="sd">"""Calculate spacial dates.</span>
|
|
||||||
|
|
||||||
<span class="sd">:Date: 2018-01-15</span>
|
|
||||||
|
|
||||||
<span class="sd">.. module:: date</span>
|
|
||||||
<span class="sd"> :platform: *nix, Windows</span>
|
|
||||||
<span class="sd"> :synopsis: Special dates.</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
|
||||||
<span class="sd">"""</span>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="gaußsche_osterformel"><a class="viewcode-back" href="../date.html#date.gaußsche_osterformel">[docs]</a><span class="k">def</span> <span class="nf">gaußsche_osterformel</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Gaußsche Osterformel.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the Easter Sunday</span>
|
|
||||||
<span class="sd"> :type year: int</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the day of Easter Sunday as a day in march.</span>
|
|
||||||
<span class="sd"> :rtype: int</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :ivar X: Das Jahr / year</span>
|
|
||||||
<span class="sd"> :vartype X: int</span>
|
|
||||||
<span class="sd"> :ivar K(X): Die Säkularzahl</span>
|
|
||||||
<span class="sd"> :vartype K(X): int</span>
|
|
||||||
<span class="sd"> :ivar M(X): Die säkulare Mondschaltung</span>
|
|
||||||
<span class="sd"> :vartype M(X): int</span>
|
|
||||||
<span class="sd"> :ivar S(K): Die säkulare Sonnenschaltung</span>
|
|
||||||
<span class="sd"> :vartype S(K): int</span>
|
|
||||||
<span class="sd"> :ivar A(X): Den Mondparameter</span>
|
|
||||||
<span class="sd"> :vartype A(X): int</span>
|
|
||||||
<span class="sd"> :ivar D(A,M): Den Keim für den ersten Vollmond im Frühling</span>
|
|
||||||
<span class="sd"> :vartype D(A,M): int</span>
|
|
||||||
<span class="sd"> :ivar R(D,A): Die kalendarische Korrekturgröße</span>
|
|
||||||
<span class="sd"> :vartype R(D,A): int</span>
|
|
||||||
<span class="sd"> :ivar OG(D,R): Die Ostergrenze</span>
|
|
||||||
<span class="sd"> :vartype OG(D,R): int</span>
|
|
||||||
<span class="sd"> :ivar SZ(X,S): Den ersten Sonntag im März</span>
|
|
||||||
<span class="sd"> :vartype SZ(X,S): int</span>
|
|
||||||
<span class="sd"> :ivar OE(OG,SZ): Die Entfernung des Ostersonntags von der Ostergrenze (Osterentfernung in Tagen)</span>
|
|
||||||
<span class="sd"> :vartype OE(OG,SZ): int</span>
|
|
||||||
<span class="sd"> :ivar OS(OG,OE): Das Datum des Ostersonntags als Märzdatum (32. März = 1. April usw.)</span>
|
|
||||||
<span class="sd"> :vartype OS(OG,OE): int</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> Algorithmus gilt für den Gregorianischen Kalender.</span>
|
|
||||||
|
|
||||||
<span class="sd"> source: https://de.wikipedia.org/wiki/Gau%C3%9Fsche_Osterformel</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">year</span>
|
|
||||||
<span class="n">k</span> <span class="o">=</span> <span class="n">x</span> <span class="o">//</span> <span class="mi">100</span>
|
|
||||||
<span class="n">m</span> <span class="o">=</span> <span class="mi">15</span> <span class="o">+</span> <span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="n">k</span> <span class="o">+</span> <span class="mi">3</span><span class="p">)</span> <span class="o">//</span> <span class="mi">4</span> <span class="o">-</span> <span class="p">(</span><span class="mi">8</span><span class="o">*</span><span class="n">k</span> <span class="o">+</span> <span class="mi">13</span><span class="p">)</span> <span class="o">//</span> <span class="mi">25</span>
|
|
||||||
<span class="n">s</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">-</span> <span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="n">k</span> <span class="o">+</span> <span class="mi">3</span><span class="p">)</span> <span class="o">//</span> <span class="mi">4</span>
|
|
||||||
<span class="n">a</span> <span class="o">=</span> <span class="n">x</span> <span class="o">%</span> <span class="mi">19</span>
|
|
||||||
<span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="mi">19</span><span class="o">*</span><span class="n">a</span> <span class="o">+</span> <span class="n">m</span><span class="p">)</span> <span class="o">%</span> <span class="mi">30</span>
|
|
||||||
<span class="n">r</span> <span class="o">=</span> <span class="p">(</span><span class="n">d</span> <span class="o">+</span> <span class="n">a</span> <span class="o">//</span> <span class="mi">11</span><span class="p">)</span> <span class="o">//</span> <span class="mi">29</span>
|
|
||||||
<span class="n">og</span> <span class="o">=</span> <span class="mi">21</span> <span class="o">+</span> <span class="n">d</span> <span class="o">-</span> <span class="n">r</span>
|
|
||||||
<span class="n">sz</span> <span class="o">=</span> <span class="mi">7</span> <span class="o">-</span> <span class="p">(</span><span class="n">x</span> <span class="o">+</span> <span class="n">x</span> <span class="o">//</span> <span class="mi">4</span> <span class="o">+</span> <span class="n">s</span><span class="p">)</span> <span class="o">%</span> <span class="mi">7</span>
|
|
||||||
<span class="n">oe</span> <span class="o">=</span> <span class="mi">7</span> <span class="o">-</span> <span class="p">(</span><span class="n">og</span> <span class="o">-</span> <span class="n">sz</span><span class="p">)</span> <span class="o">%</span> <span class="mi">7</span>
|
|
||||||
<span class="n">os</span> <span class="o">=</span> <span class="n">og</span> <span class="o">+</span> <span class="n">oe</span>
|
|
||||||
<span class="k">return</span> <span class="n">os</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="easter_sunday"><a class="viewcode-back" href="../date.html#date.easter_sunday">[docs]</a><span class="k">def</span> <span class="nf">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Easter Sunday.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the Easter Sunday</span>
|
|
||||||
<span class="sd"> :type year: int</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the day of Easter Sunday</span>
|
|
||||||
<span class="sd"> :rtype: datetime.date"""</span>
|
|
||||||
<span class="kn">import</span> <span class="nn">datetime</span>
|
|
||||||
<span class="n">march</span> <span class="o">=</span> <span class="n">datetime</span><span class="o">.</span><span class="n">date</span><span class="p">(</span><span class="n">year</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="n">day</span> <span class="o">=</span> <span class="n">march</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=</span><span class="n">gaußsche_osterformel</span><span class="p">(</span><span class="n">year</span><span class="p">))</span>
|
|
||||||
<span class="k">return</span> <span class="n">day</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="easter_friday"><a class="viewcode-back" href="../date.html#date.easter_friday">[docs]</a><span class="k">def</span> <span class="nf">easter_friday</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Easter Friday.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the Easter Friday</span>
|
|
||||||
<span class="sd"> :type year: int</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the day of Easter Friday</span>
|
|
||||||
<span class="sd"> :rtype: datetime.date"""</span>
|
|
||||||
<span class="kn">import</span> <span class="nn">datetime</span>
|
|
||||||
<span class="n">day</span> <span class="o">=</span> <span class="n">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">)</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=-</span><span class="mi">2</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">day</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="easter_monday"><a class="viewcode-back" href="../date.html#date.easter_monday">[docs]</a><span class="k">def</span> <span class="nf">easter_monday</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Easter Monday.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the Easter Monday</span>
|
|
||||||
<span class="sd"> :type year: int</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the day of Easter Monday</span>
|
|
||||||
<span class="sd"> :rtype: datetime.date"""</span>
|
|
||||||
<span class="kn">import</span> <span class="nn">datetime</span>
|
|
||||||
<span class="n">day</span> <span class="o">=</span> <span class="n">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">)</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=+</span><span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">day</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="ascension_of_jesus"><a class="viewcode-back" href="../date.html#date.ascension_of_jesus">[docs]</a><span class="k">def</span> <span class="nf">ascension_of_jesus</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Ascension of Jesus.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the ascension of Jesus</span>
|
|
||||||
<span class="sd"> :type year: int</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the day of ascension of Jesus</span>
|
|
||||||
<span class="sd"> :rtype: datetime.date"""</span>
|
|
||||||
<span class="kn">import</span> <span class="nn">datetime</span>
|
|
||||||
<span class="n">day</span> <span class="o">=</span> <span class="n">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">)</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=+</span><span class="mi">39</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">day</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="pentecost"><a class="viewcode-back" href="../date.html#date.pentecost">[docs]</a><span class="k">def</span> <span class="nf">pentecost</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Pentecost.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the Pentecost</span>
|
|
||||||
<span class="sd"> :type year: int</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the day of Pentecost</span>
|
|
||||||
<span class="sd"> :rtype: datetime.date"""</span>
|
|
||||||
<span class="kn">import</span> <span class="nn">datetime</span>
|
|
||||||
<span class="n">day</span> <span class="o">=</span> <span class="n">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">)</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=+</span><span class="mi">49</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">day</span></div>
|
|
||||||
</pre></div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
|
|
||||||
</div>
|
|
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</div>
|
|
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<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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|
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<div class="sphinxsidebarwrapper">
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|
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<h1 class="logo"><a href="../index.html">pylib</a></h1>
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|
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|
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<h3>Navigation</h3>
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<div class="relations">
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<h3>Related Topics</h3>
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<ul>
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<li><a href="../index.html">Documentation overview</a><ul>
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<li><a href="index.html">Module code</a><ul>
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|
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</div>
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</div>
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<div class="clearer"></div>
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</div>
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<div class="footer">
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©2019, Daniel Weschke.
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|
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</html>
|
|
||||||
516
docs/build/html/_modules/function.html
vendored
516
docs/build/html/_modules/function.html
vendored
@@ -1,516 +0,0 @@
|
|||||||
|
|
||||||
<!DOCTYPE html>
|
|
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|
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml">
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|
||||||
<head>
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||||||
<meta charset="utf-8" />
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<title>function — pylib 2019.5.19 documentation</title>
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<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
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<link rel="search" title="Search" href="../search.html" />
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<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
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<meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
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|
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<div class="document">
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<div class="documentwrapper">
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<div class="bodywrapper">
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|
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|
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<div class="body" role="main">
|
|
||||||
|
|
||||||
<h1>Source code for function</h1><div class="highlight"><pre>
|
|
||||||
<span></span><span class="ch">#!/usr/bin/env python</span>
|
|
||||||
<span class="c1"># -*- coding: utf-8 -*-</span>
|
|
||||||
<span class="sd">"""Mathematical equations.</span>
|
|
||||||
|
|
||||||
<span class="sd">:Date: 2019-11-15</span>
|
|
||||||
|
|
||||||
<span class="sd">.. module:: function</span>
|
|
||||||
<span class="sd"> :platform: *nix, Windows</span>
|
|
||||||
<span class="sd"> :synopsis: Mathematical equations.</span>
|
|
||||||
|
|
||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
|
||||||
<span class="sd">"""</span>
|
|
||||||
<span class="kn">import</span> <span class="nn">math</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">pylib.data</span> <span class="kn">import</span> <span class="n">seq</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">pylib.mathematics</span> <span class="kn">import</span> <span class="n">lcm</span>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="transformation"><a class="viewcode-back" href="../function.html#function.transformation">[docs]</a><span class="k">def</span> <span class="nf">transformation</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">scale_vertical</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">scale_horizontal</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
|
|
||||||
<span class="n">shift_horizontal</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">shift_vertical</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Transform functions.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param f: function or list of functions</span>
|
|
||||||
<span class="sd"> :type f: function or list</span>
|
|
||||||
<span class="sd"> :param scale_vertical: "a" scale factor in vertical direction (default</span>
|
|
||||||
<span class="sd"> = 1)</span>
|
|
||||||
<span class="sd"> :type height: float</span>
|
|
||||||
<span class="sd"> :param scale_horizontal: "b" scale factor in horizontal direction</span>
|
|
||||||
<span class="sd"> (default = 1)</span>
|
|
||||||
<span class="sd"> :type height: float</span>
|
|
||||||
<span class="sd"> :param shift_horizontal: "c" shift factor in horizontal direction</span>
|
|
||||||
<span class="sd"> (default = 0)</span>
|
|
||||||
<span class="sd"> :type height: float</span>
|
|
||||||
<span class="sd"> :param shift_vertical: "d" shift factor in vertical direction (default</span>
|
|
||||||
<span class="sd"> = 0)</span>
|
|
||||||
<span class="sd"> :type height: float</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: transformed function or list of transformed functions</span>
|
|
||||||
<span class="sd"> :rtype: function or list</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> y = a \, f(b\,(x-c)) + d</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="c1"># shorter variables</span>
|
|
||||||
<span class="n">a</span> <span class="o">=</span> <span class="n">scale_vertical</span>
|
|
||||||
<span class="n">b</span> <span class="o">=</span> <span class="n">scale_horizontal</span>
|
|
||||||
<span class="n">c</span> <span class="o">=</span> <span class="n">shift_horizontal</span>
|
|
||||||
<span class="n">d</span> <span class="o">=</span> <span class="n">shift_vertical</span>
|
|
||||||
|
|
||||||
<span class="c1"># check if f is a function than put it in a list and return only</span>
|
|
||||||
<span class="c1"># the function, not the one element list</span>
|
|
||||||
<span class="k">if</span> <span class="n">callable</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
|
|
||||||
<span class="k">return</span> <span class="n">transformation</span><span class="p">(</span>
|
|
||||||
<span class="p">[</span><span class="n">f</span><span class="p">],</span> <span class="n">scale_vertical</span><span class="o">=</span><span class="n">a</span><span class="p">,</span> <span class="n">scale_horizontal</span><span class="o">=</span><span class="n">b</span><span class="p">,</span> <span class="n">shift_horizontal</span><span class="o">=</span><span class="n">c</span><span class="p">,</span> <span class="n">shift_vertical</span><span class="o">=</span><span class="n">d</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
|
||||||
|
|
||||||
<span class="c1"># otherwise assume list of functions</span>
|
|
||||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">f</span><span class="p">:</span> <span class="c1"># if f is empty. End of the recursive fucntion</span>
|
|
||||||
<span class="k">return</span> <span class="p">[]</span>
|
|
||||||
<span class="k">return</span> <span class="p">[</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">:</span> <span class="n">a</span><span class="o">*</span><span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">](</span><span class="n">b</span><span class="o">*</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="n">c</span><span class="p">),</span> <span class="n">t</span><span class="p">)</span><span class="o">+</span><span class="n">d</span><span class="p">]</span> <span class="o">+</span>\
|
|
||||||
<span class="n">transformation</span><span class="p">(</span>
|
|
||||||
<span class="n">f</span><span class="p">[</span><span class="mi">1</span><span class="p">:],</span> <span class="n">scale_vertical</span><span class="o">=</span><span class="n">a</span><span class="p">,</span> <span class="n">scale_horizontal</span><span class="o">=</span><span class="n">b</span><span class="p">,</span> <span class="n">shift_horizontal</span><span class="o">=</span><span class="n">c</span><span class="p">,</span> <span class="n">shift_vertical</span><span class="o">=</span><span class="n">d</span><span class="p">)</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="sine_wave"><a class="viewcode-back" href="../function.html#function.sine_wave">[docs]</a><span class="k">def</span> <span class="nf">sine_wave</span><span class="p">(</span><span class="n">A</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">phi</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">D</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">degree</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""A sine wave or sinusoid is a mathematical curve that describes a</span>
|
|
||||||
<span class="sd"> smooth periodic oscillation.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param A: amplitude</span>
|
|
||||||
<span class="sd"> :type A: float or int</span>
|
|
||||||
<span class="sd"> :param k: (angular) wave number</span>
|
|
||||||
<span class="sd"> :type k: float or int</span>
|
|
||||||
<span class="sd"> :param f: ordinary frequency</span>
|
|
||||||
<span class="sd"> :type f: float or int</span>
|
|
||||||
<span class="sd"> :param phi: phase</span>
|
|
||||||
<span class="sd"> :type phi: float or int</span>
|
|
||||||
<span class="sd"> :param D: non-zero center amplitude</span>
|
|
||||||
<span class="sd"> :type D: float or int</span>
|
|
||||||
<span class="sd"> :param degree: boolean to switch between radians and degree. If</span>
|
|
||||||
<span class="sd"> False phi is interpreted in radians and if True then phi is</span>
|
|
||||||
<span class="sd"> interpreted in degrees.</span>
|
|
||||||
<span class="sd"> :type degree: bool</span>
|
|
||||||
|
|
||||||
<span class="sd"> :results: sine wave function of spatial variable x and optional</span>
|
|
||||||
<span class="sd"> time t</span>
|
|
||||||
|
|
||||||
<span class="sd"> In general, the function is:</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> y(x,t) = A\sin(kx + 2\pi f t + \varphi) + D \\</span>
|
|
||||||
<span class="sd"> y(x,t) = A\sin(kx + \omega t + \varphi) + D</span>
|
|
||||||
|
|
||||||
<span class="sd"> where:</span>
|
|
||||||
|
|
||||||
<span class="sd"> * A, amplitude, the peak deviation of the function from zero.</span>
|
|
||||||
<span class="sd"> * f, ordinary frequency, the number of oscillations (cycles) that</span>
|
|
||||||
<span class="sd"> occur each second of time.</span>
|
|
||||||
<span class="sd"> * ω = 2πf, angular frequency, the rate of change of the function</span>
|
|
||||||
<span class="sd"> argument in units of radians per second. If ω < 0 the wave is</span>
|
|
||||||
<span class="sd"> moving to the right, if ω > 0 the wave is moving to the left.</span>
|
|
||||||
<span class="sd"> * φ, phase, specifies (in radians) where in its cycle the</span>
|
|
||||||
<span class="sd"> oscillation is at t = 0.</span>
|
|
||||||
<span class="sd"> * x, spatial variable that represents the position on the</span>
|
|
||||||
<span class="sd"> dimension on which the wave propagates.</span>
|
|
||||||
<span class="sd"> * k, characteristic parameter called wave number (or angular wave</span>
|
|
||||||
<span class="sd"> number), which represents the proportionality between the</span>
|
|
||||||
<span class="sd"> angular frequency ω and the linear speed (speed of propagation)</span>
|
|
||||||
<span class="sd"> ν.</span>
|
|
||||||
<span class="sd"> * D, non-zero center amplitude.</span>
|
|
||||||
|
|
||||||
<span class="sd"> The wavenumber is related to the angular frequency by:</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> k={\omega \over v}={2\pi f \over v}={2\pi \over \lambda }</span>
|
|
||||||
|
|
||||||
<span class="sd"> where λ (lambda) is the wavelength, f is the frequency, and v is the</span>
|
|
||||||
<span class="sd"> linear speed.</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
|
||||||
<span class="sd"> :meth:`cosine_wave`</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">if</span> <span class="n">degree</span><span class="p">:</span>
|
|
||||||
<span class="n">phi</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">radians</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="o">=</span><span class="mi">0</span><span class="p">:</span> <span class="n">A</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">k</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">f</span><span class="o">*</span><span class="n">t</span> <span class="o">+</span> <span class="n">phi</span><span class="p">)</span> <span class="o">+</span> <span class="n">D</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="cosine_wave"><a class="viewcode-back" href="../function.html#function.cosine_wave">[docs]</a><span class="k">def</span> <span class="nf">cosine_wave</span><span class="p">(</span><span class="n">A</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">phi</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">D</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">degree</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""A cosine wave is said to be sinusoidal, because,</span>
|
|
||||||
<span class="sd"> :math:`\cos(x) = \sin(x + \pi/2)`, which is also a sine wave with a</span>
|
|
||||||
<span class="sd"> phase-shift of π/2 radians. Because of this head start, it is often</span>
|
|
||||||
<span class="sd"> said that the cosine function leads the sine function or the sine</span>
|
|
||||||
<span class="sd"> lags the cosine.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param A: amplitude</span>
|
|
||||||
<span class="sd"> :type A: float or int</span>
|
|
||||||
<span class="sd"> :param k: (angular) wave number</span>
|
|
||||||
<span class="sd"> :type k: float or int</span>
|
|
||||||
<span class="sd"> :param f: ordinary frequency</span>
|
|
||||||
<span class="sd"> :type f: float or int</span>
|
|
||||||
<span class="sd"> :param phi: phase</span>
|
|
||||||
<span class="sd"> :type phi: float or int</span>
|
|
||||||
<span class="sd"> :param D: non-zero center amplitude</span>
|
|
||||||
<span class="sd"> :type D: float or int</span>
|
|
||||||
<span class="sd"> :param degree: boolean to switch between radians and degree. If</span>
|
|
||||||
<span class="sd"> False phi is interpreted in radians and if True then phi is</span>
|
|
||||||
<span class="sd"> interpreted in degrees.</span>
|
|
||||||
<span class="sd"> :type degree: bool</span>
|
|
||||||
|
|
||||||
<span class="sd"> :results: sine wave function of spatial variable x and optional</span>
|
|
||||||
<span class="sd"> time t</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
|
||||||
<span class="sd"> :meth:`sine_wave`</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">if</span> <span class="n">degree</span><span class="p">:</span>
|
|
||||||
<span class="n">phi</span> <span class="o">=</span> <span class="n">phi</span> <span class="o">+</span> <span class="mi">90</span>
|
|
||||||
<span class="k">else</span><span class="p">:</span>
|
|
||||||
<span class="n">phi</span> <span class="o">=</span> <span class="n">phi</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">2</span>
|
|
||||||
<span class="k">return</span> <span class="n">sine_wave</span><span class="p">(</span><span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="n">k</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="n">f</span><span class="p">,</span> <span class="n">phi</span><span class="o">=</span><span class="n">phi</span><span class="p">,</span> <span class="n">D</span><span class="o">=</span><span class="n">D</span><span class="p">,</span> <span class="n">degree</span><span class="o">=</span><span class="n">degree</span><span class="p">)</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<span class="c1">#</span>
|
|
||||||
<span class="c1"># Parametric equations</span>
|
|
||||||
<span class="c1"># roulette</span>
|
|
||||||
<span class="c1">#</span>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="hypotrochoid"><a class="viewcode-back" href="../function.html#function.hypotrochoid">[docs]</a><span class="k">def</span> <span class="nf">hypotrochoid</span><span class="p">(</span><span class="n">R</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Hypotrochoid</span>
|
|
||||||
|
|
||||||
<span class="sd"> A point is attached with a distance d from the center of a circle</span>
|
|
||||||
<span class="sd"> of radius r. The circle is rolling around the inside of a fixed</span>
|
|
||||||
<span class="sd"> circle of radius R.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param R: radius of the fixed exterior circle</span>
|
|
||||||
<span class="sd"> :type R: float</span>
|
|
||||||
<span class="sd"> :param r: radius of the rolling circle inside of the fixed circle</span>
|
|
||||||
<span class="sd"> :typre r: float</span>
|
|
||||||
<span class="sd"> :param d: distance from the center of the interior circle</span>
|
|
||||||
<span class="sd"> :type d: float</span>
|
|
||||||
|
|
||||||
<span class="sd"> :results: functions for x of theta and y of theta</span>
|
|
||||||
<span class="sd"> :rtype: tuple</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> x(\theta) = (R - r)\cos\theta + d\cos\left(\frac{R-r}{r}\theta\right) \\</span>
|
|
||||||
<span class="sd"> y(\theta) = (R - r)\sin\theta - d\sin\left(\frac{R-r}{r}\theta\right) \\</span>
|
|
||||||
<span class="sd"> \theta = \left[0, 2\pi\frac{\mathrm{lcm}(r, R)}{R}\right]</span>
|
|
||||||
|
|
||||||
<span class="sd"> ::</span>
|
|
||||||
|
|
||||||
<span class="sd"> * * *</span>
|
|
||||||
<span class="sd"> * R *</span>
|
|
||||||
<span class="sd"> * *</span>
|
|
||||||
<span class="sd"> * * * *</span>
|
|
||||||
<span class="sd"> * * r **</span>
|
|
||||||
<span class="sd"> * * .... *</span>
|
|
||||||
<span class="sd"> * * d *</span>
|
|
||||||
<span class="sd"> * * **</span>
|
|
||||||
<span class="sd"> * * * *</span>
|
|
||||||
<span class="sd"> * *</span>
|
|
||||||
<span class="sd"> * *</span>
|
|
||||||
<span class="sd"> * * *</span>
|
|
||||||
|
|
||||||
<span class="sd"> >>> x, y = hyotrochoid(20, 6, 6)[:1]</span>
|
|
||||||
<span class="sd"> >>> x, y, theta_end = hyotrochoid(20, 6, 6)</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
|
||||||
<span class="sd"> :meth:`mathematics.lcm`</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">theta</span><span class="p">:</span> <span class="p">(</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">+</span> <span class="n">d</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">((</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">/</span><span class="n">r</span> <span class="o">*</span> <span class="n">theta</span><span class="p">)</span>
|
|
||||||
<span class="n">y</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">theta</span><span class="p">:</span> <span class="p">(</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">-</span> <span class="n">d</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">((</span><span class="n">R</span><span class="o">-</span><span class="n">r</span><span class="p">)</span><span class="o">/</span><span class="n">r</span> <span class="o">*</span> <span class="n">theta</span><span class="p">)</span>
|
|
||||||
<span class="n">theta_end</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">lcm</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">R</span><span class="p">)</span><span class="o">/</span><span class="n">R</span>
|
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">theta_end</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="epitrochoid"><a class="viewcode-back" href="../function.html#function.epitrochoid">[docs]</a><span class="k">def</span> <span class="nf">epitrochoid</span><span class="p">(</span><span class="n">R</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Epitrochoid</span>
|
|
||||||
|
|
||||||
<span class="sd"> A point is attached with a distance d from the center of a circle</span>
|
|
||||||
<span class="sd"> of radius r. The circle is rolling around the outside of a fixed</span>
|
|
||||||
<span class="sd"> circle of radius R.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param R: radius of the fixed interior circle</span>
|
|
||||||
<span class="sd"> :type R: float</span>
|
|
||||||
<span class="sd"> :param r: radius of the rolling circle outside of the fixed circle</span>
|
|
||||||
<span class="sd"> :typre r: float</span>
|
|
||||||
<span class="sd"> :param d: distance from the center of the exterior circle</span>
|
|
||||||
<span class="sd"> :type d: float</span>
|
|
||||||
|
|
||||||
<span class="sd"> :results: functions for x of theta and y of theta</span>
|
|
||||||
<span class="sd"> :rtype: tuple</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> x(\theta) = (R + r)\cos\theta - d\cos\left(\frac{R+r}{r}\theta\right) \\</span>
|
|
||||||
<span class="sd"> y(\theta) = (R + r)\sin\theta - d\sin\left(\frac{R+r}{r}\theta\right) \\</span>
|
|
||||||
<span class="sd"> \theta = \left[0, 2\pi\right]</span>
|
|
||||||
|
|
||||||
<span class="sd"> ::</span>
|
|
||||||
|
|
||||||
<span class="sd"> * * *</span>
|
|
||||||
<span class="sd"> * R *</span>
|
|
||||||
<span class="sd"> * *</span>
|
|
||||||
<span class="sd"> * * * *</span>
|
|
||||||
<span class="sd"> * * * r *</span>
|
|
||||||
<span class="sd"> * ** .... *</span>
|
|
||||||
<span class="sd"> * ** d *</span>
|
|
||||||
<span class="sd"> * * * *</span>
|
|
||||||
<span class="sd"> * * * *</span>
|
|
||||||
<span class="sd"> * *</span>
|
|
||||||
<span class="sd"> * *</span>
|
|
||||||
<span class="sd"> * * *</span>
|
|
||||||
|
|
||||||
<span class="sd"> >>> x, y = epitrochoid(3, 1, 0.5)[:1]</span>
|
|
||||||
<span class="sd"> >>> x, y, theta_end = epitrochoid(3, 1, 0.5)</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">theta</span><span class="p">:</span> <span class="p">(</span><span class="n">R</span><span class="o">+</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">-</span> <span class="n">d</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">((</span><span class="n">R</span><span class="o">+</span><span class="n">r</span><span class="p">)</span><span class="o">/</span><span class="n">r</span> <span class="o">*</span> <span class="n">theta</span><span class="p">)</span>
|
|
||||||
<span class="n">y</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">theta</span><span class="p">:</span> <span class="p">(</span><span class="n">R</span><span class="o">+</span><span class="n">r</span><span class="p">)</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">-</span> <span class="n">d</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">((</span><span class="n">R</span><span class="o">+</span><span class="n">r</span><span class="p">)</span><span class="o">/</span><span class="n">r</span> <span class="o">*</span> <span class="n">theta</span><span class="p">)</span>
|
|
||||||
<span class="n">theta_end</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span>
|
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">theta_end</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="to_str"><a class="viewcode-back" href="../function.html#function.to_str">[docs]</a><span class="k">def</span> <span class="nf">to_str</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">x_0</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">x_1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">t</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">h</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mi">80</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">char_set</span><span class="o">=</span><span class="s2">"line"</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Represent functions as string frame with a specific character set.</span>
|
|
||||||
<span class="sd"> which are normed to the range of [0, 1] to</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param f: function or list of functions normed to the range of [0, 1]</span>
|
|
||||||
<span class="sd"> :type f: function or list</span>
|
|
||||||
<span class="sd"> :param h: number of chars in vertical direction</span>
|
|
||||||
<span class="sd"> :type h: int</span>
|
|
||||||
<span class="sd"> :param w: number of chars in horizontal direction</span>
|
|
||||||
<span class="sd"> :type w: int</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param char_set: either "braille" or "block". "braille" uses Unicode</span>
|
|
||||||
<span class="sd"> Characters in the Braille Patterns Block (fisrt index U+2800, last</span>
|
|
||||||
<span class="sd"> index U+28FF [CUDB]_) and the "block" uses part of the Unicode</span>
|
|
||||||
<span class="sd"> Characters in the Block Elements Block (fisrt index U+2580, last</span>
|
|
||||||
<span class="sd"> index U+259F [CUDB]_). Alias for braille is line and alias for</span>
|
|
||||||
<span class="sd"> block is histogram</span>
|
|
||||||
<span class="sd"> :type char_set: str</span>
|
|
||||||
|
|
||||||
<span class="sd"> Usage:</span>
|
|
||||||
<span class="sd"> * case dependent arguments</span>
|
|
||||||
|
|
||||||
<span class="sd"> * 1 quasi line plot (braille characters)</span>
|
|
||||||
<span class="sd"> f = lambda function (lambda x, t=0: ...)</span>
|
|
||||||
<span class="sd"> x_1 = max x value</span>
|
|
||||||
<span class="sd"> x_0 = min x value</span>
|
|
||||||
<span class="sd"> t = time (animation)</span>
|
|
||||||
<span class="sd"> * 2 histogram (block characters)</span>
|
|
||||||
<span class="sd"> f = lambda function (lambda x, t=0: ...)</span>
|
|
||||||
<span class="sd"> x_1 = max x value</span>
|
|
||||||
<span class="sd"> x_0 = min x value</span>
|
|
||||||
<span class="sd"> t = time (animation)</span>
|
|
||||||
<span class="sd"> chart="histogram"</span>
|
|
||||||
|
|
||||||
<span class="sd"> * general arguments</span>
|
|
||||||
<span class="sd"> w = window width in number of chars</span>
|
|
||||||
<span class="sd"> density = number of data point per pixel (for line chart higher density makes thicker lines)</span>
|
|
||||||
<span class="sd"> chart = either "line" or "histogram"</span>
|
|
||||||
|
|
||||||
|
|
||||||
<span class="sd"> .. rubric:: Braille Patterns Block</span>
|
|
||||||
|
|
||||||
<span class="sd"> * Dots or pixels per character in vertical direction: 6</span>
|
|
||||||
<span class="sd"> * Dots or pixels per character in horizontal direction: 2</span>
|
|
||||||
|
|
||||||
<span class="sd"> First dot (bottom left) is the zero (0) position of the</span>
|
|
||||||
<span class="sd"> function. So, a function value of zero does not mean to have zero</span>
|
|
||||||
<span class="sd"> dots but one.</span>
|
|
||||||
<span class="sd"> Example of 3 columns and 3 rows (upside down view of 'normal' braille/drawille position)</span>
|
|
||||||
|
|
||||||
<span class="sd"> ::</span>
|
|
||||||
|
|
||||||
<span class="sd"> | ^ y axis</span>
|
|
||||||
<span class="sd"> | |</span>
|
|
||||||
<span class="sd"> | ,_____,,_____,,_____,</span>
|
|
||||||
<span class="sd"> 7 + | * *|| * *|| * *|</span>
|
|
||||||
<span class="sd"> 6 + | * *|| * *|| * *|</span>
|
|
||||||
<span class="sd"> 5 + | * *|| * *|| * *|</span>
|
|
||||||
<span class="sd"> 4 + | * *|| * *|| * *|</span>
|
|
||||||
<span class="sd"> | ;=====;;=====;;=====;</span>
|
|
||||||
<span class="sd"> 3 + | * *|| * *|| * *|</span>
|
|
||||||
<span class="sd"> 2 + | * *|| * *|| * *|</span>
|
|
||||||
<span class="sd"> 1 + | * *|| * *|| * *|</span>
|
|
||||||
<span class="sd"> 0 + - | * *|| * *|| * *| ---> x axis</span>
|
|
||||||
<span class="sd"> | ;=====;;=====;;=====;</span>
|
|
||||||
<span class="sd"> -1 + | * *|| * *|| * *|</span>
|
|
||||||
<span class="sd"> -2 + | * *|| * *|| * *|</span>
|
|
||||||
<span class="sd"> -3 + | * *|| * *|| * *|</span>
|
|
||||||
<span class="sd"> -4 + | * *|| * *|| * *|</span>
|
|
||||||
<span class="sd"> | `````````````````````</span>
|
|
||||||
<span class="sd"> | |</span>
|
|
||||||
<span class="sd"> `-----+--+---+--+---+--+-------------</span>
|
|
||||||
<span class="sd"> -2 -1 0 1 2 3</span>
|
|
||||||
|
|
||||||
|
|
||||||
<span class="sd"> .. rubric:: Block Elements Block</span>
|
|
||||||
|
|
||||||
<span class="sd"> * Dots or pixels per character in vertical direction: 8</span>
|
|
||||||
<span class="sd"> * Dots or pixels per character in horizontal direction: 1</span>
|
|
||||||
|
|
||||||
<span class="sd"> Example of 3 columns and 3 rows</span>
|
|
||||||
|
|
||||||
<span class="sd"> ::</span>
|
|
||||||
|
|
||||||
<span class="sd"> | ^ y axis</span>
|
|
||||||
<span class="sd"> | |</span>
|
|
||||||
<span class="sd"> | ,_____,,_____,,_____,</span>
|
|
||||||
<span class="sd"> 15 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 14 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 13 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 12 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 11 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 10 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 9 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 8 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> | ;=====;;=====;;=====;</span>
|
|
||||||
<span class="sd"> 7 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 6 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 5 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 4 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 3 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 2 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 1 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> 0 + - | --- || --- || --- | ---> x axis</span>
|
|
||||||
<span class="sd"> | ;=====;;=====;;=====;</span>
|
|
||||||
<span class="sd"> -1 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> -2 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> -3 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> -4 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> -5 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> -6 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> -7 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> -8 + | --- || --- || --- |</span>
|
|
||||||
<span class="sd"> | `````````````````````</span>
|
|
||||||
<span class="sd"> | |</span>
|
|
||||||
<span class="sd"> `------+------+------+---------------</span>
|
|
||||||
<span class="sd"> -1 0 1</span>
|
|
||||||
|
|
||||||
|
|
||||||
<span class="sd"> .. rubric:: References</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. [CUDB] `Unicode Database - Blocks <ftp://ftp.unicode.org/Public/UNIDATA/Blocks.txt>`_</span>
|
|
||||||
|
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
|
||||||
<span class="sd"> :meth:`pylib.function.transformation`</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="c1"># scale function to used chars and dots/pixel in y direction (4 for braille characters): from [0, 1] to [0, chars*4-1]</span>
|
|
||||||
<span class="c1"># negate the function because the y axis is pointing downwards: from [0, 1] to [-1, 0] or from [0, chars*4-1] to [-(chars*4-1), 0]</span>
|
|
||||||
<span class="c1"># and becasue of the negation shift the function by one dot/pixel, otherwise the function would need another char, because the 0 is on an another char on the "positive side".</span>
|
|
||||||
<span class="c1"># devide the time by the number of dots/pixel in x direction (2 for braille characters)</span>
|
|
||||||
<span class="n">window_factor</span> <span class="o">=</span> <span class="n">w</span><span class="o">/</span><span class="p">(</span><span class="n">x_1</span><span class="o">-</span><span class="n">x_0</span><span class="p">)</span>
|
|
||||||
<span class="n">frame</span> <span class="o">=</span> <span class="s2">""</span>
|
|
||||||
<span class="k">if</span> <span class="n">char_set</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">"line"</span><span class="p">,</span> <span class="s2">"braille"</span><span class="p">]:</span>
|
|
||||||
<span class="kn">import</span> <span class="nn">drawille</span>
|
|
||||||
|
|
||||||
<span class="n">pixels_horizontal</span> <span class="o">=</span> <span class="mi">2</span>
|
|
||||||
<span class="n">pixels_vertical</span> <span class="o">=</span> <span class="mi">4</span>
|
|
||||||
<span class="n">a</span> <span class="o">=</span> <span class="o">-</span><span class="p">(</span><span class="n">h</span><span class="o">*</span><span class="n">pixels_vertical</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="n">b</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">pixels_horizontal</span>
|
|
||||||
<span class="n">f</span> <span class="o">=</span> <span class="n">transformation</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">canvas</span> <span class="o">=</span> <span class="n">drawille</span><span class="o">.</span><span class="n">Canvas</span><span class="p">()</span>
|
|
||||||
<span class="c1"># divide step width of the sequence by 2 (double density, 2 dots/pixel per char)</span>
|
|
||||||
<span class="c1"># multiplicate x by 2 (2 dots/pixel per char)</span>
|
|
||||||
<span class="k">for</span> <span class="n">x_i</span> <span class="ow">in</span> <span class="n">seq</span><span class="p">(</span><span class="n">x_0</span><span class="o">*</span><span class="n">window_factor</span><span class="o">*</span><span class="n">pixels_horizontal</span><span class="p">,</span> <span class="n">x_1</span><span class="o">*</span><span class="n">window_factor</span><span class="o">*</span><span class="n">pixels_horizontal</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="n">density</span><span class="p">):</span>
|
|
||||||
<span class="n">canvas</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">x_i</span><span class="p">,</span> <span class="n">f</span><span class="p">(</span><span class="n">x_i</span><span class="p">,</span> <span class="n">t</span><span class="p">))</span>
|
|
||||||
<span class="c1">#frame = canvas.frame(min_x=a*pixel_per_char, min_y=1, max_x=b*pixel_per_char, max_y=21)</span>
|
|
||||||
<span class="n">frame</span> <span class="o">=</span> <span class="n">canvas</span><span class="o">.</span><span class="n">frame</span><span class="p">()</span>
|
|
||||||
<span class="k">elif</span> <span class="n">char_set</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">"histogram"</span><span class="p">,</span> <span class="s2">"block"</span><span class="p">]:</span>
|
|
||||||
<span class="kn">import</span> <span class="nn">drawblock</span>
|
|
||||||
|
|
||||||
<span class="n">pixels_horizontal</span> <span class="o">=</span> <span class="mi">1</span>
|
|
||||||
<span class="n">pixels_vertical</span> <span class="o">=</span> <span class="mi">8</span>
|
|
||||||
<span class="n">a</span> <span class="o">=</span> <span class="n">h</span><span class="o">*</span><span class="n">pixels_vertical</span><span class="o">-</span><span class="mi">1</span>
|
|
||||||
<span class="n">f</span> <span class="o">=</span> <span class="n">transformation</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">density</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">density</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="c1"># density max 1!</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">seq</span><span class="p">(</span><span class="n">x_0</span><span class="o">*</span><span class="n">window_factor</span><span class="p">,</span> <span class="n">x_1</span><span class="o">*</span><span class="n">window_factor</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="n">pixels_horizontal</span><span class="o">/</span><span class="n">density</span><span class="p">)</span>
|
|
||||||
<span class="n">f</span> <span class="o">=</span> <span class="p">[</span><span class="n">f</span><span class="p">(</span><span class="n">xi</span><span class="p">,</span> <span class="n">t</span><span class="p">)</span> <span class="k">for</span> <span class="n">xi</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]</span>
|
|
||||||
<span class="n">frame</span> <span class="o">=</span> <span class="n">drawblock</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="k">return</span> <span class="n">frame</span></div>
|
|
||||||
</pre></div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
|
|
||||||
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|
|
||||||
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|
|
||||||
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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|
||||||
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|
||||||
<h1 class="logo"><a href="../index.html">pylib</a></h1>
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|
||||||
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|
||||||
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|
||||||
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|
||||||
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|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
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|
||||||
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|
||||||
<div class="relations">
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|
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<h3>Related Topics</h3>
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||||||
185
docs/build/html/_modules/geometry_plot.html
vendored
185
docs/build/html/_modules/geometry_plot.html
vendored
@@ -1,185 +0,0 @@
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|||||||
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|
||||||
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|
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|
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<html xmlns="http://www.w3.org/1999/xhtml">
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|
||||||
<h1>Source code for geometry_plot</h1><div class="highlight"><pre>
|
|
||||||
<span></span><span class="ch">#!/usr/bin/env python</span>
|
|
||||||
<span class="c1"># -*- coding: utf-8 -*-</span>
|
|
||||||
<span class="sd">"""2D geometry plotter using matplotlib (pylab).</span>
|
|
||||||
|
|
||||||
<span class="sd">:Date: 2019-08-20</span>
|
|
||||||
|
|
||||||
<span class="sd">.. module:: geometry_plot</span>
|
|
||||||
<span class="sd"> :platform: *nix, Windows</span>
|
|
||||||
<span class="sd"> :synopsis: Geometry plotting.</span>
|
|
||||||
|
|
||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
|
||||||
<span class="sd">"""</span>
|
|
||||||
<span class="kn">import</span> <span class="nn">math</span>
|
|
||||||
<span class="kn">import</span> <span class="nn">pylab</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">geometry</span> <span class="kn">import</span> <span class="p">(</span>
|
|
||||||
<span class="n">distance</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="n">line</span><span class="p">,</span> <span class="n">interpolate_hermite</span><span class="p">,</span> <span class="n">rotate_xy</span><span class="p">,</span> <span class="n">translate_xy</span>
|
|
||||||
<span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">pylab</span><span class="o">.</span><span class="n">style</span><span class="o">.</span><span class="n">use</span><span class="p">(</span><span class="s1">'dark_background'</span><span class="p">)</span>
|
|
||||||
<span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">'grid.color'</span><span class="p">]</span> <span class="o">=</span> <span class="s1">'gray'</span>
|
|
||||||
|
|
||||||
<span class="c1"># The kwargs are Line2D properties:</span>
|
|
||||||
<span class="c1"># https://matplotlib.org/3.1.1/_modules/matplotlib/lines.html#Line2D</span>
|
|
||||||
<span class="c1"># https://matplotlib.org/devdocs/_modules/matplotlib/lines.html#Line2D</span>
|
|
||||||
<span class="n">pylab_Line2D_properties</span> <span class="o">=</span> <span class="p">[</span>
|
|
||||||
<span class="s1">'linewidth'</span><span class="p">,</span> <span class="s1">'linestyle'</span><span class="p">,</span> <span class="s1">'color'</span><span class="p">,</span>
|
|
||||||
<span class="s1">'marker'</span><span class="p">,</span> <span class="s1">'markersize'</span><span class="p">,</span> <span class="s1">'markeredgewidth'</span><span class="p">,</span> <span class="s1">'markeredgecolor'</span><span class="p">,</span>
|
|
||||||
<span class="s1">'markerfacecolor'</span><span class="p">,</span> <span class="s1">'markerfacecoloralt'</span><span class="p">,</span>
|
|
||||||
<span class="s1">'fillstyle'</span><span class="p">,</span> <span class="s1">'antialiased'</span><span class="p">,</span>
|
|
||||||
<span class="s1">'dash_capstyle'</span><span class="p">,</span> <span class="s1">'solid_capstyle'</span><span class="p">,</span>
|
|
||||||
<span class="s1">'dash_joinstyle'</span><span class="p">,</span> <span class="s1">'solid_joinstyle'</span><span class="p">,</span>
|
|
||||||
<span class="s1">'pickradius'</span><span class="p">,</span> <span class="s1">'drawstyle'</span><span class="p">,</span> <span class="s1">'markevery'</span><span class="p">,</span>
|
|
||||||
<span class="p">]</span>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="plot_lines"><a class="viewcode-back" href="../geometry_plot.html#geometry_plot.plot_lines">[docs]</a><span class="k">def</span> <span class="nf">plot_lines</span><span class="p">(</span><span class="n">lns</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'color'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="c1"># Colors from "tab10" colormap</span>
|
|
||||||
<span class="n">cmap</span> <span class="o">=</span> <span class="n">pylab</span><span class="o">.</span><span class="n">get_cmap</span><span class="p">(</span><span class="s2">"tab10"</span><span class="p">)</span>
|
|
||||||
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'color'</span><span class="p">]</span> <span class="o">=</span> <span class="n">cmap</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="c1"># Colors from color cycle</span>
|
|
||||||
<span class="n">cycle</span> <span class="o">=</span> <span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">'axes.prop_cycle'</span><span class="p">]</span><span class="o">.</span><span class="n">by_key</span><span class="p">()[</span><span class="s1">'color'</span><span class="p">]</span>
|
|
||||||
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'color'</span><span class="p">]</span> <span class="o">=</span> <span class="n">cycle</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
|
||||||
|
|
||||||
<span class="c1"># Colors from CN notation (same as the first 10 colors from the color cycle)</span>
|
|
||||||
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'color'</span><span class="p">]</span> <span class="o">=</span> <span class="s2">"C0"</span>
|
|
||||||
|
|
||||||
<span class="k">for</span> <span class="n">ln</span> <span class="ow">in</span> <span class="n">lns</span><span class="p">:</span>
|
|
||||||
<span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">line</span><span class="p">(</span><span class="o">*</span><span class="n">ln</span><span class="p">)</span>
|
|
||||||
<span class="n">pylab</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="plot_cubic_lines"><a class="viewcode-back" href="../geometry_plot.html#geometry_plot.plot_cubic_lines">[docs]</a><span class="k">def</span> <span class="nf">plot_cubic_lines</span><span class="p">(</span><span class="n">lns</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'color'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="c1"># Colors from "tab10" colormap</span>
|
|
||||||
<span class="n">cmap</span> <span class="o">=</span> <span class="n">pylab</span><span class="o">.</span><span class="n">get_cmap</span><span class="p">(</span><span class="s2">"tab10"</span><span class="p">)</span>
|
|
||||||
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'color'</span><span class="p">]</span> <span class="o">=</span> <span class="n">cmap</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="c1"># Colors from color cycle</span>
|
|
||||||
<span class="n">cycle</span> <span class="o">=</span> <span class="n">pylab</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">'axes.prop_cycle'</span><span class="p">]</span><span class="o">.</span><span class="n">by_key</span><span class="p">()[</span><span class="s1">'color'</span><span class="p">]</span>
|
|
||||||
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'color'</span><span class="p">]</span> <span class="o">=</span> <span class="n">cycle</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
|
||||||
|
|
||||||
<span class="c1"># Colors from CN notation (same as the first 10 colors from the color cycle)</span>
|
|
||||||
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'color'</span><span class="p">]</span> <span class="o">=</span> <span class="s2">"C0"</span>
|
|
||||||
|
|
||||||
<span class="n">factor</span> <span class="o">=</span> <span class="mi">1</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'factor'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="n">factor</span> <span class="o">=</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">]</span>
|
|
||||||
|
|
||||||
<span class="n">samples</span> <span class="o">=</span> <span class="mi">10</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'samples'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="n">samples</span> <span class="o">=</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'samples'</span><span class="p">]</span>
|
|
||||||
|
|
||||||
<span class="n">kwargs</span> <span class="o">=</span> <span class="p">{</span><span class="n">k</span><span class="p">:</span> <span class="n">v</span> <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">items</span><span class="p">()</span> <span class="k">if</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">pylab_Line2D_properties</span><span class="p">}</span>
|
|
||||||
|
|
||||||
<span class="k">for</span> <span class="n">ln</span> <span class="ow">in</span> <span class="n">lns</span><span class="p">:</span>
|
|
||||||
<span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">d</span> <span class="o">=</span> <span class="n">ln</span>
|
|
||||||
<span class="n">L</span> <span class="o">=</span> <span class="n">distance</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
|
|
||||||
<span class="n">ang</span> <span class="o">=</span> <span class="n">angle</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
|
|
||||||
<span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">interpolate_hermite</span><span class="p">(</span><span class="n">d</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="mi">4</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="mi">5</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span>
|
|
||||||
<span class="n">scale_x</span><span class="o">=</span><span class="n">L</span><span class="p">,</span> <span class="n">scale_y</span><span class="o">=</span><span class="n">factor</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="n">samples</span><span class="p">)</span>
|
|
||||||
<span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">rotate_xy</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">ang</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
|
|
||||||
<span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">translate_xy</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">pylab</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span></div>
|
|
||||||
</pre></div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
|
||||||
<div class="sphinxsidebarwrapper">
|
|
||||||
<h1 class="logo"><a href="../index.html">pylib</a></h1>
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
|
||||||
|
|
||||||
<div class="relations">
|
|
||||||
<h3>Related Topics</h3>
|
|
||||||
<ul>
|
|
||||||
<li><a href="../index.html">Documentation overview</a><ul>
|
|
||||||
<li><a href="index.html">Module code</a><ul>
|
|
||||||
</ul></li>
|
|
||||||
</ul></li>
|
|
||||||
</ul>
|
|
||||||
</div>
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|
||||||
<div id="searchbox" style="display: none" role="search">
|
|
||||||
<h3 id="searchlabel">Quick search</h3>
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|
||||||
<div class="searchformwrapper">
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||||||
<form class="search" action="../search.html" method="get">
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<input type="text" name="q" aria-labelledby="searchlabel" />
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|
||||||
<input type="submit" value="Go" />
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|
||||||
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|
||||||
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||||||
|
|
||||||
|
|
||||||
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|
||||||
|
|
||||||
</div>
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|
||||||
</div>
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||||||
<div class="clearer"></div>
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||||||
</div>
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<div class="footer">
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©2019, Daniel Weschke.
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</body>
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</html>
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||||||
22
docs/build/html/_modules/index.html
vendored
22
docs/build/html/_modules/index.html
vendored
@@ -4,7 +4,7 @@
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|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
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<html xmlns="http://www.w3.org/1999/xhtml">
|
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<head>
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<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
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<title>Overview: module code — pylib 2019.5.19 documentation</title>
|
<title>Overview: module code — pylib 2019.12.21 documentation</title>
|
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<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
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<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
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<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
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<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
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@@ -33,29 +33,19 @@
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<div class="body" role="main">
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|
||||||
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||||||
<h1>All modules for which code is available</h1>
|
<h1>All modules for which code is available</h1>
|
||||||
<ul><li><a href="data.html">data</a></li>
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<ul><li><a href="pylib/data.html">pylib.data</a></li>
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<li><a href="numerical/fit.html">numerical.fit</a></li>
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||||||
<li><a href="numerical/integration.html">numerical.integration</a></li>
|
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||||||
<li><a href="numerical/ode.html">numerical.ode</a></li>
|
|
||||||
<li><a href="numerical/ode_model.html">numerical.ode_model</a></li>
|
|
||||||
<li><a href="pylib/data.html">pylib.data</a></li>
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|
||||||
<li><a href="pylib/date.html">pylib.date</a></li>
|
<li><a href="pylib/date.html">pylib.date</a></li>
|
||||||
<li><a href="pylib/drawblock.html">pylib.drawblock</a></li>
|
<li><a href="pylib/drawblock.html">pylib.drawblock</a></li>
|
||||||
<li><a href="pylib/function.html">pylib.function</a></li>
|
<li><a href="pylib/function.html">pylib.function</a></li>
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<li><a href="pylib/geometry.html">pylib.geometry</a></li>
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<li><a href="pylib/geometry.html">pylib.geometry</a></li>
|
||||||
<li><a href="pylib/geometry_plot.html">pylib.geometry_plot</a></li>
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<li><a href="pylib/geometry2d.html">pylib.geometry2d</a></li>
|
||||||
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<li><a href="pylib/geometry2d_plot.html">pylib.geometry2d_plot</a></li>
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||||||
<li><a href="pylib/mathematics.html">pylib.mathematics</a></li>
|
<li><a href="pylib/mathematics.html">pylib.mathematics</a></li>
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||||||
<li><a href="pylib/numerical/fit.html">pylib.numerical.fit</a></li>
|
<li><a href="pylib/numerical/fit.html">pylib.numerical.fit</a></li>
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||||||
<li><a href="pylib/numerical/integration.html">pylib.numerical.integration</a></li>
|
<li><a href="pylib/numerical/integration.html">pylib.numerical.integration</a></li>
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||||||
<li><a href="pylib/numerical/ode.html">pylib.numerical.ode</a></li>
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<li><a href="pylib/numerical/ode_model.html">pylib.numerical.ode_model</a></li>
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<li><a href="pylib/time_of_day.html">pylib.time_of_day</a></li>
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<li><a href="time_of_day.html">time_of_day</a></li>
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</ul>
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</div>
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1025
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||||||
<h1>Source code for numerical.fit</h1><div class="highlight"><pre>
|
|
||||||
<span></span><span class="ch">#!/usr/bin/env python</span>
|
|
||||||
<span class="c1"># -*- coding: utf-8 -*-</span>
|
|
||||||
<span class="sd">"""Function and approximation.</span>
|
|
||||||
|
|
||||||
<span class="sd">:Date: 2019-10-15</span>
|
|
||||||
|
|
||||||
<span class="sd">.. module:: fit</span>
|
|
||||||
<span class="sd"> :platform: *nix, Windows</span>
|
|
||||||
<span class="sd"> :synopsis: Function and approximation.</span>
|
|
||||||
|
|
||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
|
||||||
<span class="sd">"""</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">print_function</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">pylab</span> <span class="kn">import</span> <span class="n">array</span><span class="p">,</span> <span class="n">argmax</span><span class="p">,</span> <span class="n">gradient</span><span class="p">,</span> <span class="n">exp</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">,</span> <span class="n">log</span><span class="p">,</span> <span class="n">linspace</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">scipy.optimize</span> <span class="kn">import</span> <span class="n">curve_fit</span>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="gauss"><a class="viewcode-back" href="../../numerical.html#numerical.fit.gauss">[docs]</a><span class="k">def</span> <span class="nf">gauss</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Gauss distribution function.</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> f(x)=ae^{-(x-b)^{2}/(2c^{2})}</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param x: positions where the gauss function will be calculated</span>
|
|
||||||
<span class="sd"> :type x: int or float or list or numpy.ndarray</span>
|
|
||||||
<span class="sd"> :param p: gauss parameters [a, b, c, d]:</span>
|
|
||||||
|
|
||||||
<span class="sd"> * a -- amplitude (:math:`\\int y \\,\\mathrm{d}x=1 \\Leftrightarrow a=1/(c\\sqrt{2\\pi})` )</span>
|
|
||||||
<span class="sd"> * b -- expected value :math:`\\mu` (position of maximum, default = 0)</span>
|
|
||||||
<span class="sd"> * c -- standard deviation :math:`\\sigma` (variance :math:`\\sigma^2=c^2`)</span>
|
|
||||||
<span class="sd"> * d -- vertical offset (default = 0)</span>
|
|
||||||
<span class="sd"> :type p: list</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: gauss values at given positions x</span>
|
|
||||||
<span class="sd"> :rtype: numpy.ndarray</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="c1"># cast e. g. list to numpy array</span>
|
|
||||||
<span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="o">=</span> <span class="n">p</span>
|
|
||||||
<span class="k">return</span> <span class="n">a</span><span class="o">*</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span><span class="o">**</span><span class="mf">2.</span><span class="o">/</span><span class="p">(</span><span class="mf">2.</span> <span class="o">*</span> <span class="n">c</span><span class="o">**</span><span class="mf">2.</span><span class="p">))</span> <span class="o">+</span> <span class="n">d</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="gauss_fit"><a class="viewcode-back" href="../../numerical.html#numerical.fit.gauss_fit">[docs]</a><span class="k">def</span> <span class="nf">gauss_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">e</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">x_fit</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Fit Gauss distribution function to data.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param x: positions</span>
|
|
||||||
<span class="sd"> :type x: int or float or list or numpy.ndarray</span>
|
|
||||||
<span class="sd"> :param y: values</span>
|
|
||||||
<span class="sd"> :type y: int or float or list or numpy.ndarray</span>
|
|
||||||
<span class="sd"> :param e: error values (default = None)</span>
|
|
||||||
<span class="sd"> :type e: int or float or list or numpy.ndarray</span>
|
|
||||||
<span class="sd"> :param x_fit: positions of fitted function (default = None, if None then x</span>
|
|
||||||
<span class="sd"> is used)</span>
|
|
||||||
<span class="sd"> :type x_fit: int or float or list or numpy.ndarray</span>
|
|
||||||
<span class="sd"> :param verbose: verbose information (default = False)</span>
|
|
||||||
<span class="sd"> :type verbose: bool</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns:</span>
|
|
||||||
<span class="sd"> * numpy.ndarray -- fitted values (y_fit)</span>
|
|
||||||
<span class="sd"> * numpy.ndarray -- parameters of gauss distribution function (popt:</span>
|
|
||||||
<span class="sd"> amplitude a, expected value :math:`\\mu`, standard deviation</span>
|
|
||||||
<span class="sd"> :math:`\\sigma`, vertical offset d)</span>
|
|
||||||
<span class="sd"> * numpy.float64 -- full width at half maximum (FWHM)</span>
|
|
||||||
<span class="sd"> :rtype: tuple</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
|
||||||
<span class="sd"> :meth:`gauss`</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="c1"># cast e. g. list to numpy array</span>
|
|
||||||
<span class="n">y</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="c1"># cast e. g. list to numpy array</span>
|
|
||||||
<span class="n">y_max</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
|
||||||
<span class="n">y_max_pos</span> <span class="o">=</span> <span class="n">argmax</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
|
||||||
<span class="n">x_y_max</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">y_max_pos</span><span class="p">]</span>
|
|
||||||
|
|
||||||
<span class="c1"># starting parameter</span>
|
|
||||||
<span class="n">p0</span> <span class="o">=</span> <span class="p">[</span><span class="n">y_max</span><span class="p">,</span> <span class="n">x_y_max</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
|
|
||||||
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'p0:'</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s1">' '</span><span class="p">)</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="n">p0</span><span class="p">)</span>
|
|
||||||
<span class="k">if</span> <span class="n">e</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
|
||||||
<span class="n">popt</span><span class="p">,</span> <span class="n">pcov</span> <span class="o">=</span> <span class="n">curve_fit</span><span class="p">(</span><span class="n">gauss</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">p0</span><span class="o">=</span><span class="n">p0</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">e</span><span class="p">)</span>
|
|
||||||
<span class="k">else</span><span class="p">:</span>
|
|
||||||
<span class="n">popt</span><span class="p">,</span> <span class="n">pcov</span> <span class="o">=</span> <span class="n">curve_fit</span><span class="p">(</span><span class="n">gauss</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">p0</span><span class="o">=</span><span class="n">p0</span><span class="p">)</span>
|
|
||||||
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'popt:'</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s1">' '</span><span class="p">)</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="n">popt</span><span class="p">)</span>
|
|
||||||
<span class="c1">#print(pcov)</span>
|
|
||||||
|
|
||||||
<span class="n">FWHM</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">log</span><span class="p">(</span><span class="mi">2</span><span class="p">))</span><span class="o">*</span><span class="n">popt</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
|
|
||||||
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'FWHM'</span><span class="p">,</span> <span class="n">FWHM</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="k">if</span> <span class="n">x_fit</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
|
||||||
<span class="n">x_fit</span> <span class="o">=</span> <span class="n">x</span>
|
|
||||||
<span class="n">y_fit</span> <span class="o">=</span> <span class="n">gauss</span><span class="p">(</span><span class="n">x_fit</span><span class="p">,</span> <span class="o">*</span><span class="n">popt</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="k">return</span> <span class="n">y_fit</span><span class="p">,</span> <span class="n">popt</span><span class="p">,</span> <span class="n">FWHM</span></div>
|
|
||||||
|
|
||||||
<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s2">"__main__"</span><span class="p">:</span>
|
|
||||||
<span class="k">pass</span>
|
|
||||||
</pre></div>
|
|
||||||
|
|
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250
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<div class="bodywrapper">
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<div class="body" role="main">
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||||||
<h1>Source code for numerical.integration</h1><div class="highlight"><pre>
|
|
||||||
<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
|
|
||||||
<span class="sd">"""Numerical integration, numerical quadrature.</span>
|
|
||||||
|
|
||||||
<span class="sd">de: numerische Integration, numerische Quadratur.</span>
|
|
||||||
|
|
||||||
<span class="sd">:Date: 2015-10-15</span>
|
|
||||||
|
|
||||||
<span class="sd">.. module:: integration</span>
|
|
||||||
<span class="sd"> :platform: *nix, Windows</span>
|
|
||||||
<span class="sd"> :synopsis: Numerical integration.</span>
|
|
||||||
|
|
||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
|
||||||
<span class="sd">"""</span>
|
|
||||||
|
|
||||||
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">linspace</span><span class="p">,</span> <span class="n">trapz</span><span class="p">,</span> <span class="n">zeros</span>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="trapez"><a class="viewcode-back" href="../../numerical.html#numerical.integration.trapez">[docs]</a><span class="k">def</span> <span class="nf">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">a</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">b</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
|
|
||||||
<span class="n">save_values</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""</span>
|
|
||||||
<span class="sd"> Integration of :math:`f(x)` using the trapezoidal rule</span>
|
|
||||||
<span class="sd"> (Simpson's rule, Kepler's rule).</span>
|
|
||||||
|
|
||||||
<span class="sd"> de: Trapezregel, Simpsonregel (Thomas Simpson), Keplersche</span>
|
|
||||||
<span class="sd"> Fassregel (Johannes Kepler)</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param f: function to integrate.</span>
|
|
||||||
<span class="sd"> :type f: function or list</span>
|
|
||||||
<span class="sd"> :param a: lower limit of integration (default = 0).</span>
|
|
||||||
<span class="sd"> :type a: float</span>
|
|
||||||
<span class="sd"> :param b: upper limit of integration (default = 1).</span>
|
|
||||||
<span class="sd"> :type b: float</span>
|
|
||||||
<span class="sd"> :param N: specify the number of subintervals.</span>
|
|
||||||
<span class="sd"> :type N: int</span>
|
|
||||||
<span class="sd"> :param x: variable of integration, necessary if f is a list</span>
|
|
||||||
<span class="sd"> (default = None).</span>
|
|
||||||
<span class="sd"> :type x: list</span>
|
|
||||||
<span class="sd"> :param verbose: print information (default = False)</span>
|
|
||||||
<span class="sd"> :type verbose: bool</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: the definite integral as approximated by trapezoidal</span>
|
|
||||||
<span class="sd"> rule.</span>
|
|
||||||
<span class="sd"> :rtype: float</span>
|
|
||||||
|
|
||||||
<span class="sd"> The trapezoidal rule approximates the integral by the area of a</span>
|
|
||||||
<span class="sd"> trapezoid with base h=b-a and sides equal to the values of the</span>
|
|
||||||
<span class="sd"> integrand at the two end points.</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> f_n(x) = f(a)+\frac{f(b)-f(a)}{b-a}(x-a)</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> I &= \int\limits_a^b f(x) \,\mathrm{d}x \\</span>
|
|
||||||
<span class="sd"> I &\approx \int\limits_a^b f_n(x) \,\mathrm{d}x \\</span>
|
|
||||||
<span class="sd"> &= \int\limits_a^b</span>
|
|
||||||
<span class="sd"> \left( f(a)+\frac{f(b)-f(a)}{b-a}(x-a) \right)</span>
|
|
||||||
<span class="sd"> \mathrm{d}x \\</span>
|
|
||||||
<span class="sd"> &= \left.\left( f(a)-a\frac{f(b)-f(a)}{b-a} \right)</span>
|
|
||||||
<span class="sd"> x \right\vert_a^b +</span>
|
|
||||||
<span class="sd"> \left. \frac{f(b)-f(a)}{b-a} \frac{x^2}{2}</span>
|
|
||||||
<span class="sd"> \right\vert_a^b \\</span>
|
|
||||||
<span class="sd"> &= \frac{b-a}{2}\left[f(a)+f(b)\right]</span>
|
|
||||||
|
|
||||||
<span class="sd"> The composite trapezium rule. If the interval is divided into n</span>
|
|
||||||
<span class="sd"> segments (not necessarily equal)</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> a = x_0 \leq x_1 \leq x_2 \leq \ldots \leq x_n = b</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> I &\approx \sum\limits_{i=0}^{n-1} \frac{1}{2} (x_{i+1}-x_i)</span>
|
|
||||||
<span class="sd"> \left[f(x_{i+1})+f(x_i)\right] \\</span>
|
|
||||||
|
|
||||||
<span class="sd"> Special Case (Equaliy spaced base points)</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> x_{i+1}-x_i = h \quad \forall i</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> I \approx h \left\{ \frac{1}{2} \left[f(x_0)+f(x_n)\right] +</span>
|
|
||||||
<span class="sd"> \sum\limits_{i=1}^{n-1} f(x_i) \right\}</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. rubric:: Example</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> I &= \int\limits_a^b f(x) \,\mathrm{d}x \\</span>
|
|
||||||
<span class="sd"> f(x) &= x^2 \\</span>
|
|
||||||
<span class="sd"> a &= 0 \\</span>
|
|
||||||
<span class="sd"> b &= 1</span>
|
|
||||||
|
|
||||||
<span class="sd"> analytical solution</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> I = \int\limits_{0}^{1} x^2 \,\mathrm{d}x</span>
|
|
||||||
<span class="sd"> = \left. \frac{1}{3} x^3 \right\vert_0^1</span>
|
|
||||||
<span class="sd"> = \frac{1}{3}</span>
|
|
||||||
|
|
||||||
<span class="sd"> numerical solution</span>
|
|
||||||
|
|
||||||
<span class="sd"> >>> f = lambda(x): x**2</span>
|
|
||||||
<span class="sd"> >>> trapez(f, 0, 1, 1)</span>
|
|
||||||
<span class="sd"> 0.5</span>
|
|
||||||
<span class="sd"> >>> trapez(f, 0, 1, 10)</span>
|
|
||||||
<span class="sd"> 0.3350000000000001</span>
|
|
||||||
<span class="sd"> >>> trapez(f, 0, 1, 100)</span>
|
|
||||||
<span class="sd"> 0.33335000000000004</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">N</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>
|
|
||||||
<span class="c1"># f is function or list</span>
|
|
||||||
<span class="k">if</span> <span class="n">callable</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
|
|
||||||
<span class="c1"># h width of each subinterval</span>
|
|
||||||
<span class="n">h</span> <span class="o">=</span> <span class="p">(</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="p">)</span><span class="o">/</span><span class="n">N</span>
|
|
||||||
|
|
||||||
<span class="c1"># x variable of integration</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">linspace</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="k">if</span> <span class="n">save_values</span><span class="p">:</span>
|
|
||||||
<span class="c1"># ff contribution from the points</span>
|
|
||||||
<span class="n">ff</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span>
|
|
||||||
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span> <span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
|
|
||||||
<span class="n">ff</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">n</span><span class="p">])</span>
|
|
||||||
<span class="n">T</span> <span class="o">=</span> <span class="p">(</span><span class="n">ff</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">/</span><span class="mf">2.</span><span class="o">+</span><span class="nb">sum</span><span class="p">(</span><span class="n">ff</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="n">N</span><span class="p">])</span><span class="o">+</span><span class="n">ff</span><span class="p">[</span><span class="n">N</span><span class="p">]</span><span class="o">/</span><span class="mf">2.</span><span class="p">)</span><span class="o">*</span><span class="n">h</span>
|
|
||||||
<span class="k">else</span><span class="p">:</span>
|
|
||||||
<span class="n">TL</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
|
||||||
<span class="n">TR</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">N</span><span class="p">])</span>
|
|
||||||
<span class="n">TI</span> <span class="o">=</span> <span class="mi">0</span>
|
|
||||||
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
|
|
||||||
<span class="n">TI</span> <span class="o">=</span> <span class="n">TI</span> <span class="o">+</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">n</span><span class="p">])</span>
|
|
||||||
<span class="n">T</span> <span class="o">=</span> <span class="p">(</span><span class="n">TL</span><span class="o">/</span><span class="mf">2.</span><span class="o">+</span><span class="n">TI</span><span class="o">+</span><span class="n">TR</span><span class="o">/</span><span class="mf">2.</span><span class="p">)</span><span class="o">*</span><span class="n">h</span>
|
|
||||||
<span class="k">else</span><span class="p">:</span>
|
|
||||||
<span class="n">N</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">f</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
|
|
||||||
<span class="n">T</span> <span class="o">=</span> <span class="mi">0</span>
|
|
||||||
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">):</span>
|
|
||||||
<span class="n">T</span> <span class="o">=</span> <span class="n">T</span> <span class="o">+</span> <span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">x</span><span class="p">[</span><span class="n">n</span><span class="p">])</span><span class="o">/</span><span class="mi">2</span><span class="o">*</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="n">f</span><span class="p">[</span><span class="n">n</span><span class="p">])</span>
|
|
||||||
|
|
||||||
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="k">return</span> <span class="n">T</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
|
|
||||||
<span class="n">func</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span>
|
|
||||||
<span class="n">trapez</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
|
||||||
<span class="c1">#print(trapz(func, linspace(0,1,10)))</span>
|
|
||||||
|
|
||||||
<span class="n">trapez</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">9</span><span class="p">],</span> <span class="n">x</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
|
||||||
<span class="c1">#print(trapz([0,1,4,9]))</span>
|
|
||||||
|
|
||||||
<span class="n">trapez</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="n">x</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">trapez</span><span class="p">([</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">x</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
|
||||||
</pre></div>
|
|
||||||
|
|
||||||
</div>
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|
||||||
|
|
||||||
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<h1>Source code for numerical.ode</h1><div class="highlight"><pre>
|
|
||||||
<span></span><span class="ch">#!/usr/bin/env python</span>
|
|
||||||
<span class="c1"># -*- coding: utf-8 -*-</span>
|
|
||||||
<span class="sd">"""Numerical solver of ordinary differential equations.</span>
|
|
||||||
|
|
||||||
<span class="sd">Solves the initial value problem for systems of first order</span>
|
|
||||||
<span class="sd">ordinary differential equations.</span>
|
|
||||||
|
|
||||||
<span class="sd">:Date: 2015-09-21</span>
|
|
||||||
|
|
||||||
<span class="sd">.. module:: ode</span>
|
|
||||||
<span class="sd"> :platform: *nix, Windows</span>
|
|
||||||
<span class="sd"> :synopsis: Numerical solver.</span>
|
|
||||||
|
|
||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
|
||||||
<span class="sd">"""</span>
|
|
||||||
|
|
||||||
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span><span class="p">,</span> <span class="n">print_function</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span><span class="p">,</span> <span class="n">isnan</span><span class="p">,</span> <span class="nb">sum</span><span class="p">,</span> <span class="n">zeros</span><span class="p">,</span> <span class="n">dot</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">numpy.linalg</span> <span class="kn">import</span> <span class="n">norm</span><span class="p">,</span> <span class="n">inv</span>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="e1"><a class="viewcode-back" href="../../numerical.html#numerical.ode.e1">[docs]</a><span class="k">def</span> <span class="nf">e1</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Explicit first-order method /</span>
|
|
||||||
<span class="sd"> (standard, or forward) Euler method /</span>
|
|
||||||
<span class="sd"> Runge-Kutta 1st order method.</span>
|
|
||||||
|
|
||||||
<span class="sd"> de:</span>
|
|
||||||
<span class="sd"> Euler'sche Polygonzugverfahren / explizite Euler-Verfahren /</span>
|
|
||||||
<span class="sd"> Euler-Cauchy-Verfahren / Euler-vorwärts-Verfahren</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param f: the function to solve</span>
|
|
||||||
<span class="sd"> :type f: function</span>
|
|
||||||
<span class="sd"> :param x0: initial condition</span>
|
|
||||||
<span class="sd"> :type x0: list</span>
|
|
||||||
<span class="sd"> :param t: time</span>
|
|
||||||
<span class="sd"> :type t: list</span>
|
|
||||||
<span class="sd"> :param `*p`: parameters of the function (thickness, diameter,</span>
|
|
||||||
<span class="sd"> ...)</span>
|
|
||||||
<span class="sd"> :param verbose: print information (default = False)</span>
|
|
||||||
<span class="sd"> :type verbose: bool</span>
|
|
||||||
|
|
||||||
<span class="sd"> Approximate the solution of the initial value problem</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> \dot{x} &= f(t,x) \\</span>
|
|
||||||
<span class="sd"> x(t_0) &= x_0</span>
|
|
||||||
|
|
||||||
<span class="sd"> Choose a value h for the size of every step and set</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> t_i = t_0 + i h ~,\quad i=1,2,\ldots,n</span>
|
|
||||||
|
|
||||||
<span class="sd"> The derivative of the solution is approximated as the forward</span>
|
|
||||||
<span class="sd"> difference equation</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> \dot{x}_i = f(t_i, x_i) = \frac{x_{i+1} - x_i}{t_{i+1}-t_i}</span>
|
|
||||||
|
|
||||||
<span class="sd"> Therefore one step :math:`h` of the Euler method from</span>
|
|
||||||
<span class="sd"> :math:`t_i` to :math:`t_{i+1}` is</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> x_{i+1} &= x_i + (t_{i+1}-t_i) f(t_i, x_i) \\</span>
|
|
||||||
<span class="sd"> x_{i+1} &= x_i + h f(t_i, x_i) \\</span>
|
|
||||||
|
|
||||||
<span class="sd"> Example 1:</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> m\ddot{u} + d\dot{u} + ku = f(t) \\</span>
|
|
||||||
<span class="sd"> \ddot{u} = m^{-1}(f(t) - d\dot{u} - ku) \\</span>
|
|
||||||
|
|
||||||
<span class="sd"> with</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> x_1 &= u &\quad \dot{x}_1 = \dot{u} = x_2 \\</span>
|
|
||||||
<span class="sd"> x_2 &= \dot{u} &\quad \dot{x}_2 = \ddot{u} \\</span>
|
|
||||||
|
|
||||||
<span class="sd"> becomes</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> \dot{x}_1 &= x_2 \\</span>
|
|
||||||
<span class="sd"> \dot{x}_2 &= m^{-1}(f(t) - d x_2 - k x_1) \\</span>
|
|
||||||
|
|
||||||
<span class="sd"> or</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> \dot{x} &= f(t,x) \\</span>
|
|
||||||
<span class="sd"> \begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} &=</span>
|
|
||||||
<span class="sd"> \begin{bmatrix} x_2 \\ m^{-1}(f(t) - d x_2 - k x_1)</span>
|
|
||||||
<span class="sd"> \end{bmatrix} \\</span>
|
|
||||||
<span class="sd"> &=</span>
|
|
||||||
<span class="sd"> \begin{bmatrix} 0 \\ m^{-1} f(t) \end{bmatrix} +</span>
|
|
||||||
<span class="sd"> \begin{bmatrix} 0 & 1 \\ -m^{-1} k & -m^{-1} d \end{bmatrix}</span>
|
|
||||||
<span class="sd"> \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}</span>
|
|
||||||
|
|
||||||
<span class="sd"> Example 2:</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> m(u)\ddot{u} + d(u,\dot{u})\dot{u} + k(u)u = f(t) \\</span>
|
|
||||||
<span class="sd"> \ddot{u} = m^{-1}(u)(f(t) - d(u,\dot{u})\dot{u} - k(u)u) \\</span>
|
|
||||||
|
|
||||||
<span class="sd"> with</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> x_1 &= u &\quad \dot{x}_1 = \dot{u} = x_2 \\</span>
|
|
||||||
<span class="sd"> x_2 &= \dot{u} &\quad \dot{x}_2 = \ddot{u} \\</span>
|
|
||||||
|
|
||||||
<span class="sd"> becomes</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> \dot{x}_1 &= x_2 \\</span>
|
|
||||||
<span class="sd"> \dot{x}_2 &=</span>
|
|
||||||
<span class="sd"> m^{-1}(x_1)(f(t) - d(x_1,x_2) x_2 - k(x_1) x_1) \\</span>
|
|
||||||
|
|
||||||
<span class="sd"> or</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> \dot{x} &= f(t,x) \\</span>
|
|
||||||
<span class="sd"> \begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} &=</span>
|
|
||||||
<span class="sd"> \begin{bmatrix}</span>
|
|
||||||
<span class="sd"> x_2 \\ m^{-1}(x_1)(f(t) - d(x_1,x_2) x_2 - k(x_1) x_1)</span>
|
|
||||||
<span class="sd"> \end{bmatrix} \\</span>
|
|
||||||
<span class="sd"> &=</span>
|
|
||||||
<span class="sd"> \begin{bmatrix} 0 \\ m^{-1}(x_1) f(t) \end{bmatrix} +</span>
|
|
||||||
<span class="sd"> \begin{bmatrix}</span>
|
|
||||||
<span class="sd"> 0 & 1 \\ -m^{-1}(x_1) k(x_1) & -m^{-1} d(x_1,x_2)</span>
|
|
||||||
<span class="sd"> \end{bmatrix}</span>
|
|
||||||
<span class="sd"> \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}</span>
|
|
||||||
|
|
||||||
<span class="sd"> The Euler method is a first-order method, which means that the</span>
|
|
||||||
<span class="sd"> local error (error per step) is proportional to the square of</span>
|
|
||||||
<span class="sd"> the step size, and the global error (error at a given time) is</span>
|
|
||||||
<span class="sd"> proportional to the step size.</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)))</span> <span class="c1"># Preallocate array</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">x0</span> <span class="c1"># Initial condition gives solution at first t</span>
|
|
||||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span> <span class="c1"># Calculation loop</span>
|
|
||||||
<span class="n">Dt</span> <span class="o">=</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
|
||||||
<span class="n">dxdt</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:],</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="o">*</span><span class="n">p</span><span class="p">))</span>
|
|
||||||
<span class="c1"># Approximate solution at next value of x</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span> <span class="o">+</span> <span class="n">dxdt</span><span class="o">*</span><span class="n">Dt</span>
|
|
||||||
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Numerical integration of ODE using explicit '</span> <span class="o">+</span>
|
|
||||||
<span class="s1">'first-order method (Euler / Runge-Kutta) was successful.'</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">x</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="e2"><a class="viewcode-back" href="../../numerical.html#numerical.ode.e2">[docs]</a><span class="k">def</span> <span class="nf">e2</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Explicit second-order method / Runge-Kutta 2nd order method.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param f: the function to solve</span>
|
|
||||||
<span class="sd"> :type f: function</span>
|
|
||||||
<span class="sd"> :param x0: initial condition</span>
|
|
||||||
<span class="sd"> :type x0: list</span>
|
|
||||||
<span class="sd"> :param t: time</span>
|
|
||||||
<span class="sd"> :type t: list</span>
|
|
||||||
<span class="sd"> :param `*p`: parameters of the function (thickness, diameter,</span>
|
|
||||||
<span class="sd"> ...)</span>
|
|
||||||
<span class="sd"> :param verbose: print information (default = False)</span>
|
|
||||||
<span class="sd"> :type verbose: bool</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)))</span> <span class="c1"># Preallocate array</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">x0</span> <span class="c1"># Initial condition gives solution at first t</span>
|
|
||||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span> <span class="c1"># Calculation loop</span>
|
|
||||||
<span class="n">Dt</span> <span class="o">=</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
|
||||||
<span class="n">k_1</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:],</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="o">*</span><span class="n">p</span><span class="p">))</span>
|
|
||||||
<span class="n">k_2</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span><span class="o">+</span><span class="mf">0.5</span><span class="o">*</span><span class="n">Dt</span><span class="o">*</span><span class="n">k_1</span><span class="p">,</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">+</span><span class="mf">0.5</span><span class="o">*</span><span class="n">Dt</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">))</span>
|
|
||||||
<span class="c1"># Approximate solution at next value of x</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span> <span class="o">+</span> <span class="n">k_2</span><span class="o">*</span><span class="n">Dt</span>
|
|
||||||
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Numerical integration of ODE using explicit '</span> <span class="o">+</span>
|
|
||||||
<span class="s1">'2th-order method (Runge-Kutta) was successful.'</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">x</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="e4"><a class="viewcode-back" href="../../numerical.html#numerical.ode.e4">[docs]</a><span class="k">def</span> <span class="nf">e4</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Explicit fourth-order method / Runge-Kutta 4th order method.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param f: the function to solve</span>
|
|
||||||
<span class="sd"> :type f: function</span>
|
|
||||||
<span class="sd"> :param x0: initial condition</span>
|
|
||||||
<span class="sd"> :type x0: list</span>
|
|
||||||
<span class="sd"> :param t: time</span>
|
|
||||||
<span class="sd"> :type t: list</span>
|
|
||||||
<span class="sd"> :param `*p`: parameters of the function (thickness, diameter,</span>
|
|
||||||
<span class="sd"> ...)</span>
|
|
||||||
<span class="sd"> :param verbose: print information (default = False)</span>
|
|
||||||
<span class="sd"> :type verbose: bool</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)))</span> <span class="c1"># Preallocate array</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">x0</span> <span class="c1"># Initial condition</span>
|
|
||||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span> <span class="c1"># Calculation loop</span>
|
|
||||||
<span class="n">Dt</span> <span class="o">=</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
|
||||||
<span class="n">k_1</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:],</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="o">*</span><span class="n">p</span><span class="p">))</span>
|
|
||||||
<span class="n">k_2</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span><span class="o">+</span><span class="mf">0.5</span><span class="o">*</span><span class="n">Dt</span><span class="o">*</span><span class="n">k_1</span><span class="p">,</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">+</span><span class="mf">0.5</span><span class="o">*</span><span class="n">Dt</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">))</span>
|
|
||||||
<span class="n">k_3</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span><span class="o">+</span><span class="mf">0.5</span><span class="o">*</span><span class="n">Dt</span><span class="o">*</span><span class="n">k_2</span><span class="p">,</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">+</span><span class="mf">0.5</span><span class="o">*</span><span class="n">Dt</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">))</span>
|
|
||||||
<span class="n">k_4</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span><span class="o">+</span><span class="n">k_3</span><span class="o">*</span><span class="n">Dt</span><span class="p">,</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">+</span><span class="n">Dt</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">))</span>
|
|
||||||
<span class="c1"># Approximate solution at next value of x</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span> <span class="o">+</span> <span class="mf">1.</span><span class="o">/</span><span class="mi">6</span><span class="o">*</span><span class="p">(</span><span class="n">k_1</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">k_2</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">k_3</span><span class="o">+</span><span class="n">k_4</span><span class="p">)</span><span class="o">*</span><span class="n">Dt</span>
|
|
||||||
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Numerical integration of ODE using explicit '</span> <span class="o">+</span>
|
|
||||||
<span class="s1">'4th-order method (Runge-Kutta) was successful.'</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">x</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="fpi"><a class="viewcode-back" href="../../numerical.html#numerical.ode.fpi">[docs]</a><span class="k">def</span> <span class="nf">fpi</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">ti</span><span class="p">,</span> <span class="n">ti1</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span>
|
|
||||||
<span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Fixed-point iteration.</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :param f: the function to iterate :math:`f = \dot{x}(x,t)`</span>
|
|
||||||
<span class="sd"> :type f: function</span>
|
|
||||||
<span class="sd"> :param xi: initial condition :math:`x_i`</span>
|
|
||||||
<span class="sd"> :type xi: list</span>
|
|
||||||
<span class="sd"> :param ti: time :math:`t_i`</span>
|
|
||||||
<span class="sd"> :type ti: float</span>
|
|
||||||
<span class="sd"> :param ti1: time :math:`t_{i+1}`</span>
|
|
||||||
<span class="sd"> :type ti1: float</span>
|
|
||||||
<span class="sd"> :param `*p`: parameters of the function (thickness, diameter,</span>
|
|
||||||
<span class="sd"> ...)</span>
|
|
||||||
<span class="sd"> :param max_iterations: maximum number of iterations</span>
|
|
||||||
<span class="sd"> :type max_iterations: int</span>
|
|
||||||
<span class="sd"> :param tol: tolerance against residuum :math:`\varepsilon`</span>
|
|
||||||
<span class="sd"> (default = 1e-9)</span>
|
|
||||||
<span class="sd"> :type tol: float</span>
|
|
||||||
<span class="sd"> :param verbose: print information (default = False)</span>
|
|
||||||
<span class="sd"> :type verbose: bool</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: :math:`x_{i}`</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> x_{i,j=0} = x_{i}</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> x_{i,j+1} = x_i + \dot{x}(x_{i,j}, t_{i+1})\cdot(t_{i+1}-t_i)</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> \text{residuum} = \frac{\lVert x_{i,j+1}-x_{i,j}\rVert}</span>
|
|
||||||
<span class="sd"> {\lVert x_{i,j+1} \rVert} < \varepsilon</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> .. math ::</span>
|
|
||||||
<span class="sd"> x_{i} = x_{i,j=\text{end}}</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">xij</span> <span class="o">=</span> <span class="n">xi</span>
|
|
||||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">max_iterations</span><span class="p">):</span>
|
|
||||||
<span class="n">dxdt</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">xij</span><span class="p">,</span> <span class="n">ti1</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">))</span>
|
|
||||||
<span class="c1"># Approximate solution at next value of x</span>
|
|
||||||
<span class="n">xij1</span> <span class="o">=</span> <span class="n">xi</span> <span class="o">+</span> <span class="n">dxdt</span> <span class="o">*</span> <span class="p">(</span><span class="n">ti1</span><span class="o">-</span><span class="n">ti</span><span class="p">)</span>
|
|
||||||
<span class="n">residuum</span> <span class="o">=</span> <span class="n">norm</span><span class="p">(</span><span class="n">xij1</span><span class="o">-</span><span class="n">xij</span><span class="p">)</span><span class="o">/</span><span class="n">norm</span><span class="p">(</span><span class="n">xij1</span><span class="p">)</span>
|
|
||||||
<span class="n">xij</span> <span class="o">=</span> <span class="n">xij1</span>
|
|
||||||
<span class="k">if</span> <span class="n">residuum</span> <span class="o"><</span> <span class="n">tol</span><span class="p">:</span>
|
|
||||||
<span class="k">break</span>
|
|
||||||
<span class="n">iterations</span> <span class="o">=</span> <span class="n">j</span><span class="o">+</span><span class="mi">1</span> <span class="c1"># number beginning with 1 therefore + 1</span>
|
|
||||||
<span class="k">return</span> <span class="n">xij</span><span class="p">,</span> <span class="n">iterations</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="i1"><a class="viewcode-back" href="../../numerical.html#numerical.ode.i1">[docs]</a><span class="k">def</span> <span class="nf">i1</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span>
|
|
||||||
<span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Implicite first-order method / backward Euler method.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param f: the function to solve</span>
|
|
||||||
<span class="sd"> :type f: function</span>
|
|
||||||
<span class="sd"> :param x0: initial condition</span>
|
|
||||||
<span class="sd"> :type x0: list</span>
|
|
||||||
<span class="sd"> :param t: time</span>
|
|
||||||
<span class="sd"> :type t: list</span>
|
|
||||||
<span class="sd"> :param `*p`: parameters of the function (thickness, diameter,</span>
|
|
||||||
<span class="sd"> ...)</span>
|
|
||||||
<span class="sd"> :param max_iterations: maximum number of iterations</span>
|
|
||||||
<span class="sd"> :type max_iterations: int</span>
|
|
||||||
<span class="sd"> :param tol: tolerance against residuum (default = 1e-9)</span>
|
|
||||||
<span class="sd"> :type tol: float</span>
|
|
||||||
<span class="sd"> :param verbose: print information (default = False)</span>
|
|
||||||
<span class="sd"> :type verbose: bool</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> The backward Euler method has order one and is A-stable.</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">iterations</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)))</span> <span class="c1"># Preallocate array</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">x0</span> <span class="c1"># Initial condition gives solution at first t</span>
|
|
||||||
<span class="c1"># x(i+1) = x(i) + f(x(i+1), t(i+1)), exact value of</span>
|
|
||||||
<span class="c1"># f(x(i+1), t(i+1)) is not available therefore using</span>
|
|
||||||
<span class="c1"># Newton-Raphson method</span>
|
|
||||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
|
|
||||||
<span class="n">Dt</span> <span class="o">=</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
|
||||||
<span class="n">xi</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span>
|
|
||||||
<span class="n">xi</span><span class="p">,</span> <span class="n">iteration</span> <span class="o">=</span> <span class="n">fpi</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">],</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">max_iterations</span><span class="p">,</span>
|
|
||||||
<span class="n">tol</span><span class="p">,</span> <span class="n">verbose</span><span class="p">)</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">xi</span>
|
|
||||||
<span class="n">iterations</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">iteration</span>
|
|
||||||
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Numerical integration of ODE using implicite '</span> <span class="o">+</span>
|
|
||||||
<span class="s1">'first-order method (Euler) was successful.'</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">iterations</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="newmark_newtonraphson"><a class="viewcode-back" href="../../numerical.html#numerical.ode.newmark_newtonraphson">[docs]</a><span class="k">def</span> <span class="nf">newmark_newtonraphson</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">xp0</span><span class="p">,</span> <span class="n">xpp0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=.</span><span class="mi">5</span><span class="p">,</span>
|
|
||||||
<span class="n">beta</span><span class="o">=.</span><span class="mi">25</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Newmark method.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param f: the function to solve</span>
|
|
||||||
<span class="sd"> :type f: function</span>
|
|
||||||
<span class="sd"> :param x0: initial condition</span>
|
|
||||||
<span class="sd"> :type x0: list</span>
|
|
||||||
<span class="sd"> :param xp0: initial condition</span>
|
|
||||||
<span class="sd"> :type xp0: list</span>
|
|
||||||
<span class="sd"> :param xpp0: initial condition</span>
|
|
||||||
<span class="sd"> :type xpp0: list</span>
|
|
||||||
<span class="sd"> :param t: time</span>
|
|
||||||
<span class="sd"> :type t: list</span>
|
|
||||||
<span class="sd"> :param `*p`: parameters of the function (thickness, diameter,</span>
|
|
||||||
<span class="sd"> ...)</span>
|
|
||||||
<span class="sd"> :param gamma: newmark parameter for velocity (default = 0.5)</span>
|
|
||||||
<span class="sd"> :type gamma: float</span>
|
|
||||||
<span class="sd"> :param beta: newmark parameter for displacement (default = 0.25)</span>
|
|
||||||
<span class="sd"> :type beta: float</span>
|
|
||||||
<span class="sd"> :param max_iterations: maximum number of iterations</span>
|
|
||||||
<span class="sd"> :type max_iterations: int</span>
|
|
||||||
<span class="sd"> :param tol: tolerance against residuum (default = 1e-9)</span>
|
|
||||||
<span class="sd"> :type tol: float</span>
|
|
||||||
<span class="sd"> :param verbose: print information (default = False)</span>
|
|
||||||
<span class="sd"> :type verbose: bool</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">iterations</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)))</span> <span class="c1"># Preallocate array</span>
|
|
||||||
<span class="n">xp</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">xp0</span><span class="p">)))</span> <span class="c1"># Preallocate array</span>
|
|
||||||
<span class="n">xpp</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">xpp0</span><span class="p">)))</span> <span class="c1"># Preallocate array</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">x0</span> <span class="c1"># Initial condition gives solution at first t</span>
|
|
||||||
<span class="n">xp</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">xp0</span> <span class="c1"># Initial condition gives solution at first t</span>
|
|
||||||
<span class="n">xpp</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">xpp0</span> <span class="c1"># Initial condition gives solution at first t</span>
|
|
||||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
|
|
||||||
<span class="n">Dt</span> <span class="o">=</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
|
||||||
|
|
||||||
<span class="n">xi</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="n">xpi</span> <span class="o">=</span> <span class="n">xp</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="n">xppi</span> <span class="o">=</span> <span class="n">xpp</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="n">x1</span> <span class="o">=</span> <span class="n">xi</span>
|
|
||||||
<span class="n">xp1</span> <span class="o">=</span> <span class="n">xpi</span>
|
|
||||||
<span class="n">xpp1</span> <span class="o">=</span> <span class="n">xppi</span>
|
|
||||||
<span class="n">j</span> <span class="o">=</span> <span class="mi">0</span>
|
|
||||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">max_iterations</span><span class="p">):</span> <span class="c1"># Fixed-point iteration</span>
|
|
||||||
<span class="c1">#dxdt = array(f(t[i+1], x1, p))</span>
|
|
||||||
<span class="c1"># Approximate solution at next value of x</span>
|
|
||||||
<span class="c1">#x11 = x[i,:] + dxdt*Dt</span>
|
|
||||||
|
|
||||||
<span class="n">N</span><span class="p">,</span> <span class="n">dN</span><span class="p">,</span> <span class="n">dNp</span><span class="p">,</span> <span class="n">dNpp</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">x1</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">(),</span>
|
|
||||||
<span class="n">xp1</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">(),</span> <span class="n">xpp1</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">(),</span>
|
|
||||||
<span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="o">*</span><span class="n">p</span><span class="p">)</span>
|
|
||||||
<span class="k">if</span> <span class="n">isnan</span><span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="n">dN</span><span class="p">))</span> <span class="ow">or</span> <span class="n">isnan</span><span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="n">dNp</span><span class="p">))</span> <span class="ow">or</span> <span class="n">isnan</span><span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="n">dNpp</span><span class="p">)):</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'divergiert'</span><span class="p">)</span>
|
|
||||||
<span class="k">break</span>
|
|
||||||
|
|
||||||
<span class="n">xpp11</span> <span class="o">=</span> <span class="n">xpp1</span> <span class="o">-</span> <span class="n">dot</span><span class="p">(</span><span class="n">inv</span><span class="p">(</span><span class="n">dNpp</span><span class="p">),</span> <span class="p">(</span><span class="n">N</span> <span class="o">+</span> <span class="n">dot</span><span class="p">(</span><span class="n">dN</span><span class="p">,</span> <span class="p">(</span><span class="n">x1</span><span class="o">-</span><span class="n">xi</span><span class="p">))</span> <span class="o">+</span> \
|
|
||||||
<span class="n">dot</span><span class="p">(</span><span class="n">dNp</span><span class="p">,</span> <span class="p">(</span><span class="n">xp1</span><span class="o">-</span><span class="n">xpi</span><span class="p">))))</span>
|
|
||||||
<span class="n">xp1</span> <span class="o">=</span> <span class="n">xpi</span> <span class="o">+</span> <span class="n">Dt</span><span class="o">*</span><span class="p">(</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">gamma</span><span class="p">)</span><span class="o">*</span><span class="n">xppi</span> <span class="o">+</span> <span class="n">gamma</span><span class="o">*</span><span class="n">xpp11</span> <span class="p">)</span>
|
|
||||||
<span class="n">x1</span> <span class="o">=</span> <span class="n">xi</span> <span class="o">+</span> <span class="n">Dt</span><span class="o">*</span><span class="n">xpi</span> <span class="o">+</span> <span class="n">Dt</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="p">(</span> <span class="p">(</span><span class="o">.</span><span class="mi">5</span><span class="o">-</span><span class="n">beta</span><span class="p">)</span><span class="o">*</span><span class="n">xppi</span> <span class="o">+</span> <span class="n">beta</span><span class="o">*</span><span class="n">xpp11</span> <span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">residuum</span> <span class="o">=</span> <span class="n">norm</span><span class="p">(</span><span class="n">xpp11</span><span class="o">-</span><span class="n">xpp1</span><span class="p">)</span><span class="o">/</span><span class="n">norm</span><span class="p">(</span><span class="n">xpp11</span><span class="p">)</span>
|
|
||||||
<span class="n">xpp1</span> <span class="o">=</span> <span class="n">xpp11</span>
|
|
||||||
<span class="k">if</span> <span class="n">residuum</span> <span class="o"><</span> <span class="n">tol</span><span class="p">:</span>
|
|
||||||
<span class="k">break</span>
|
|
||||||
<span class="n">iterations</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">j</span><span class="o">+</span><span class="mi">1</span>
|
|
||||||
|
|
||||||
<span class="n">xpp</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">xpp1</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
|
|
||||||
<span class="n">xp</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">xp1</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">x1</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
|
|
||||||
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Numerical integration of ODE using explicite '</span> <span class="o">+</span>
|
|
||||||
<span class="s1">'newmark method was successful.'</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">xp</span><span class="p">,</span> <span class="n">xpp</span><span class="p">,</span> <span class="n">iterations</span></div>
|
|
||||||
<span class="c1"># x = concatenate((x, xp, xpp), axis=1)</span>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="newmark_newtonraphson_rdk"><a class="viewcode-back" href="../../numerical.html#numerical.ode.newmark_newtonraphson_rdk">[docs]</a><span class="k">def</span> <span class="nf">newmark_newtonraphson_rdk</span><span class="p">(</span><span class="n">fnm</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">xp0</span><span class="p">,</span> <span class="n">xpp0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=.</span><span class="mi">5</span><span class="p">,</span>
|
|
||||||
<span class="n">beta</span><span class="o">=.</span><span class="mi">25</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Newmark method.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param f: the function to solve</span>
|
|
||||||
<span class="sd"> :type f: function</span>
|
|
||||||
<span class="sd"> :param x0: initial condition</span>
|
|
||||||
<span class="sd"> :type x0: list</span>
|
|
||||||
<span class="sd"> :param xp0: initial condition</span>
|
|
||||||
<span class="sd"> :type xp0: list</span>
|
|
||||||
<span class="sd"> :param xpp0: initial condition</span>
|
|
||||||
<span class="sd"> :type xpp0: list</span>
|
|
||||||
<span class="sd"> :param t: time</span>
|
|
||||||
<span class="sd"> :type t: list</span>
|
|
||||||
<span class="sd"> :param `*p`: parameters of the function (thickness, diameter,</span>
|
|
||||||
<span class="sd"> ...)</span>
|
|
||||||
<span class="sd"> :param gamma: newmark parameter for velocity (default = 0.5)</span>
|
|
||||||
<span class="sd"> :type gamma: float</span>
|
|
||||||
<span class="sd"> :param beta: newmark parameter for displacement (default = 0.25)</span>
|
|
||||||
<span class="sd"> :type beta: float</span>
|
|
||||||
<span class="sd"> :param max_iterations: maximum number of iterations</span>
|
|
||||||
<span class="sd"> :type max_iterations: int</span>
|
|
||||||
<span class="sd"> :param tol: tolerance against residuum (default = 1e-9)</span>
|
|
||||||
<span class="sd"> :type tol: float</span>
|
|
||||||
<span class="sd"> :param verbose: print information (default = False)</span>
|
|
||||||
<span class="sd"> :type verbose: bool</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">iterations</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="mi">1</span><span class="p">))</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)))</span> <span class="c1"># Preallocate array</span>
|
|
||||||
<span class="n">xp</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">xp0</span><span class="p">)))</span> <span class="c1"># Preallocate array</span>
|
|
||||||
<span class="n">xpp</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">xpp0</span><span class="p">)))</span> <span class="c1"># Preallocate array</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">x0</span> <span class="c1"># Initial condition gives solution at first t</span>
|
|
||||||
<span class="n">xp</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">xp0</span> <span class="c1"># Initial condition gives solution at first t</span>
|
|
||||||
<span class="n">xpp</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">xpp0</span> <span class="c1"># Initial condition gives solution at first t</span>
|
|
||||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
|
|
||||||
<span class="n">Dt</span> <span class="o">=</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
|
||||||
|
|
||||||
<span class="n">rm</span><span class="p">,</span> <span class="n">rmx</span><span class="p">,</span> <span class="n">rmxpp</span><span class="p">,</span> <span class="n">rd</span><span class="p">,</span> <span class="n">rdx</span><span class="p">,</span> <span class="n">rdxp</span><span class="p">,</span> <span class="n">rk</span><span class="p">,</span> <span class="n">rkx</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">fnm</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:],</span>
|
|
||||||
<span class="n">xp</span><span class="p">[</span><span class="n">i</span><span class="p">,:],</span> <span class="n">xpp</span><span class="p">[</span><span class="n">i</span><span class="p">,:],</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="o">*</span><span class="n">p</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">xi</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="n">xpi</span> <span class="o">=</span> <span class="n">xp</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="n">xppi</span> <span class="o">=</span> <span class="n">xpp</span><span class="p">[</span><span class="n">i</span><span class="p">,:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="n">x1</span> <span class="o">=</span> <span class="n">xi</span>
|
|
||||||
<span class="n">xp1</span> <span class="o">=</span> <span class="n">xpi</span>
|
|
||||||
<span class="n">xpp1</span> <span class="o">=</span> <span class="n">xppi</span>
|
|
||||||
<span class="n">j</span> <span class="o">=</span> <span class="mi">0</span>
|
|
||||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">max_iterations</span><span class="p">):</span> <span class="c1"># Fixed-point iteration</span>
|
|
||||||
<span class="c1">#dxdt = array(f(t[i+1], x1, p))</span>
|
|
||||||
<span class="c1"># Approximate solution at next value of x</span>
|
|
||||||
<span class="c1">#x11 = x[i,:] + dxdt*Dt</span>
|
|
||||||
|
|
||||||
<span class="n">r</span> <span class="o">=</span> <span class="p">(</span><span class="n">rmx</span><span class="o">+</span><span class="n">rdx</span><span class="o">+</span><span class="n">rkx</span><span class="p">)</span><span class="o">*</span><span class="n">Dt</span><span class="o">**</span><span class="mf">2.</span><span class="o">/</span><span class="mi">4</span> <span class="o">+</span> <span class="n">rdxp</span><span class="o">*</span><span class="n">Dt</span><span class="o">/</span><span class="mi">2</span> <span class="o">+</span> <span class="n">rmxpp</span>
|
|
||||||
<span class="n">rp</span> <span class="o">=</span> <span class="n">f</span> <span class="o">-</span> <span class="p">(</span><span class="n">rm</span> <span class="o">+</span> <span class="n">dot</span><span class="p">(</span><span class="n">rmx</span><span class="p">,</span> <span class="p">(</span><span class="n">Dt</span><span class="o">*</span><span class="n">xpi</span><span class="o">+</span><span class="n">Dt</span><span class="o">**</span><span class="mf">2.</span><span class="o">/</span><span class="mi">4</span><span class="o">*</span><span class="n">xppi</span><span class="p">))</span> <span class="o">-</span> \
|
|
||||||
<span class="n">dot</span><span class="p">(</span><span class="n">rmxpp</span><span class="p">,</span> <span class="n">xppi</span><span class="p">)</span> <span class="o">+</span> \
|
|
||||||
<span class="n">rd</span> <span class="o">+</span> <span class="n">dot</span><span class="p">(</span><span class="n">rdx</span><span class="p">,</span> <span class="p">(</span><span class="n">Dt</span><span class="o">*</span><span class="n">xpi</span><span class="o">+</span><span class="n">Dt</span><span class="o">**</span><span class="mf">2.</span><span class="o">/</span><span class="mi">4</span><span class="o">*</span><span class="n">xppi</span><span class="p">))</span> <span class="o">+</span> \
|
|
||||||
<span class="n">dot</span><span class="p">(</span><span class="n">rdxp</span><span class="p">,</span> <span class="n">Dt</span><span class="o">/</span><span class="mi">2</span><span class="o">*</span><span class="n">xppi</span><span class="p">)</span> <span class="o">+</span> \
|
|
||||||
<span class="n">rk</span> <span class="o">+</span> <span class="n">dot</span><span class="p">(</span><span class="n">rkx</span><span class="p">,</span> <span class="p">(</span><span class="n">Dt</span><span class="o">*</span><span class="n">xpi</span><span class="o">+</span><span class="n">Dt</span><span class="o">**</span><span class="mf">2.</span><span class="o">/</span><span class="mi">4</span><span class="o">*</span><span class="n">xppi</span><span class="p">))</span> <span class="p">)</span>
|
|
||||||
<span class="n">xpp11</span> <span class="o">=</span> <span class="n">dot</span><span class="p">(</span><span class="n">inv</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">rp</span><span class="p">)</span>
|
|
||||||
<span class="n">xp1</span> <span class="o">=</span> <span class="n">xpi</span> <span class="o">+</span> <span class="n">Dt</span><span class="o">*</span><span class="p">(</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">gamma</span><span class="p">)</span><span class="o">*</span><span class="n">xppi</span> <span class="o">+</span> <span class="n">gamma</span><span class="o">*</span><span class="n">xpp11</span> <span class="p">)</span>
|
|
||||||
<span class="n">x1</span> <span class="o">=</span> <span class="n">xi</span> <span class="o">+</span> <span class="n">Dt</span><span class="o">*</span><span class="n">xpi</span> <span class="o">+</span> <span class="n">Dt</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="p">(</span> <span class="p">(</span><span class="o">.</span><span class="mi">5</span><span class="o">-</span><span class="n">beta</span><span class="p">)</span><span class="o">*</span><span class="n">xppi</span> <span class="o">+</span> <span class="n">beta</span><span class="o">*</span><span class="n">xpp11</span> <span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">residuum</span> <span class="o">=</span> <span class="n">norm</span><span class="p">(</span><span class="n">xpp11</span><span class="o">-</span><span class="n">xpp1</span><span class="p">)</span><span class="o">/</span><span class="n">norm</span><span class="p">(</span><span class="n">xpp11</span><span class="p">)</span>
|
|
||||||
<span class="n">xpp1</span> <span class="o">=</span> <span class="n">xpp11</span>
|
|
||||||
<span class="k">if</span> <span class="n">residuum</span> <span class="o"><</span> <span class="n">tol</span><span class="p">:</span>
|
|
||||||
<span class="k">break</span>
|
|
||||||
<span class="n">iterations</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">j</span><span class="o">+</span><span class="mi">1</span>
|
|
||||||
|
|
||||||
<span class="n">xpp</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">xpp1</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
|
|
||||||
<span class="n">xp</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">xp1</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
|
|
||||||
<span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,:]</span> <span class="o">=</span> <span class="n">x1</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
|
|
||||||
<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Numerical integration of ODE using explicite '</span> <span class="o">+</span>
|
|
||||||
<span class="s1">'newmark method was successful.'</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">xp</span><span class="p">,</span> <span class="n">xpp</span><span class="p">,</span> <span class="n">iterations</span></div>
|
|
||||||
<span class="c1"># x = concatenate((x, xp, xpp), axis=1)</span>
|
|
||||||
</pre></div>
|
|
||||||
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|
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219
docs/build/html/_modules/numerical/ode_model.html
vendored
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@@ -1,219 +0,0 @@
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<h1>Source code for numerical.ode_model</h1><div class="highlight"><pre>
|
|
||||||
<span></span><span class="ch">#!/usr/bin/env python</span>
|
|
||||||
<span class="c1"># -*- coding: utf-8 -*-</span>
|
|
||||||
<span class="sd">"""Mathmatical models governed by ordinary differential equations.</span>
|
|
||||||
|
|
||||||
<span class="sd">Describes initial value problems as systems of first order ordinary differential</span>
|
|
||||||
<span class="sd">equations.</span>
|
|
||||||
|
|
||||||
<span class="sd">:Date: 2019-05-25</span>
|
|
||||||
|
|
||||||
<span class="sd">.. module:: ode_model</span>
|
|
||||||
<span class="sd"> :platform: *nix, Windows</span>
|
|
||||||
<span class="sd"> :synopsis: Models of ordinary differential equations.</span>
|
|
||||||
|
|
||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
|
||||||
<span class="sd">"""</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span><span class="p">,</span> <span class="n">print_function</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span><span class="p">,</span> <span class="n">cos</span><span class="p">,</span> <span class="n">sin</span><span class="p">,</span> <span class="n">dot</span><span class="p">,</span> <span class="n">square</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">numpy.linalg</span> <span class="kn">import</span> <span class="n">inv</span>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="disk"><a class="viewcode-back" href="../../numerical.html#numerical.ode_model.disk">[docs]</a><span class="k">def</span> <span class="nf">disk</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Rotation of an eccentric disk.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param x: values of the function</span>
|
|
||||||
<span class="sd"> :type x: list</span>
|
|
||||||
<span class="sd"> :param t: time</span>
|
|
||||||
<span class="sd"> :type t: list</span>
|
|
||||||
<span class="sd"> :param `*p`: parameters of the function</span>
|
|
||||||
|
|
||||||
<span class="sd"> * diameter</span>
|
|
||||||
<span class="sd"> * eccentricity</span>
|
|
||||||
<span class="sd"> * torque</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">qp1</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span>
|
|
||||||
<span class="n">qp2</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span>
|
|
||||||
<span class="n">qp3</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span>
|
|
||||||
<span class="n">M</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
|
||||||
<span class="n">y</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">+</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">-</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span> \
|
|
||||||
<span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span><span class="o">+</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">-</span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span> \
|
|
||||||
<span class="p">[</span><span class="n">p</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">+</span><span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">])]])</span>
|
|
||||||
<span class="n">qp46</span> <span class="o">=</span> <span class="n">dot</span><span class="p">(</span><span class="n">inv</span><span class="p">(</span><span class="n">M</span><span class="p">),</span> <span class="n">y</span><span class="p">)</span>
|
|
||||||
<span class="n">qp4</span><span class="p">,</span> <span class="n">qp5</span><span class="p">,</span> <span class="n">qp6</span> <span class="o">=</span> <span class="n">qp46</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span> <span class="c1"># 2d array to 1d array to list</span>
|
|
||||||
<span class="k">return</span> <span class="n">qp1</span><span class="p">,</span> <span class="n">qp2</span><span class="p">,</span> <span class="n">qp3</span><span class="p">,</span> <span class="n">qp4</span><span class="p">,</span> <span class="n">qp5</span><span class="p">,</span> <span class="n">qp6</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="disk_nm"><a class="viewcode-back" href="../../numerical.html#numerical.ode_model.disk_nm">[docs]</a><span class="k">def</span> <span class="nf">disk_nm</span><span class="p">(</span><span class="n">xn</span><span class="p">,</span> <span class="n">xpn</span><span class="p">,</span> <span class="n">xppn</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Rotation of an eccentric disk.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param xn: values of the function</span>
|
|
||||||
<span class="sd"> :type xn: list</span>
|
|
||||||
<span class="sd"> :param xpn: first derivative values of the function</span>
|
|
||||||
<span class="sd"> :type xpn: list</span>
|
|
||||||
<span class="sd"> :param xppn: second derivative values of the function</span>
|
|
||||||
<span class="sd"> :type xppn: list</span>
|
|
||||||
<span class="sd"> :param t: time</span>
|
|
||||||
<span class="sd"> :type t: list</span>
|
|
||||||
<span class="sd"> :param `*p`: parameters of the function</span>
|
|
||||||
|
|
||||||
<span class="sd"> * diameter</span>
|
|
||||||
<span class="sd"> * eccentricity</span>
|
|
||||||
<span class="sd"> * torque</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">N</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="n">xppn</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xppn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">square</span><span class="p">(</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">+</span><span class="n">xn</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
|
|
||||||
<span class="p">[</span><span class="n">xppn</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xppn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">square</span><span class="p">(</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">+</span><span class="n">xn</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
|
|
||||||
<span class="p">[</span><span class="n">xppn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">+</span><span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="o">-</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xn</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xn</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">-</span><span class="n">p</span><span class="p">[</span><span class="mi">2</span><span class="p">]]])</span>
|
|
||||||
<span class="n">dN</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">xppn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">square</span><span class="p">(</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">xppn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">+</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">square</span><span class="p">(</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="o">-</span><span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xn</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xn</span><span class="p">[</span><span class="mi">1</span><span class="p">])]])</span>
|
|
||||||
<span class="n">dNp</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
|
|
||||||
<span class="n">dNpp</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
|
||||||
<span class="k">return</span> <span class="n">N</span><span class="p">,</span> <span class="n">dN</span><span class="p">,</span> <span class="n">dNp</span><span class="p">,</span> <span class="n">dNpp</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="disk_nmmdk"><a class="viewcode-back" href="../../numerical.html#numerical.ode_model.disk_nmmdk">[docs]</a><span class="k">def</span> <span class="nf">disk_nmmdk</span><span class="p">(</span><span class="n">xn</span><span class="p">,</span> <span class="n">xpn</span><span class="p">,</span> <span class="n">xppn</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Rotation of an eccentric disk.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param xn: values of the function</span>
|
|
||||||
<span class="sd"> :type xn: list</span>
|
|
||||||
<span class="sd"> :param xpn: derivative values of the function</span>
|
|
||||||
<span class="sd"> :type xpn: list</span>
|
|
||||||
<span class="sd"> :param xppn: second derivative values of the function</span>
|
|
||||||
<span class="sd"> :type xppn: list</span>
|
|
||||||
<span class="sd"> :param t: time</span>
|
|
||||||
<span class="sd"> :type t: list</span>
|
|
||||||
<span class="sd"> :param `*p`: parameters of the function</span>
|
|
||||||
|
|
||||||
<span class="sd"> * diameter</span>
|
|
||||||
<span class="sd"> * eccentricity</span>
|
|
||||||
<span class="sd"> * torque</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">rm</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="n">xppn</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xppn</span><span class="p">[</span><span class="mi">2</span><span class="p">]],</span>
|
|
||||||
<span class="p">[</span><span class="n">xppn</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xppn</span><span class="p">[</span><span class="mi">2</span><span class="p">]],</span>
|
|
||||||
<span class="p">[</span><span class="n">xppn</span><span class="p">[</span><span class="mi">2</span><span class="p">]]])</span>
|
|
||||||
<span class="n">rmx</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">xppn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">xppn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
|
|
||||||
<span class="n">rmxpp</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
|
||||||
<span class="n">rd</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">square</span><span class="p">(</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">square</span><span class="p">(</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">]])</span>
|
|
||||||
<span class="n">rdx</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">square</span><span class="p">(</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">+</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">square</span><span class="p">(</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
|
|
||||||
<span class="n">rdxp</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xpn</span><span class="p">[</span><span class="mi">2</span><span class="p">]],</span>
|
|
||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
|
|
||||||
<span class="n">rk</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="n">xn</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
|
|
||||||
<span class="p">[</span><span class="n">xn</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
|
|
||||||
<span class="p">[</span><span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="o">-</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xn</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xn</span><span class="p">[</span><span class="mi">1</span><span class="p">])]])</span>
|
|
||||||
<span class="n">rkx</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
|
|
||||||
<span class="p">[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
|
|
||||||
<span class="p">[</span><span class="o">-</span><span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="n">sin</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xn</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="n">cos</span><span class="p">(</span><span class="n">xn</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">xn</span><span class="p">[</span><span class="mi">1</span><span class="p">])]])</span>
|
|
||||||
<span class="n">f</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="n">p</span><span class="p">[</span><span class="mi">2</span><span class="p">]]])</span>
|
|
||||||
<span class="k">return</span> <span class="n">rm</span><span class="p">,</span> <span class="n">rmx</span><span class="p">,</span> <span class="n">rmxpp</span><span class="p">,</span> <span class="n">rd</span><span class="p">,</span> <span class="n">rdx</span><span class="p">,</span> <span class="n">rdxp</span><span class="p">,</span> <span class="n">rk</span><span class="p">,</span> <span class="n">rkx</span><span class="p">,</span> <span class="n">f</span></div>
|
|
||||||
|
|
||||||
<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
|
|
||||||
<span class="kc">True</span>
|
|
||||||
</pre></div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
|
|
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</div>
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<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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<div class="sphinxsidebarwrapper">
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<h1 class="logo"><a href="../../index.html">pylib</a></h1>
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|
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|
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<h3>Navigation</h3>
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<div class="relations">
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<h3>Related Topics</h3>
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<ul>
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<li><a href="../../index.html">Documentation overview</a><ul>
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<li><a href="../index.html">Module code</a><ul>
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</ul></li>
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||||||
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©2019, Daniel Weschke.
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</html>
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||||||
22
docs/build/html/_modules/pylib/data.html
vendored
22
docs/build/html/_modules/pylib/data.html
vendored
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.data — pylib 2019.5.19 documentation</title>
|
<title>pylib.data — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
||||||
@@ -48,7 +48,7 @@
|
|||||||
<span class="kn">import</span> <span class="nn">math</span>
|
<span class="kn">import</span> <span class="nn">math</span>
|
||||||
<span class="kn">import</span> <span class="nn">pickle</span>
|
<span class="kn">import</span> <span class="nn">pickle</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="read"><a class="viewcode-back" href="../../pylib.html#pylib.data.read">[docs]</a><span class="k">def</span> <span class="nf">read</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">x_column</span><span class="p">,</span> <span class="n">y_column</span><span class="p">,</span> <span class="n">default</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<div class="viewcode-block" id="read"><a class="viewcode-back" href="../../pylib.data.html#pylib.data.read">[docs]</a><span class="k">def</span> <span class="nf">read</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">x_column</span><span class="p">,</span> <span class="n">y_column</span><span class="p">,</span> <span class="n">default</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sd">"""Read ascii data file.</span>
|
<span class="sd">"""Read ascii data file.</span>
|
||||||
|
|
||||||
<span class="sd"> :param filename: file to read</span>
|
<span class="sd"> :param filename: file to read</span>
|
||||||
@@ -86,7 +86,7 @@
|
|||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'data file not found'</span><span class="p">)</span>
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'data file not found'</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></div>
|
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="write"><a class="viewcode-back" href="../../pylib.html#pylib.data.write">[docs]</a><span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">data</span><span class="p">):</span>
|
<div class="viewcode-block" id="write"><a class="viewcode-back" href="../../pylib.data.html#pylib.data.write">[docs]</a><span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">data</span><span class="p">):</span>
|
||||||
<span class="sd">"""Write ascii file.</span>
|
<span class="sd">"""Write ascii file.</span>
|
||||||
|
|
||||||
<span class="sd"> :param file_name: file to write</span>
|
<span class="sd"> :param file_name: file to write</span>
|
||||||
@@ -97,7 +97,7 @@
|
|||||||
<span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="s1">'w'</span><span class="p">)</span> <span class="k">as</span> <span class="n">file</span><span class="p">:</span>
|
<span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="s1">'w'</span><span class="p">)</span> <span class="k">as</span> <span class="n">file</span><span class="p">:</span>
|
||||||
<span class="n">file</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="n">data</span><span class="p">)</span></div>
|
<span class="n">file</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="n">data</span><span class="p">)</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="load"><a class="viewcode-back" href="../../pylib.html#pylib.data.load">[docs]</a><span class="k">def</span> <span class="nf">load</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">default</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<div class="viewcode-block" id="load"><a class="viewcode-back" href="../../pylib.data.html#pylib.data.load">[docs]</a><span class="k">def</span> <span class="nf">load</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">default</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sd">"""Load stored program objects from binary file.</span>
|
<span class="sd">"""Load stored program objects from binary file.</span>
|
||||||
|
|
||||||
<span class="sd"> :param file_name: file to load</span>
|
<span class="sd"> :param file_name: file to load</span>
|
||||||
@@ -125,7 +125,7 @@
|
|||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'no saved datas found'</span><span class="p">)</span>
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'no saved datas found'</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">object_data</span></div>
|
<span class="k">return</span> <span class="n">object_data</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="store"><a class="viewcode-back" href="../../pylib.html#pylib.data.store">[docs]</a><span class="k">def</span> <span class="nf">store</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">object_data</span><span class="p">):</span>
|
<div class="viewcode-block" id="store"><a class="viewcode-back" href="../../pylib.data.html#pylib.data.store">[docs]</a><span class="k">def</span> <span class="nf">store</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">object_data</span><span class="p">):</span>
|
||||||
<span class="sd">"""Store program objects to binary file.</span>
|
<span class="sd">"""Store program objects to binary file.</span>
|
||||||
|
|
||||||
<span class="sd"> :param file_name: file to store</span>
|
<span class="sd"> :param file_name: file to store</span>
|
||||||
@@ -137,7 +137,7 @@
|
|||||||
<span class="c1"># every dump needs a load</span>
|
<span class="c1"># every dump needs a load</span>
|
||||||
<span class="n">pickle</span><span class="o">.</span><span class="n">dump</span><span class="p">(</span><span class="n">object_data</span><span class="p">,</span> <span class="n">output</span><span class="p">,</span> <span class="n">pickle</span><span class="o">.</span><span class="n">HIGHEST_PROTOCOL</span><span class="p">)</span></div>
|
<span class="n">pickle</span><span class="o">.</span><span class="n">dump</span><span class="p">(</span><span class="n">object_data</span><span class="p">,</span> <span class="n">output</span><span class="p">,</span> <span class="n">pickle</span><span class="o">.</span><span class="n">HIGHEST_PROTOCOL</span><span class="p">)</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="fold_list"><a class="viewcode-back" href="../../pylib.html#pylib.data.fold_list">[docs]</a><span class="k">def</span> <span class="nf">fold_list</span><span class="p">(</span><span class="n">lst</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
|
<div class="viewcode-block" id="fold_list"><a class="viewcode-back" href="../../pylib.data.html#pylib.data.fold_list">[docs]</a><span class="k">def</span> <span class="nf">fold_list</span><span class="p">(</span><span class="n">lst</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
|
||||||
<span class="sd">"""Convert one-dimensional kx1 array (list) to two-dimensional mxn</span>
|
<span class="sd">"""Convert one-dimensional kx1 array (list) to two-dimensional mxn</span>
|
||||||
<span class="sd"> array. m = k / n</span>
|
<span class="sd"> array. m = k / n</span>
|
||||||
|
|
||||||
@@ -154,7 +154,7 @@
|
|||||||
<span class="n">length</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">k</span><span class="o">/</span><span class="n">n</span><span class="p">)</span>
|
<span class="n">length</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">k</span><span class="o">/</span><span class="n">n</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="p">[</span><span class="n">lst</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">n</span><span class="p">:</span><span class="n">i</span><span class="o">*</span><span class="n">n</span><span class="o">+</span><span class="n">n</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">length</span><span class="p">)]</span></div>
|
<span class="k">return</span> <span class="p">[</span><span class="n">lst</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">n</span><span class="p">:</span><span class="n">i</span><span class="o">*</span><span class="n">n</span><span class="o">+</span><span class="n">n</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">length</span><span class="p">)]</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="seq"><a class="viewcode-back" href="../../pylib.html#pylib.data.seq">[docs]</a><span class="k">def</span> <span class="nf">seq</span><span class="p">(</span><span class="n">start</span><span class="p">,</span> <span class="n">stop</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">step</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
|
<div class="viewcode-block" id="seq"><a class="viewcode-back" href="../../pylib.data.html#pylib.data.seq">[docs]</a><span class="k">def</span> <span class="nf">seq</span><span class="p">(</span><span class="n">start</span><span class="p">,</span> <span class="n">stop</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">step</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Create an arithmetic bounded sequence.</span>
|
<span class="sa">r</span><span class="sd">"""Create an arithmetic bounded sequence.</span>
|
||||||
|
|
||||||
<span class="sd"> The sequence is one of the following;</span>
|
<span class="sd"> The sequence is one of the following;</span>
|
||||||
@@ -208,7 +208,7 @@
|
|||||||
<span class="n">lst</span> <span class="o">=</span> <span class="p">[</span><span class="nb">round</span><span class="p">(</span><span class="n">start</span> <span class="o">+</span> <span class="n">step</span><span class="o">*</span><span class="n">i</span><span class="p">,</span> <span class="n">exponent</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
|
<span class="n">lst</span> <span class="o">=</span> <span class="p">[</span><span class="nb">round</span><span class="p">(</span><span class="n">start</span> <span class="o">+</span> <span class="n">step</span><span class="o">*</span><span class="n">i</span><span class="p">,</span> <span class="n">exponent</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
|
||||||
<span class="k">return</span> <span class="n">lst</span></div>
|
<span class="k">return</span> <span class="n">lst</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="unique_ending"><a class="viewcode-back" href="../../pylib.html#pylib.data.unique_ending">[docs]</a><span class="k">def</span> <span class="nf">unique_ending</span><span class="p">(</span><span class="n">ids</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
|
<div class="viewcode-block" id="unique_ending"><a class="viewcode-back" href="../../pylib.data.html#pylib.data.unique_ending">[docs]</a><span class="k">def</span> <span class="nf">unique_ending</span><span class="p">(</span><span class="n">ids</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
|
||||||
<span class="sd">"""From id list get list with unique ending.</span>
|
<span class="sd">"""From id list get list with unique ending.</span>
|
||||||
|
|
||||||
<span class="sd"> :param ids: ids</span>
|
<span class="sd"> :param ids: ids</span>
|
||||||
@@ -226,7 +226,7 @@
|
|||||||
<span class="k">else</span><span class="p">:</span>
|
<span class="k">else</span><span class="p">:</span>
|
||||||
<span class="k">return</span> <span class="n">x</span></div>
|
<span class="k">return</span> <span class="n">x</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="get_id"><a class="viewcode-back" href="../../pylib.html#pylib.data.get_id">[docs]</a><span class="k">def</span> <span class="nf">get_id</span><span class="p">(</span><span class="n">ids</span><span class="p">,</span> <span class="n">uide</span><span class="p">):</span>
|
<div class="viewcode-block" id="get_id"><a class="viewcode-back" href="../../pylib.data.html#pylib.data.get_id">[docs]</a><span class="k">def</span> <span class="nf">get_id</span><span class="p">(</span><span class="n">ids</span><span class="p">,</span> <span class="n">uide</span><span class="p">):</span>
|
||||||
<span class="sd">"""Get full id from unique id ending.</span>
|
<span class="sd">"""Get full id from unique id ending.</span>
|
||||||
|
|
||||||
<span class="sd"> :param ids: ids</span>
|
<span class="sd"> :param ids: ids</span>
|
||||||
@@ -257,6 +257,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
18
docs/build/html/_modules/pylib/date.html
vendored
18
docs/build/html/_modules/pylib/date.html
vendored
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.date — pylib 2019.5.19 documentation</title>
|
<title>pylib.date — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
||||||
@@ -46,7 +46,7 @@
|
|||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
||||||
<span class="sd">"""</span>
|
<span class="sd">"""</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="gaußsche_osterformel"><a class="viewcode-back" href="../../pylib.html#pylib.date.gaußsche_osterformel">[docs]</a><span class="k">def</span> <span class="nf">gaußsche_osterformel</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
<div class="viewcode-block" id="gaußsche_osterformel"><a class="viewcode-back" href="../../pylib.date.html#pylib.date.gaußsche_osterformel">[docs]</a><span class="k">def</span> <span class="nf">gaußsche_osterformel</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
||||||
<span class="sd">"""Gaußsche Osterformel.</span>
|
<span class="sd">"""Gaußsche Osterformel.</span>
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the Easter Sunday</span>
|
<span class="sd"> :param year: the year to calculate the Easter Sunday</span>
|
||||||
@@ -95,7 +95,7 @@
|
|||||||
<span class="n">os</span> <span class="o">=</span> <span class="n">og</span> <span class="o">+</span> <span class="n">oe</span>
|
<span class="n">os</span> <span class="o">=</span> <span class="n">og</span> <span class="o">+</span> <span class="n">oe</span>
|
||||||
<span class="k">return</span> <span class="n">os</span></div>
|
<span class="k">return</span> <span class="n">os</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="easter_sunday"><a class="viewcode-back" href="../../pylib.html#pylib.date.easter_sunday">[docs]</a><span class="k">def</span> <span class="nf">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
<div class="viewcode-block" id="easter_sunday"><a class="viewcode-back" href="../../pylib.date.html#pylib.date.easter_sunday">[docs]</a><span class="k">def</span> <span class="nf">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
||||||
<span class="sd">"""Easter Sunday.</span>
|
<span class="sd">"""Easter Sunday.</span>
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the Easter Sunday</span>
|
<span class="sd"> :param year: the year to calculate the Easter Sunday</span>
|
||||||
@@ -108,7 +108,7 @@
|
|||||||
<span class="n">day</span> <span class="o">=</span> <span class="n">march</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=</span><span class="n">gaußsche_osterformel</span><span class="p">(</span><span class="n">year</span><span class="p">))</span>
|
<span class="n">day</span> <span class="o">=</span> <span class="n">march</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=</span><span class="n">gaußsche_osterformel</span><span class="p">(</span><span class="n">year</span><span class="p">))</span>
|
||||||
<span class="k">return</span> <span class="n">day</span></div>
|
<span class="k">return</span> <span class="n">day</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="easter_friday"><a class="viewcode-back" href="../../pylib.html#pylib.date.easter_friday">[docs]</a><span class="k">def</span> <span class="nf">easter_friday</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
<div class="viewcode-block" id="easter_friday"><a class="viewcode-back" href="../../pylib.date.html#pylib.date.easter_friday">[docs]</a><span class="k">def</span> <span class="nf">easter_friday</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
||||||
<span class="sd">"""Easter Friday.</span>
|
<span class="sd">"""Easter Friday.</span>
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the Easter Friday</span>
|
<span class="sd"> :param year: the year to calculate the Easter Friday</span>
|
||||||
@@ -120,7 +120,7 @@
|
|||||||
<span class="n">day</span> <span class="o">=</span> <span class="n">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">)</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=-</span><span class="mi">2</span><span class="p">)</span>
|
<span class="n">day</span> <span class="o">=</span> <span class="n">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">)</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=-</span><span class="mi">2</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">day</span></div>
|
<span class="k">return</span> <span class="n">day</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="easter_monday"><a class="viewcode-back" href="../../pylib.html#pylib.date.easter_monday">[docs]</a><span class="k">def</span> <span class="nf">easter_monday</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
<div class="viewcode-block" id="easter_monday"><a class="viewcode-back" href="../../pylib.date.html#pylib.date.easter_monday">[docs]</a><span class="k">def</span> <span class="nf">easter_monday</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
||||||
<span class="sd">"""Easter Monday.</span>
|
<span class="sd">"""Easter Monday.</span>
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the Easter Monday</span>
|
<span class="sd"> :param year: the year to calculate the Easter Monday</span>
|
||||||
@@ -132,7 +132,7 @@
|
|||||||
<span class="n">day</span> <span class="o">=</span> <span class="n">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">)</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=+</span><span class="mi">1</span><span class="p">)</span>
|
<span class="n">day</span> <span class="o">=</span> <span class="n">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">)</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=+</span><span class="mi">1</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">day</span></div>
|
<span class="k">return</span> <span class="n">day</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="ascension_of_jesus"><a class="viewcode-back" href="../../pylib.html#pylib.date.ascension_of_jesus">[docs]</a><span class="k">def</span> <span class="nf">ascension_of_jesus</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
<div class="viewcode-block" id="ascension_of_jesus"><a class="viewcode-back" href="../../pylib.date.html#pylib.date.ascension_of_jesus">[docs]</a><span class="k">def</span> <span class="nf">ascension_of_jesus</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
||||||
<span class="sd">"""Ascension of Jesus.</span>
|
<span class="sd">"""Ascension of Jesus.</span>
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the ascension of Jesus</span>
|
<span class="sd"> :param year: the year to calculate the ascension of Jesus</span>
|
||||||
@@ -144,7 +144,7 @@
|
|||||||
<span class="n">day</span> <span class="o">=</span> <span class="n">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">)</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=+</span><span class="mi">39</span><span class="p">)</span>
|
<span class="n">day</span> <span class="o">=</span> <span class="n">easter_sunday</span><span class="p">(</span><span class="n">year</span><span class="p">)</span> <span class="o">+</span> <span class="n">datetime</span><span class="o">.</span><span class="n">timedelta</span><span class="p">(</span><span class="n">days</span><span class="o">=+</span><span class="mi">39</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">day</span></div>
|
<span class="k">return</span> <span class="n">day</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="pentecost"><a class="viewcode-back" href="../../pylib.html#pylib.date.pentecost">[docs]</a><span class="k">def</span> <span class="nf">pentecost</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
<div class="viewcode-block" id="pentecost"><a class="viewcode-back" href="../../pylib.date.html#pylib.date.pentecost">[docs]</a><span class="k">def</span> <span class="nf">pentecost</span><span class="p">(</span><span class="n">year</span><span class="p">):</span>
|
||||||
<span class="sd">"""Pentecost.</span>
|
<span class="sd">"""Pentecost.</span>
|
||||||
|
|
||||||
<span class="sd"> :param year: the year to calculate the Pentecost</span>
|
<span class="sd"> :param year: the year to calculate the Pentecost</span>
|
||||||
@@ -173,6 +173,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
21
docs/build/html/_modules/pylib/drawblock.html
vendored
21
docs/build/html/_modules/pylib/drawblock.html
vendored
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.drawblock — pylib 2019.5.19 documentation</title>
|
<title>pylib.drawblock — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
||||||
@@ -35,12 +35,23 @@
|
|||||||
<h1>Source code for pylib.drawblock</h1><div class="highlight"><pre>
|
<h1>Source code for pylib.drawblock</h1><div class="highlight"><pre>
|
||||||
<span></span><span class="ch">#!/usr/bin/env python</span>
|
<span></span><span class="ch">#!/usr/bin/env python</span>
|
||||||
<span class="c1"># -*- coding: utf-8 -*-</span>
|
<span class="c1"># -*- coding: utf-8 -*-</span>
|
||||||
|
<span class="sd">"""Draw with block characters.</span>
|
||||||
|
|
||||||
|
<span class="sd">:Date: 2019-11-15</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="histogram"><a class="viewcode-back" href="../../pylib.html#pylib.drawblock.histogram">[docs]</a><span class="k">def</span> <span class="nf">histogram</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
<span class="sd">.. module:: drawblock</span>
|
||||||
|
<span class="sd"> :platform: *nix, Windows</span>
|
||||||
|
<span class="sd"> :synopsis: Draw with block characters.</span>
|
||||||
|
|
||||||
|
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
||||||
|
<span class="sd">"""</span>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="histogram"><a class="viewcode-back" href="../../pylib.drawblock.html#pylib.drawblock.histogram">[docs]</a><span class="k">def</span> <span class="nf">histogram</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||||
<span class="sd">"""Histogram chart with block symbols.</span>
|
<span class="sd">"""Histogram chart with block symbols.</span>
|
||||||
|
|
||||||
<span class="sd"> dots:</span>
|
<span class="sd"> ::</span>
|
||||||
|
|
||||||
|
<span class="sd"> dots</span>
|
||||||
<span class="sd"> ,_,</span>
|
<span class="sd"> ,_,</span>
|
||||||
<span class="sd"> |8|</span>
|
<span class="sd"> |8|</span>
|
||||||
<span class="sd"> |7|</span>
|
<span class="sd"> |7|</span>
|
||||||
@@ -176,6 +187,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
18
docs/build/html/_modules/pylib/function.html
vendored
18
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<html xmlns="http://www.w3.org/1999/xhtml">
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<html xmlns="http://www.w3.org/1999/xhtml">
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<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.function — pylib 2019.5.19 documentation</title>
|
<title>pylib.function — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
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|
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<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
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<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
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@@ -49,7 +49,7 @@
|
|||||||
<span class="kn">from</span> <span class="nn">pylib.data</span> <span class="kn">import</span> <span class="n">seq</span>
|
<span class="kn">from</span> <span class="nn">pylib.data</span> <span class="kn">import</span> <span class="n">seq</span>
|
||||||
<span class="kn">from</span> <span class="nn">pylib.mathematics</span> <span class="kn">import</span> <span class="n">lcm</span>
|
<span class="kn">from</span> <span class="nn">pylib.mathematics</span> <span class="kn">import</span> <span class="n">lcm</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="transformation"><a class="viewcode-back" href="../../pylib.html#pylib.function.transformation">[docs]</a><span class="k">def</span> <span class="nf">transformation</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">scale_vertical</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">scale_horizontal</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
|
<div class="viewcode-block" id="transformation"><a class="viewcode-back" href="../../pylib.function.html#pylib.function.transformation">[docs]</a><span class="k">def</span> <span class="nf">transformation</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">scale_vertical</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">scale_horizontal</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
|
||||||
<span class="n">shift_horizontal</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">shift_vertical</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
|
<span class="n">shift_horizontal</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">shift_vertical</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Transform functions.</span>
|
<span class="sa">r</span><span class="sd">"""Transform functions.</span>
|
||||||
|
|
||||||
@@ -93,7 +93,7 @@
|
|||||||
<span class="n">transformation</span><span class="p">(</span>
|
<span class="n">transformation</span><span class="p">(</span>
|
||||||
<span class="n">f</span><span class="p">[</span><span class="mi">1</span><span class="p">:],</span> <span class="n">scale_vertical</span><span class="o">=</span><span class="n">a</span><span class="p">,</span> <span class="n">scale_horizontal</span><span class="o">=</span><span class="n">b</span><span class="p">,</span> <span class="n">shift_horizontal</span><span class="o">=</span><span class="n">c</span><span class="p">,</span> <span class="n">shift_vertical</span><span class="o">=</span><span class="n">d</span><span class="p">)</span></div>
|
<span class="n">f</span><span class="p">[</span><span class="mi">1</span><span class="p">:],</span> <span class="n">scale_vertical</span><span class="o">=</span><span class="n">a</span><span class="p">,</span> <span class="n">scale_horizontal</span><span class="o">=</span><span class="n">b</span><span class="p">,</span> <span class="n">shift_horizontal</span><span class="o">=</span><span class="n">c</span><span class="p">,</span> <span class="n">shift_vertical</span><span class="o">=</span><span class="n">d</span><span class="p">)</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="sine_wave"><a class="viewcode-back" href="../../pylib.html#pylib.function.sine_wave">[docs]</a><span class="k">def</span> <span class="nf">sine_wave</span><span class="p">(</span><span class="n">A</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">phi</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">D</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">degree</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<div class="viewcode-block" id="sine_wave"><a class="viewcode-back" href="../../pylib.function.html#pylib.function.sine_wave">[docs]</a><span class="k">def</span> <span class="nf">sine_wave</span><span class="p">(</span><span class="n">A</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">phi</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">D</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">degree</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""A sine wave or sinusoid is a mathematical curve that describes a</span>
|
<span class="sa">r</span><span class="sd">"""A sine wave or sinusoid is a mathematical curve that describes a</span>
|
||||||
<span class="sd"> smooth periodic oscillation.</span>
|
<span class="sd"> smooth periodic oscillation.</span>
|
||||||
|
|
||||||
@@ -154,7 +154,7 @@
|
|||||||
<span class="n">phi</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">radians</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span>
|
<span class="n">phi</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">radians</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="o">=</span><span class="mi">0</span><span class="p">:</span> <span class="n">A</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">k</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">f</span><span class="o">*</span><span class="n">t</span> <span class="o">+</span> <span class="n">phi</span><span class="p">)</span> <span class="o">+</span> <span class="n">D</span></div>
|
<span class="k">return</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="o">=</span><span class="mi">0</span><span class="p">:</span> <span class="n">A</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">k</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">f</span><span class="o">*</span><span class="n">t</span> <span class="o">+</span> <span class="n">phi</span><span class="p">)</span> <span class="o">+</span> <span class="n">D</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="cosine_wave"><a class="viewcode-back" href="../../pylib.html#pylib.function.cosine_wave">[docs]</a><span class="k">def</span> <span class="nf">cosine_wave</span><span class="p">(</span><span class="n">A</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">phi</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">D</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">degree</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<div class="viewcode-block" id="cosine_wave"><a class="viewcode-back" href="../../pylib.function.html#pylib.function.cosine_wave">[docs]</a><span class="k">def</span> <span class="nf">cosine_wave</span><span class="p">(</span><span class="n">A</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">phi</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">D</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">degree</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""A cosine wave is said to be sinusoidal, because,</span>
|
<span class="sa">r</span><span class="sd">"""A cosine wave is said to be sinusoidal, because,</span>
|
||||||
<span class="sd"> :math:`\cos(x) = \sin(x + \pi/2)`, which is also a sine wave with a</span>
|
<span class="sd"> :math:`\cos(x) = \sin(x + \pi/2)`, which is also a sine wave with a</span>
|
||||||
<span class="sd"> phase-shift of π/2 radians. Because of this head start, it is often</span>
|
<span class="sd"> phase-shift of π/2 radians. Because of this head start, it is often</span>
|
||||||
@@ -194,7 +194,7 @@
|
|||||||
<span class="c1"># roulette</span>
|
<span class="c1"># roulette</span>
|
||||||
<span class="c1">#</span>
|
<span class="c1">#</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="hypotrochoid"><a class="viewcode-back" href="../../pylib.html#pylib.function.hypotrochoid">[docs]</a><span class="k">def</span> <span class="nf">hypotrochoid</span><span class="p">(</span><span class="n">R</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
|
<div class="viewcode-block" id="hypotrochoid"><a class="viewcode-back" href="../../pylib.function.html#pylib.function.hypotrochoid">[docs]</a><span class="k">def</span> <span class="nf">hypotrochoid</span><span class="p">(</span><span class="n">R</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Hypotrochoid</span>
|
<span class="sa">r</span><span class="sd">"""Hypotrochoid</span>
|
||||||
|
|
||||||
<span class="sd"> A point is attached with a distance d from the center of a circle</span>
|
<span class="sd"> A point is attached with a distance d from the center of a circle</span>
|
||||||
@@ -242,7 +242,7 @@
|
|||||||
<span class="n">theta_end</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">lcm</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">R</span><span class="p">)</span><span class="o">/</span><span class="n">R</span>
|
<span class="n">theta_end</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">lcm</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">R</span><span class="p">)</span><span class="o">/</span><span class="n">R</span>
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">theta_end</span></div>
|
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">theta_end</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="epitrochoid"><a class="viewcode-back" href="../../pylib.html#pylib.function.epitrochoid">[docs]</a><span class="k">def</span> <span class="nf">epitrochoid</span><span class="p">(</span><span class="n">R</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
|
<div class="viewcode-block" id="epitrochoid"><a class="viewcode-back" href="../../pylib.function.html#pylib.function.epitrochoid">[docs]</a><span class="k">def</span> <span class="nf">epitrochoid</span><span class="p">(</span><span class="n">R</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Epitrochoid</span>
|
<span class="sa">r</span><span class="sd">"""Epitrochoid</span>
|
||||||
|
|
||||||
<span class="sd"> A point is attached with a distance d from the center of a circle</span>
|
<span class="sd"> A point is attached with a distance d from the center of a circle</span>
|
||||||
@@ -287,7 +287,7 @@
|
|||||||
<span class="n">theta_end</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span>
|
<span class="n">theta_end</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span>
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">theta_end</span></div>
|
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">theta_end</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="to_str"><a class="viewcode-back" href="../../pylib.html#pylib.function.to_str">[docs]</a><span class="k">def</span> <span class="nf">to_str</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">x_0</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">x_1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">t</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">h</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mi">80</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">char_set</span><span class="o">=</span><span class="s2">"line"</span><span class="p">):</span>
|
<div class="viewcode-block" id="to_str"><a class="viewcode-back" href="../../pylib.function.html#pylib.function.to_str">[docs]</a><span class="k">def</span> <span class="nf">to_str</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">x_0</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">x_1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">t</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">h</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mi">80</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">char_set</span><span class="o">=</span><span class="s2">"line"</span><span class="p">):</span>
|
||||||
<span class="sd">"""Represent functions as string frame with a specific character set.</span>
|
<span class="sd">"""Represent functions as string frame with a specific character set.</span>
|
||||||
<span class="sd"> which are normed to the range of [0, 1] to</span>
|
<span class="sd"> which are normed to the range of [0, 1] to</span>
|
||||||
|
|
||||||
@@ -468,6 +468,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
680
docs/build/html/_modules/pylib/geometry.html
vendored
680
docs/build/html/_modules/pylib/geometry.html
vendored
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.geometry — pylib 2019.5.19 documentation</title>
|
<title>pylib.geometry — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
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|
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@@ -37,7 +37,7 @@
|
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<span class="c1"># -*- coding: utf-8 -*-</span>
|
<span class="c1"># -*- coding: utf-8 -*-</span>
|
||||||
<span class="sd">"""2D geometry objects.</span>
|
<span class="sd">"""2D geometry objects.</span>
|
||||||
|
|
||||||
<span class="sd">:Date: 2019-08-28</span>
|
<span class="sd">:Date: 2019-12-21</span>
|
||||||
|
|
||||||
<span class="sd">.. module:: geometry</span>
|
<span class="sd">.. module:: geometry</span>
|
||||||
<span class="sd"> :platform: *nix, Windows</span>
|
<span class="sd"> :platform: *nix, Windows</span>
|
||||||
@@ -46,504 +46,218 @@
|
|||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
||||||
<span class="sd">"""</span>
|
<span class="sd">"""</span>
|
||||||
<span class="kn">import</span> <span class="nn">math</span>
|
<span class="kn">import</span> <span class="nn">math</span>
|
||||||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
<span class="kn">import</span> <span class="nn">copy</span>
|
||||||
|
<span class="kn">from</span> <span class="nn">mathematics</span> <span class="kn">import</span> <span class="n">vector</span><span class="p">,</span> <span class="n">matrix</span>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="Direction"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Direction">[docs]</a><span class="k">class</span> <span class="nc">Direction</span><span class="p">(</span><span class="n">vector</span><span class="p">):</span>
|
||||||
|
<span class="sd">"""Direction in local coordinate system"""</span>
|
||||||
|
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">z</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
|
||||||
|
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="distance"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.distance">[docs]</a><span class="k">def</span> <span class="nf">distance</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="p">):</span>
|
<span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
<span class="sd">"""Distance between two points (or length of a straight line).</span>
|
<span class="k">return</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">xyz</span><span class="p">())</span></div>
|
||||||
|
|
||||||
<span class="sd"> :param point1: first point (first end point of straight line)</span>
|
<div class="viewcode-block" id="Point"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Point">[docs]</a><span class="k">class</span> <span class="nc">Point</span><span class="p">(</span><span class="n">vector</span><span class="p">):</span>
|
||||||
<span class="sd"> :type point1: tuple</span>
|
<span class="sd">"""Point in local coordinate system"""</span>
|
||||||
<span class="sd"> :param point2: second point (second end point of straight line)</span>
|
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">z</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
|
||||||
<span class="sd"> :type point2: tuple</span>
|
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
|
||||||
|
|
||||||
<span class="sd"> :returns: distance between the two points</span>
|
<span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
<span class="sd"> :rtype: float</span>
|
<span class="k">return</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">xyz</span><span class="p">())</span></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="CS"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.CS">[docs]</a><span class="k">class</span> <span class="nc">CS</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
|
||||||
|
<span class="sd">"""Coordinate system</span>
|
||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">((</span><span class="n">point2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="p">(</span><span class="n">point2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span></div>
|
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">y</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">z</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]):</span>
|
||||||
|
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">([[</span><span class="o">*</span><span class="n">x</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="o">*</span><span class="n">y</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="o">*</span><span class="n">z</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
||||||
|
|
||||||
|
<span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
|
<span class="k">return</span> <span class="s1">'['</span> <span class="o">+</span> <span class="s1">', '</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_coordinates</span><span class="p">()])</span> <span class="o">+</span> <span class="s1">']'</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="angle"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.angle">[docs]</a><span class="k">def</span> <span class="nf">angle</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
<div class="viewcode-block" id="CS.x90"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.CS.x90">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="sd">"""Angle of point or between two points.</span>
|
<span class="k">def</span> <span class="nf">x90</span><span class="p">():</span>
|
||||||
|
<span class="k">return</span> <span class="n">CS</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span></div>
|
||||||
|
|
||||||
<span class="sd"> :param point1: (first) point</span>
|
<div class="viewcode-block" id="CS.xm90"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.CS.xm90">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="sd"> :type point1: tuple</span>
|
<span class="k">def</span> <span class="nf">xm90</span><span class="p">():</span>
|
||||||
<span class="sd"> :param point2: second point (default = None)</span>
|
<span class="k">return</span> <span class="n">CS</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span></div>
|
||||||
<span class="sd"> :type point2: tuple</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: angle of point or between two points</span>
|
<div class="viewcode-block" id="CS.y90"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.CS.y90">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="sd"> :rtype: float</span>
|
<span class="k">def</span> <span class="nf">y90</span><span class="p">():</span>
|
||||||
|
<span class="k">return</span> <span class="n">CS</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="CS.ym90"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.CS.ym90">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
|
<span class="k">def</span> <span class="nf">ym90</span><span class="p">():</span>
|
||||||
|
<span class="k">return</span> <span class="n">CS</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="CS.get_coordinates"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.CS.get_coordinates">[docs]</a> <span class="k">def</span> <span class="nf">get_coordinates</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
|
<span class="sd">"""Get coordinates in 3d space"""</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span><span class="p">[:</span><span class="mi">3</span><span class="p">,:</span><span class="mi">3</span><span class="p">]</span></div></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="World"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World">[docs]</a><span class="k">class</span> <span class="nc">World</span><span class="p">():</span>
|
||||||
|
<span class="sd">"""World-space with world-space coordinates</span>
|
||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">if</span> <span class="n">point2</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">point1</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">point1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_cs</span> <span class="o">=</span> <span class="n">CS</span><span class="p">()</span> <span class="c1"># Camera</span>
|
||||||
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">point2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">point2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span></div>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_objects</span> <span class="o">=</span> <span class="p">[]</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">_store_init</span><span class="p">()</span>
|
||||||
|
|
||||||
|
<span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
|
<span class="sd">"""Returns the Iterator object"""</span>
|
||||||
|
<span class="k">return</span> <span class="nb">iter</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">objects</span><span class="p">())</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="translate"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.translate">[docs]</a><span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="n">vec</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">_store_init</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
<span class="sd">"""Translate a point or polygon by a given vector.</span>
|
<span class="sd">"""Initialize or reset calculated values, because a new object was added.</span>
|
||||||
|
|
||||||
<span class="sd"> :param vec: translation vector</span>
|
|
||||||
<span class="sd"> :type vec: tuple</span>
|
|
||||||
<span class="sd"> :param `*pts`: points to translate</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: (point_x, point_y) or (point1, point2, ...)</span>
|
|
||||||
<span class="sd"> :rtype: tuple</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
|
||||||
<span class="sd"> :meth:`translate_xy`</span>
|
|
||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="n">vx</span><span class="p">,</span> <span class="n">vy</span> <span class="o">=</span> <span class="n">vec</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_bb</span> <span class="o">=</span> <span class="kc">None</span>
|
||||||
<span class="k">return</span> <span class="nb">tuple</span><span class="p">([(</span><span class="n">x</span><span class="o">+</span><span class="n">vx</span><span class="p">,</span> <span class="n">y</span><span class="o">+</span><span class="n">vy</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="n">pts</span><span class="p">])</span></div>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_sd</span> <span class="o">=</span> <span class="kc">None</span>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="World.cs"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.cs">[docs]</a> <span class="k">def</span> <span class="nf">cs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cs</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||||
|
<span class="k">if</span> <span class="n">cs</span><span class="p">:</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">_cs</span> <span class="o">=</span> <span class="n">cs</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_cs</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="translate_xy"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.translate_xy">[docs]</a><span class="k">def</span> <span class="nf">translate_xy</span><span class="p">(</span><span class="n">vec</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
|
<div class="viewcode-block" id="World.ch_cs"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.ch_cs">[docs]</a> <span class="k">def</span> <span class="nf">ch_cs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cs</span><span class="p">):</span>
|
||||||
<span class="sd">"""Translate a point or polygon by a given vector.</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_cs</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_cs</span> <span class="o">*</span> <span class="n">cs</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
<span class="sd"> :param vec: translation vector</span>
|
<div class="viewcode-block" id="World.rotate_x"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.rotate_x">[docs]</a> <span class="k">def</span> <span class="nf">rotate_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sd"> :type vec: tuple</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_cs</span><span class="o">.</span><span class="n">rotate_x</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
|
||||||
<span class="sd"> :param x: points to translate</span>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
<span class="sd"> :type x: int or float or list</span>
|
|
||||||
<span class="sd"> :param y: points to translate</span>
|
|
||||||
<span class="sd"> :type y: int or float or list</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: (x', y')</span>
|
<div class="viewcode-block" id="World.rotate_y"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.rotate_y">[docs]</a> <span class="k">def</span> <span class="nf">rotate_y</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sd"> :rtype: tuple</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_cs</span><span class="o">.</span><span class="n">rotate_y</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
<div class="viewcode-block" id="World.rotate_z"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.rotate_z">[docs]</a> <span class="k">def</span> <span class="nf">rotate_z</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sd"> :meth:`translate`</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_cs</span><span class="o">.</span><span class="n">rotate_z</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="World.translate"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.translate">[docs]</a> <span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">_cs</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">)</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="World.scale"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.scale">[docs]</a> <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sz</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">_cs</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="World.objects"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.objects">[docs]</a> <span class="k">def</span> <span class="nf">objects</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
|
<span class="k">return</span> <span class="p">[</span><span class="n">copy</span><span class="o">.</span><span class="n">deepcopy</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">ch_cs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_cs</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_objects</span><span class="p">]</span></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="World.add"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.add">[docs]</a> <span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">objects</span><span class="p">):</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">_store_init</span><span class="p">()</span> <span class="c1"># calculated values are not correct anymore</span>
|
||||||
|
<span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_objects</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">objects</span><span class="p">]</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="World.bounding_box"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.bounding_box">[docs]</a> <span class="k">def</span> <span class="nf">bounding_box</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
|
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_bb</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_bb</span>
|
||||||
|
|
||||||
|
<span class="n">xmin</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">inf</span>
|
||||||
|
<span class="n">ymin</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">inf</span>
|
||||||
|
<span class="n">zmin</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">inf</span>
|
||||||
|
<span class="n">xmax</span> <span class="o">=</span> <span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">inf</span>
|
||||||
|
<span class="n">ymax</span> <span class="o">=</span> <span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">inf</span>
|
||||||
|
<span class="n">zmax</span> <span class="o">=</span> <span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">inf</span>
|
||||||
|
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_objects</span><span class="p">:</span>
|
||||||
|
<span class="n">xi</span><span class="p">,</span> <span class="n">yi</span><span class="p">,</span> <span class="n">zi</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="nb">min</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">xyz</span><span class="p">())</span>
|
||||||
|
<span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">zs</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="nb">max</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">xyz</span><span class="p">())</span>
|
||||||
|
<span class="c1">#xmax = x if x > xmax: xmax = x</span>
|
||||||
|
<span class="n">xmin</span> <span class="o">=</span> <span class="n">xi</span> <span class="k">if</span> <span class="n">xi</span> <span class="o"><</span> <span class="n">xmin</span> <span class="k">else</span> <span class="n">xmin</span>
|
||||||
|
<span class="n">ymin</span> <span class="o">=</span> <span class="n">yi</span> <span class="k">if</span> <span class="n">yi</span> <span class="o"><</span> <span class="n">ymin</span> <span class="k">else</span> <span class="n">ymin</span>
|
||||||
|
<span class="n">zmin</span> <span class="o">=</span> <span class="n">zi</span> <span class="k">if</span> <span class="n">zi</span> <span class="o"><</span> <span class="n">zmin</span> <span class="k">else</span> <span class="n">zmin</span>
|
||||||
|
<span class="n">xmax</span> <span class="o">=</span> <span class="n">xs</span> <span class="k">if</span> <span class="n">xs</span> <span class="o">></span> <span class="n">xmax</span> <span class="k">else</span> <span class="n">xmax</span>
|
||||||
|
<span class="n">ymax</span> <span class="o">=</span> <span class="n">ys</span> <span class="k">if</span> <span class="n">ys</span> <span class="o">></span> <span class="n">ymax</span> <span class="k">else</span> <span class="n">ymax</span>
|
||||||
|
<span class="n">zmax</span> <span class="o">=</span> <span class="n">zs</span> <span class="k">if</span> <span class="n">zs</span> <span class="o">></span> <span class="n">zmax</span> <span class="k">else</span> <span class="n">zmax</span>
|
||||||
|
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">_bb</span> <span class="o">=</span> <span class="n">xmin</span><span class="p">,</span> <span class="n">xmax</span><span class="p">,</span> <span class="n">ymin</span><span class="p">,</span> <span class="n">ymax</span><span class="p">,</span> <span class="n">zmin</span><span class="p">,</span> <span class="n">zmax</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_bb</span></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="World.space_diagonal"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.space_diagonal">[docs]</a> <span class="k">def</span> <span class="nf">space_diagonal</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
|
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_sd</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_sd</span>
|
||||||
|
|
||||||
|
<span class="n">bb</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounding_box</span><span class="p">()</span>
|
||||||
|
<span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span> <span class="o">=</span> <span class="n">bb</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">bb</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">bb</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="n">bb</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">bb</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">-</span><span class="n">bb</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span>
|
||||||
|
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">a</span><span class="o">**</span><span class="mi">2</span><span class="o">+</span><span class="n">b</span><span class="o">**</span><span class="mi">2</span><span class="o">+</span><span class="n">c</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="World.center"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.World.center">[docs]</a> <span class="k">def</span> <span class="nf">center</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
|
<span class="n">bb</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bounding_box</span><span class="p">()</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">ch_cs</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="o">-</span><span class="p">(</span><span class="n">bb</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">bb</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">/</span><span class="mi">2</span><span class="p">],[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="o">-</span><span class="p">(</span><span class="n">bb</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">-</span><span class="n">bb</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">/</span><span class="mi">2</span><span class="p">],[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">-</span><span class="p">(</span><span class="n">bb</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">-</span><span class="n">bb</span><span class="p">[</span><span class="mi">4</span><span class="p">])</span><span class="o">/</span><span class="mi">2</span><span class="p">],[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">]])</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span></div></div>
|
||||||
|
|
||||||
|
<span class="c1"># TODO: Wireframe(list) or Wireframe(matrix) ?</span>
|
||||||
|
<span class="c1"># list of Points</span>
|
||||||
|
<div class="viewcode-block" id="Wireframe"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe">[docs]</a><span class="k">class</span> <span class="nc">Wireframe</span><span class="p">():</span>
|
||||||
|
<span class="sd">"""Open and closed wireframe object in local coordinate system</span>
|
||||||
|
|
||||||
|
<span class="sd"> This class create its own points (copy).</span>
|
||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="n">vx</span><span class="p">,</span> <span class="n">vy</span> <span class="o">=</span> <span class="n">vec</span>
|
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">points</span><span class="p">,</span> <span class="n">closed</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">copy</span><span class="o">.</span><span class="n">copy</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">points</span><span class="p">]</span>
|
||||||
<span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s2">"__len__"</span><span class="p">):</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">closed</span> <span class="o">=</span> <span class="n">closed</span>
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span><span class="p">]</span>
|
|
||||||
|
<span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
<span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="s2">"__len__"</span><span class="p">):</span>
|
<span class="k">return</span> <span class="s1">'['</span> <span class="o">+</span> <span class="s1">', '</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="nb">str</span><span class="p">(</span><span class="n">point</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">])</span> <span class="o">+</span> <span class="s1">']'</span>
|
||||||
<span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="n">y</span><span class="p">]</span>
|
|
||||||
|
<span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
<span class="n">xp</span> <span class="o">=</span> <span class="p">[</span><span class="n">xi</span><span class="o">+</span><span class="n">vx</span> <span class="k">for</span> <span class="n">xi</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]</span>
|
<span class="sd">"""Returns the Iterator object"""</span>
|
||||||
<span class="n">yp</span> <span class="o">=</span> <span class="p">[</span><span class="n">yi</span><span class="o">+</span><span class="n">vy</span> <span class="k">for</span> <span class="n">yi</span> <span class="ow">in</span> <span class="n">y</span><span class="p">]</span>
|
<span class="k">return</span> <span class="nb">iter</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">points</span><span class="p">())</span>
|
||||||
|
|
||||||
<span class="c1"># no list if it is only one value</span>
|
<div class="viewcode-block" id="Wireframe.points"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.points">[docs]</a> <span class="k">def</span> <span class="nf">points</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">xp</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
<span class="sd">"""Get coordinates in 3d space"""</span>
|
||||||
<span class="k">return</span> <span class="n">xp</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">yp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
<span class="n">result</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
|
||||||
|
<span class="k">return</span> <span class="n">result</span> <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">closed</span> <span class="k">else</span> <span class="n">result</span> <span class="o">+</span> <span class="p">[</span><span class="n">result</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span></div>
|
||||||
<span class="k">return</span> <span class="n">xp</span><span class="p">,</span> <span class="n">yp</span></div>
|
|
||||||
|
<div class="viewcode-block" id="Wireframe.xyz"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.xyz">[docs]</a> <span class="k">def</span> <span class="nf">xyz</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
|
<span class="k">return</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="p">[</span><span class="n">i</span><span class="o">.</span><span class="n">xyz</span><span class="p">()</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">points</span><span class="p">()])</span></div>
|
||||||
<div class="viewcode-block" id="rotate"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.rotate">[docs]</a><span class="k">def</span> <span class="nf">rotate</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Rotate a point or polygon counterclockwise by a given angle</span>
|
<div class="viewcode-block" id="Wireframe.rotate_x"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.rotate_x">[docs]</a> <span class="k">def</span> <span class="nf">rotate_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sd"> around a given origin. The angle should be given in radians.</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">rotate_x</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
<span class="sd"> :param origin: the center of rotation</span>
|
|
||||||
<span class="sd"> :type origin: tuple</span>
|
<div class="viewcode-block" id="Wireframe.rotate_y"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.rotate_y">[docs]</a> <span class="k">def</span> <span class="nf">rotate_y</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sd"> :param angle: the rotation angle</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">rotate_y</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
|
||||||
<span class="sd"> :type angle: int or float</span>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
<span class="sd"> :param `*pts`: points to rotate</span>
|
|
||||||
<span class="sd"> :param `**kwargs`: options</span>
|
<div class="viewcode-block" id="Wireframe.rotate_z"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.rotate_z">[docs]</a> <span class="k">def</span> <span class="nf">rotate_z</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
|
<span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">rotate_z</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
|
||||||
<span class="sd"> :returns: (point_x, point_y) or (point1, point2, ...)</span>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
<span class="sd"> :rtype: tuple</span>
|
|
||||||
|
<div class="viewcode-block" id="Wireframe.translate"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.translate">[docs]</a> <span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
|
||||||
<span class="sd"> .. seealso::</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
|
||||||
<span class="sd"> :meth:`rotate_xy`</span>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">ox</span><span class="p">,</span> <span class="n">oy</span> <span class="o">=</span> <span class="n">origin</span>
|
<div class="viewcode-block" id="Wireframe.scale"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.scale">[docs]</a> <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sz</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||||
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">sy</span><span class="p">:</span>
|
||||||
<span class="c1"># add first point to the end</span>
|
<span class="n">sy</span> <span class="o">=</span> <span class="n">sx</span>
|
||||||
<span class="k">if</span> <span class="s2">"closed"</span> <span class="ow">in</span> <span class="n">kwargs</span> <span class="ow">and</span> <span class="n">kwargs</span><span class="p">[</span><span class="s2">"closed"</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
<span class="n">sz</span> <span class="o">=</span> <span class="n">sx</span>
|
||||||
<span class="n">pts</span> <span class="o">+=</span> <span class="p">(</span><span class="n">pts</span><span class="p">[</span><span class="mi">0</span><span class="p">],)</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
<span class="n">result</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">([(</span><span class="n">ox</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">px</span> <span class="o">-</span> <span class="n">ox</span><span class="p">)</span> <span class="o">-</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">py</span> <span class="o">-</span> <span class="n">oy</span><span class="p">),</span>
|
|
||||||
<span class="n">oy</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">px</span> <span class="o">-</span> <span class="n">ox</span><span class="p">)</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">py</span> <span class="o">-</span> <span class="n">oy</span><span class="p">))</span>
|
<div class="viewcode-block" id="Wireframe.ch_cs"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Wireframe.ch_cs">[docs]</a> <span class="k">def</span> <span class="nf">ch_cs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cs</span><span class="p">):</span>
|
||||||
<span class="k">for</span> <span class="p">(</span><span class="n">px</span><span class="p">,</span> <span class="n">py</span><span class="p">)</span> <span class="ow">in</span> <span class="n">pts</span><span class="p">])</span>
|
<span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">point</span><span class="o">.</span><span class="n">ch_cs</span><span class="p">(</span><span class="n">cs</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span><span class="p">]</span>
|
||||||
|
<span class="k">return</span> <span class="bp">self</span></div></div>
|
||||||
<span class="c1"># no tuple in tuple if it is only one point</span>
|
|
||||||
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">pts</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
<div class="viewcode-block" id="Line"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Line">[docs]</a><span class="k">class</span> <span class="nc">Line</span><span class="p">(</span><span class="n">Wireframe</span><span class="p">):</span>
|
||||||
<span class="k">return</span> <span class="n">result</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">],</span> <span class="n">result</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
|
<span class="sd">"""Line a open wireframe object in local coordinate system"""</span>
|
||||||
|
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">point1</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">point2</span><span class="o">=</span><span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)):</span>
|
||||||
<span class="k">return</span> <span class="n">result</span></div>
|
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="p">)</span></div>
|
||||||
|
|
||||||
|
<div class="viewcode-block" id="Polygon"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Polygon">[docs]</a><span class="k">class</span> <span class="nc">Polygon</span><span class="p">(</span><span class="n">Wireframe</span><span class="p">):</span>
|
||||||
<div class="viewcode-block" id="rotate_deg"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.rotate_deg">[docs]</a><span class="k">def</span> <span class="nf">rotate_deg</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
<span class="sd">"""Polygon as closed wireframe object in local coordinate system"""</span>
|
||||||
<span class="sd">"""Rotate a point or polygon counterclockwise by a given angle</span>
|
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">points</span><span class="p">):</span>
|
||||||
<span class="sd"> around a given origin. The angle should be given in degrees.</span>
|
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">*</span><span class="n">points</span><span class="p">,</span> <span class="n">closed</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></div>
|
||||||
|
|
||||||
<span class="sd"> :param origin: the center of rotation</span>
|
<div class="viewcode-block" id="Circle"><a class="viewcode-back" href="../../pylib.geometry.html#pylib.geometry.Circle">[docs]</a><span class="k">class</span> <span class="nc">Circle</span><span class="p">(</span><span class="n">Polygon</span><span class="p">):</span>
|
||||||
<span class="sd"> :type origin: tuple</span>
|
<span class="sd">"""Circle a closed wireframe object in local coordinate system"""</span>
|
||||||
<span class="sd"> :param angle: the rotation angle</span>
|
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">radius</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
|
||||||
<span class="sd"> :type angle: int or float</span>
|
<span class="n">points</span> <span class="o">=</span> <span class="p">[]</span>
|
||||||
<span class="sd"> :param `*pts`: points to rotate</span>
|
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||||
<span class="sd"> :param `**kwargs`: options</span>
|
<span class="n">x</span> <span class="o">=</span> <span class="n">radius</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="n">n</span><span class="p">)</span>
|
||||||
|
<span class="n">y</span> <span class="o">=</span> <span class="n">radius</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="mi">2</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="n">n</span><span class="p">)</span>
|
||||||
<span class="sd"> :returns: (point_x, point_y) or (point1, point2, ...)</span>
|
<span class="n">points</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Point</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
|
||||||
<span class="sd"> :rtype: tuple</span>
|
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">*</span><span class="n">points</span><span class="p">)</span></div>
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
|
||||||
<span class="sd"> :meth:`rotate`</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">rotate</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">180</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="rotate_xy"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.rotate_xy">[docs]</a><span class="k">def</span> <span class="nf">rotate_xy</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Rotate x and y coordinates counterclockwise by a given angle</span>
|
|
||||||
<span class="sd"> around a given origin. The angle should be given in radians.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param origin: the center of rotation</span>
|
|
||||||
<span class="sd"> :type origin: tuple</span>
|
|
||||||
<span class="sd"> :param angle: the rotation angle</span>
|
|
||||||
<span class="sd"> :type angle: int or float</span>
|
|
||||||
<span class="sd"> :param x: x coordinates</span>
|
|
||||||
<span class="sd"> :type x: int or float or list</span>
|
|
||||||
<span class="sd"> :param y: y coordinates</span>
|
|
||||||
<span class="sd"> :type y: int or float or list</span>
|
|
||||||
<span class="sd"> :param `**kwargs`: options</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
|
||||||
<span class="sd"> :meth:`rotate`</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">ox</span><span class="p">,</span> <span class="n">oy</span> <span class="o">=</span> <span class="n">origin</span>
|
|
||||||
|
|
||||||
<span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s2">"__len__"</span><span class="p">):</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span><span class="p">]</span>
|
|
||||||
|
|
||||||
<span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="s2">"__len__"</span><span class="p">):</span>
|
|
||||||
<span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="n">y</span><span class="p">]</span>
|
|
||||||
|
|
||||||
<span class="c1"># add first point to the end</span>
|
|
||||||
<span class="k">if</span> <span class="s2">"closed"</span> <span class="ow">in</span> <span class="n">kwargs</span> <span class="ow">and</span> <span class="n">kwargs</span><span class="p">[</span><span class="s2">"closed"</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
|
||||||
<span class="n">x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
|
||||||
<span class="n">y</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
|
||||||
|
|
||||||
<span class="n">x_result</span> <span class="o">=</span> <span class="p">[</span><span class="n">ox</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">xi</span> <span class="o">-</span> <span class="n">ox</span><span class="p">)</span> <span class="o">-</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">yi</span> <span class="o">-</span> <span class="n">oy</span><span class="p">)</span>
|
|
||||||
<span class="k">for</span> <span class="n">xi</span><span class="p">,</span> <span class="n">yi</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)]</span>
|
|
||||||
|
|
||||||
<span class="n">y_result</span> <span class="o">=</span> <span class="p">[</span><span class="n">oy</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">xi</span> <span class="o">-</span> <span class="n">ox</span><span class="p">)</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">yi</span> <span class="o">-</span> <span class="n">oy</span><span class="p">)</span>
|
|
||||||
<span class="k">for</span> <span class="n">xi</span><span class="p">,</span> <span class="n">yi</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)]</span>
|
|
||||||
|
|
||||||
<span class="c1"># no list if it is only one value</span>
|
|
||||||
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x_result</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
|
||||||
<span class="k">return</span> <span class="n">x_result</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">y_result</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
|
||||||
|
|
||||||
<span class="k">return</span> <span class="n">x_result</span><span class="p">,</span> <span class="n">y_result</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="rectangle"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.rectangle">[docs]</a><span class="k">def</span> <span class="nf">rectangle</span><span class="p">(</span><span class="n">width</span><span class="p">,</span> <span class="n">height</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""\</span>
|
|
||||||
<span class="sd"> :param width: the width of the rectangle</span>
|
|
||||||
<span class="sd"> :type width: int or float</span>
|
|
||||||
<span class="sd"> :param height: the height of the rectangle</span>
|
|
||||||
<span class="sd"> :type height: int or float</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: (point1, point2, point3, point4)</span>
|
|
||||||
<span class="sd"> :rtype: tuple</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">pt1</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="n">width</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="n">height</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
|
|
||||||
<span class="n">pt2</span> <span class="o">=</span> <span class="p">(</span><span class="n">width</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="n">height</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
|
|
||||||
<span class="n">pt3</span> <span class="o">=</span> <span class="p">(</span><span class="n">width</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">height</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
|
|
||||||
<span class="n">pt4</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="n">width</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">height</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">pt1</span><span class="p">,</span> <span class="n">pt2</span><span class="p">,</span> <span class="n">pt3</span><span class="p">,</span> <span class="n">pt4</span><span class="p">,</span> <span class="n">pt1</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="square"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.square">[docs]</a><span class="k">def</span> <span class="nf">square</span><span class="p">(</span><span class="n">width</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""\</span>
|
|
||||||
<span class="sd"> :param width: the edge size of the square</span>
|
|
||||||
<span class="sd"> :type width: int or float</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: (point1, point2, point3, point4)</span>
|
|
||||||
<span class="sd"> :rtype: tuple</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
|
||||||
<span class="sd"> :meth:`rectangle`</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">rectangle</span><span class="p">(</span><span class="n">width</span><span class="p">,</span> <span class="n">width</span><span class="p">)</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="lines"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.lines">[docs]</a><span class="k">def</span> <span class="nf">lines</span><span class="p">(</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Lines defined by a list of end points.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param pts: list of points in absolute global coordinate system. If</span>
|
|
||||||
<span class="sd"> keyword inc is given than the inc decides what the left and the</span>
|
|
||||||
<span class="sd"> right end point of the line is, otherwise it is assumed that the</span>
|
|
||||||
<span class="sd"> points build a solid line, that is lines between the given points</span>
|
|
||||||
<span class="sd"> in given order.</span>
|
|
||||||
<span class="sd"> :type pts: list</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param `**kwargs`: options:</span>
|
|
||||||
|
|
||||||
<span class="sd"> * deformation -- list of points. Additional deformation</span>
|
|
||||||
<span class="sd"> (translation) at point.</span>
|
|
||||||
<span class="sd"> * factor -- factor of the deformation (default = 1).</span>
|
|
||||||
<span class="sd"> * inc -- the incidence table, a list of 2 element lists. The inc</span>
|
|
||||||
<span class="sd"> decides what the left and the right end point of the line is.</span>
|
|
||||||
<span class="sd"> * index_offset -- starting index of lists (default = 0).</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: list of endpoints for each line;</span>
|
|
||||||
<span class="sd"> [((point1_x, point1_y), (point2_x, point2_y)),</span>
|
|
||||||
<span class="sd"> (p1, p2),</span>
|
|
||||||
<span class="sd"> ...]</span>
|
|
||||||
<span class="sd"> :rtype: list</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
|
||||||
<span class="sd"> :meth:`~geometry_plot.plot_lines` of the :mod:`geometry_plot`</span>
|
|
||||||
<span class="sd"> module to plot the lines</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'index_offset'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'deformation'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'factor'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
|
|
||||||
<span class="n">pts</span> <span class="o">=</span> <span class="p">[(</span><span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="n">d</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="n">d</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">])</span> <span class="k">for</span>
|
|
||||||
<span class="n">p</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">pts</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'deformation'</span><span class="p">])]</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'inc'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="k">return</span> <span class="p">[(</span><span class="n">pts</span><span class="p">[</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">]],</span>
|
|
||||||
<span class="n">pts</span><span class="p">[</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">]])</span> <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'inc'</span><span class="p">]]</span>
|
|
||||||
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">pts</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">pts</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="cubics"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.cubics">[docs]</a><span class="k">def</span> <span class="nf">cubics</span><span class="p">(</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Cubic lines defined by a list of two end points. The deformation</span>
|
|
||||||
<span class="sd"> as displacement and rotation (radians) is defined element wise as</span>
|
|
||||||
<span class="sd"> keyword argument deformation or global node wise as</span>
|
|
||||||
<span class="sd"> global_deformation. The global coordinate system is xy. x in the</span>
|
|
||||||
<span class="sd"> right direction and y in the top direction.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param pts: list of points in absolute global coordinate system. If</span>
|
|
||||||
<span class="sd"> keyword inc is given than the inc decides what the left and the</span>
|
|
||||||
<span class="sd"> right end point of the line is, otherwise it is assumed that the</span>
|
|
||||||
<span class="sd"> points build a solid line, that is lines between the given points</span>
|
|
||||||
<span class="sd"> in given order.</span>
|
|
||||||
<span class="sd"> :type pts_rot: list</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param `**kwargs`: options:</span>
|
|
||||||
|
|
||||||
<span class="sd"> * deformation -- list of deformation element wise. Additional</span>
|
|
||||||
<span class="sd"> deformation (translation and rotation in radians) at element</span>
|
|
||||||
<span class="sd"> left and right node.</span>
|
|
||||||
<span class="sd"> * rotation_plane -- rotation plane of the element wise</span>
|
|
||||||
<span class="sd"> deformation defined by a string; either 'xy' or 'xz' (default</span>
|
|
||||||
<span class="sd"> = 'xy'). x in the right direction and y in the top direction</span>
|
|
||||||
<span class="sd"> or z in the bottom direction.</span>
|
|
||||||
<span class="sd"> * global_deformation -- list of deformation global node wise.</span>
|
|
||||||
<span class="sd"> Additional deformation (horizontal translation, vertical</span>
|
|
||||||
<span class="sd"> translation and rotation in radians) at node.</span>
|
|
||||||
<span class="sd"> * factor -- factor of the derformation (default = 1).</span>
|
|
||||||
<span class="sd"> * inc -- the incidence table, a list of 2 element lists. The inc</span>
|
|
||||||
<span class="sd"> decides what the left and the right end point of the line is.</span>
|
|
||||||
<span class="sd"> * index_offset -- starting index of lists (default = 0).</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: list of endpoints for each line;</span>
|
|
||||||
<span class="sd"> [(((point1_x, point1_y) angle1), ((point2_x, point2_y), angle2),</span>
|
|
||||||
<span class="sd"> (p1, angle1, p2, angle2),</span>
|
|
||||||
<span class="sd"> ...]</span>
|
|
||||||
<span class="sd"> :rtype: list</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'index_offset'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'deformation'</span> <span class="ow">in</span> <span class="n">kwargs</span> <span class="ow">or</span> <span class="s1">'global_deformation'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'factor'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'inc'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'global_deformation'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
||||||
<span class="n">lr</span> <span class="o">=</span> <span class="p">[(</span><span class="n">pts</span><span class="p">[</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">]],</span>
|
|
||||||
<span class="n">pts</span><span class="p">[</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">]])</span> <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'inc'</span><span class="p">]]</span>
|
|
||||||
<span class="n">ang</span> <span class="o">=</span> <span class="p">[</span><span class="n">angle</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">lr</span><span class="p">]</span>
|
|
||||||
<span class="c1"># system deformation</span>
|
|
||||||
<span class="n">U</span> <span class="o">=</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'global_deformation'</span><span class="p">]</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'rotation_plane'</span> <span class="ow">in</span> <span class="n">kwargs</span> <span class="ow">and</span> <span class="s1">'xz'</span> <span class="o">==</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'rotation_plane'</span><span class="p">]:</span>
|
|
||||||
<span class="c1"># system deformation left X Z RY right X Z RY element wise</span>
|
|
||||||
<span class="c1"># Z downwards -> convert to X Y RZ</span>
|
|
||||||
<span class="n">Ue</span> <span class="o">=</span> <span class="p">[[</span> <span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">0</span><span class="p">],</span>
|
|
||||||
<span class="o">-</span><span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">1</span><span class="p">],</span>
|
|
||||||
<span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">2</span><span class="p">],</span>
|
|
||||||
<span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">0</span><span class="p">],</span>
|
|
||||||
<span class="o">-</span><span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">1</span><span class="p">],</span>
|
|
||||||
<span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">2</span><span class="p">]]</span> <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'inc'</span><span class="p">]]</span>
|
|
||||||
<span class="k">else</span><span class="p">:</span>
|
|
||||||
<span class="c1"># system deformation left X Y RZ right X Y RZ element wise</span>
|
|
||||||
<span class="n">Ue</span> <span class="o">=</span> <span class="p">[[</span><span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">0</span><span class="p">],</span>
|
|
||||||
<span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">1</span><span class="p">],</span>
|
|
||||||
<span class="n">U</span><span class="p">[(</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">2</span><span class="p">],</span>
|
|
||||||
<span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">0</span><span class="p">],</span>
|
|
||||||
<span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">1</span><span class="p">],</span>
|
|
||||||
<span class="n">U</span><span class="p">[(</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">])][</span><span class="mi">2</span><span class="p">]]</span> <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'inc'</span><span class="p">]]</span>
|
|
||||||
<span class="c1"># element deformation, X Y RZ to x r rz</span>
|
|
||||||
<span class="c1"># back transformation T^T = [[c, s, 0], [-s, c, 0], [0, 0, 1]]</span>
|
|
||||||
<span class="n">u</span> <span class="o">=</span> <span class="p">[[(</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">],</span>
|
|
||||||
<span class="p">(</span><span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">],</span>
|
|
||||||
<span class="n">Uei</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">],</span>
|
|
||||||
<span class="p">(</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">+</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">4</span><span class="p">])</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">],</span>
|
|
||||||
<span class="p">(</span><span class="o">-</span><span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">+</span><span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angi</span><span class="p">)</span><span class="o">*</span><span class="n">Uei</span><span class="p">[</span><span class="mi">4</span><span class="p">])</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">],</span>
|
|
||||||
<span class="n">Uei</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span> <span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">]]</span>
|
|
||||||
<span class="k">for</span> <span class="n">Uei</span><span class="p">,</span> <span class="n">angi</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">Ue</span><span class="p">,</span> <span class="n">ang</span><span class="p">)]</span>
|
|
||||||
<span class="k">else</span><span class="p">:</span> <span class="c1"># deformation</span>
|
|
||||||
<span class="c1"># the deformation is in element coordinate system, therefore the angle is needed</span>
|
|
||||||
<span class="k">if</span> <span class="s1">'rotation_plane'</span> <span class="ow">in</span> <span class="n">kwargs</span> <span class="ow">and</span> <span class="s1">'xz'</span> <span class="o">==</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'rotation_plane'</span><span class="p">]:</span>
|
|
||||||
<span class="n">u</span> <span class="o">=</span> <span class="p">[[</span> <span class="n">ue</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">],</span>
|
|
||||||
<span class="o">-</span><span class="n">ue</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">],</span>
|
|
||||||
<span class="n">ue</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">],</span>
|
|
||||||
<span class="n">ue</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">],</span>
|
|
||||||
<span class="o">-</span><span class="n">ue</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">],</span>
|
|
||||||
<span class="n">ue</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">]]</span> <span class="k">for</span> <span class="n">ue</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'deformation'</span><span class="p">]]</span>
|
|
||||||
<span class="k">else</span><span class="p">:</span>
|
|
||||||
<span class="n">u</span> <span class="o">=</span> <span class="p">[[</span><span class="n">ui</span><span class="o">*</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'factor'</span><span class="p">]</span> <span class="k">for</span> <span class="n">ui</span> <span class="ow">in</span> <span class="n">ue</span><span class="p">]</span> <span class="k">for</span> <span class="n">ue</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'deformation'</span><span class="p">]]</span>
|
|
||||||
<span class="k">return</span> <span class="p">[(</span><span class="n">pts</span><span class="p">[</span><span class="n">l</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">]],</span>
|
|
||||||
<span class="n">pts</span><span class="p">[</span><span class="n">r</span><span class="o">-</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'index_offset'</span><span class="p">]],</span>
|
|
||||||
<span class="n">d</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">),</span> <span class="n">d</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">kwargs</span><span class="p">[</span><span class="s1">'inc'</span><span class="p">],</span> <span class="n">u</span><span class="p">)]</span>
|
|
||||||
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">pts</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">pts</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="interpolate_hermite"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.interpolate_hermite">[docs]</a><span class="k">def</span> <span class="nf">interpolate_hermite</span><span class="p">(</span><span class="n">lvd</span><span class="p">,</span> <span class="n">lr</span><span class="p">,</span> <span class="n">rvd</span><span class="p">,</span> <span class="n">rr</span><span class="p">,</span> <span class="n">lhd</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">rhd</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">scale_x</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">scale_y</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
|
|
||||||
<span class="sa">r</span><span class="sd">"""Interpolate cubic line with hermite boundary conditions.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param lvd: left vertcal deflection</span>
|
|
||||||
<span class="sd"> :type lvd: int or float</span>
|
|
||||||
<span class="sd"> :param lr: left rotation</span>
|
|
||||||
<span class="sd"> :type lr: int or float</span>
|
|
||||||
<span class="sd"> :param rvd: right vertical deflection</span>
|
|
||||||
<span class="sd"> :type rvd: int or float</span>
|
|
||||||
<span class="sd"> :param rr: right rotation</span>
|
|
||||||
<span class="sd"> :type rr: int or float</span>
|
|
||||||
<span class="sd"> :param lhd: left horizontal deformation (default = 0)</span>
|
|
||||||
<span class="sd"> :type lhd: int or float</span>
|
|
||||||
<span class="sd"> :param rhd: right horizontal deformation (default = 0)</span>
|
|
||||||
<span class="sd"> :type rhd: int or float</span>
|
|
||||||
<span class="sd"> :param scale_x: length of element (default = 1)</span>
|
|
||||||
<span class="sd"> :type scale_x: int or float</span>
|
|
||||||
<span class="sd"> :param scale_y: factor of the deformation (default = 1).</span>
|
|
||||||
<span class="sd"> This does not change the length.</span>
|
|
||||||
<span class="sd"> :type scale_y: int or float</span>
|
|
||||||
<span class="sd"> :param samples: number of sampling points (default = 10)</span>
|
|
||||||
<span class="sd"> :type samples: int</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> s = \frac{x - x_1}{L} \\</span>
|
|
||||||
<span class="sd"> x = s\,L + x_1</span>
|
|
||||||
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">L</span> <span class="o">=</span> <span class="n">scale_x</span>
|
|
||||||
<span class="n">Lp</span> <span class="o">=</span> <span class="n">L</span> <span class="o">+</span> <span class="n">rhd</span> <span class="o">-</span> <span class="n">lhd</span>
|
|
||||||
|
|
||||||
<span class="c1"># x=[0,1] in non-dimensional coordinates</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="n">samples</span><span class="p">)</span>
|
|
||||||
<span class="n">N1</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">3</span>
|
|
||||||
<span class="n">N2</span> <span class="o">=</span> <span class="p">(</span> <span class="n">x</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span><span class="o">*</span><span class="n">Lp</span>
|
|
||||||
<span class="n">N3</span> <span class="o">=</span> <span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">3</span>
|
|
||||||
<span class="n">N4</span> <span class="o">=</span> <span class="p">(</span> <span class="o">-</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span><span class="o">*</span><span class="n">Lp</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">*</span><span class="n">Lp</span>
|
|
||||||
|
|
||||||
|
|
||||||
<span class="c1"># x=[0,L] in global coordinates</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">Lp</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="n">samples</span><span class="p">)</span>
|
|
||||||
<span class="n">N1</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">3</span>
|
|
||||||
<span class="n">N2</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="n">Lp</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">2</span>
|
|
||||||
<span class="n">N3</span> <span class="o">=</span> <span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">3</span>
|
|
||||||
<span class="n">N4</span> <span class="o">=</span> <span class="o">-</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="n">Lp</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span><span class="o">/</span><span class="n">Lp</span><span class="o">**</span><span class="mi">2</span>
|
|
||||||
|
|
||||||
|
|
||||||
<span class="n">v</span> <span class="o">=</span> <span class="n">N1</span><span class="o">*</span><span class="n">lvd</span> <span class="o">+</span> <span class="n">N2</span><span class="o">*</span><span class="n">lr</span> <span class="o">+</span> <span class="n">N3</span><span class="o">*</span><span class="n">rvd</span> <span class="o">+</span> <span class="n">N4</span><span class="o">*</span><span class="n">rr</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="n">lhd</span>
|
|
||||||
<span class="n">y</span> <span class="o">=</span> <span class="n">v</span><span class="o">*</span><span class="n">scale_y</span>
|
|
||||||
|
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<span class="c1">#</span>
|
|
||||||
<span class="c1"># matplotlib format, return lists for x and y</span>
|
|
||||||
<span class="c1">#</span>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="line"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.line">[docs]</a><span class="k">def</span> <span class="nf">line</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Line defined by two end points.</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
|
||||||
<span class="sd"> y = \\frac{y_2-y_1}{x_2-x_1}(x-x_1) + y_1</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param point1: one end point</span>
|
|
||||||
<span class="sd"> :type point1: tuple</span>
|
|
||||||
<span class="sd"> :param point2: other end point</span>
|
|
||||||
<span class="sd"> :type point2: tuple</span>
|
|
||||||
<span class="sd"> :param samples: number of sampling points (default = 2)</span>
|
|
||||||
<span class="sd"> :type samples: int</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: ((point1_x, point2_x), (points1_y, point2_y)) or</span>
|
|
||||||
<span class="sd"> ([sample_point1_x, sample_point2_x, ...],</span>
|
|
||||||
<span class="sd"> [sample_points1_y, sample_point2_y, ...])</span>
|
|
||||||
<span class="sd"> :rtype: tuple</span>
|
|
||||||
|
|
||||||
<span class="sd"> :Example:</span>
|
|
||||||
|
|
||||||
<span class="sd"> >>> x, y = line((0, 0), (1, 0))</span>
|
|
||||||
<span class="sd"> >>> print(x, y)</span>
|
|
||||||
<span class="sd"> ((0, 1), (0, 0))</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">p1x</span><span class="p">,</span> <span class="n">p1y</span> <span class="o">=</span> <span class="n">point1</span>
|
|
||||||
<span class="n">p2x</span><span class="p">,</span> <span class="n">p2y</span> <span class="o">=</span> <span class="n">point2</span>
|
|
||||||
|
|
||||||
<span class="n">denominator</span> <span class="o">=</span> <span class="p">(</span><span class="n">p1x</span> <span class="o">-</span> <span class="n">p2x</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="k">if</span> <span class="n">samples</span> <span class="o">></span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">denominator</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">p1x</span><span class="p">,</span> <span class="n">p2x</span><span class="p">,</span> <span class="n">samples</span><span class="p">)</span>
|
|
||||||
<span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">p1y</span> <span class="o">-</span> <span class="n">p2y</span><span class="p">)</span> <span class="o">/</span> <span class="n">denominator</span>
|
|
||||||
<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2y</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">*</span><span class="n">p1y</span><span class="p">)</span> <span class="o">/</span> <span class="n">denominator</span>
|
|
||||||
<span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">b</span>
|
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span>
|
|
||||||
<span class="k">return</span> <span class="p">(</span><span class="n">p1x</span><span class="p">,</span> <span class="n">p2x</span><span class="p">),</span> <span class="p">(</span><span class="n">p1y</span><span class="p">,</span> <span class="n">p2y</span><span class="p">)</span> <span class="c1"># matplotlib format</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="cubic"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.cubic">[docs]</a><span class="k">def</span> <span class="nf">cubic</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">angle1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">angle2</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Cubic line defined by two end points and the rotation in radians</span>
|
|
||||||
<span class="sd"> at the points.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param point1: one end point</span>
|
|
||||||
<span class="sd"> :type point1: tuple</span>
|
|
||||||
<span class="sd"> :param angle1: the slope at the one end point</span>
|
|
||||||
<span class="sd"> :type angle1: int or float</span>
|
|
||||||
<span class="sd"> :param point2: other end point</span>
|
|
||||||
<span class="sd"> :type point2: tuple</span>
|
|
||||||
<span class="sd"> :param angle2: the slope at the other end point</span>
|
|
||||||
<span class="sd"> :type angle2: int or float</span>
|
|
||||||
<span class="sd"> :param samples: number of sampling points (default = 10)</span>
|
|
||||||
<span class="sd"> :type samples: int</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: ([sample_point1_x, sample_point2_x, ...],</span>
|
|
||||||
<span class="sd"> [sample_points1_y, sample_point2_y, ...])</span>
|
|
||||||
<span class="sd"> :rtype: tuple</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="n">p1x</span><span class="p">,</span> <span class="n">p1y</span> <span class="o">=</span> <span class="n">point1</span>
|
|
||||||
<span class="n">p2x</span><span class="p">,</span> <span class="n">p2y</span> <span class="o">=</span> <span class="n">point2</span>
|
|
||||||
|
|
||||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">p1x</span><span class="p">,</span> <span class="n">p2x</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="n">samples</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">p1ys</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">tan</span><span class="p">(</span><span class="n">angle1</span><span class="p">)</span>
|
|
||||||
<span class="n">p2ys</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">tan</span><span class="p">(</span><span class="n">angle2</span><span class="p">)</span>
|
|
||||||
<span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">p1x</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">p1y</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">p2y</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">p1x</span><span class="o">**</span><span class="mi">3</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span>
|
|
||||||
<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p1y</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2y</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p1y</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2y</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">p1x</span><span class="o">**</span><span class="mi">3</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span>
|
|
||||||
<span class="n">c</span> <span class="o">=</span> <span class="p">(</span><span class="n">p1x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="mi">6</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p1y</span> <span class="o">+</span> <span class="mi">6</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2y</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p1ys</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">p1x</span><span class="o">**</span><span class="mi">3</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span>
|
|
||||||
<span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p2y</span> <span class="o">-</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2ys</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span><span class="o">*</span><span class="n">p2y</span> <span class="o">+</span> <span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p1ys</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p1y</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="n">p1y</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">p1x</span><span class="o">**</span><span class="mi">3</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">p2x</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">p1x</span><span class="o">*</span><span class="n">p2x</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">p2x</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span>
|
|
||||||
<span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">3</span> <span class="o">+</span> <span class="n">b</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">c</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">d</span>
|
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></div>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="cubic_deg"><a class="viewcode-back" href="../../pylib.html#pylib.geometry.cubic_deg">[docs]</a><span class="k">def</span> <span class="nf">cubic_deg</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">angle1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">angle2</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Cubic line defined by two end points and the roation in degree</span>
|
|
||||||
<span class="sd"> at the points.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param point1: one end point</span>
|
|
||||||
<span class="sd"> :type point1: tuple</span>
|
|
||||||
<span class="sd"> :param angle1: the slope at the one end point</span>
|
|
||||||
<span class="sd"> :type angle1: int or float</span>
|
|
||||||
<span class="sd"> :param point2: other end point</span>
|
|
||||||
<span class="sd"> :type point2: tuple</span>
|
|
||||||
<span class="sd"> :param angle2: the slope at the other end point</span>
|
|
||||||
<span class="sd"> :type angle2: int or float</span>
|
|
||||||
|
|
||||||
<span class="sd"> :returns: ([sample_point1_x, sample_point2_x, ...],</span>
|
|
||||||
<span class="sd"> [sample_points1_y, sample_point2_y, ...])</span>
|
|
||||||
<span class="sd"> :rtype: tuple</span>
|
|
||||||
|
|
||||||
<span class="sd"> .. seealso::</span>
|
|
||||||
<span class="sd"> :meth:`cubic`</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">cubic</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">angle1</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">180</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">angle2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">180</span><span class="p">)</span></div>
|
|
||||||
</pre></div>
|
</pre></div>
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
@@ -562,6 +276,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
@@ -4,20 +4,20 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>geometry — pylib 2019.5.19 documentation</title>
|
<title>pylib.geometry2d — pylib 2019.12.21 documentation</title>
|
||||||
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<div class="body" role="main">
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||||||
<h1>Source code for geometry</h1><div class="highlight"><pre>
|
<h1>Source code for pylib.geometry2d</h1><div class="highlight"><pre>
|
||||||
<span></span><span class="ch">#!/usr/bin/env python</span>
|
<span></span><span class="ch">#!/usr/bin/env python</span>
|
||||||
<span class="c1"># -*- coding: utf-8 -*-</span>
|
<span class="c1"># -*- coding: utf-8 -*-</span>
|
||||||
<span class="sd">"""2D geometry objects.</span>
|
<span class="sd">"""2D geometry objects.</span>
|
||||||
|
|
||||||
<span class="sd">:Date: 2019-08-28</span>
|
<span class="sd">:Date: 2019-08-28</span>
|
||||||
|
|
||||||
<span class="sd">.. module:: geometry</span>
|
<span class="sd">.. module:: geometry2d</span>
|
||||||
<span class="sd"> :platform: *nix, Windows</span>
|
<span class="sd"> :platform: *nix, Windows</span>
|
||||||
<span class="sd"> :synopsis: Geometry objects.</span>
|
<span class="sd"> :synopsis: 2D geometry objects.</span>
|
||||||
|
|
||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
||||||
<span class="sd">"""</span>
|
<span class="sd">"""</span>
|
||||||
@@ -49,7 +49,7 @@
|
|||||||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="distance"><a class="viewcode-back" href="../geometry.html#geometry.distance">[docs]</a><span class="k">def</span> <span class="nf">distance</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="p">):</span>
|
<div class="viewcode-block" id="distance"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.distance">[docs]</a><span class="k">def</span> <span class="nf">distance</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="p">):</span>
|
||||||
<span class="sd">"""Distance between two points (or length of a straight line).</span>
|
<span class="sd">"""Distance between two points (or length of a straight line).</span>
|
||||||
|
|
||||||
<span class="sd"> :param point1: first point (first end point of straight line)</span>
|
<span class="sd"> :param point1: first point (first end point of straight line)</span>
|
||||||
@@ -63,7 +63,7 @@
|
|||||||
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">((</span><span class="n">point2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="p">(</span><span class="n">point2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span></div>
|
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">((</span><span class="n">point2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="p">(</span><span class="n">point2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="angle"><a class="viewcode-back" href="../geometry.html#geometry.angle">[docs]</a><span class="k">def</span> <span class="nf">angle</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
<div class="viewcode-block" id="angle"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.angle">[docs]</a><span class="k">def</span> <span class="nf">angle</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||||
<span class="sd">"""Angle of point or between two points.</span>
|
<span class="sd">"""Angle of point or between two points.</span>
|
||||||
|
|
||||||
<span class="sd"> :param point1: (first) point</span>
|
<span class="sd"> :param point1: (first) point</span>
|
||||||
@@ -79,7 +79,7 @@
|
|||||||
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">point2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">point2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span></div>
|
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">point2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">point2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="n">point1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="translate"><a class="viewcode-back" href="../geometry.html#geometry.translate">[docs]</a><span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="n">vec</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">):</span>
|
<div class="viewcode-block" id="translate"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.translate">[docs]</a><span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="n">vec</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">):</span>
|
||||||
<span class="sd">"""Translate a point or polygon by a given vector.</span>
|
<span class="sd">"""Translate a point or polygon by a given vector.</span>
|
||||||
|
|
||||||
<span class="sd"> :param vec: translation vector</span>
|
<span class="sd"> :param vec: translation vector</span>
|
||||||
@@ -96,7 +96,7 @@
|
|||||||
<span class="k">return</span> <span class="nb">tuple</span><span class="p">([(</span><span class="n">x</span><span class="o">+</span><span class="n">vx</span><span class="p">,</span> <span class="n">y</span><span class="o">+</span><span class="n">vy</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="n">pts</span><span class="p">])</span></div>
|
<span class="k">return</span> <span class="nb">tuple</span><span class="p">([(</span><span class="n">x</span><span class="o">+</span><span class="n">vx</span><span class="p">,</span> <span class="n">y</span><span class="o">+</span><span class="n">vy</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="n">pts</span><span class="p">])</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="translate_xy"><a class="viewcode-back" href="../geometry.html#geometry.translate_xy">[docs]</a><span class="k">def</span> <span class="nf">translate_xy</span><span class="p">(</span><span class="n">vec</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
|
<div class="viewcode-block" id="translate_xy"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.translate_xy">[docs]</a><span class="k">def</span> <span class="nf">translate_xy</span><span class="p">(</span><span class="n">vec</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
|
||||||
<span class="sd">"""Translate a point or polygon by a given vector.</span>
|
<span class="sd">"""Translate a point or polygon by a given vector.</span>
|
||||||
|
|
||||||
<span class="sd"> :param vec: translation vector</span>
|
<span class="sd"> :param vec: translation vector</span>
|
||||||
@@ -130,7 +130,7 @@
|
|||||||
<span class="k">return</span> <span class="n">xp</span><span class="p">,</span> <span class="n">yp</span></div>
|
<span class="k">return</span> <span class="n">xp</span><span class="p">,</span> <span class="n">yp</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="rotate"><a class="viewcode-back" href="../geometry.html#geometry.rotate">[docs]</a><span class="k">def</span> <span class="nf">rotate</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
<div class="viewcode-block" id="rotate"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.rotate">[docs]</a><span class="k">def</span> <span class="nf">rotate</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||||||
<span class="sd">"""Rotate a point or polygon counterclockwise by a given angle</span>
|
<span class="sd">"""Rotate a point or polygon counterclockwise by a given angle</span>
|
||||||
<span class="sd"> around a given origin. The angle should be given in radians.</span>
|
<span class="sd"> around a given origin. The angle should be given in radians.</span>
|
||||||
|
|
||||||
@@ -164,7 +164,7 @@
|
|||||||
<span class="k">return</span> <span class="n">result</span></div>
|
<span class="k">return</span> <span class="n">result</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="rotate_deg"><a class="viewcode-back" href="../geometry.html#geometry.rotate_deg">[docs]</a><span class="k">def</span> <span class="nf">rotate_deg</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
<div class="viewcode-block" id="rotate_deg"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.rotate_deg">[docs]</a><span class="k">def</span> <span class="nf">rotate_deg</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||||||
<span class="sd">"""Rotate a point or polygon counterclockwise by a given angle</span>
|
<span class="sd">"""Rotate a point or polygon counterclockwise by a given angle</span>
|
||||||
<span class="sd"> around a given origin. The angle should be given in degrees.</span>
|
<span class="sd"> around a given origin. The angle should be given in degrees.</span>
|
||||||
|
|
||||||
@@ -184,7 +184,7 @@
|
|||||||
<span class="k">return</span> <span class="n">rotate</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">180</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span></div>
|
<span class="k">return</span> <span class="n">rotate</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mi">180</span><span class="p">,</span> <span class="o">*</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="rotate_xy"><a class="viewcode-back" href="../geometry.html#geometry.rotate_xy">[docs]</a><span class="k">def</span> <span class="nf">rotate_xy</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
<div class="viewcode-block" id="rotate_xy"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.rotate_xy">[docs]</a><span class="k">def</span> <span class="nf">rotate_xy</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||||||
<span class="sd">"""Rotate x and y coordinates counterclockwise by a given angle</span>
|
<span class="sd">"""Rotate x and y coordinates counterclockwise by a given angle</span>
|
||||||
<span class="sd"> around a given origin. The angle should be given in radians.</span>
|
<span class="sd"> around a given origin. The angle should be given in radians.</span>
|
||||||
|
|
||||||
@@ -227,7 +227,7 @@
|
|||||||
<span class="k">return</span> <span class="n">x_result</span><span class="p">,</span> <span class="n">y_result</span></div>
|
<span class="k">return</span> <span class="n">x_result</span><span class="p">,</span> <span class="n">y_result</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="rectangle"><a class="viewcode-back" href="../geometry.html#geometry.rectangle">[docs]</a><span class="k">def</span> <span class="nf">rectangle</span><span class="p">(</span><span class="n">width</span><span class="p">,</span> <span class="n">height</span><span class="p">):</span>
|
<div class="viewcode-block" id="rectangle"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.rectangle">[docs]</a><span class="k">def</span> <span class="nf">rectangle</span><span class="p">(</span><span class="n">width</span><span class="p">,</span> <span class="n">height</span><span class="p">):</span>
|
||||||
<span class="sd">"""\</span>
|
<span class="sd">"""\</span>
|
||||||
<span class="sd"> :param width: the width of the rectangle</span>
|
<span class="sd"> :param width: the width of the rectangle</span>
|
||||||
<span class="sd"> :type width: int or float</span>
|
<span class="sd"> :type width: int or float</span>
|
||||||
@@ -244,7 +244,7 @@
|
|||||||
<span class="k">return</span> <span class="n">pt1</span><span class="p">,</span> <span class="n">pt2</span><span class="p">,</span> <span class="n">pt3</span><span class="p">,</span> <span class="n">pt4</span><span class="p">,</span> <span class="n">pt1</span></div>
|
<span class="k">return</span> <span class="n">pt1</span><span class="p">,</span> <span class="n">pt2</span><span class="p">,</span> <span class="n">pt3</span><span class="p">,</span> <span class="n">pt4</span><span class="p">,</span> <span class="n">pt1</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="square"><a class="viewcode-back" href="../geometry.html#geometry.square">[docs]</a><span class="k">def</span> <span class="nf">square</span><span class="p">(</span><span class="n">width</span><span class="p">):</span>
|
<div class="viewcode-block" id="square"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.square">[docs]</a><span class="k">def</span> <span class="nf">square</span><span class="p">(</span><span class="n">width</span><span class="p">):</span>
|
||||||
<span class="sd">"""\</span>
|
<span class="sd">"""\</span>
|
||||||
<span class="sd"> :param width: the edge size of the square</span>
|
<span class="sd"> :param width: the edge size of the square</span>
|
||||||
<span class="sd"> :type width: int or float</span>
|
<span class="sd"> :type width: int or float</span>
|
||||||
@@ -258,7 +258,7 @@
|
|||||||
<span class="k">return</span> <span class="n">rectangle</span><span class="p">(</span><span class="n">width</span><span class="p">,</span> <span class="n">width</span><span class="p">)</span></div>
|
<span class="k">return</span> <span class="n">rectangle</span><span class="p">(</span><span class="n">width</span><span class="p">,</span> <span class="n">width</span><span class="p">)</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="lines"><a class="viewcode-back" href="../geometry.html#geometry.lines">[docs]</a><span class="k">def</span> <span class="nf">lines</span><span class="p">(</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
<div class="viewcode-block" id="lines"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.lines">[docs]</a><span class="k">def</span> <span class="nf">lines</span><span class="p">(</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||||||
<span class="sd">"""Lines defined by a list of end points.</span>
|
<span class="sd">"""Lines defined by a list of end points.</span>
|
||||||
|
|
||||||
<span class="sd"> :param pts: list of points in absolute global coordinate system. If</span>
|
<span class="sd"> :param pts: list of points in absolute global coordinate system. If</span>
|
||||||
@@ -300,7 +300,7 @@
|
|||||||
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">pts</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">pts</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span></div>
|
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">pts</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">pts</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="cubics"><a class="viewcode-back" href="../geometry.html#geometry.cubics">[docs]</a><span class="k">def</span> <span class="nf">cubics</span><span class="p">(</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
<div class="viewcode-block" id="cubics"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.cubics">[docs]</a><span class="k">def</span> <span class="nf">cubics</span><span class="p">(</span><span class="n">pts</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||||||
<span class="sd">"""Cubic lines defined by a list of two end points. The deformation</span>
|
<span class="sd">"""Cubic lines defined by a list of two end points. The deformation</span>
|
||||||
<span class="sd"> as displacement and rotation (radians) is defined element wise as</span>
|
<span class="sd"> as displacement and rotation (radians) is defined element wise as</span>
|
||||||
<span class="sd"> keyword argument deformation or global node wise as</span>
|
<span class="sd"> keyword argument deformation or global node wise as</span>
|
||||||
@@ -392,7 +392,7 @@
|
|||||||
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">pts</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">pts</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span></div>
|
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">pts</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">pts</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="interpolate_hermite"><a class="viewcode-back" href="../geometry.html#geometry.interpolate_hermite">[docs]</a><span class="k">def</span> <span class="nf">interpolate_hermite</span><span class="p">(</span><span class="n">lvd</span><span class="p">,</span> <span class="n">lr</span><span class="p">,</span> <span class="n">rvd</span><span class="p">,</span> <span class="n">rr</span><span class="p">,</span> <span class="n">lhd</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">rhd</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">scale_x</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">scale_y</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
|
<div class="viewcode-block" id="interpolate_hermite"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.interpolate_hermite">[docs]</a><span class="k">def</span> <span class="nf">interpolate_hermite</span><span class="p">(</span><span class="n">lvd</span><span class="p">,</span> <span class="n">lr</span><span class="p">,</span> <span class="n">rvd</span><span class="p">,</span> <span class="n">rr</span><span class="p">,</span> <span class="n">lhd</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">rhd</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">scale_x</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">scale_y</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Interpolate cubic line with hermite boundary conditions.</span>
|
<span class="sa">r</span><span class="sd">"""Interpolate cubic line with hermite boundary conditions.</span>
|
||||||
|
|
||||||
<span class="sd"> :param lvd: left vertcal deflection</span>
|
<span class="sd"> :param lvd: left vertcal deflection</span>
|
||||||
@@ -451,7 +451,7 @@
|
|||||||
<span class="c1"># matplotlib format, return lists for x and y</span>
|
<span class="c1"># matplotlib format, return lists for x and y</span>
|
||||||
<span class="c1">#</span>
|
<span class="c1">#</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="line"><a class="viewcode-back" href="../geometry.html#geometry.line">[docs]</a><span class="k">def</span> <span class="nf">line</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
|
<div class="viewcode-block" id="line"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.line">[docs]</a><span class="k">def</span> <span class="nf">line</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
|
||||||
<span class="sd">"""Line defined by two end points.</span>
|
<span class="sd">"""Line defined by two end points.</span>
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
<span class="sd"> .. math::</span>
|
||||||
@@ -489,7 +489,7 @@
|
|||||||
<span class="k">return</span> <span class="p">(</span><span class="n">p1x</span><span class="p">,</span> <span class="n">p2x</span><span class="p">),</span> <span class="p">(</span><span class="n">p1y</span><span class="p">,</span> <span class="n">p2y</span><span class="p">)</span> <span class="c1"># matplotlib format</span></div>
|
<span class="k">return</span> <span class="p">(</span><span class="n">p1x</span><span class="p">,</span> <span class="n">p2x</span><span class="p">),</span> <span class="p">(</span><span class="n">p1y</span><span class="p">,</span> <span class="n">p2y</span><span class="p">)</span> <span class="c1"># matplotlib format</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="cubic"><a class="viewcode-back" href="../geometry.html#geometry.cubic">[docs]</a><span class="k">def</span> <span class="nf">cubic</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">angle1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">angle2</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
|
<div class="viewcode-block" id="cubic"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.cubic">[docs]</a><span class="k">def</span> <span class="nf">cubic</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">angle1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">angle2</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">10</span><span class="p">):</span>
|
||||||
<span class="sd">"""Cubic line defined by two end points and the rotation in radians</span>
|
<span class="sd">"""Cubic line defined by two end points and the rotation in radians</span>
|
||||||
<span class="sd"> at the points.</span>
|
<span class="sd"> at the points.</span>
|
||||||
|
|
||||||
@@ -523,7 +523,7 @@
|
|||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></div>
|
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="cubic_deg"><a class="viewcode-back" href="../geometry.html#geometry.cubic_deg">[docs]</a><span class="k">def</span> <span class="nf">cubic_deg</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">angle1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">angle2</span><span class="p">):</span>
|
<div class="viewcode-block" id="cubic_deg"><a class="viewcode-back" href="../../pylib.geometry2d.html#pylib.geometry2d.cubic_deg">[docs]</a><span class="k">def</span> <span class="nf">cubic_deg</span><span class="p">(</span><span class="n">point1</span><span class="p">,</span> <span class="n">angle1</span><span class="p">,</span> <span class="n">point2</span><span class="p">,</span> <span class="n">angle2</span><span class="p">):</span>
|
||||||
<span class="sd">"""Cubic line defined by two end points and the roation in degree</span>
|
<span class="sd">"""Cubic line defined by two end points and the roation in degree</span>
|
||||||
<span class="sd"> at the points.</span>
|
<span class="sd"> at the points.</span>
|
||||||
|
|
||||||
@@ -552,7 +552,7 @@
|
|||||||
</div>
|
</div>
|
||||||
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
<div class="sphinxsidebarwrapper">
|
<div class="sphinxsidebarwrapper">
|
||||||
<h1 class="logo"><a href="../index.html">pylib</a></h1>
|
<h1 class="logo"><a href="../../index.html">pylib</a></h1>
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
@@ -562,12 +562,16 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="../index.html">Documentation overview</a><ul>
|
<li><a href="../../index.html">Documentation overview</a><ul>
|
||||||
<li><a href="index.html">Module code</a><ul>
|
<li><a href="../index.html">Module code</a><ul>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
</ul>
|
</ul>
|
||||||
@@ -575,7 +579,7 @@
|
|||||||
<div id="searchbox" style="display: none" role="search">
|
<div id="searchbox" style="display: none" role="search">
|
||||||
<h3 id="searchlabel">Quick search</h3>
|
<h3 id="searchlabel">Quick search</h3>
|
||||||
<div class="searchformwrapper">
|
<div class="searchformwrapper">
|
||||||
<form class="search" action="../search.html" method="get">
|
<form class="search" action="../../search.html" method="get">
|
||||||
<input type="text" name="q" aria-labelledby="searchlabel" />
|
<input type="text" name="q" aria-labelledby="searchlabel" />
|
||||||
<input type="submit" value="Go" />
|
<input type="submit" value="Go" />
|
||||||
</form>
|
</form>
|
||||||
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.geometry_plot — pylib 2019.5.19 documentation</title>
|
<title>pylib.geometry2d_plot — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
||||||
@@ -32,22 +32,21 @@
|
|||||||
|
|
||||||
<div class="body" role="main">
|
<div class="body" role="main">
|
||||||
|
|
||||||
<h1>Source code for pylib.geometry_plot</h1><div class="highlight"><pre>
|
<h1>Source code for pylib.geometry2d_plot</h1><div class="highlight"><pre>
|
||||||
<span></span><span class="ch">#!/usr/bin/env python</span>
|
<span></span><span class="ch">#!/usr/bin/env python</span>
|
||||||
<span class="c1"># -*- coding: utf-8 -*-</span>
|
<span class="c1"># -*- coding: utf-8 -*-</span>
|
||||||
<span class="sd">"""2D geometry plotter using matplotlib (pylab).</span>
|
<span class="sd">"""2D geometry plotter using matplotlib (pylab).</span>
|
||||||
|
|
||||||
<span class="sd">:Date: 2019-08-20</span>
|
<span class="sd">:Date: 2019-08-20</span>
|
||||||
|
|
||||||
<span class="sd">.. module:: geometry_plot</span>
|
<span class="sd">.. module:: geometry2d_plot</span>
|
||||||
<span class="sd"> :platform: *nix, Windows</span>
|
<span class="sd"> :platform: *nix, Windows</span>
|
||||||
<span class="sd"> :synopsis: Geometry plotting.</span>
|
<span class="sd"> :synopsis: 2D geometry plotting.</span>
|
||||||
|
|
||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
||||||
<span class="sd">"""</span>
|
<span class="sd">"""</span>
|
||||||
<span class="kn">import</span> <span class="nn">math</span>
|
|
||||||
<span class="kn">import</span> <span class="nn">pylab</span>
|
<span class="kn">import</span> <span class="nn">pylab</span>
|
||||||
<span class="kn">from</span> <span class="nn">geometry</span> <span class="kn">import</span> <span class="p">(</span>
|
<span class="kn">from</span> <span class="nn">geometry2d</span> <span class="kn">import</span> <span class="p">(</span>
|
||||||
<span class="n">distance</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="n">line</span><span class="p">,</span> <span class="n">interpolate_hermite</span><span class="p">,</span> <span class="n">rotate_xy</span><span class="p">,</span> <span class="n">translate_xy</span>
|
<span class="n">distance</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="n">line</span><span class="p">,</span> <span class="n">interpolate_hermite</span><span class="p">,</span> <span class="n">rotate_xy</span><span class="p">,</span> <span class="n">translate_xy</span>
|
||||||
<span class="p">)</span>
|
<span class="p">)</span>
|
||||||
|
|
||||||
@@ -68,7 +67,7 @@
|
|||||||
<span class="p">]</span>
|
<span class="p">]</span>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="plot_lines"><a class="viewcode-back" href="../../pylib.html#pylib.geometry_plot.plot_lines">[docs]</a><span class="k">def</span> <span class="nf">plot_lines</span><span class="p">(</span><span class="n">lns</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
<div class="viewcode-block" id="plot_lines"><a class="viewcode-back" href="../../pylib.geometry2d_plot.html#pylib.geometry2d_plot.plot_lines">[docs]</a><span class="k">def</span> <span class="nf">plot_lines</span><span class="p">(</span><span class="n">lns</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||||||
<span class="k">if</span> <span class="s1">'color'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
<span class="k">if</span> <span class="s1">'color'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
||||||
<span class="c1"># Colors from "tab10" colormap</span>
|
<span class="c1"># Colors from "tab10" colormap</span>
|
||||||
<span class="n">cmap</span> <span class="o">=</span> <span class="n">pylab</span><span class="o">.</span><span class="n">get_cmap</span><span class="p">(</span><span class="s2">"tab10"</span><span class="p">)</span>
|
<span class="n">cmap</span> <span class="o">=</span> <span class="n">pylab</span><span class="o">.</span><span class="n">get_cmap</span><span class="p">(</span><span class="s2">"tab10"</span><span class="p">)</span>
|
||||||
@@ -86,7 +85,7 @@
|
|||||||
<span class="n">pylab</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span></div>
|
<span class="n">pylab</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="plot_cubic_lines"><a class="viewcode-back" href="../../pylib.html#pylib.geometry_plot.plot_cubic_lines">[docs]</a><span class="k">def</span> <span class="nf">plot_cubic_lines</span><span class="p">(</span><span class="n">lns</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
<div class="viewcode-block" id="plot_cubic_lines"><a class="viewcode-back" href="../../pylib.geometry2d_plot.html#pylib.geometry2d_plot.plot_cubic_lines">[docs]</a><span class="k">def</span> <span class="nf">plot_cubic_lines</span><span class="p">(</span><span class="n">lns</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||||||
<span class="k">if</span> <span class="s1">'color'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
<span class="k">if</span> <span class="s1">'color'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
||||||
<span class="c1"># Colors from "tab10" colormap</span>
|
<span class="c1"># Colors from "tab10" colormap</span>
|
||||||
<span class="n">cmap</span> <span class="o">=</span> <span class="n">pylab</span><span class="o">.</span><span class="n">get_cmap</span><span class="p">(</span><span class="s2">"tab10"</span><span class="p">)</span>
|
<span class="n">cmap</span> <span class="o">=</span> <span class="n">pylab</span><span class="o">.</span><span class="n">get_cmap</span><span class="p">(</span><span class="s2">"tab10"</span><span class="p">)</span>
|
||||||
@@ -137,6 +136,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
70
docs/build/html/_modules/pylib/mathematics.html
vendored
70
docs/build/html/_modules/pylib/mathematics.html
vendored
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.mathematics — pylib 2019.5.19 documentation</title>
|
<title>pylib.mathematics — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
||||||
@@ -48,12 +48,12 @@
|
|||||||
<span class="kn">import</span> <span class="nn">math</span>
|
<span class="kn">import</span> <span class="nn">math</span>
|
||||||
<span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">gcd</span>
|
<span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">gcd</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="lcm"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.lcm">[docs]</a><span class="k">def</span> <span class="nf">lcm</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
<div class="viewcode-block" id="lcm"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.lcm">[docs]</a><span class="k">def</span> <span class="nf">lcm</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||||||
<span class="sd">"""Compute the lowest common multiple of a and b"""</span>
|
<span class="sd">"""Compute the lowest common multiple of a and b"""</span>
|
||||||
<span class="k">return</span> <span class="n">a</span><span class="o">/</span><span class="n">gcd</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span><span class="o">*</span><span class="n">b</span></div>
|
<span class="k">return</span> <span class="n">a</span><span class="o">/</span><span class="n">gcd</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span><span class="o">*</span><span class="n">b</span></div>
|
||||||
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector">[docs]</a><span class="k">class</span> <span class="nc">vector</span><span class="p">(</span><span class="nb">list</span><span class="p">):</span>
|
<div class="viewcode-block" id="vector"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector">[docs]</a><span class="k">class</span> <span class="nc">vector</span><span class="p">(</span><span class="nb">list</span><span class="p">):</span>
|
||||||
<span class="sd">"""Use/create vector like lists</span>
|
<span class="sd">"""Use/create vector like lists</span>
|
||||||
|
|
||||||
<span class="sd"> * size -> len(a)</span>
|
<span class="sd"> * size -> len(a)</span>
|
||||||
@@ -311,7 +311,7 @@
|
|||||||
<span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
<span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
<span class="k">return</span> <span class="s2">"vector("</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">+</span> <span class="s2">")"</span>
|
<span class="k">return</span> <span class="s2">"vector("</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">+</span> <span class="s2">")"</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.full"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.full">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.full"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.full">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">full</span><span class="p">(</span><span class="n">length</span><span class="p">,</span> <span class="n">fill_value</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">full</span><span class="p">(</span><span class="n">length</span><span class="p">,</span> <span class="n">fill_value</span><span class="p">):</span>
|
||||||
<span class="sd">"""Returns a vector of length m or matrix of size m rows, n</span>
|
<span class="sd">"""Returns a vector of length m or matrix of size m rows, n</span>
|
||||||
<span class="sd"> columns filled with v.</span>
|
<span class="sd"> columns filled with v.</span>
|
||||||
@@ -329,7 +329,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">fill_value</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">length</span><span class="p">)])</span></div>
|
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">fill_value</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">length</span><span class="p">)])</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.zeros"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.zeros">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.zeros"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.zeros">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">zeros</span><span class="p">(</span><span class="n">length</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">zeros</span><span class="p">(</span><span class="n">length</span><span class="p">):</span>
|
||||||
<span class="sd">"""Returns a zero vector of length m or matrix of size rows, n</span>
|
<span class="sd">"""Returns a zero vector of length m or matrix of size rows, n</span>
|
||||||
<span class="sd"> columns filled with zeros.</span>
|
<span class="sd"> columns filled with zeros.</span>
|
||||||
@@ -345,7 +345,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">vector</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">length</span><span class="p">,</span> <span class="mf">0.</span><span class="p">)</span></div>
|
<span class="k">return</span> <span class="n">vector</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">length</span><span class="p">,</span> <span class="mf">0.</span><span class="p">)</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.ones"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.ones">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.ones"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.ones">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">ones</span><span class="p">(</span><span class="n">length</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">ones</span><span class="p">(</span><span class="n">length</span><span class="p">):</span>
|
||||||
<span class="sd">"""Returns a vector of length m or matrix of size rows, n</span>
|
<span class="sd">"""Returns a vector of length m or matrix of size rows, n</span>
|
||||||
<span class="sd"> columns filled with ones.</span>
|
<span class="sd"> columns filled with ones.</span>
|
||||||
@@ -361,7 +361,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">vector</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">length</span><span class="p">,</span> <span class="mf">1.</span><span class="p">)</span></div>
|
<span class="k">return</span> <span class="n">vector</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">length</span><span class="p">,</span> <span class="mf">1.</span><span class="p">)</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.random"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.random">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.random"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.random">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">random</span><span class="p">(</span><span class="n">shape</span><span class="p">,</span> <span class="n">lmin</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">lmax</span><span class="o">=</span><span class="mf">1.0</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">random</span><span class="p">(</span><span class="n">shape</span><span class="p">,</span> <span class="n">lmin</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">lmax</span><span class="o">=</span><span class="mf">1.0</span><span class="p">):</span>
|
||||||
<span class="sd">"""Returns a random vector of length n or matrix of size m rows, n</span>
|
<span class="sd">"""Returns a random vector of length n or matrix of size m rows, n</span>
|
||||||
<span class="sd"> columns filled with random numbers.</span>
|
<span class="sd"> columns filled with random numbers.</span>
|
||||||
@@ -379,7 +379,7 @@
|
|||||||
<span class="n">dl</span> <span class="o">=</span> <span class="n">lmax</span><span class="o">-</span><span class="n">lmin</span>
|
<span class="n">dl</span> <span class="o">=</span> <span class="n">lmax</span><span class="o">-</span><span class="n">lmin</span>
|
||||||
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">dl</span><span class="o">*</span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</span><span class="o">+</span><span class="n">lmin</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">shape</span><span class="p">)])</span></div>
|
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">dl</span><span class="o">*</span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</span><span class="o">+</span><span class="n">lmin</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">shape</span><span class="p">)])</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.normalize"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.normalize">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.normalize"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.normalize">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">normalize</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">normalize</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Normalize a vector (i. e. the vector has a length of 1)</span>
|
<span class="sa">r</span><span class="sd">"""Normalize a vector (i. e. the vector has a length of 1)</span>
|
||||||
|
|
||||||
@@ -394,11 +394,11 @@
|
|||||||
<span class="n">a_mag</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
|
<span class="n">a_mag</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">/</span><span class="n">a_mag</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">/</span><span class="n">a_mag</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.ang"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.ang">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.ang"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.ang">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">ang</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">ang</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||||||
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">acos</span><span class="p">(</span><span class="n">a</span> <span class="o">*</span> <span class="n">b</span> <span class="o">/</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="o">*</span> <span class="nb">abs</span><span class="p">(</span><span class="n">b</span><span class="p">)))</span></div>
|
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">acos</span><span class="p">(</span><span class="n">a</span> <span class="o">*</span> <span class="n">b</span> <span class="o">/</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="o">*</span> <span class="nb">abs</span><span class="p">(</span><span class="n">b</span><span class="p">)))</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.conjugate"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.conjugate">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.conjugate"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.conjugate">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">conjugate</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">conjugate</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
||||||
<span class="sd">"""</span>
|
<span class="sd">"""</span>
|
||||||
<span class="sd"> New vector object</span>
|
<span class="sd"> New vector object</span>
|
||||||
@@ -407,7 +407,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">.</span><span class="n">conjugate</span><span class="p">()</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">.</span><span class="n">conjugate</span><span class="p">()</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.re"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.re">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.re"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.re">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">re</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">re</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
||||||
<span class="sd">"""Return the real parts of a complex vector</span>
|
<span class="sd">"""Return the real parts of a complex vector</span>
|
||||||
|
|
||||||
@@ -415,7 +415,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">.</span><span class="n">real</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">.</span><span class="n">real</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.im"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.im">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.im"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.im">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">im</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">im</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
||||||
<span class="sd">"""Return the imaginary parts of a complex vector</span>
|
<span class="sd">"""Return the imaginary parts of a complex vector</span>
|
||||||
|
|
||||||
@@ -423,7 +423,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">.</span><span class="n">imag</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">i</span><span class="o">.</span><span class="n">imag</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.abs"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.abs">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.abs"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.abs">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">abs</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">abs</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
||||||
<span class="sd">"""Return modulus parts of a complex vector</span>
|
<span class="sd">"""Return modulus parts of a complex vector</span>
|
||||||
|
|
||||||
@@ -431,7 +431,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="nb">abs</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="nb">abs</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.arg"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.arg">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.arg"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.arg">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">arg</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">arg</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
||||||
<span class="sd">"""Return phase parts of a complex vector</span>
|
<span class="sd">"""Return phase parts of a complex vector</span>
|
||||||
|
|
||||||
@@ -439,7 +439,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">imag</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">real</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
<span class="k">return</span> <span class="n">vector</span><span class="p">([</span><span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">i</span><span class="o">.</span><span class="n">imag</span><span class="p">,</span> <span class="n">i</span><span class="o">.</span><span class="n">real</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">a</span><span class="p">])</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.cross"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.cross">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="vector.cross"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.cross">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">cross</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">cross</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Cross product</span>
|
<span class="sa">r</span><span class="sd">"""Cross product</span>
|
||||||
|
|
||||||
@@ -456,10 +456,10 @@
|
|||||||
<span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span>
|
<span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span>
|
||||||
<span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span></div>
|
<span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.xyz"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.xyz">[docs]</a> <span class="k">def</span> <span class="nf">xyz</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
<div class="viewcode-block" id="vector.xyz"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.xyz">[docs]</a> <span class="k">def</span> <span class="nf">xyz</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
<span class="k">return</span> <span class="bp">self</span><span class="p">[:</span><span class="mi">3</span><span class="p">]</span></div>
|
<span class="k">return</span> <span class="bp">self</span><span class="p">[:</span><span class="mi">3</span><span class="p">]</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.rotate_x"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.rotate_x">[docs]</a> <span class="k">def</span> <span class="nf">rotate_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
<div class="viewcode-block" id="vector.rotate_x"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.rotate_x">[docs]</a> <span class="k">def</span> <span class="nf">rotate_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Rotation about the x dirction.</span>
|
<span class="sa">r</span><span class="sd">"""Rotation about the x dirction.</span>
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
<span class="sd"> .. math::</span>
|
||||||
@@ -475,7 +475,7 @@
|
|||||||
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">rx</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">rx</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
||||||
<span class="k">return</span> <span class="bp">self</span></div>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.rotate_y"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.rotate_y">[docs]</a> <span class="k">def</span> <span class="nf">rotate_y</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
<div class="viewcode-block" id="vector.rotate_y"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.rotate_y">[docs]</a> <span class="k">def</span> <span class="nf">rotate_y</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Rotation about the y dirction.</span>
|
<span class="sa">r</span><span class="sd">"""Rotation about the y dirction.</span>
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
<span class="sd"> .. math::</span>
|
||||||
@@ -491,7 +491,7 @@
|
|||||||
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">ry</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">ry</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
||||||
<span class="k">return</span> <span class="bp">self</span></div>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.rotate_z"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.rotate_z">[docs]</a> <span class="k">def</span> <span class="nf">rotate_z</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
<div class="viewcode-block" id="vector.rotate_z"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.rotate_z">[docs]</a> <span class="k">def</span> <span class="nf">rotate_z</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Rotation about the z dirction.</span>
|
<span class="sa">r</span><span class="sd">"""Rotation about the z dirction.</span>
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
<span class="sd"> .. math::</span>
|
||||||
@@ -507,7 +507,7 @@
|
|||||||
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">rz</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">rz</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
||||||
<span class="k">return</span> <span class="bp">self</span></div>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.translate"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.translate">[docs]</a> <span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
|
<div class="viewcode-block" id="vector.translate"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.translate">[docs]</a> <span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Translation</span>
|
<span class="sa">r</span><span class="sd">"""Translation</span>
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
<span class="sd"> .. math::</span>
|
||||||
@@ -523,7 +523,7 @@
|
|||||||
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">t</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">t</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
||||||
<span class="k">return</span> <span class="bp">self</span></div>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.scale"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.scale">[docs]</a> <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sz</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
<div class="viewcode-block" id="vector.scale"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.scale">[docs]</a> <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sz</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Scaling</span>
|
<span class="sa">r</span><span class="sd">"""Scaling</span>
|
||||||
|
|
||||||
<span class="sd"> uniform scaling if sx=sy=sz=s.</span>
|
<span class="sd"> uniform scaling if sx=sy=sz=s.</span>
|
||||||
@@ -549,7 +549,7 @@
|
|||||||
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">s</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">s</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="p">,</span> <span class="n">sz</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
||||||
<span class="k">return</span> <span class="bp">self</span></div>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="vector.ch_cs"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.vector.ch_cs">[docs]</a> <span class="k">def</span> <span class="nf">ch_cs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cs</span><span class="p">):</span>
|
<div class="viewcode-block" id="vector.ch_cs"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.vector.ch_cs">[docs]</a> <span class="k">def</span> <span class="nf">ch_cs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cs</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Transform this vector from its defined coordinate system to a</span>
|
<span class="sa">r</span><span class="sd">"""Transform this vector from its defined coordinate system to a</span>
|
||||||
<span class="sd"> new coordinate system, defined by the given coordinate system (u,</span>
|
<span class="sd"> new coordinate system, defined by the given coordinate system (u,</span>
|
||||||
<span class="sd"> v and w direction vectors).</span>
|
<span class="sd"> v and w direction vectors).</span>
|
||||||
@@ -567,7 +567,7 @@
|
|||||||
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">cs</span> <span class="o">*</span> <span class="bp">self</span>
|
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">cs</span> <span class="o">*</span> <span class="bp">self</span>
|
||||||
<span class="k">return</span> <span class="bp">self</span></div></div>
|
<span class="k">return</span> <span class="bp">self</span></div></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="matrix"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.matrix">[docs]</a><span class="k">class</span> <span class="nc">matrix</span><span class="p">(</span><span class="nb">list</span><span class="p">):</span>
|
<div class="viewcode-block" id="matrix"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix">[docs]</a><span class="k">class</span> <span class="nc">matrix</span><span class="p">(</span><span class="nb">list</span><span class="p">):</span>
|
||||||
<span class="sd">"""Use/create matrix like list of lists</span>
|
<span class="sd">"""Use/create matrix like list of lists</span>
|
||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
|
|
||||||
@@ -596,7 +596,7 @@
|
|||||||
<span class="n">item</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getitem__</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
|
<span class="n">item</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getitem__</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">matrix</span><span class="p">(</span><span class="n">item</span><span class="p">)</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="nb">list</span><span class="p">)</span> <span class="k">else</span> <span class="n">item</span>
|
<span class="k">return</span> <span class="n">matrix</span><span class="p">(</span><span class="n">item</span><span class="p">)</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="nb">list</span><span class="p">)</span> <span class="k">else</span> <span class="n">item</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="matrix.rx"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.matrix.rx">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="matrix.rx"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.rx">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">rx</span><span class="p">(</span><span class="n">theta</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">rx</span><span class="p">(</span><span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Rotation matrix about the x direction.</span>
|
<span class="sa">r</span><span class="sd">"""Rotation matrix about the x direction.</span>
|
||||||
|
|
||||||
@@ -619,7 +619,7 @@
|
|||||||
<span class="p">[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
<span class="p">[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
||||||
<span class="k">return</span> <span class="n">T</span></div>
|
<span class="k">return</span> <span class="n">T</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="matrix.ry"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.matrix.ry">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="matrix.ry"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.ry">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">ry</span><span class="p">(</span><span class="n">theta</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">ry</span><span class="p">(</span><span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Rotation matrix about the y direction.</span>
|
<span class="sa">r</span><span class="sd">"""Rotation matrix about the y direction.</span>
|
||||||
|
|
||||||
@@ -642,7 +642,7 @@
|
|||||||
<span class="p">[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
<span class="p">[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
||||||
<span class="k">return</span> <span class="n">T</span></div>
|
<span class="k">return</span> <span class="n">T</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="matrix.rz"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.matrix.rz">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="matrix.rz"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.rz">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">rz</span><span class="p">(</span><span class="n">theta</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">rz</span><span class="p">(</span><span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Rotation matrix about the z direction.</span>
|
<span class="sa">r</span><span class="sd">"""Rotation matrix about the z direction.</span>
|
||||||
|
|
||||||
@@ -685,7 +685,7 @@
|
|||||||
<span class="p">[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
<span class="p">[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
||||||
<span class="k">return</span> <span class="n">T</span></div>
|
<span class="k">return</span> <span class="n">T</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="matrix.t"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.matrix.t">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="matrix.t"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.t">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">t</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">t</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Translation matrix</span>
|
<span class="sa">r</span><span class="sd">"""Translation matrix</span>
|
||||||
|
|
||||||
@@ -704,7 +704,7 @@
|
|||||||
<span class="p">[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
<span class="p">[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
||||||
<span class="k">return</span> <span class="n">T</span></div>
|
<span class="k">return</span> <span class="n">T</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="matrix.s"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.matrix.s">[docs]</a> <span class="nd">@staticmethod</span>
|
<div class="viewcode-block" id="matrix.s"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.s">[docs]</a> <span class="nd">@staticmethod</span>
|
||||||
<span class="k">def</span> <span class="nf">s</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sz</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
<span class="k">def</span> <span class="nf">s</span><span class="p">(</span><span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sz</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Scaling matrix</span>
|
<span class="sa">r</span><span class="sd">"""Scaling matrix</span>
|
||||||
|
|
||||||
@@ -820,7 +820,7 @@
|
|||||||
<span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
<span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
<span class="k">return</span> <span class="s2">"matrix("</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">+</span> <span class="s2">")"</span>
|
<span class="k">return</span> <span class="s2">"matrix("</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">+</span> <span class="s2">")"</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="matrix.rotate_x"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.matrix.rotate_x">[docs]</a> <span class="k">def</span> <span class="nf">rotate_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
<div class="viewcode-block" id="matrix.rotate_x"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.rotate_x">[docs]</a> <span class="k">def</span> <span class="nf">rotate_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Rotation about the x dirction.</span>
|
<span class="sa">r</span><span class="sd">"""Rotation about the x dirction.</span>
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
<span class="sd"> .. math::</span>
|
||||||
@@ -846,7 +846,7 @@
|
|||||||
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">rx</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">rx</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
||||||
<span class="k">return</span> <span class="bp">self</span></div>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="matrix.rotate_y"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.matrix.rotate_y">[docs]</a> <span class="k">def</span> <span class="nf">rotate_y</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
<div class="viewcode-block" id="matrix.rotate_y"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.rotate_y">[docs]</a> <span class="k">def</span> <span class="nf">rotate_y</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Rotation about the y dirction.</span>
|
<span class="sa">r</span><span class="sd">"""Rotation about the y dirction.</span>
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
<span class="sd"> .. math::</span>
|
||||||
@@ -872,7 +872,7 @@
|
|||||||
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">ry</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">ry</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
||||||
<span class="k">return</span> <span class="bp">self</span></div>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="matrix.rotate_z"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.matrix.rotate_z">[docs]</a> <span class="k">def</span> <span class="nf">rotate_z</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
<div class="viewcode-block" id="matrix.rotate_z"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.rotate_z">[docs]</a> <span class="k">def</span> <span class="nf">rotate_z</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Rotation about the z dirction.</span>
|
<span class="sa">r</span><span class="sd">"""Rotation about the z dirction.</span>
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
<span class="sd"> .. math::</span>
|
||||||
@@ -898,7 +898,7 @@
|
|||||||
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">rz</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">rz</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
||||||
<span class="k">return</span> <span class="bp">self</span></div>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="matrix.translate"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.matrix.translate">[docs]</a> <span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
|
<div class="viewcode-block" id="matrix.translate"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.translate">[docs]</a> <span class="k">def</span> <span class="nf">translate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Translation</span>
|
<span class="sa">r</span><span class="sd">"""Translation</span>
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
<span class="sd"> .. math::</span>
|
||||||
@@ -924,7 +924,7 @@
|
|||||||
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">t</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
<span class="bp">self</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">t</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">ty</span><span class="p">,</span> <span class="n">tz</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span>
|
||||||
<span class="k">return</span> <span class="bp">self</span></div>
|
<span class="k">return</span> <span class="bp">self</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="matrix.scale"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.matrix.scale">[docs]</a> <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sz</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
<div class="viewcode-block" id="matrix.scale"><a class="viewcode-back" href="../../pylib.mathematics.html#pylib.mathematics.matrix.scale">[docs]</a> <span class="k">def</span> <span class="nf">scale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sx</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sz</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Scaling</span>
|
<span class="sa">r</span><span class="sd">"""Scaling</span>
|
||||||
|
|
||||||
<span class="sd"> uniform scaling if sx=sy=sz=s.</span>
|
<span class="sd"> uniform scaling if sx=sy=sz=s.</span>
|
||||||
@@ -977,6 +977,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.numerical.fit — pylib 2019.5.19 documentation</title>
|
<title>pylib.numerical.fit — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../../_static/custom.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/custom.css" type="text/css" />
|
||||||
@@ -49,7 +49,7 @@
|
|||||||
<span class="kn">from</span> <span class="nn">pylab</span> <span class="kn">import</span> <span class="n">array</span><span class="p">,</span> <span class="n">argmax</span><span class="p">,</span> <span class="n">gradient</span><span class="p">,</span> <span class="n">exp</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">,</span> <span class="n">log</span><span class="p">,</span> <span class="n">linspace</span>
|
<span class="kn">from</span> <span class="nn">pylab</span> <span class="kn">import</span> <span class="n">array</span><span class="p">,</span> <span class="n">argmax</span><span class="p">,</span> <span class="n">gradient</span><span class="p">,</span> <span class="n">exp</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">,</span> <span class="n">log</span><span class="p">,</span> <span class="n">linspace</span>
|
||||||
<span class="kn">from</span> <span class="nn">scipy.optimize</span> <span class="kn">import</span> <span class="n">curve_fit</span>
|
<span class="kn">from</span> <span class="nn">scipy.optimize</span> <span class="kn">import</span> <span class="n">curve_fit</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="gauss"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.fit.gauss">[docs]</a><span class="k">def</span> <span class="nf">gauss</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
<div class="viewcode-block" id="gauss"><a class="viewcode-back" href="../../../pylib.numerical.fit.html#pylib.numerical.fit.gauss">[docs]</a><span class="k">def</span> <span class="nf">gauss</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
||||||
<span class="sd">"""Gauss distribution function.</span>
|
<span class="sd">"""Gauss distribution function.</span>
|
||||||
|
|
||||||
<span class="sd"> .. math::</span>
|
<span class="sd"> .. math::</span>
|
||||||
@@ -72,7 +72,7 @@
|
|||||||
<span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="o">=</span> <span class="n">p</span>
|
<span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="o">=</span> <span class="n">p</span>
|
||||||
<span class="k">return</span> <span class="n">a</span><span class="o">*</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span><span class="o">**</span><span class="mf">2.</span><span class="o">/</span><span class="p">(</span><span class="mf">2.</span> <span class="o">*</span> <span class="n">c</span><span class="o">**</span><span class="mf">2.</span><span class="p">))</span> <span class="o">+</span> <span class="n">d</span></div>
|
<span class="k">return</span> <span class="n">a</span><span class="o">*</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span><span class="o">**</span><span class="mf">2.</span><span class="o">/</span><span class="p">(</span><span class="mf">2.</span> <span class="o">*</span> <span class="n">c</span><span class="o">**</span><span class="mf">2.</span><span class="p">))</span> <span class="o">+</span> <span class="n">d</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="gauss_fit"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.fit.gauss_fit">[docs]</a><span class="k">def</span> <span class="nf">gauss_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">e</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">x_fit</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<div class="viewcode-block" id="gauss_fit"><a class="viewcode-back" href="../../../pylib.numerical.fit.html#pylib.numerical.fit.gauss_fit">[docs]</a><span class="k">def</span> <span class="nf">gauss_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">e</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">x_fit</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sd">"""Fit Gauss distribution function to data.</span>
|
<span class="sd">"""Fit Gauss distribution function to data.</span>
|
||||||
|
|
||||||
<span class="sd"> :param x: positions</span>
|
<span class="sd"> :param x: positions</span>
|
||||||
@@ -148,6 +148,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.numerical.integration — pylib 2019.5.19 documentation</title>
|
<title>pylib.numerical.integration — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../../_static/custom.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/custom.css" type="text/css" />
|
||||||
@@ -50,7 +50,7 @@
|
|||||||
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span>
|
<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span>
|
||||||
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">linspace</span><span class="p">,</span> <span class="n">trapz</span><span class="p">,</span> <span class="n">zeros</span>
|
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">linspace</span><span class="p">,</span> <span class="n">trapz</span><span class="p">,</span> <span class="n">zeros</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="trapez"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.integration.trapez">[docs]</a><span class="k">def</span> <span class="nf">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">a</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">b</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
|
<div class="viewcode-block" id="trapez"><a class="viewcode-back" href="../../../pylib.numerical.integration.html#pylib.numerical.integration.trapez">[docs]</a><span class="k">def</span> <span class="nf">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">a</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">b</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
|
||||||
<span class="n">save_values</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<span class="n">save_values</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""</span>
|
<span class="sa">r</span><span class="sd">"""</span>
|
||||||
<span class="sd"> Integration of :math:`f(x)` using the trapezoidal rule</span>
|
<span class="sd"> Integration of :math:`f(x)` using the trapezoidal rule</span>
|
||||||
@@ -202,6 +202,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.numerical.ode — pylib 2019.5.19 documentation</title>
|
<title>pylib.numerical.ode — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../../_static/custom.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/custom.css" type="text/css" />
|
||||||
@@ -53,7 +53,7 @@
|
|||||||
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span><span class="p">,</span> <span class="n">isnan</span><span class="p">,</span> <span class="nb">sum</span><span class="p">,</span> <span class="n">zeros</span><span class="p">,</span> <span class="n">dot</span>
|
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span><span class="p">,</span> <span class="n">isnan</span><span class="p">,</span> <span class="nb">sum</span><span class="p">,</span> <span class="n">zeros</span><span class="p">,</span> <span class="n">dot</span>
|
||||||
<span class="kn">from</span> <span class="nn">numpy.linalg</span> <span class="kn">import</span> <span class="n">norm</span><span class="p">,</span> <span class="n">inv</span>
|
<span class="kn">from</span> <span class="nn">numpy.linalg</span> <span class="kn">import</span> <span class="n">norm</span><span class="p">,</span> <span class="n">inv</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="e1"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.ode.e1">[docs]</a><span class="k">def</span> <span class="nf">e1</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<div class="viewcode-block" id="e1"><a class="viewcode-back" href="../../../pylib.numerical.ode.html#pylib.numerical.ode.e1">[docs]</a><span class="k">def</span> <span class="nf">e1</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Explicit first-order method /</span>
|
<span class="sa">r</span><span class="sd">"""Explicit first-order method /</span>
|
||||||
<span class="sd"> (standard, or forward) Euler method /</span>
|
<span class="sd"> (standard, or forward) Euler method /</span>
|
||||||
<span class="sd"> Runge-Kutta 1st order method.</span>
|
<span class="sd"> Runge-Kutta 1st order method.</span>
|
||||||
@@ -178,7 +178,7 @@
|
|||||||
<span class="s1">'first-order method (Euler / Runge-Kutta) was successful.'</span><span class="p">)</span>
|
<span class="s1">'first-order method (Euler / Runge-Kutta) was successful.'</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">x</span></div>
|
<span class="k">return</span> <span class="n">x</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="e2"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.ode.e2">[docs]</a><span class="k">def</span> <span class="nf">e2</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<div class="viewcode-block" id="e2"><a class="viewcode-back" href="../../../pylib.numerical.ode.html#pylib.numerical.ode.e2">[docs]</a><span class="k">def</span> <span class="nf">e2</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Explicit second-order method / Runge-Kutta 2nd order method.</span>
|
<span class="sa">r</span><span class="sd">"""Explicit second-order method / Runge-Kutta 2nd order method.</span>
|
||||||
|
|
||||||
<span class="sd"> :param f: the function to solve</span>
|
<span class="sd"> :param f: the function to solve</span>
|
||||||
@@ -205,7 +205,7 @@
|
|||||||
<span class="s1">'2th-order method (Runge-Kutta) was successful.'</span><span class="p">)</span>
|
<span class="s1">'2th-order method (Runge-Kutta) was successful.'</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">x</span></div>
|
<span class="k">return</span> <span class="n">x</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="e4"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.ode.e4">[docs]</a><span class="k">def</span> <span class="nf">e4</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<div class="viewcode-block" id="e4"><a class="viewcode-back" href="../../../pylib.numerical.ode.html#pylib.numerical.ode.e4">[docs]</a><span class="k">def</span> <span class="nf">e4</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Explicit fourth-order method / Runge-Kutta 4th order method.</span>
|
<span class="sa">r</span><span class="sd">"""Explicit fourth-order method / Runge-Kutta 4th order method.</span>
|
||||||
|
|
||||||
<span class="sd"> :param f: the function to solve</span>
|
<span class="sd"> :param f: the function to solve</span>
|
||||||
@@ -234,7 +234,7 @@
|
|||||||
<span class="s1">'4th-order method (Runge-Kutta) was successful.'</span><span class="p">)</span>
|
<span class="s1">'4th-order method (Runge-Kutta) was successful.'</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">x</span></div>
|
<span class="k">return</span> <span class="n">x</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="fpi"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.ode.fpi">[docs]</a><span class="k">def</span> <span class="nf">fpi</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">ti</span><span class="p">,</span> <span class="n">ti1</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span>
|
<div class="viewcode-block" id="fpi"><a class="viewcode-back" href="../../../pylib.numerical.ode.html#pylib.numerical.ode.fpi">[docs]</a><span class="k">def</span> <span class="nf">fpi</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">ti</span><span class="p">,</span> <span class="n">ti1</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span>
|
||||||
<span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Fixed-point iteration.</span>
|
<span class="sa">r</span><span class="sd">"""Fixed-point iteration.</span>
|
||||||
<span class="sd"> </span>
|
<span class="sd"> </span>
|
||||||
@@ -283,7 +283,7 @@
|
|||||||
<span class="n">iterations</span> <span class="o">=</span> <span class="n">j</span><span class="o">+</span><span class="mi">1</span> <span class="c1"># number beginning with 1 therefore + 1</span>
|
<span class="n">iterations</span> <span class="o">=</span> <span class="n">j</span><span class="o">+</span><span class="mi">1</span> <span class="c1"># number beginning with 1 therefore + 1</span>
|
||||||
<span class="k">return</span> <span class="n">xij</span><span class="p">,</span> <span class="n">iterations</span></div>
|
<span class="k">return</span> <span class="n">xij</span><span class="p">,</span> <span class="n">iterations</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="i1"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.ode.i1">[docs]</a><span class="k">def</span> <span class="nf">i1</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span>
|
<div class="viewcode-block" id="i1"><a class="viewcode-back" href="../../../pylib.numerical.ode.html#pylib.numerical.ode.i1">[docs]</a><span class="k">def</span> <span class="nf">i1</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span>
|
||||||
<span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Implicite first-order method / backward Euler method.</span>
|
<span class="sa">r</span><span class="sd">"""Implicite first-order method / backward Euler method.</span>
|
||||||
|
|
||||||
@@ -322,7 +322,7 @@
|
|||||||
<span class="s1">'first-order method (Euler) was successful.'</span><span class="p">)</span>
|
<span class="s1">'first-order method (Euler) was successful.'</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">iterations</span></div>
|
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">iterations</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="newmark_newtonraphson"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.ode.newmark_newtonraphson">[docs]</a><span class="k">def</span> <span class="nf">newmark_newtonraphson</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">xp0</span><span class="p">,</span> <span class="n">xpp0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=.</span><span class="mi">5</span><span class="p">,</span>
|
<div class="viewcode-block" id="newmark_newtonraphson"><a class="viewcode-back" href="../../../pylib.numerical.ode.html#pylib.numerical.ode.newmark_newtonraphson">[docs]</a><span class="k">def</span> <span class="nf">newmark_newtonraphson</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">xp0</span><span class="p">,</span> <span class="n">xpp0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=.</span><span class="mi">5</span><span class="p">,</span>
|
||||||
<span class="n">beta</span><span class="o">=.</span><span class="mi">25</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<span class="n">beta</span><span class="o">=.</span><span class="mi">25</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Newmark method.</span>
|
<span class="sa">r</span><span class="sd">"""Newmark method.</span>
|
||||||
|
|
||||||
@@ -398,7 +398,7 @@
|
|||||||
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">xp</span><span class="p">,</span> <span class="n">xpp</span><span class="p">,</span> <span class="n">iterations</span></div>
|
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">xp</span><span class="p">,</span> <span class="n">xpp</span><span class="p">,</span> <span class="n">iterations</span></div>
|
||||||
<span class="c1"># x = concatenate((x, xp, xpp), axis=1)</span>
|
<span class="c1"># x = concatenate((x, xp, xpp), axis=1)</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="newmark_newtonraphson_rdk"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.ode.newmark_newtonraphson_rdk">[docs]</a><span class="k">def</span> <span class="nf">newmark_newtonraphson_rdk</span><span class="p">(</span><span class="n">fnm</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">xp0</span><span class="p">,</span> <span class="n">xpp0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=.</span><span class="mi">5</span><span class="p">,</span>
|
<div class="viewcode-block" id="newmark_newtonraphson_rdk"><a class="viewcode-back" href="../../../pylib.numerical.ode.html#pylib.numerical.ode.newmark_newtonraphson_rdk">[docs]</a><span class="k">def</span> <span class="nf">newmark_newtonraphson_rdk</span><span class="p">(</span><span class="n">fnm</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">xp0</span><span class="p">,</span> <span class="n">xpp0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=.</span><span class="mi">5</span><span class="p">,</span>
|
||||||
<span class="n">beta</span><span class="o">=.</span><span class="mi">25</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
<span class="n">beta</span><span class="o">=.</span><span class="mi">25</span><span class="p">,</span> <span class="n">max_iterations</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||||
<span class="sa">r</span><span class="sd">"""Newmark method.</span>
|
<span class="sa">r</span><span class="sd">"""Newmark method.</span>
|
||||||
|
|
||||||
@@ -492,6 +492,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.numerical.ode_model — pylib 2019.5.19 documentation</title>
|
<title>pylib.numerical.ode_model — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../../_static/custom.css" type="text/css" />
|
<link rel="stylesheet" href="../../../_static/custom.css" type="text/css" />
|
||||||
@@ -52,7 +52,7 @@
|
|||||||
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span><span class="p">,</span> <span class="n">cos</span><span class="p">,</span> <span class="n">sin</span><span class="p">,</span> <span class="n">dot</span><span class="p">,</span> <span class="n">square</span>
|
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span><span class="p">,</span> <span class="n">cos</span><span class="p">,</span> <span class="n">sin</span><span class="p">,</span> <span class="n">dot</span><span class="p">,</span> <span class="n">square</span>
|
||||||
<span class="kn">from</span> <span class="nn">numpy.linalg</span> <span class="kn">import</span> <span class="n">inv</span>
|
<span class="kn">from</span> <span class="nn">numpy.linalg</span> <span class="kn">import</span> <span class="n">inv</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="disk"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.ode_model.disk">[docs]</a><span class="k">def</span> <span class="nf">disk</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
<div class="viewcode-block" id="disk"><a class="viewcode-back" href="../../../pylib.numerical.ode_model.html#pylib.numerical.ode_model.disk">[docs]</a><span class="k">def</span> <span class="nf">disk</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
||||||
<span class="sd">"""Rotation of an eccentric disk.</span>
|
<span class="sd">"""Rotation of an eccentric disk.</span>
|
||||||
|
|
||||||
<span class="sd"> :param x: values of the function</span>
|
<span class="sd"> :param x: values of the function</span>
|
||||||
@@ -76,7 +76,7 @@
|
|||||||
<span class="n">qp4</span><span class="p">,</span> <span class="n">qp5</span><span class="p">,</span> <span class="n">qp6</span> <span class="o">=</span> <span class="n">qp46</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span> <span class="c1"># 2d array to 1d array to list</span>
|
<span class="n">qp4</span><span class="p">,</span> <span class="n">qp5</span><span class="p">,</span> <span class="n">qp6</span> <span class="o">=</span> <span class="n">qp46</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,)</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span> <span class="c1"># 2d array to 1d array to list</span>
|
||||||
<span class="k">return</span> <span class="n">qp1</span><span class="p">,</span> <span class="n">qp2</span><span class="p">,</span> <span class="n">qp3</span><span class="p">,</span> <span class="n">qp4</span><span class="p">,</span> <span class="n">qp5</span><span class="p">,</span> <span class="n">qp6</span></div>
|
<span class="k">return</span> <span class="n">qp1</span><span class="p">,</span> <span class="n">qp2</span><span class="p">,</span> <span class="n">qp3</span><span class="p">,</span> <span class="n">qp4</span><span class="p">,</span> <span class="n">qp5</span><span class="p">,</span> <span class="n">qp6</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="disk_nm"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.ode_model.disk_nm">[docs]</a><span class="k">def</span> <span class="nf">disk_nm</span><span class="p">(</span><span class="n">xn</span><span class="p">,</span> <span class="n">xpn</span><span class="p">,</span> <span class="n">xppn</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
<div class="viewcode-block" id="disk_nm"><a class="viewcode-back" href="../../../pylib.numerical.ode_model.html#pylib.numerical.ode_model.disk_nm">[docs]</a><span class="k">def</span> <span class="nf">disk_nm</span><span class="p">(</span><span class="n">xn</span><span class="p">,</span> <span class="n">xpn</span><span class="p">,</span> <span class="n">xppn</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
||||||
<span class="sd">"""Rotation of an eccentric disk.</span>
|
<span class="sd">"""Rotation of an eccentric disk.</span>
|
||||||
|
|
||||||
<span class="sd"> :param xn: values of the function</span>
|
<span class="sd"> :param xn: values of the function</span>
|
||||||
@@ -107,7 +107,7 @@
|
|||||||
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
|
||||||
<span class="k">return</span> <span class="n">N</span><span class="p">,</span> <span class="n">dN</span><span class="p">,</span> <span class="n">dNp</span><span class="p">,</span> <span class="n">dNpp</span></div>
|
<span class="k">return</span> <span class="n">N</span><span class="p">,</span> <span class="n">dN</span><span class="p">,</span> <span class="n">dNp</span><span class="p">,</span> <span class="n">dNpp</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="disk_nmmdk"><a class="viewcode-back" href="../../../pylib.numerical.html#pylib.numerical.ode_model.disk_nmmdk">[docs]</a><span class="k">def</span> <span class="nf">disk_nmmdk</span><span class="p">(</span><span class="n">xn</span><span class="p">,</span> <span class="n">xpn</span><span class="p">,</span> <span class="n">xppn</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
<div class="viewcode-block" id="disk_nmmdk"><a class="viewcode-back" href="../../../pylib.numerical.ode_model.html#pylib.numerical.ode_model.disk_nmmdk">[docs]</a><span class="k">def</span> <span class="nf">disk_nmmdk</span><span class="p">(</span><span class="n">xn</span><span class="p">,</span> <span class="n">xpn</span><span class="p">,</span> <span class="n">xppn</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
|
||||||
<span class="sd">"""Rotation of an eccentric disk.</span>
|
<span class="sd">"""Rotation of an eccentric disk.</span>
|
||||||
|
|
||||||
<span class="sd"> :param xn: values of the function</span>
|
<span class="sd"> :param xn: values of the function</span>
|
||||||
@@ -171,6 +171,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
26
docs/build/html/_modules/pylib/time_of_day.html
vendored
26
docs/build/html/_modules/pylib/time_of_day.html
vendored
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>pylib.time_of_day — pylib 2019.5.19 documentation</title>
|
<title>pylib.time_of_day — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
|
||||||
@@ -47,7 +47,7 @@
|
|||||||
<span class="sd">"""</span>
|
<span class="sd">"""</span>
|
||||||
<span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <span class="n">struct_time</span><span class="p">,</span> <span class="n">mktime</span>
|
<span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <span class="n">struct_time</span><span class="p">,</span> <span class="n">mktime</span>
|
||||||
|
|
||||||
<div class="viewcode-block" id="in_seconds"><a class="viewcode-back" href="../../pylib.html#pylib.time_of_day.in_seconds">[docs]</a><span class="k">def</span> <span class="nf">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
<div class="viewcode-block" id="in_seconds"><a class="viewcode-back" href="../../pylib.time_of_day.html#pylib.time_of_day.in_seconds">[docs]</a><span class="k">def</span> <span class="nf">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
||||||
<span class="sd">"""If time is `time.struct_time` convert to float seconds.</span>
|
<span class="sd">"""If time is `time.struct_time` convert to float seconds.</span>
|
||||||
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
<span class="sd"> :param time: the time in seconds</span>
|
||||||
@@ -60,7 +60,7 @@
|
|||||||
<span class="n">time</span> <span class="o">=</span> <span class="n">mktime</span><span class="p">(</span><span class="n">time</span><span class="p">)</span>
|
<span class="n">time</span> <span class="o">=</span> <span class="n">mktime</span><span class="p">(</span><span class="n">time</span><span class="p">)</span>
|
||||||
<span class="k">return</span> <span class="n">time</span></div>
|
<span class="k">return</span> <span class="n">time</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="seconds"><a class="viewcode-back" href="../../pylib.html#pylib.time_of_day.seconds">[docs]</a><span class="k">def</span> <span class="nf">seconds</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
<div class="viewcode-block" id="seconds"><a class="viewcode-back" href="../../pylib.time_of_day.html#pylib.time_of_day.seconds">[docs]</a><span class="k">def</span> <span class="nf">seconds</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
||||||
<span class="sd">"""The seconds of the time.</span>
|
<span class="sd">"""The seconds of the time.</span>
|
||||||
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
<span class="sd"> :param time: the time in seconds</span>
|
||||||
@@ -71,7 +71,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">%</span><span class="mi">60</span></div>
|
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">%</span><span class="mi">60</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="seconds_norm"><a class="viewcode-back" href="../../pylib.html#pylib.time_of_day.seconds_norm">[docs]</a><span class="k">def</span> <span class="nf">seconds_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
<div class="viewcode-block" id="seconds_norm"><a class="viewcode-back" href="../../pylib.time_of_day.html#pylib.time_of_day.seconds_norm">[docs]</a><span class="k">def</span> <span class="nf">seconds_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
||||||
<span class="sd">"""The seconds normalized to 60 seconds.</span>
|
<span class="sd">"""The seconds normalized to 60 seconds.</span>
|
||||||
<span class="sd"> </span>
|
<span class="sd"> </span>
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
<span class="sd"> :param time: the time in seconds</span>
|
||||||
@@ -82,7 +82,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span></div>
|
<span class="k">return</span> <span class="n">seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="minutes"><a class="viewcode-back" href="../../pylib.html#pylib.time_of_day.minutes">[docs]</a><span class="k">def</span> <span class="nf">minutes</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
<div class="viewcode-block" id="minutes"><a class="viewcode-back" href="../../pylib.time_of_day.html#pylib.time_of_day.minutes">[docs]</a><span class="k">def</span> <span class="nf">minutes</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
||||||
<span class="sd">"""The minutes of the time.</span>
|
<span class="sd">"""The minutes of the time.</span>
|
||||||
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
<span class="sd"> :param time: the time in seconds</span>
|
||||||
@@ -93,7 +93,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span><span class="o">%</span><span class="mi">60</span></div>
|
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span><span class="o">%</span><span class="mi">60</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="minutes_norm"><a class="viewcode-back" href="../../pylib.html#pylib.time_of_day.minutes_norm">[docs]</a><span class="k">def</span> <span class="nf">minutes_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
<div class="viewcode-block" id="minutes_norm"><a class="viewcode-back" href="../../pylib.time_of_day.html#pylib.time_of_day.minutes_norm">[docs]</a><span class="k">def</span> <span class="nf">minutes_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
||||||
<span class="sd">"""The minutes normalized to 60 minutes.</span>
|
<span class="sd">"""The minutes normalized to 60 minutes.</span>
|
||||||
<span class="sd"> </span>
|
<span class="sd"> </span>
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
<span class="sd"> :param time: the time in seconds</span>
|
||||||
@@ -104,7 +104,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">minutes</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span></div>
|
<span class="k">return</span> <span class="n">minutes</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="hours"><a class="viewcode-back" href="../../pylib.html#pylib.time_of_day.hours">[docs]</a><span class="k">def</span> <span class="nf">hours</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
<div class="viewcode-block" id="hours"><a class="viewcode-back" href="../../pylib.time_of_day.html#pylib.time_of_day.hours">[docs]</a><span class="k">def</span> <span class="nf">hours</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
||||||
<span class="sd">"""The hours of the time.</span>
|
<span class="sd">"""The hours of the time.</span>
|
||||||
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
<span class="sd"> :param time: the time in seconds</span>
|
||||||
@@ -115,7 +115,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span><span class="o">/</span><span class="mi">60</span><span class="o">%</span><span class="mi">24</span></div>
|
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span><span class="o">/</span><span class="mi">60</span><span class="o">%</span><span class="mi">24</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="hours_norm"><a class="viewcode-back" href="../../pylib.html#pylib.time_of_day.hours_norm">[docs]</a><span class="k">def</span> <span class="nf">hours_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
<div class="viewcode-block" id="hours_norm"><a class="viewcode-back" href="../../pylib.time_of_day.html#pylib.time_of_day.hours_norm">[docs]</a><span class="k">def</span> <span class="nf">hours_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
||||||
<span class="sd">"""The hours normalized to 24 hours.</span>
|
<span class="sd">"""The hours normalized to 24 hours.</span>
|
||||||
<span class="sd"> </span>
|
<span class="sd"> </span>
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
<span class="sd"> :param time: the time in seconds</span>
|
||||||
@@ -126,7 +126,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">hours</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">24</span></div>
|
<span class="k">return</span> <span class="n">hours</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">24</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="days"><a class="viewcode-back" href="../../pylib.html#pylib.time_of_day.days">[docs]</a><span class="k">def</span> <span class="nf">days</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
<div class="viewcode-block" id="days"><a class="viewcode-back" href="../../pylib.time_of_day.html#pylib.time_of_day.days">[docs]</a><span class="k">def</span> <span class="nf">days</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
||||||
<span class="sd">"""The days of the time (year).</span>
|
<span class="sd">"""The days of the time (year).</span>
|
||||||
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
<span class="sd"> :param time: the time in seconds</span>
|
||||||
@@ -137,7 +137,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span><span class="o">/</span><span class="mi">60</span><span class="o">/</span><span class="mi">24</span><span class="o">%</span><span class="mf">365.2425</span></div>
|
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span><span class="o">/</span><span class="mi">60</span><span class="o">/</span><span class="mi">24</span><span class="o">%</span><span class="mf">365.2425</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="days_norm"><a class="viewcode-back" href="../../pylib.html#pylib.time_of_day.days_norm">[docs]</a><span class="k">def</span> <span class="nf">days_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
<div class="viewcode-block" id="days_norm"><a class="viewcode-back" href="../../pylib.time_of_day.html#pylib.time_of_day.days_norm">[docs]</a><span class="k">def</span> <span class="nf">days_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
||||||
<span class="sd">"""The days normalized to 365.2425 (Gregorian, on average) days.</span>
|
<span class="sd">"""The days normalized to 365.2425 (Gregorian, on average) days.</span>
|
||||||
<span class="sd"> </span>
|
<span class="sd"> </span>
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
<span class="sd"> :param time: the time in seconds</span>
|
||||||
@@ -148,7 +148,7 @@
|
|||||||
<span class="sd"> """</span>
|
<span class="sd"> """</span>
|
||||||
<span class="k">return</span> <span class="n">days</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mf">365.2425</span></div>
|
<span class="k">return</span> <span class="n">days</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mf">365.2425</span></div>
|
||||||
|
|
||||||
<div class="viewcode-block" id="transform"><a class="viewcode-back" href="../../pylib.html#pylib.time_of_day.transform">[docs]</a><span class="k">def</span> <span class="nf">transform</span><span class="p">(</span><span class="n">time_norm</span><span class="p">,</span> <span class="n">length</span><span class="p">,</span> <span class="n">offset</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
|
<div class="viewcode-block" id="transform"><a class="viewcode-back" href="../../pylib.time_of_day.html#pylib.time_of_day.transform">[docs]</a><span class="k">def</span> <span class="nf">transform</span><span class="p">(</span><span class="n">time_norm</span><span class="p">,</span> <span class="n">length</span><span class="p">,</span> <span class="n">offset</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
|
||||||
<span class="sd">"""Transform normalized time value to new length.</span>
|
<span class="sd">"""Transform normalized time value to new length.</span>
|
||||||
<span class="sd"> </span>
|
<span class="sd"> </span>
|
||||||
<span class="sd"> :param position_norm: the normalized time value to transform</span>
|
<span class="sd"> :param position_norm: the normalized time value to transform</span>
|
||||||
@@ -205,6 +205,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="../../modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
253
docs/build/html/_modules/time_of_day.html
vendored
253
docs/build/html/_modules/time_of_day.html
vendored
@@ -1,253 +0,0 @@
|
|||||||
|
|
||||||
<!DOCTYPE html>
|
|
||||||
|
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
|
||||||
<head>
|
|
||||||
<meta charset="utf-8" />
|
|
||||||
<title>time_of_day — pylib 2019.5.19 documentation</title>
|
|
||||||
<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
|
|
||||||
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
|
|
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<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
|
|
||||||
<script type="text/javascript" id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script>
|
|
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<script type="text/javascript" src="../_static/jquery.js"></script>
|
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||||||
<script type="text/javascript" src="../_static/underscore.js"></script>
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<script type="text/javascript" src="../_static/doctools.js"></script>
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<script type="text/javascript" src="../_static/language_data.js"></script>
|
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<script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
|
|
||||||
<link rel="index" title="Index" href="../genindex.html" />
|
|
||||||
<link rel="search" title="Search" href="../search.html" />
|
|
||||||
|
|
||||||
<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
|
|
||||||
|
|
||||||
|
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
|
|
||||||
|
|
||||||
</head><body>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="document">
|
|
||||||
<div class="documentwrapper">
|
|
||||||
<div class="bodywrapper">
|
|
||||||
|
|
||||||
|
|
||||||
<div class="body" role="main">
|
|
||||||
|
|
||||||
<h1>Source code for time_of_day</h1><div class="highlight"><pre>
|
|
||||||
<span></span><span class="ch">#!/usr/bin/env python</span>
|
|
||||||
<span class="c1"># -*- coding: utf-8 -*-</span>
|
|
||||||
<span class="sd">"""Calculate time.</span>
|
|
||||||
|
|
||||||
<span class="sd">:Date: 2019-06-01</span>
|
|
||||||
|
|
||||||
<span class="sd">.. module:: time_of_day</span>
|
|
||||||
<span class="sd"> :platform: *nix, Windows</span>
|
|
||||||
<span class="sd"> :synopsis: Calculate time.</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
|
|
||||||
<span class="sd">"""</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <span class="n">struct_time</span><span class="p">,</span> <span class="n">mktime</span>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="in_seconds"><a class="viewcode-back" href="../time_of_day.html#time_of_day.in_seconds">[docs]</a><span class="k">def</span> <span class="nf">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""If time is `time.struct_time` convert to float seconds.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
|
||||||
<span class="sd"> :type time: float or `time.struct_time`</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the time in seconds</span>
|
|
||||||
<span class="sd"> :rtype: float</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">struct_time</span><span class="p">):</span>
|
|
||||||
<span class="n">time</span> <span class="o">=</span> <span class="n">mktime</span><span class="p">(</span><span class="n">time</span><span class="p">)</span>
|
|
||||||
<span class="k">return</span> <span class="n">time</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="seconds"><a class="viewcode-back" href="../time_of_day.html#time_of_day.seconds">[docs]</a><span class="k">def</span> <span class="nf">seconds</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""The seconds of the time.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
|
||||||
<span class="sd"> :type time: float or `time.struct_time`</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: seconds, range [0, 60]</span>
|
|
||||||
<span class="sd"> :rtype: float</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">%</span><span class="mi">60</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="seconds_norm"><a class="viewcode-back" href="../time_of_day.html#time_of_day.seconds_norm">[docs]</a><span class="k">def</span> <span class="nf">seconds_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""The seconds normalized to 60 seconds.</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
|
||||||
<span class="sd"> :type time: float or `time.struct_time`</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the normalized seconds, range [0, 1]</span>
|
|
||||||
<span class="sd"> :rtype: float</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="minutes"><a class="viewcode-back" href="../time_of_day.html#time_of_day.minutes">[docs]</a><span class="k">def</span> <span class="nf">minutes</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""The minutes of the time.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
|
||||||
<span class="sd"> :type time: float or `time.struct_time`</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: minutes, range [0, 60]</span>
|
|
||||||
<span class="sd"> :rtype: float</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span><span class="o">%</span><span class="mi">60</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="minutes_norm"><a class="viewcode-back" href="../time_of_day.html#time_of_day.minutes_norm">[docs]</a><span class="k">def</span> <span class="nf">minutes_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""The minutes normalized to 60 minutes.</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
|
||||||
<span class="sd"> :type time: float or `time.struct_time`</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the normalized minutes, range [0, 1]</span>
|
|
||||||
<span class="sd"> :rtype: float</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">minutes</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="hours"><a class="viewcode-back" href="../time_of_day.html#time_of_day.hours">[docs]</a><span class="k">def</span> <span class="nf">hours</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""The hours of the time.</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
|
||||||
<span class="sd"> :type time: float or `time.struct_time`</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: hours, range [0, 24]</span>
|
|
||||||
<span class="sd"> :rtype: float</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span><span class="o">/</span><span class="mi">60</span><span class="o">%</span><span class="mi">24</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="hours_norm"><a class="viewcode-back" href="../time_of_day.html#time_of_day.hours_norm">[docs]</a><span class="k">def</span> <span class="nf">hours_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""The hours normalized to 24 hours.</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
|
||||||
<span class="sd"> :type time: float or `time.struct_time`</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the normalized hours, range [0, 1]</span>
|
|
||||||
<span class="sd"> :rtype: float</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">hours</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">24</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="days"><a class="viewcode-back" href="../time_of_day.html#time_of_day.days">[docs]</a><span class="k">def</span> <span class="nf">days</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""The days of the time (year).</span>
|
|
||||||
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
|
||||||
<span class="sd"> :type time: float or `time.struct_time`</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: hours, range [0, 365.2425]</span>
|
|
||||||
<span class="sd"> :rtype: float</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">in_seconds</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mi">60</span><span class="o">/</span><span class="mi">60</span><span class="o">/</span><span class="mi">24</span><span class="o">%</span><span class="mf">365.2425</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="days_norm"><a class="viewcode-back" href="../time_of_day.html#time_of_day.days_norm">[docs]</a><span class="k">def</span> <span class="nf">days_norm</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""The days normalized to 365.2425 (Gregorian, on average) days.</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :param time: the time in seconds</span>
|
|
||||||
<span class="sd"> :type time: float or `time.struct_time`</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the normalized days, range [0, 1]</span>
|
|
||||||
<span class="sd"> :rtype: float</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">days</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="mf">365.2425</span></div>
|
|
||||||
|
|
||||||
<div class="viewcode-block" id="transform"><a class="viewcode-back" href="../time_of_day.html#time_of_day.transform">[docs]</a><span class="k">def</span> <span class="nf">transform</span><span class="p">(</span><span class="n">time_norm</span><span class="p">,</span> <span class="n">length</span><span class="p">,</span> <span class="n">offset</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
|
|
||||||
<span class="sd">"""Transform normalized time value to new length.</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :param position_norm: the normalized time value to transform</span>
|
|
||||||
<span class="sd"> :type position_norm: float</span>
|
|
||||||
<span class="sd"> :param length: the transformation</span>
|
|
||||||
<span class="sd"> :type length: float</span>
|
|
||||||
<span class="sd"> :param offset: the offset (default = 0)</span>
|
|
||||||
<span class="sd"> :type offset: float</span>
|
|
||||||
<span class="sd"> </span>
|
|
||||||
<span class="sd"> :returns: the transformation value</span>
|
|
||||||
<span class="sd"> :rtype: float</span>
|
|
||||||
<span class="sd"> """</span>
|
|
||||||
<span class="k">return</span> <span class="n">time_norm</span><span class="o">*</span><span class="n">length</span> <span class="o">+</span> <span class="n">offset</span></div>
|
|
||||||
|
|
||||||
<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s2">"__main__"</span><span class="p">:</span>
|
|
||||||
<span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <span class="n">time</span><span class="p">,</span> <span class="n">gmtime</span><span class="p">,</span> <span class="n">localtime</span>
|
|
||||||
<span class="c1"># time in seconds</span>
|
|
||||||
<span class="n">t</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
|
|
||||||
<span class="nb">min</span> <span class="o">=</span> <span class="n">minutes</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
|
|
||||||
<span class="n">h</span> <span class="o">=</span> <span class="n">hours</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
|
|
||||||
<span class="n">min_norm</span> <span class="o">=</span> <span class="n">minutes_norm</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
|
|
||||||
<span class="n">h_norm</span> <span class="o">=</span> <span class="n">hours_norm</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'min '</span><span class="p">,</span> <span class="nb">min</span><span class="p">)</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'h '</span><span class="p">,</span> <span class="n">h</span><span class="p">)</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'min_norm '</span><span class="p">,</span> <span class="n">min_norm</span><span class="p">)</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'h_norm '</span><span class="p">,</span> <span class="n">h_norm</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">x_len</span> <span class="o">=</span> <span class="mi">30</span>
|
|
||||||
<span class="n">x_offset</span> <span class="o">=</span> <span class="o">-</span><span class="mi">8</span>
|
|
||||||
<span class="n">x_pos</span> <span class="o">=</span> <span class="n">transform</span><span class="p">(</span><span class="n">min_norm</span><span class="p">,</span> <span class="n">x_len</span><span class="p">,</span> <span class="n">x_offset</span><span class="p">)</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'m[-8,22] '</span><span class="p">,</span> <span class="n">x_pos</span><span class="p">)</span>
|
|
||||||
|
|
||||||
<span class="n">y_len</span> <span class="o">=</span> <span class="mi">20</span>
|
|
||||||
<span class="n">y_offset</span> <span class="o">=</span> <span class="o">-</span><span class="mi">10</span>
|
|
||||||
<span class="n">y_pos</span> <span class="o">=</span> <span class="n">transform</span><span class="p">(</span><span class="n">h_norm</span><span class="p">,</span> <span class="n">y_len</span><span class="p">,</span> <span class="n">y_offset</span><span class="p">)</span>
|
|
||||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'h[-10,10]'</span><span class="p">,</span> <span class="n">y_pos</span><span class="p">)</span>
|
|
||||||
|
|
||||||
</pre></div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
|
||||||
<div class="sphinxsidebarwrapper">
|
|
||||||
<h1 class="logo"><a href="../index.html">pylib</a></h1>
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
|
||||||
|
|
||||||
<div class="relations">
|
|
||||||
<h3>Related Topics</h3>
|
|
||||||
<ul>
|
|
||||||
<li><a href="../index.html">Documentation overview</a><ul>
|
|
||||||
<li><a href="index.html">Module code</a><ul>
|
|
||||||
</ul></li>
|
|
||||||
</ul></li>
|
|
||||||
</ul>
|
|
||||||
</div>
|
|
||||||
<div id="searchbox" style="display: none" role="search">
|
|
||||||
<h3 id="searchlabel">Quick search</h3>
|
|
||||||
<div class="searchformwrapper">
|
|
||||||
<form class="search" action="../search.html" method="get">
|
|
||||||
<input type="text" name="q" aria-labelledby="searchlabel" />
|
|
||||||
<input type="submit" value="Go" />
|
|
||||||
</form>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
<script type="text/javascript">$('#searchbox').show(0);</script>
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
<div class="clearer"></div>
|
|
||||||
</div>
|
|
||||||
<div class="footer">
|
|
||||||
©2019, Daniel Weschke.
|
|
||||||
|
|
||||||
|
|
|
||||||
Powered by <a href="http://sphinx-doc.org/">Sphinx 2.2.1</a>
|
|
||||||
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
</body>
|
|
||||||
</html>
|
|
||||||
7
docs/build/html/_sources/data.rst.txt
vendored
7
docs/build/html/_sources/data.rst.txt
vendored
@@ -1,7 +0,0 @@
|
|||||||
data module
|
|
||||||
===========
|
|
||||||
|
|
||||||
.. automodule:: data
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
7
docs/build/html/_sources/date.rst.txt
vendored
7
docs/build/html/_sources/date.rst.txt
vendored
@@ -1,7 +0,0 @@
|
|||||||
date module
|
|
||||||
===========
|
|
||||||
|
|
||||||
.. automodule:: date
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
7
docs/build/html/_sources/function.rst.txt
vendored
7
docs/build/html/_sources/function.rst.txt
vendored
@@ -1,7 +0,0 @@
|
|||||||
function module
|
|
||||||
===============
|
|
||||||
|
|
||||||
.. automodule:: function
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
7
docs/build/html/_sources/geometry.rst.txt
vendored
7
docs/build/html/_sources/geometry.rst.txt
vendored
@@ -1,7 +0,0 @@
|
|||||||
geometry module
|
|
||||||
===============
|
|
||||||
|
|
||||||
.. automodule:: geometry
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
2
docs/build/html/_sources/index.rst.txt
vendored
2
docs/build/html/_sources/index.rst.txt
vendored
@@ -10,6 +10,8 @@ Welcome to pylib's documentation!
|
|||||||
:maxdepth: 2
|
:maxdepth: 2
|
||||||
:caption: Contents:
|
:caption: Contents:
|
||||||
|
|
||||||
|
modules
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
Indices and tables
|
Indices and tables
|
||||||
|
|||||||
7
docs/build/html/_sources/mathematics.rst.txt
vendored
7
docs/build/html/_sources/mathematics.rst.txt
vendored
@@ -1,7 +0,0 @@
|
|||||||
mathematics module
|
|
||||||
==================
|
|
||||||
|
|
||||||
.. automodule:: mathematics
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
46
docs/build/html/_sources/numerical.rst.txt
vendored
46
docs/build/html/_sources/numerical.rst.txt
vendored
@@ -1,46 +0,0 @@
|
|||||||
numerical package
|
|
||||||
=================
|
|
||||||
|
|
||||||
Submodules
|
|
||||||
----------
|
|
||||||
|
|
||||||
numerical.fit module
|
|
||||||
--------------------
|
|
||||||
|
|
||||||
.. automodule:: numerical.fit
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
numerical.integration module
|
|
||||||
----------------------------
|
|
||||||
|
|
||||||
.. automodule:: numerical.integration
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
numerical.ode module
|
|
||||||
--------------------
|
|
||||||
|
|
||||||
.. automodule:: numerical.ode
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
numerical.ode\_model module
|
|
||||||
---------------------------
|
|
||||||
|
|
||||||
.. automodule:: numerical.ode_model
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
|
|
||||||
Module contents
|
|
||||||
---------------
|
|
||||||
|
|
||||||
.. automodule:: numerical
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
7
docs/build/html/_sources/pylib.data.rst.txt
vendored
Normal file
7
docs/build/html/_sources/pylib.data.rst.txt
vendored
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.data module
|
||||||
|
=================
|
||||||
|
|
||||||
|
.. automodule:: pylib.data
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/build/html/_sources/pylib.date.rst.txt
vendored
Normal file
7
docs/build/html/_sources/pylib.date.rst.txt
vendored
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.date module
|
||||||
|
=================
|
||||||
|
|
||||||
|
.. automodule:: pylib.date
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/build/html/_sources/pylib.drawblock.rst.txt
vendored
Normal file
7
docs/build/html/_sources/pylib.drawblock.rst.txt
vendored
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.drawblock module
|
||||||
|
======================
|
||||||
|
|
||||||
|
.. automodule:: pylib.drawblock
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
@@ -1,7 +1,7 @@
|
|||||||
geometry\_plot module
|
pylib.function module
|
||||||
=====================
|
=====================
|
||||||
|
|
||||||
.. automodule:: geometry_plot
|
.. automodule:: pylib.function
|
||||||
:members:
|
:members:
|
||||||
:undoc-members:
|
:undoc-members:
|
||||||
:show-inheritance:
|
:show-inheritance:
|
||||||
@@ -1,7 +1,7 @@
|
|||||||
geometry\_plot module
|
pylib.geometry module
|
||||||
=====================
|
=====================
|
||||||
|
|
||||||
.. automodule:: geometry_plot
|
.. automodule:: pylib.geometry
|
||||||
:members:
|
:members:
|
||||||
:undoc-members:
|
:undoc-members:
|
||||||
:show-inheritance:
|
:show-inheritance:
|
||||||
7
docs/build/html/_sources/pylib.geometry2d.rst.txt
vendored
Normal file
7
docs/build/html/_sources/pylib.geometry2d.rst.txt
vendored
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.geometry2d module
|
||||||
|
=======================
|
||||||
|
|
||||||
|
.. automodule:: pylib.geometry2d
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/build/html/_sources/pylib.geometry2d_plot.rst.txt
vendored
Normal file
7
docs/build/html/_sources/pylib.geometry2d_plot.rst.txt
vendored
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.geometry2d\_plot module
|
||||||
|
=============================
|
||||||
|
|
||||||
|
.. automodule:: pylib.geometry2d_plot
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/build/html/_sources/pylib.mathematics.rst.txt
vendored
Normal file
7
docs/build/html/_sources/pylib.mathematics.rst.txt
vendored
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.mathematics module
|
||||||
|
========================
|
||||||
|
|
||||||
|
.. automodule:: pylib.mathematics
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/build/html/_sources/pylib.numerical.fit.rst.txt
vendored
Normal file
7
docs/build/html/_sources/pylib.numerical.fit.rst.txt
vendored
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.numerical.fit module
|
||||||
|
==========================
|
||||||
|
|
||||||
|
.. automodule:: pylib.numerical.fit
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/build/html/_sources/pylib.numerical.integration.rst.txt
vendored
Normal file
7
docs/build/html/_sources/pylib.numerical.integration.rst.txt
vendored
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.numerical.integration module
|
||||||
|
==================================
|
||||||
|
|
||||||
|
.. automodule:: pylib.numerical.integration
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/build/html/_sources/pylib.numerical.ode.rst.txt
vendored
Normal file
7
docs/build/html/_sources/pylib.numerical.ode.rst.txt
vendored
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.numerical.ode module
|
||||||
|
==========================
|
||||||
|
|
||||||
|
.. automodule:: pylib.numerical.ode
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/build/html/_sources/pylib.numerical.ode_model.rst.txt
vendored
Normal file
7
docs/build/html/_sources/pylib.numerical.ode_model.rst.txt
vendored
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.numerical.ode\_model module
|
||||||
|
=================================
|
||||||
|
|
||||||
|
.. automodule:: pylib.numerical.ode_model
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
49
docs/build/html/_sources/pylib.numerical.rst.txt
vendored
49
docs/build/html/_sources/pylib.numerical.rst.txt
vendored
@@ -1,46 +1,17 @@
|
|||||||
pylib.numerical package
|
pylib.numerical package
|
||||||
=======================
|
=======================
|
||||||
|
|
||||||
Submodules
|
|
||||||
----------
|
|
||||||
|
|
||||||
pylib.numerical.fit module
|
|
||||||
--------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.numerical.fit
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.numerical.integration module
|
|
||||||
----------------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.numerical.integration
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.numerical.ode module
|
|
||||||
--------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.numerical.ode
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.numerical.ode\_model module
|
|
||||||
---------------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.numerical.ode_model
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
|
|
||||||
Module contents
|
|
||||||
---------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.numerical
|
.. automodule:: pylib.numerical
|
||||||
:members:
|
:members:
|
||||||
:undoc-members:
|
:undoc-members:
|
||||||
:show-inheritance:
|
:show-inheritance:
|
||||||
|
|
||||||
|
Submodules
|
||||||
|
----------
|
||||||
|
|
||||||
|
.. toctree::
|
||||||
|
|
||||||
|
pylib.numerical.fit
|
||||||
|
pylib.numerical.integration
|
||||||
|
pylib.numerical.ode
|
||||||
|
pylib.numerical.ode_model
|
||||||
|
|||||||
86
docs/build/html/_sources/pylib.rst.txt
vendored
86
docs/build/html/_sources/pylib.rst.txt
vendored
@@ -1,6 +1,11 @@
|
|||||||
pylib package
|
pylib package
|
||||||
=============
|
=============
|
||||||
|
|
||||||
|
.. automodule:: pylib
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
|
|
||||||
Subpackages
|
Subpackages
|
||||||
-----------
|
-----------
|
||||||
|
|
||||||
@@ -11,75 +16,14 @@ Subpackages
|
|||||||
Submodules
|
Submodules
|
||||||
----------
|
----------
|
||||||
|
|
||||||
pylib.data module
|
.. toctree::
|
||||||
-----------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.data
|
pylib.data
|
||||||
:members:
|
pylib.date
|
||||||
:undoc-members:
|
pylib.drawblock
|
||||||
:show-inheritance:
|
pylib.function
|
||||||
|
pylib.geometry
|
||||||
pylib.date module
|
pylib.geometry2d
|
||||||
-----------------
|
pylib.geometry2d_plot
|
||||||
|
pylib.mathematics
|
||||||
.. automodule:: pylib.date
|
pylib.time_of_day
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.drawblock module
|
|
||||||
----------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.drawblock
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.function module
|
|
||||||
---------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.function
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.geometry module
|
|
||||||
---------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.geometry
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.geometry\_plot module
|
|
||||||
---------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.geometry_plot
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.mathematics module
|
|
||||||
------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.mathematics
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.time\_of\_day module
|
|
||||||
--------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.time_of_day
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
|
|
||||||
Module contents
|
|
||||||
---------------
|
|
||||||
|
|
||||||
.. automodule:: pylib
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|||||||
7
docs/build/html/_sources/pylib.time_of_day.rst.txt
vendored
Normal file
7
docs/build/html/_sources/pylib.time_of_day.rst.txt
vendored
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.time\_of\_day module
|
||||||
|
==========================
|
||||||
|
|
||||||
|
.. automodule:: pylib.time_of_day
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/build/html/_sources/time_of_day.rst.txt
vendored
7
docs/build/html/_sources/time_of_day.rst.txt
vendored
@@ -1,7 +0,0 @@
|
|||||||
time\_of\_day module
|
|
||||||
====================
|
|
||||||
|
|
||||||
.. automodule:: time_of_day
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
@@ -1,6 +1,6 @@
|
|||||||
var DOCUMENTATION_OPTIONS = {
|
var DOCUMENTATION_OPTIONS = {
|
||||||
URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
|
URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
|
||||||
VERSION: '2019.5.19',
|
VERSION: '2019.12.21',
|
||||||
LANGUAGE: 'None',
|
LANGUAGE: 'None',
|
||||||
COLLAPSE_INDEX: false,
|
COLLAPSE_INDEX: false,
|
||||||
FILE_SUFFIX: '.html',
|
FILE_SUFFIX: '.html',
|
||||||
|
|||||||
606
docs/build/html/genindex.html
vendored
606
docs/build/html/genindex.html
vendored
@@ -5,7 +5,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>Index — pylib 2019.5.19 documentation</title>
|
<title>Index — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="_static/custom.css" type="text/css" />
|
<link rel="stylesheet" href="_static/custom.css" type="text/css" />
|
||||||
@@ -38,6 +38,7 @@
|
|||||||
|
|
||||||
<div class="genindex-jumpbox">
|
<div class="genindex-jumpbox">
|
||||||
<a href="#A"><strong>A</strong></a>
|
<a href="#A"><strong>A</strong></a>
|
||||||
|
| <a href="#B"><strong>B</strong></a>
|
||||||
| <a href="#C"><strong>C</strong></a>
|
| <a href="#C"><strong>C</strong></a>
|
||||||
| <a href="#D"><strong>D</strong></a>
|
| <a href="#D"><strong>D</strong></a>
|
||||||
| <a href="#E"><strong>E</strong></a>
|
| <a href="#E"><strong>E</strong></a>
|
||||||
@@ -57,193 +58,138 @@
|
|||||||
| <a href="#V"><strong>V</strong></a>
|
| <a href="#V"><strong>V</strong></a>
|
||||||
| <a href="#W"><strong>W</strong></a>
|
| <a href="#W"><strong>W</strong></a>
|
||||||
| <a href="#X"><strong>X</strong></a>
|
| <a href="#X"><strong>X</strong></a>
|
||||||
|
| <a href="#Y"><strong>Y</strong></a>
|
||||||
| <a href="#Z"><strong>Z</strong></a>
|
| <a href="#Z"><strong>Z</strong></a>
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
<h2 id="A">A</h2>
|
<h2 id="A">A</h2>
|
||||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="mathematics.html#mathematics.vector.abs">abs() (vector static method)</a>, <a href="pylib.html#pylib.mathematics.vector.abs">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.abs">abs() (vector static method)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="mathematics.html#mathematics.vector.ang">ang() (vector static method)</a>, <a href="pylib.html#pylib.mathematics.vector.ang">[1]</a>
|
<li><a href="pylib.geometry.html#pylib.geometry.World.add">add() (World method)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="geometry.html#geometry.angle">angle() (in module geometry)</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.ang">ang() (vector static method)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry.angle">(in module pylib.geometry)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="mathematics.html#mathematics.vector.arg">arg() (vector static method)</a>, <a href="pylib.html#pylib.mathematics.vector.arg">[1]</a>
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.angle">angle() (in module pylib.geometry2d)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="date.html#date.ascension_of_jesus">ascension_of_jesus() (in module date)</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.arg">arg() (vector static method)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.date.html#pylib.date.ascension_of_jesus">ascension_of_jesus() (in module pylib.date)</a>
|
||||||
|
</li>
|
||||||
|
</ul></td>
|
||||||
|
</tr></table>
|
||||||
|
|
||||||
<ul>
|
<h2 id="B">B</h2>
|
||||||
<li><a href="pylib.html#pylib.date.ascension_of_jesus">(in module pylib.date)</a>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.World.bounding_box">bounding_box() (World method)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
</tr></table>
|
</tr></table>
|
||||||
|
|
||||||
<h2 id="C">C</h2>
|
<h2 id="C">C</h2>
|
||||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="mathematics.html#mathematics.vector.ch_cs">ch_cs() (vector method)</a>, <a href="pylib.html#pylib.mathematics.vector.ch_cs">[1]</a>
|
<li><a href="pylib.geometry.html#pylib.geometry.World.center">center() (World method)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="mathematics.html#mathematics.vector.conjugate">conjugate() (vector static method)</a>, <a href="pylib.html#pylib.mathematics.vector.conjugate">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.ch_cs">ch_cs() (vector method)</a>
|
||||||
</li>
|
|
||||||
<li><a href="function.html#function.cosine_wave">cosine_wave() (in module function)</a>
|
|
||||||
|
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="pylib.html#pylib.function.cosine_wave">(in module pylib.function)</a>
|
<li><a href="pylib.geometry.html#pylib.geometry.Wireframe.ch_cs">(Wireframe method)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.World.ch_cs">(World method)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
<li><a href="mathematics.html#mathematics.vector.cross">cross() (vector static method)</a>, <a href="pylib.html#pylib.mathematics.vector.cross">[1]</a>
|
<li><a href="pylib.geometry.html#pylib.geometry.Circle">Circle (class in pylib.geometry)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.conjugate">conjugate() (vector static method)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></td>
|
</ul></td>
|
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<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="geometry.html#geometry.cubic">cubic() (in module geometry)</a>
|
<li><a href="pylib.function.html#pylib.function.cosine_wave">cosine_wave() (in module pylib.function)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry.cubic">(in module pylib.geometry)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.cross">cross() (vector static method)</a>
|
||||||
<li><a href="geometry.html#geometry.cubic_deg">cubic_deg() (in module geometry)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry.cubic_deg">(in module pylib.geometry)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.geometry.html#pylib.geometry.CS">CS (class in pylib.geometry)</a>
|
||||||
<li><a href="geometry.html#geometry.cubics">cubics() (in module geometry)</a>
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.World.cs">cs() (World method)</a>
|
||||||
<ul>
|
</li>
|
||||||
<li><a href="pylib.html#pylib.geometry.cubics">(in module pylib.geometry)</a>
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.cubic">cubic() (in module pylib.geometry2d)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.cubic_deg">cubic_deg() (in module pylib.geometry2d)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.cubics">cubics() (in module pylib.geometry2d)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
</tr></table>
|
</tr></table>
|
||||||
|
|
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<h2 id="D">D</h2>
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<h2 id="D">D</h2>
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<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="data.html#module-data">data (module)</a>, <a href="data.html#module-data">[1]</a>, <a href="pylib.html#module-data">[2]</a>
|
<li><a href="pylib.data.html#module-data">data (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="date.html#module-date">date (module)</a>, <a href="date.html#module-date">[1]</a>, <a href="pylib.html#module-date">[2]</a>
|
<li><a href="pylib.date.html#module-date">date (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.html#pylib.time_of_day.days">days() (in module pylib.time_of_day)</a>
|
<li><a href="pylib.time_of_day.html#pylib.time_of_day.days">days() (in module pylib.time_of_day)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="time_of_day.html#time_of_day.days">(in module time_of_day)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.time_of_day.html#pylib.time_of_day.days_norm">days_norm() (in module pylib.time_of_day)</a>
|
||||||
<li><a href="pylib.html#pylib.time_of_day.days_norm">days_norm() (in module pylib.time_of_day)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="time_of_day.html#time_of_day.days_norm">(in module time_of_day)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.geometry.html#pylib.geometry.Direction">Direction (class in pylib.geometry)</a>
|
||||||
<li><a href="numerical.html#numerical.ode_model.disk">disk() (in module numerical.ode_model)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.ode_model.disk">(in module pylib.numerical.ode_model)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="numerical.html#numerical.ode_model.disk_nm">disk_nm() (in module numerical.ode_model)</a>
|
<li><a href="pylib.numerical.ode_model.html#pylib.numerical.ode_model.disk">disk() (in module pylib.numerical.ode_model)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.ode_model.disk_nm">(in module pylib.numerical.ode_model)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.numerical.ode_model.html#pylib.numerical.ode_model.disk_nm">disk_nm() (in module pylib.numerical.ode_model)</a>
|
||||||
<li><a href="numerical.html#numerical.ode_model.disk_nmmdk">disk_nmmdk() (in module numerical.ode_model)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.ode_model.disk_nmmdk">(in module pylib.numerical.ode_model)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.numerical.ode_model.html#pylib.numerical.ode_model.disk_nmmdk">disk_nmmdk() (in module pylib.numerical.ode_model)</a>
|
||||||
<li><a href="geometry.html#geometry.distance">distance() (in module geometry)</a>
|
</li>
|
||||||
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.distance">distance() (in module pylib.geometry2d)</a>
|
||||||
<ul>
|
</li>
|
||||||
<li><a href="pylib.html#pylib.geometry.distance">(in module pylib.geometry)</a>
|
<li><a href="pylib.drawblock.html#module-drawblock">drawblock (module)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
</tr></table>
|
</tr></table>
|
||||||
|
|
||||||
<h2 id="E">E</h2>
|
<h2 id="E">E</h2>
|
||||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="numerical.html#numerical.ode.e1">e1() (in module numerical.ode)</a>
|
<li><a href="pylib.numerical.ode.html#pylib.numerical.ode.e1">e1() (in module pylib.numerical.ode)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.ode.e1">(in module pylib.numerical.ode)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.numerical.ode.html#pylib.numerical.ode.e2">e2() (in module pylib.numerical.ode)</a>
|
||||||
<li><a href="numerical.html#numerical.ode.e2">e2() (in module numerical.ode)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.ode.e2">(in module pylib.numerical.ode)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.numerical.ode.html#pylib.numerical.ode.e4">e4() (in module pylib.numerical.ode)</a>
|
||||||
<li><a href="numerical.html#numerical.ode.e4">e4() (in module numerical.ode)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.ode.e4">(in module pylib.numerical.ode)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
<li><a href="date.html#date.easter_friday">easter_friday() (in module date)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.date.easter_friday">(in module pylib.date)</a>
|
|
||||||
</li>
|
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="date.html#date.easter_monday">easter_monday() (in module date)</a>
|
<li><a href="pylib.date.html#pylib.date.easter_friday">easter_friday() (in module pylib.date)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.date.easter_monday">(in module pylib.date)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.date.html#pylib.date.easter_monday">easter_monday() (in module pylib.date)</a>
|
||||||
<li><a href="date.html#date.easter_sunday">easter_sunday() (in module date)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.date.easter_sunday">(in module pylib.date)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.date.html#pylib.date.easter_sunday">easter_sunday() (in module pylib.date)</a>
|
||||||
<li><a href="function.html#function.epitrochoid">epitrochoid() (in module function)</a>
|
</li>
|
||||||
|
<li><a href="pylib.function.html#pylib.function.epitrochoid">epitrochoid() (in module pylib.function)</a>
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.function.epitrochoid">(in module pylib.function)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
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</tr></table>
|
</tr></table>
|
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|
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<h2 id="F">F</h2>
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<h2 id="F">F</h2>
|
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<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="numerical.html#module-fit">fit (module)</a>, <a href="pylib.numerical.html#module-fit">[1]</a>
|
<li><a href="pylib.numerical.fit.html#module-fit">fit (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="data.html#data.fold_list">fold_list() (in module data)</a>
|
<li><a href="pylib.data.html#pylib.data.fold_list">fold_list() (in module pylib.data)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.data.fold_list">(in module pylib.data)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="numerical.html#numerical.ode.fpi">fpi() (in module numerical.ode)</a>
|
<li><a href="pylib.numerical.ode.html#pylib.numerical.ode.fpi">fpi() (in module pylib.numerical.ode)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.ode.fpi">(in module pylib.numerical.ode)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.full">full() (vector static method)</a>
|
||||||
<li><a href="mathematics.html#mathematics.vector.full">full() (vector static method)</a>, <a href="pylib.html#pylib.mathematics.vector.full">[1]</a>
|
|
||||||
</li>
|
</li>
|
||||||
<li><a href="function.html#module-function">function (module)</a>, <a href="function.html#module-function">[1]</a>, <a href="pylib.html#module-function">[2]</a>
|
<li><a href="pylib.function.html#module-function">function (module)</a>
|
||||||
</li>
|
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|
||||||
</ul></td>
|
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|
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</tr></table>
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|
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<h2 id="G">G</h2>
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<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
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<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="numerical.html#numerical.fit.gauss">gauss() (in module numerical.fit)</a>
|
<li><a href="pylib.numerical.fit.html#pylib.numerical.fit.gauss">gauss() (in module pylib.numerical.fit)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.fit.gauss">(in module pylib.numerical.fit)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.numerical.fit.html#pylib.numerical.fit.gauss_fit">gauss_fit() (in module pylib.numerical.fit)</a>
|
||||||
<li><a href="numerical.html#numerical.fit.gauss_fit">gauss_fit() (in module numerical.fit)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.fit.gauss_fit">(in module pylib.numerical.fit)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.date.html#pylib.date.gaußsche_osterformel">gaußsche_osterformel() (in module pylib.date)</a>
|
||||||
<li><a href="date.html#date.gaußsche_osterformel">gaußsche_osterformel() (in module date)</a>
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#module-geometry">geometry (module)</a>
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.date.gaußsche_osterformel">(in module pylib.date)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="geometry.html#module-geometry">geometry (module)</a>, <a href="geometry.html#module-geometry">[1]</a>, <a href="pylib.html#module-geometry">[2]</a>
|
<li><a href="pylib.geometry2d.html#module-geometry2d">geometry2d (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="geometry_plot.html#module-geometry_plot">geometry_plot (module)</a>, <a href="geometry_plot.html#module-geometry_plot">[1]</a>, <a href="pylib.html#module-geometry_plot">[2]</a>
|
<li><a href="pylib.geometry2d_plot.html#module-geometry2d_plot">geometry2d_plot (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="data.html#data.get_id">get_id() (in module data)</a>
|
<li><a href="pylib.geometry.html#pylib.geometry.CS.get_coordinates">get_coordinates() (CS method)</a>
|
||||||
|
</li>
|
||||||
<ul>
|
<li><a href="pylib.data.html#pylib.data.get_id">get_id() (in module pylib.data)</a>
|
||||||
<li><a href="pylib.html#pylib.data.get_id">(in module pylib.data)</a>
|
|
||||||
</li>
|
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|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
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|
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</tr></table>
|
</tr></table>
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|
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<h2 id="H">H</h2>
|
<h2 id="H">H</h2>
|
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<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="pylib.html#pylib.drawblock.histogram">histogram() (in module pylib.drawblock)</a>
|
<li><a href="pylib.drawblock.html#pylib.drawblock.histogram">histogram() (in module pylib.drawblock)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.html#pylib.time_of_day.hours">hours() (in module pylib.time_of_day)</a>
|
<li><a href="pylib.time_of_day.html#pylib.time_of_day.hours">hours() (in module pylib.time_of_day)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="time_of_day.html#time_of_day.hours">(in module time_of_day)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="pylib.html#pylib.time_of_day.hours_norm">hours_norm() (in module pylib.time_of_day)</a>
|
<li><a href="pylib.time_of_day.html#pylib.time_of_day.hours_norm">hours_norm() (in module pylib.time_of_day)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="time_of_day.html#time_of_day.hours_norm">(in module time_of_day)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.function.html#pylib.function.hypotrochoid">hypotrochoid() (in module pylib.function)</a>
|
||||||
<li><a href="function.html#function.hypotrochoid">hypotrochoid() (in module function)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.function.hypotrochoid">(in module pylib.function)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
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|
||||||
</tr></table>
|
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|
||||||
|
|
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<h2 id="I">I</h2>
|
<h2 id="I">I</h2>
|
||||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
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<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
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<li><a href="numerical.html#numerical.ode.i1">i1() (in module numerical.ode)</a>
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<li><a href="pylib.numerical.ode.html#pylib.numerical.ode.i1">i1() (in module pylib.numerical.ode)</a>
|
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|
|
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<ul>
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|
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<li><a href="pylib.numerical.html#pylib.numerical.ode.i1">(in module pylib.numerical.ode)</a>
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</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.im">im() (vector static method)</a>
|
||||||
<li><a href="mathematics.html#mathematics.vector.im">im() (vector static method)</a>, <a href="pylib.html#pylib.mathematics.vector.im">[1]</a>
|
|
||||||
</li>
|
</li>
|
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<li><a href="pylib.html#pylib.time_of_day.in_seconds">in_seconds() (in module pylib.time_of_day)</a>
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|
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<ul>
|
|
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<li><a href="time_of_day.html#time_of_day.in_seconds">(in module time_of_day)</a>
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</li>
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|
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</ul></li>
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</ul></td>
|
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<td style="width: 33%; vertical-align: top;"><ul>
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<td style="width: 33%; vertical-align: top;"><ul>
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<li><a href="numerical.html#module-integration">integration (module)</a>, <a href="pylib.numerical.html#module-integration">[1]</a>
|
<li><a href="pylib.time_of_day.html#pylib.time_of_day.in_seconds">in_seconds() (in module pylib.time_of_day)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="geometry.html#geometry.interpolate_hermite">interpolate_hermite() (in module geometry)</a>
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<li><a href="pylib.numerical.integration.html#module-integration">integration (module)</a>
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|
</li>
|
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<ul>
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.interpolate_hermite">interpolate_hermite() (in module pylib.geometry2d)</a>
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<li><a href="pylib.html#pylib.geometry.interpolate_hermite">(in module pylib.geometry)</a>
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</li>
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<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
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<li><a href="mathematics.html#mathematics.lcm">lcm() (in module mathematics)</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.lcm">lcm() (in module pylib.mathematics)</a>
|
||||||
|
|
||||||
<ul>
|
|
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<li><a href="pylib.html#pylib.mathematics.lcm">(in module pylib.mathematics)</a>
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|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.geometry.html#pylib.geometry.Line">Line (class in pylib.geometry)</a>
|
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<li><a href="geometry.html#geometry.line">line() (in module geometry)</a>
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|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry.line">(in module pylib.geometry)</a>
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</li>
|
</li>
|
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</ul></li>
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</ul></td>
|
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<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
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<li><a href="geometry.html#geometry.lines">lines() (in module geometry)</a>
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.line">line() (in module pylib.geometry2d)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry.lines">(in module pylib.geometry)</a>
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|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.lines">lines() (in module pylib.geometry2d)</a>
|
||||||
<li><a href="data.html#data.load">load() (in module data)</a>
|
</li>
|
||||||
|
<li><a href="pylib.data.html#pylib.data.load">load() (in module pylib.data)</a>
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.data.load">(in module pylib.data)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
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|
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<h2 id="M">M</h2>
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<h2 id="M">M</h2>
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<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
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<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
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<li><a href="mathematics.html#module-mathematics">mathematics (module)</a>, <a href="mathematics.html#module-mathematics">[1]</a>, <a href="pylib.html#module-mathematics">[2]</a>
|
<li><a href="pylib.mathematics.html#module-mathematics">mathematics (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="mathematics.html#mathematics.matrix">matrix (class in mathematics)</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.matrix">matrix (class in pylib.mathematics)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.mathematics.matrix">(class in pylib.mathematics)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="pylib.html#pylib.time_of_day.minutes">minutes() (in module pylib.time_of_day)</a>
|
<li><a href="pylib.time_of_day.html#pylib.time_of_day.minutes">minutes() (in module pylib.time_of_day)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="time_of_day.html#time_of_day.minutes">(in module time_of_day)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.time_of_day.html#pylib.time_of_day.minutes_norm">minutes_norm() (in module pylib.time_of_day)</a>
|
||||||
<li><a href="pylib.html#pylib.time_of_day.minutes_norm">minutes_norm() (in module pylib.time_of_day)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="time_of_day.html#time_of_day.minutes_norm">(in module time_of_day)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
</tr></table>
|
</tr></table>
|
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<h2 id="N">N</h2>
|
<h2 id="N">N</h2>
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<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
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<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="numerical.html#numerical.ode.newmark_newtonraphson">newmark_newtonraphson() (in module numerical.ode)</a>
|
<li><a href="pylib.numerical.ode.html#pylib.numerical.ode.newmark_newtonraphson">newmark_newtonraphson() (in module pylib.numerical.ode)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.ode.newmark_newtonraphson">(in module pylib.numerical.ode)</a>
|
|
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</li>
|
|
||||||
</ul></li>
|
|
||||||
<li><a href="numerical.html#numerical.ode.newmark_newtonraphson_rdk">newmark_newtonraphson_rdk() (in module numerical.ode)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.ode.newmark_newtonraphson_rdk">(in module pylib.numerical.ode)</a>
|
|
||||||
</li>
|
|
||||||
</ul></li>
|
|
||||||
<li><a href="mathematics.html#mathematics.vector.normalize">normalize() (vector static method)</a>, <a href="pylib.html#pylib.mathematics.vector.normalize">[1]</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
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<li><a href="numerical.html#module-numerical">numerical (module)</a>
|
<li><a href="pylib.numerical.ode.html#pylib.numerical.ode.newmark_newtonraphson_rdk">newmark_newtonraphson_rdk() (in module pylib.numerical.ode)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="numerical.html#module-numerical.fit">numerical.fit (module)</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.normalize">normalize() (vector static method)</a>
|
||||||
</li>
|
|
||||||
<li><a href="numerical.html#module-numerical.integration">numerical.integration (module)</a>
|
|
||||||
</li>
|
|
||||||
<li><a href="numerical.html#module-numerical.ode">numerical.ode (module)</a>
|
|
||||||
</li>
|
|
||||||
<li><a href="numerical.html#module-numerical.ode_model">numerical.ode_model (module)</a>
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|
||||||
</li>
|
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|
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|
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|
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@@ -437,13 +303,15 @@
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<h2 id="O">O</h2>
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|
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<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="numerical.html#module-ode">ode (module)</a>, <a href="pylib.numerical.html#module-ode">[1]</a>
|
<li><a href="pylib.geometry.html#pylib.geometry.World.objects">objects() (World method)</a>
|
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|
</li>
|
||||||
|
<li><a href="pylib.numerical.ode.html#module-ode">ode (module)</a>
|
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</li>
|
</li>
|
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</ul></td>
|
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|
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<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
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<li><a href="numerical.html#module-ode_model">ode_model (module)</a>, <a href="pylib.numerical.html#module-ode_model">[1]</a>
|
<li><a href="pylib.numerical.ode_model.html#module-ode_model">ode_model (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="mathematics.html#mathematics.vector.ones">ones() (vector static method)</a>, <a href="pylib.html#pylib.mathematics.vector.ones">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.ones">ones() (vector static method)</a>
|
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</li>
|
</li>
|
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</ul></td>
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<table style="width: 100%" class="indextable genindextable"><tr>
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<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
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<li><a href="date.html#date.pentecost">pentecost() (in module date)</a>
|
<li><a href="pylib.date.html#pylib.date.pentecost">pentecost() (in module pylib.date)</a>
|
||||||
|
|
||||||
<ul>
|
|
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<li><a href="pylib.html#pylib.date.pentecost">(in module pylib.date)</a>
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</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.geometry2d_plot.html#pylib.geometry2d_plot.plot_cubic_lines">plot_cubic_lines() (in module pylib.geometry2d_plot)</a>
|
||||||
<li><a href="geometry_plot.html#geometry_plot.plot_cubic_lines">plot_cubic_lines() (in module geometry_plot)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry_plot.plot_cubic_lines">(in module pylib.geometry_plot)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.geometry2d_plot.html#pylib.geometry2d_plot.plot_lines">plot_lines() (in module pylib.geometry2d_plot)</a>
|
||||||
<li><a href="geometry_plot.html#geometry_plot.plot_lines">plot_lines() (in module geometry_plot)</a>
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.Point">Point (class in pylib.geometry)</a>
|
||||||
<ul>
|
</li>
|
||||||
<li><a href="pylib.html#pylib.geometry_plot.plot_lines">(in module pylib.geometry_plot)</a>
|
<li><a href="pylib.geometry.html#pylib.geometry.Wireframe.points">points() (Wireframe method)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.Polygon">Polygon (class in pylib.geometry)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
<li><a href="pylib.html#module-pylib">pylib (module)</a>
|
<li><a href="pylib.html#module-pylib">pylib (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.html#module-pylib.data">pylib.data (module)</a>
|
<li><a href="pylib.data.html#module-pylib.data">pylib.data (module)</a>
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</li>
|
</li>
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||||||
<li><a href="pylib.html#module-pylib.date">pylib.date (module)</a>
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<li><a href="pylib.date.html#module-pylib.date">pylib.date (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.html#module-pylib.drawblock">pylib.drawblock (module)</a>
|
<li><a href="pylib.drawblock.html#module-pylib.drawblock">pylib.drawblock (module)</a>
|
||||||
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|
</li>
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
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<li><a href="pylib.html#module-pylib.function">pylib.function (module)</a>
|
<li><a href="pylib.function.html#module-pylib.function">pylib.function (module)</a>
|
||||||
</li>
|
</li>
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||||||
<li><a href="pylib.html#module-pylib.geometry">pylib.geometry (module)</a>
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<li><a href="pylib.geometry.html#module-pylib.geometry">pylib.geometry (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.html#module-pylib.geometry_plot">pylib.geometry_plot (module)</a>
|
<li><a href="pylib.geometry2d.html#module-pylib.geometry2d">pylib.geometry2d (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.html#module-pylib.mathematics">pylib.mathematics (module)</a>
|
<li><a href="pylib.geometry2d_plot.html#module-pylib.geometry2d_plot">pylib.geometry2d_plot (module)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.mathematics.html#module-pylib.mathematics">pylib.mathematics (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.numerical.html#module-pylib.numerical">pylib.numerical (module)</a>
|
<li><a href="pylib.numerical.html#module-pylib.numerical">pylib.numerical (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.numerical.html#module-pylib.numerical.fit">pylib.numerical.fit (module)</a>
|
<li><a href="pylib.numerical.fit.html#module-pylib.numerical.fit">pylib.numerical.fit (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.numerical.html#module-pylib.numerical.integration">pylib.numerical.integration (module)</a>
|
<li><a href="pylib.numerical.integration.html#module-pylib.numerical.integration">pylib.numerical.integration (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.numerical.html#module-pylib.numerical.ode">pylib.numerical.ode (module)</a>
|
<li><a href="pylib.numerical.ode.html#module-pylib.numerical.ode">pylib.numerical.ode (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.numerical.html#module-pylib.numerical.ode_model">pylib.numerical.ode_model (module)</a>
|
<li><a href="pylib.numerical.ode_model.html#module-pylib.numerical.ode_model">pylib.numerical.ode_model (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.html#module-pylib.time_of_day">pylib.time_of_day (module)</a>
|
<li><a href="pylib.time_of_day.html#module-pylib.time_of_day">pylib.time_of_day (module)</a>
|
||||||
</li>
|
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|
||||||
</ul></td>
|
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|
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</tr></table>
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@@ -505,65 +369,57 @@
|
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<h2 id="R">R</h2>
|
<h2 id="R">R</h2>
|
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<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="mathematics.html#mathematics.vector.random">random() (vector static method)</a>, <a href="pylib.html#pylib.mathematics.vector.random">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.random">random() (vector static method)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="mathematics.html#mathematics.vector.re">re() (vector static method)</a>, <a href="pylib.html#pylib.mathematics.vector.re">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.re">re() (vector static method)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="data.html#data.read">read() (in module data)</a>
|
<li><a href="pylib.data.html#pylib.data.read">read() (in module pylib.data)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.rectangle">rectangle() (in module pylib.geometry2d)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.rotate">rotate() (in module pylib.geometry2d)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.rotate_deg">rotate_deg() (in module pylib.geometry2d)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.mathematics.html#pylib.mathematics.matrix.rotate_x">rotate_x() (matrix method)</a>
|
||||||
|
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="pylib.html#pylib.data.read">(in module pylib.data)</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.rotate_x">(vector method)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.Wireframe.rotate_x">(Wireframe method)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.World.rotate_x">(World method)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
<li><a href="geometry.html#geometry.rectangle">rectangle() (in module geometry)</a>
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.rotate_xy">rotate_xy() (in module pylib.geometry2d)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry.rectangle">(in module pylib.geometry)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
<li><a href="geometry.html#geometry.rotate">rotate() (in module geometry)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry.rotate">(in module pylib.geometry)</a>
|
|
||||||
</li>
|
|
||||||
</ul></li>
|
|
||||||
<li><a href="geometry.html#geometry.rotate_deg">rotate_deg() (in module geometry)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry.rotate_deg">(in module pylib.geometry)</a>
|
|
||||||
</li>
|
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="mathematics.html#mathematics.matrix.rotate_x">rotate_x() (matrix method)</a>, <a href="pylib.html#pylib.mathematics.matrix.rotate_x">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.matrix.rotate_y">rotate_y() (matrix method)</a>
|
||||||
|
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="mathematics.html#mathematics.vector.rotate_x">(vector method)</a>, <a href="pylib.html#pylib.mathematics.vector.rotate_x">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.rotate_y">(vector method)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.Wireframe.rotate_y">(Wireframe method)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.World.rotate_y">(World method)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
<li><a href="geometry.html#geometry.rotate_xy">rotate_xy() (in module geometry)</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.matrix.rotate_z">rotate_z() (matrix method)</a>
|
||||||
|
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="pylib.html#pylib.geometry.rotate_xy">(in module pylib.geometry)</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.rotate_z">(vector method)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.Wireframe.rotate_z">(Wireframe method)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.World.rotate_z">(World method)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
<li><a href="mathematics.html#mathematics.matrix.rotate_y">rotate_y() (matrix method)</a>, <a href="pylib.html#pylib.mathematics.matrix.rotate_y">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.matrix.rx">rx() (matrix static method)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="mathematics.html#mathematics.vector.rotate_y">(vector method)</a>, <a href="pylib.html#pylib.mathematics.vector.rotate_y">[1]</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.matrix.ry">ry() (matrix static method)</a>
|
||||||
<li><a href="mathematics.html#mathematics.matrix.rotate_z">rotate_z() (matrix method)</a>, <a href="pylib.html#pylib.mathematics.matrix.rotate_z">[1]</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="mathematics.html#mathematics.vector.rotate_z">(vector method)</a>, <a href="pylib.html#pylib.mathematics.vector.rotate_z">[1]</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.matrix.rz">rz() (matrix static method)</a>
|
||||||
<li><a href="mathematics.html#mathematics.matrix.rx">rx() (matrix static method)</a>, <a href="pylib.html#pylib.mathematics.matrix.rx">[1]</a>
|
|
||||||
</li>
|
|
||||||
<li><a href="mathematics.html#mathematics.matrix.ry">ry() (matrix static method)</a>, <a href="pylib.html#pylib.mathematics.matrix.ry">[1]</a>
|
|
||||||
</li>
|
|
||||||
<li><a href="mathematics.html#mathematics.matrix.rz">rz() (matrix static method)</a>, <a href="pylib.html#pylib.mathematics.matrix.rz">[1]</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></td>
|
</ul></td>
|
||||||
</tr></table>
|
</tr></table>
|
||||||
@@ -571,147 +427,127 @@
|
|||||||
<h2 id="S">S</h2>
|
<h2 id="S">S</h2>
|
||||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="mathematics.html#mathematics.matrix.s">s() (matrix static method)</a>, <a href="pylib.html#pylib.mathematics.matrix.s">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.matrix.s">s() (matrix static method)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="mathematics.html#mathematics.matrix.scale">scale() (matrix method)</a>, <a href="pylib.html#pylib.mathematics.matrix.scale">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.matrix.scale">scale() (matrix method)</a>
|
||||||
|
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="mathematics.html#mathematics.vector.scale">(vector method)</a>, <a href="pylib.html#pylib.mathematics.vector.scale">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.scale">(vector method)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.Wireframe.scale">(Wireframe method)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.World.scale">(World method)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
<li><a href="pylib.html#pylib.time_of_day.seconds">seconds() (in module pylib.time_of_day)</a>
|
<li><a href="pylib.time_of_day.html#pylib.time_of_day.seconds">seconds() (in module pylib.time_of_day)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="time_of_day.html#time_of_day.seconds">(in module time_of_day)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
<li><a href="pylib.html#pylib.time_of_day.seconds_norm">seconds_norm() (in module pylib.time_of_day)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="time_of_day.html#time_of_day.seconds_norm">(in module time_of_day)</a>
|
|
||||||
</li>
|
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="data.html#data.seq">seq() (in module data)</a>
|
<li><a href="pylib.time_of_day.html#pylib.time_of_day.seconds_norm">seconds_norm() (in module pylib.time_of_day)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.data.seq">(in module pylib.data)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.data.html#pylib.data.seq">seq() (in module pylib.data)</a>
|
||||||
<li><a href="function.html#function.sine_wave">sine_wave() (in module function)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.function.sine_wave">(in module pylib.function)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.function.html#pylib.function.sine_wave">sine_wave() (in module pylib.function)</a>
|
||||||
<li><a href="geometry.html#geometry.square">square() (in module geometry)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry.square">(in module pylib.geometry)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.geometry.html#pylib.geometry.World.space_diagonal">space_diagonal() (World method)</a>
|
||||||
<li><a href="data.html#data.store">store() (in module data)</a>
|
</li>
|
||||||
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.square">square() (in module pylib.geometry2d)</a>
|
||||||
<ul>
|
</li>
|
||||||
<li><a href="pylib.html#pylib.data.store">(in module pylib.data)</a>
|
<li><a href="pylib.data.html#pylib.data.store">store() (in module pylib.data)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
</tr></table>
|
</tr></table>
|
||||||
|
|
||||||
<h2 id="T">T</h2>
|
<h2 id="T">T</h2>
|
||||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="mathematics.html#mathematics.matrix.t">t() (matrix static method)</a>, <a href="pylib.html#pylib.mathematics.matrix.t">[1]</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.matrix.t">t() (matrix static method)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="pylib.html#module-time_of_day">time_of_day (module)</a>, <a href="time_of_day.html#module-time_of_day">[1]</a>, <a href="time_of_day.html#module-time_of_day">[2]</a>
|
<li><a href="pylib.time_of_day.html#module-time_of_day">time_of_day (module)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="function.html#function.to_str">to_str() (in module function)</a>
|
<li><a href="pylib.function.html#pylib.function.to_str">to_str() (in module pylib.function)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.time_of_day.html#pylib.time_of_day.transform">transform() (in module pylib.time_of_day)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.function.html#pylib.function.transformation">transformation() (in module pylib.function)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.translate">translate() (in module pylib.geometry2d)</a>
|
||||||
|
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="pylib.html#pylib.function.to_str">(in module pylib.function)</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.matrix.translate">(matrix method)</a>
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector.translate">(vector method)</a>
|
||||||
<li><a href="pylib.html#pylib.time_of_day.transform">transform() (in module pylib.time_of_day)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="time_of_day.html#time_of_day.transform">(in module time_of_day)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
<li><a href="pylib.geometry.html#pylib.geometry.Wireframe.translate">(Wireframe method)</a>
|
||||||
<li><a href="function.html#function.transformation">transformation() (in module function)</a>
|
</li>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.World.translate">(World method)</a>
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.function.transformation">(in module pylib.function)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
</ul></td>
|
</ul></td>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="geometry.html#geometry.translate">translate() (in module geometry)</a>
|
<li><a href="pylib.geometry2d.html#pylib.geometry2d.translate_xy">translate_xy() (in module pylib.geometry2d)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry.translate">(in module pylib.geometry)</a>
|
|
||||||
</li>
|
</li>
|
||||||
<li><a href="mathematics.html#mathematics.matrix.translate">(matrix method)</a>, <a href="pylib.html#pylib.mathematics.matrix.translate">[1]</a>
|
<li><a href="pylib.numerical.integration.html#pylib.numerical.integration.trapez">trapez() (in module pylib.numerical.integration)</a>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="mathematics.html#mathematics.vector.translate">(vector method)</a>, <a href="pylib.html#pylib.mathematics.vector.translate">[1]</a>
|
|
||||||
</li>
|
|
||||||
</ul></li>
|
|
||||||
<li><a href="geometry.html#geometry.translate_xy">translate_xy() (in module geometry)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.geometry.translate_xy">(in module pylib.geometry)</a>
|
|
||||||
</li>
|
|
||||||
</ul></li>
|
|
||||||
<li><a href="numerical.html#numerical.integration.trapez">trapez() (in module numerical.integration)</a>
|
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.numerical.html#pylib.numerical.integration.trapez">(in module pylib.numerical.integration)</a>
|
|
||||||
</li>
|
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
</tr></table>
|
</tr></table>
|
||||||
|
|
||||||
<h2 id="U">U</h2>
|
<h2 id="U">U</h2>
|
||||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="data.html#data.unique_ending">unique_ending() (in module data)</a>
|
<li><a href="pylib.data.html#pylib.data.unique_ending">unique_ending() (in module pylib.data)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.data.unique_ending">(in module pylib.data)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
</tr></table>
|
</tr></table>
|
||||||
|
|
||||||
<h2 id="V">V</h2>
|
<h2 id="V">V</h2>
|
||||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="mathematics.html#mathematics.vector">vector (class in mathematics)</a>
|
<li><a href="pylib.mathematics.html#pylib.mathematics.vector">vector (class in pylib.mathematics)</a>
|
||||||
|
|
||||||
<ul>
|
|
||||||
<li><a href="pylib.html#pylib.mathematics.vector">(class in pylib.mathematics)</a>
|
|
||||||
</li>
|
</li>
|
||||||
</ul></li>
|
|
||||||
</ul></td>
|
</ul></td>
|
||||||
</tr></table>
|
</tr></table>
|
||||||
|
|
||||||
<h2 id="W">W</h2>
|
<h2 id="W">W</h2>
|
||||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||||
<td style="width: 33%; vertical-align: top;"><ul>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
<li><a href="data.html#data.write">write() (in module data)</a>
|
<li><a href="pylib.geometry.html#pylib.geometry.Wireframe">Wireframe (class in pylib.geometry)</a>
|
||||||
|
</li>
|
||||||
<ul>
|
</ul></td>
|
||||||
<li><a href="pylib.html#pylib.data.write">(in module pylib.data)</a>
|
<td style="width: 33%; vertical-align: top;"><ul>
|
||||||
|
<li><a href="pylib.geometry.html#pylib.geometry.World">World (class in pylib.geometry)</a>
|
||||||
|
</li>
|
||||||
|
<li><a href="pylib.data.html#pylib.data.write">write() (in module pylib.data)</a>
|
||||||
</li>
|
</li>
|
||||||
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<h1>Welcome to pylib’s documentation!<a class="headerlink" href="#welcome-to-pylib-s-documentation" title="Permalink to this headline">¶</a></h1>
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|
||||||
<li><p><strong>p</strong> (<em>list</em>) – <p>gauss parameters [a, b, c, d]:</p>
|
|
||||||
<ul>
|
|
||||||
<li><p>a – amplitude (<span class="math notranslate nohighlight">\(\int y \,\mathrm{d}x=1 \Leftrightarrow a=1/(c\sqrt{2\pi})\)</span> )</p></li>
|
|
||||||
<li><p>b – expected value <span class="math notranslate nohighlight">\(\mu\)</span> (position of maximum, default = 0)</p></li>
|
|
||||||
<li><p>c – standard deviation <span class="math notranslate nohighlight">\(\sigma\)</span> (variance <span class="math notranslate nohighlight">\(\sigma^2=c^2\)</span>)</p></li>
|
|
||||||
<li><p>d – vertical offset (default = 0)</p></li>
|
|
||||||
</ul>
|
|
||||||
</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-even">Returns</dt>
|
|
||||||
<dd class="field-even"><p>gauss values at given positions x</p>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-odd">Return type</dt>
|
|
||||||
<dd class="field-odd"><p>numpy.ndarray</p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="numerical.fit.gauss_fit">
|
|
||||||
<code class="sig-name descname">gauss_fit</code><span class="sig-paren">(</span><em class="sig-param">x</em>, <em class="sig-param">y</em>, <em class="sig-param">e=None</em>, <em class="sig-param">x_fit=None</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/fit.html#gauss_fit"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.fit.gauss_fit" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Fit Gauss distribution function to data.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>x</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – positions</p></li>
|
|
||||||
<li><p><strong>y</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – values</p></li>
|
|
||||||
<li><p><strong>e</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – error values (default = None)</p></li>
|
|
||||||
<li><p><strong>x_fit</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – positions of fitted function (default = None, if None then x
|
|
||||||
is used)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – verbose information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-even">Returns</dt>
|
|
||||||
<dd class="field-even"><p><ul class="simple">
|
|
||||||
<li><p>numpy.ndarray – fitted values (y_fit)</p></li>
|
|
||||||
<li><p>numpy.ndarray – parameters of gauss distribution function (popt:
|
|
||||||
amplitude a, expected value <span class="math notranslate nohighlight">\(\mu\)</span>, standard deviation
|
|
||||||
<span class="math notranslate nohighlight">\(\sigma\)</span>, vertical offset d)</p></li>
|
|
||||||
<li><p>numpy.float64 – full width at half maximum (FWHM)</p></li>
|
|
||||||
</ul>
|
|
||||||
</p>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-odd">Return type</dt>
|
|
||||||
<dd class="field-odd"><p>tuple</p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<div class="admonition seealso">
|
|
||||||
<p class="admonition-title">See also</p>
|
|
||||||
<p><a class="reference internal" href="#numerical.fit.gauss" title="numerical.fit.gauss"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gauss()</span></code></a></p>
|
|
||||||
</div>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
<div class="section" id="module-numerical.integration">
|
|
||||||
<span id="numerical-integration-module"></span><h2>numerical.integration module<a class="headerlink" href="#module-numerical.integration" title="Permalink to this headline">¶</a></h2>
|
|
||||||
<p>Numerical integration, numerical quadrature.</p>
|
|
||||||
<p>de: numerische Integration, numerische Quadratur.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Date</dt>
|
|
||||||
<dd class="field-odd"><p>2015-10-15</p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<span class="target" id="module-integration"></span><dl class="function">
|
|
||||||
<dt id="numerical.integration.trapez">
|
|
||||||
<code class="sig-name descname">trapez</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">a=0</em>, <em class="sig-param">b=1</em>, <em class="sig-param">N=10</em>, <em class="sig-param">x=None</em>, <em class="sig-param">verbose=False</em>, <em class="sig-param">save_values=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/integration.html#trapez"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.integration.trapez" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Integration of <span class="math notranslate nohighlight">\(f(x)\)</span> using the trapezoidal rule
|
|
||||||
(Simpson’s rule, Kepler’s rule).</p>
|
|
||||||
<p>de: Trapezregel, Simpsonregel (Thomas Simpson), Keplersche
|
|
||||||
Fassregel (Johannes Kepler)</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em><em> or </em><em>list</em>) – function to integrate.</p></li>
|
|
||||||
<li><p><strong>a</strong> (<em>float</em>) – lower limit of integration (default = 0).</p></li>
|
|
||||||
<li><p><strong>b</strong> (<em>float</em>) – upper limit of integration (default = 1).</p></li>
|
|
||||||
<li><p><strong>N</strong> (<em>int</em>) – specify the number of subintervals.</p></li>
|
|
||||||
<li><p><strong>x</strong> (<em>list</em>) – variable of integration, necessary if f is a list
|
|
||||||
(default = None).</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-even">Returns</dt>
|
|
||||||
<dd class="field-even"><p>the definite integral as approximated by trapezoidal
|
|
||||||
rule.</p>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-odd">Return type</dt>
|
|
||||||
<dd class="field-odd"><p>float</p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<p>The trapezoidal rule approximates the integral by the area of a
|
|
||||||
trapezoid with base h=b-a and sides equal to the values of the
|
|
||||||
integrand at the two end points.</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[f_n(x) = f(a)+\frac{f(b)-f(a)}{b-a}(x-a)\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}I &= \int\limits_a^b f(x) \,\mathrm{d}x \\
|
|
||||||
I &\approx \int\limits_a^b f_n(x) \,\mathrm{d}x \\
|
|
||||||
&= \int\limits_a^b
|
|
||||||
\left( f(a)+\frac{f(b)-f(a)}{b-a}(x-a) \right)
|
|
||||||
\mathrm{d}x \\
|
|
||||||
&= \left.\left( f(a)-a\frac{f(b)-f(a)}{b-a} \right)
|
|
||||||
x \right\vert_a^b +
|
|
||||||
\left. \frac{f(b)-f(a)}{b-a} \frac{x^2}{2}
|
|
||||||
\right\vert_a^b \\
|
|
||||||
&= \frac{b-a}{2}\left[f(a)+f(b)\right]\end{split}\]</div>
|
|
||||||
<p>The composite trapezium rule. If the interval is divided into n
|
|
||||||
segments (not necessarily equal)</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[a = x_0 \leq x_1 \leq x_2 \leq \ldots \leq x_n = b\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}I &\approx \sum\limits_{i=0}^{n-1} \frac{1}{2} (x_{i+1}-x_i)
|
|
||||||
\left[f(x_{i+1})+f(x_i)\right] \\\end{split}\]</div>
|
|
||||||
<p>Special Case (Equaliy spaced base points)</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[x_{i+1}-x_i = h \quad \forall i\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[I \approx h \left\{ \frac{1}{2} \left[f(x_0)+f(x_n)\right] +
|
|
||||||
\sum\limits_{i=1}^{n-1} f(x_i) \right\}\]</div>
|
|
||||||
<p class="rubric">Example</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}I &= \int\limits_a^b f(x) \,\mathrm{d}x \\
|
|
||||||
f(x) &= x^2 \\
|
|
||||||
a &= 0 \\
|
|
||||||
b &= 1\end{split}\]</div>
|
|
||||||
<p>analytical solution</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[I = \int\limits_{0}^{1} x^2 \,\mathrm{d}x
|
|
||||||
= \left. \frac{1}{3} x^3 \right\vert_0^1
|
|
||||||
= \frac{1}{3}\]</div>
|
|
||||||
<p>numerical solution</p>
|
|
||||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">f</span> <span class="o">=</span> <span class="k">lambda</span><span class="p">(</span><span class="n">x</span><span class="p">):</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span>
|
|
||||||
<span class="gp">>>> </span><span class="n">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="go">0.5</span>
|
|
||||||
<span class="gp">>>> </span><span class="n">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
|
|
||||||
<span class="go">0.3350000000000001</span>
|
|
||||||
<span class="gp">>>> </span><span class="n">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
|
|
||||||
<span class="go">0.33335000000000004</span>
|
|
||||||
</pre></div>
|
|
||||||
</div>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
<div class="section" id="module-numerical.ode">
|
|
||||||
<span id="numerical-ode-module"></span><h2>numerical.ode module<a class="headerlink" href="#module-numerical.ode" title="Permalink to this headline">¶</a></h2>
|
|
||||||
<p>Numerical solver of ordinary differential equations.</p>
|
|
||||||
<p>Solves the initial value problem for systems of first order
|
|
||||||
ordinary differential equations.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Date</dt>
|
|
||||||
<dd class="field-odd"><p>2015-09-21</p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<span class="target" id="module-ode"></span><dl class="function">
|
|
||||||
<dt id="numerical.ode.e1">
|
|
||||||
<code class="sig-name descname">e1</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/ode.html#e1"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.ode.e1" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Explicit first-order method /
|
|
||||||
(standard, or forward) Euler method /
|
|
||||||
Runge-Kutta 1st order method.</p>
|
|
||||||
<p>de:
|
|
||||||
Euler’sche Polygonzugverfahren / explizite Euler-Verfahren /
|
|
||||||
Euler-Cauchy-Verfahren / Euler-vorwärts-Verfahren</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<p>Approximate the solution of the initial value problem</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}\dot{x} &= f(t,x) \\
|
|
||||||
x(t_0) &= x_0\end{split}\]</div>
|
|
||||||
<p>Choose a value h for the size of every step and set</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[t_i = t_0 + i h ~,\quad i=1,2,\ldots,n\]</div>
|
|
||||||
<p>The derivative of the solution is approximated as the forward
|
|
||||||
difference equation</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\dot{x}_i = f(t_i, x_i) = \frac{x_{i+1} - x_i}{t_{i+1}-t_i}\]</div>
|
|
||||||
<p>Therefore one step <span class="math notranslate nohighlight">\(h\)</span> of the Euler method from
|
|
||||||
<span class="math notranslate nohighlight">\(t_i\)</span> to <span class="math notranslate nohighlight">\(t_{i+1}\)</span> is</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}x_{i+1} &= x_i + (t_{i+1}-t_i) f(t_i, x_i) \\
|
|
||||||
x_{i+1} &= x_i + h f(t_i, x_i) \\\end{split}\]</div>
|
|
||||||
<p>Example 1:</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}m\ddot{u} + d\dot{u} + ku = f(t) \\
|
|
||||||
\ddot{u} = m^{-1}(f(t) - d\dot{u} - ku) \\\end{split}\]</div>
|
|
||||||
<p>with</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}x_1 &= u &\quad \dot{x}_1 = \dot{u} = x_2 \\
|
|
||||||
x_2 &= \dot{u} &\quad \dot{x}_2 = \ddot{u} \\\end{split}\]</div>
|
|
||||||
<p>becomes</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}\dot{x}_1 &= x_2 \\
|
|
||||||
\dot{x}_2 &= m^{-1}(f(t) - d x_2 - k x_1) \\\end{split}\]</div>
|
|
||||||
<p>or</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}\dot{x} &= f(t,x) \\
|
|
||||||
\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} &=
|
|
||||||
\begin{bmatrix} x_2 \\ m^{-1}(f(t) - d x_2 - k x_1)
|
|
||||||
\end{bmatrix} \\
|
|
||||||
&=
|
|
||||||
\begin{bmatrix} 0 \\ m^{-1} f(t) \end{bmatrix} +
|
|
||||||
\begin{bmatrix} 0 & 1 \\ -m^{-1} k & -m^{-1} d \end{bmatrix}
|
|
||||||
\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\end{split}\]</div>
|
|
||||||
<p>Example 2:</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}m(u)\ddot{u} + d(u,\dot{u})\dot{u} + k(u)u = f(t) \\
|
|
||||||
\ddot{u} = m^{-1}(u)(f(t) - d(u,\dot{u})\dot{u} - k(u)u) \\\end{split}\]</div>
|
|
||||||
<p>with</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}x_1 &= u &\quad \dot{x}_1 = \dot{u} = x_2 \\
|
|
||||||
x_2 &= \dot{u} &\quad \dot{x}_2 = \ddot{u} \\\end{split}\]</div>
|
|
||||||
<p>becomes</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}\dot{x}_1 &= x_2 \\
|
|
||||||
\dot{x}_2 &=
|
|
||||||
m^{-1}(x_1)(f(t) - d(x_1,x_2) x_2 - k(x_1) x_1) \\\end{split}\]</div>
|
|
||||||
<p>or</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}\dot{x} &= f(t,x) \\
|
|
||||||
\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} &=
|
|
||||||
\begin{bmatrix}
|
|
||||||
x_2 \\ m^{-1}(x_1)(f(t) - d(x_1,x_2) x_2 - k(x_1) x_1)
|
|
||||||
\end{bmatrix} \\
|
|
||||||
&=
|
|
||||||
\begin{bmatrix} 0 \\ m^{-1}(x_1) f(t) \end{bmatrix} +
|
|
||||||
\begin{bmatrix}
|
|
||||||
0 & 1 \\ -m^{-1}(x_1) k(x_1) & -m^{-1} d(x_1,x_2)
|
|
||||||
\end{bmatrix}
|
|
||||||
\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\end{split}\]</div>
|
|
||||||
<p>The Euler method is a first-order method, which means that the
|
|
||||||
local error (error per step) is proportional to the square of
|
|
||||||
the step size, and the global error (error at a given time) is
|
|
||||||
proportional to the step size.</p>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="numerical.ode.e2">
|
|
||||||
<code class="sig-name descname">e2</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/ode.html#e2"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.ode.e2" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Explicit second-order method / Runge-Kutta 2nd order method.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="numerical.ode.e4">
|
|
||||||
<code class="sig-name descname">e4</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/ode.html#e4"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.ode.e4" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Explicit fourth-order method / Runge-Kutta 4th order method.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="numerical.ode.fpi">
|
|
||||||
<code class="sig-name descname">fpi</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">xi</em>, <em class="sig-param">ti</em>, <em class="sig-param">ti1</em>, <em class="sig-param">*p</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/ode.html#fpi"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.ode.fpi" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Fixed-point iteration.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to iterate <span class="math notranslate nohighlight">\(f = \dot{x}(x,t)\)</span></p></li>
|
|
||||||
<li><p><strong>xi</strong> (<em>list</em>) – initial condition <span class="math notranslate nohighlight">\(x_i\)</span></p></li>
|
|
||||||
<li><p><strong>ti</strong> (<em>float</em>) – time <span class="math notranslate nohighlight">\(t_i\)</span></p></li>
|
|
||||||
<li><p><strong>ti1</strong> (<em>float</em>) – time <span class="math notranslate nohighlight">\(t_{i+1}\)</span></p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
|
||||||
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum <span class="math notranslate nohighlight">\(\varepsilon\)</span>
|
|
||||||
(default = 1e-9)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-even">Returns</dt>
|
|
||||||
<dd class="field-even"><p><span class="math notranslate nohighlight">\(x_{i}\)</span></p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[x_{i,j=0} = x_{i}\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[x_{i,j+1} = x_i + \dot{x}(x_{i,j}, t_{i+1})\cdot(t_{i+1}-t_i)\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\text{residuum} = \frac{\lVert x_{i,j+1}-x_{i,j}\rVert}
|
|
||||||
{\lVert x_{i,j+1} \rVert} < \varepsilon\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[x_{i} = x_{i,j=\text{end}}\]</div>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="numerical.ode.i1">
|
|
||||||
<code class="sig-name descname">i1</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/ode.html#i1"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.ode.i1" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Implicite first-order method / backward Euler method.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
|
||||||
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum (default = 1e-9)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<p>The backward Euler method has order one and is A-stable.</p>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="numerical.ode.newmark_newtonraphson">
|
|
||||||
<code class="sig-name descname">newmark_newtonraphson</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">xp0</em>, <em class="sig-param">xpp0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">gamma=0.5</em>, <em class="sig-param">beta=0.25</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/ode.html#newmark_newtonraphson"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.ode.newmark_newtonraphson" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Newmark method.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>xp0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>xpp0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>gamma</strong> (<em>float</em>) – newmark parameter for velocity (default = 0.5)</p></li>
|
|
||||||
<li><p><strong>beta</strong> (<em>float</em>) – newmark parameter for displacement (default = 0.25)</p></li>
|
|
||||||
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
|
||||||
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum (default = 1e-9)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="numerical.ode.newmark_newtonraphson_rdk">
|
|
||||||
<code class="sig-name descname">newmark_newtonraphson_rdk</code><span class="sig-paren">(</span><em class="sig-param">fnm</em>, <em class="sig-param">x0</em>, <em class="sig-param">xp0</em>, <em class="sig-param">xpp0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">gamma=0.5</em>, <em class="sig-param">beta=0.25</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/ode.html#newmark_newtonraphson_rdk"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.ode.newmark_newtonraphson_rdk" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Newmark method.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>xp0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>xpp0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>gamma</strong> (<em>float</em>) – newmark parameter for velocity (default = 0.5)</p></li>
|
|
||||||
<li><p><strong>beta</strong> (<em>float</em>) – newmark parameter for displacement (default = 0.25)</p></li>
|
|
||||||
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
|
||||||
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum (default = 1e-9)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
<div class="section" id="module-numerical.ode_model">
|
|
||||||
<span id="numerical-ode-model-module"></span><h2>numerical.ode_model module<a class="headerlink" href="#module-numerical.ode_model" title="Permalink to this headline">¶</a></h2>
|
|
||||||
<p>Mathmatical models governed by ordinary differential equations.</p>
|
|
||||||
<p>Describes initial value problems as systems of first order ordinary differential
|
|
||||||
equations.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Date</dt>
|
|
||||||
<dd class="field-odd"><p>2019-05-25</p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<span class="target" id="module-ode_model"></span><dl class="function">
|
|
||||||
<dt id="numerical.ode_model.disk">
|
|
||||||
<code class="sig-name descname">disk</code><span class="sig-paren">(</span><em class="sig-param">x</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/ode_model.html#disk"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.ode_model.disk" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Rotation of an eccentric disk.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>x</strong> (<em>list</em>) – values of the function</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – <p>parameters of the function</p>
|
|
||||||
<ul>
|
|
||||||
<li><p>diameter</p></li>
|
|
||||||
<li><p>eccentricity</p></li>
|
|
||||||
<li><p>torque</p></li>
|
|
||||||
</ul>
|
|
||||||
</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="numerical.ode_model.disk_nm">
|
|
||||||
<code class="sig-name descname">disk_nm</code><span class="sig-paren">(</span><em class="sig-param">xn</em>, <em class="sig-param">xpn</em>, <em class="sig-param">xppn</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/ode_model.html#disk_nm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.ode_model.disk_nm" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Rotation of an eccentric disk.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>xn</strong> (<em>list</em>) – values of the function</p></li>
|
|
||||||
<li><p><strong>xpn</strong> (<em>list</em>) – first derivative values of the function</p></li>
|
|
||||||
<li><p><strong>xppn</strong> (<em>list</em>) – second derivative values of the function</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – <p>parameters of the function</p>
|
|
||||||
<ul>
|
|
||||||
<li><p>diameter</p></li>
|
|
||||||
<li><p>eccentricity</p></li>
|
|
||||||
<li><p>torque</p></li>
|
|
||||||
</ul>
|
|
||||||
</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="numerical.ode_model.disk_nmmdk">
|
|
||||||
<code class="sig-name descname">disk_nmmdk</code><span class="sig-paren">(</span><em class="sig-param">xn</em>, <em class="sig-param">xpn</em>, <em class="sig-param">xppn</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/numerical/ode_model.html#disk_nmmdk"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numerical.ode_model.disk_nmmdk" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Rotation of an eccentric disk.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>xn</strong> (<em>list</em>) – values of the function</p></li>
|
|
||||||
<li><p><strong>xpn</strong> (<em>list</em>) – derivative values of the function</p></li>
|
|
||||||
<li><p><strong>xppn</strong> (<em>list</em>) – second derivative values of the function</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – <p>parameters of the function</p>
|
|
||||||
<ul>
|
|
||||||
<li><p>diameter</p></li>
|
|
||||||
<li><p>eccentricity</p></li>
|
|
||||||
<li><p>torque</p></li>
|
|
||||||
</ul>
|
|
||||||
</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
<div class="section" id="module-numerical">
|
|
||||||
<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-numerical" title="Permalink to this headline">¶</a></h2>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
|
|
||||||
</div>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
|
||||||
<div class="sphinxsidebarwrapper">
|
|
||||||
<h1 class="logo"><a href="index.html">pylib</a></h1>
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
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<a href="pylib.numerical.html#module-fit"><code class="xref">fit</code></a> <em>(*nix, Windows)</em></td><td>
|
<a href="pylib.numerical.fit.html#module-fit"><code class="xref">fit</code></a> <em>(*nix, Windows)</em></td><td>
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<em>Function and approximation.</em></td></tr>
|
<em>Function and approximation.</em></td></tr>
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<em>Mathematical equations.</em></td></tr>
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||||||
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<a href="pylib.html#module-geometry"><code class="xref">geometry</code></a> <em>(*nix, Windows)</em></td><td>
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|
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|
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|
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|
||||||
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<a href="pylib.numerical.html#module-integration"><code class="xref">integration</code></a> <em>(*nix, Windows)</em></td><td>
|
<a href="pylib.numerical.integration.html#module-integration"><code class="xref">integration</code></a> <em>(*nix, Windows)</em></td><td>
|
||||||
<em>Numerical integration.</em></td></tr>
|
<em>Numerical integration.</em></td></tr>
|
||||||
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|
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|
||||||
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|
<em>Mathematical functions and objects.</em></td></tr>
|
||||||
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|
||||||
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|
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|
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|
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|
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|
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|
||||||
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||||||
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||||||
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|
||||||
<a href="pylib.numerical.html#module-ode"><code class="xref">ode</code></a> <em>(*nix, Windows)</em></td><td>
|
<a href="pylib.numerical.ode.html#module-ode"><code class="xref">ode</code></a> <em>(*nix, Windows)</em></td><td>
|
||||||
<em>Numerical solver.</em></td></tr>
|
<em>Numerical solver.</em></td></tr>
|
||||||
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||||||
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||||||
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||||||
<a href="pylib.numerical.html#module-ode_model"><code class="xref">ode_model</code></a> <em>(*nix, Windows)</em></td><td>
|
<a href="pylib.numerical.ode_model.html#module-ode_model"><code class="xref">ode_model</code></a> <em>(*nix, Windows)</em></td><td>
|
||||||
<em>Models of ordinary differential equations.</em></td></tr>
|
<em>Models of ordinary differential equations.</em></td></tr>
|
||||||
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||||||
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|
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|
||||||
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||||||
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||||||
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||||||
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||||||
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|
||||||
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||||||
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||||||
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||||||
<a href="pylib.numerical.html#module-pylib.numerical"><code class="xref">pylib.numerical</code></a></td><td>
|
<a href="pylib.numerical.html#module-pylib.numerical"><code class="xref">pylib.numerical</code></a></td><td>
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||||||
<a href="pylib.numerical.html#module-pylib.numerical.fit"><code class="xref">pylib.numerical.fit</code></a></td><td>
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<a href="pylib.numerical.fit.html#module-pylib.numerical.fit"><code class="xref">pylib.numerical.fit</code></a></td><td>
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||||||
<a href="pylib.numerical.html#module-pylib.numerical.integration"><code class="xref">pylib.numerical.integration</code></a></td><td>
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<a href="pylib.numerical.integration.html#module-pylib.numerical.integration"><code class="xref">pylib.numerical.integration</code></a></td><td>
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<a href="pylib.numerical.html#module-pylib.numerical.ode"><code class="xref">pylib.numerical.ode</code></a></td><td>
|
<a href="pylib.numerical.ode.html#module-pylib.numerical.ode"><code class="xref">pylib.numerical.ode</code></a></td><td>
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||||||
<a href="pylib.numerical.html#module-pylib.numerical.ode_model"><code class="xref">pylib.numerical.ode_model</code></a></td><td>
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<a href="pylib.numerical.ode_model.html#module-pylib.numerical.ode_model"><code class="xref">pylib.numerical.ode_model</code></a></td><td>
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||||||
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|
||||||
<a href="pylib.html#module-pylib.time_of_day"><code class="xref">pylib.time_of_day</code></a></td><td>
|
<a href="pylib.time_of_day.html#module-pylib.time_of_day"><code class="xref">pylib.time_of_day</code></a></td><td>
|
||||||
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||||||
<tr class="pcap"><td></td><td> </td><td></td></tr>
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|||||||
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||||||
<td>
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||||||
<a href="pylib.html#module-time_of_day"><code class="xref">time_of_day</code></a> <em>(*nix, Windows)</em></td><td>
|
<a href="pylib.time_of_day.html#module-time_of_day"><code class="xref">time_of_day</code></a> <em>(*nix, Windows)</em></td><td>
|
||||||
<em>Calculate time.</em></td></tr>
|
<em>Calculate time.</em></td></tr>
|
||||||
</table>
|
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||||||
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||||||
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|
|||||||
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||||||
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||||||
<h3>Navigation</h3>
|
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|
||||||
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<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
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|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
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|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
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||||||
<meta charset="utf-8" />
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||||||
<title>data module — pylib 2019.5.19 documentation</title>
|
<title>pylib.data module — pylib 2019.12.21 documentation</title>
|
||||||
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<script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
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<link rel="search" title="Search" href="search.html" />
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<link rel="search" title="Search" href="search.html" />
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<link rel="next" title="pylib.date module" href="pylib.date.html" />
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|||||||
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||||||
<div class="body" role="main">
|
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||||||
|
|
||||||
<div class="section" id="module-data">
|
<div class="section" id="module-pylib.data">
|
||||||
<span id="data-module"></span><h1>data module<a class="headerlink" href="#module-data" title="Permalink to this headline">¶</a></h1>
|
<span id="pylib-data-module"></span><h1>pylib.data module<a class="headerlink" href="#module-pylib.data" title="Permalink to this headline">¶</a></h1>
|
||||||
<p>Read and write data to or from file and manipulate data structures.</p>
|
<p>Read and write data to or from file and manipulate data structures.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Date</dt>
|
<dt class="field-odd">Date</dt>
|
||||||
@@ -41,8 +43,8 @@
|
|||||||
</dd>
|
</dd>
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||||||
</dl>
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|
||||||
<span class="target" id="module-data"></span><dl class="function">
|
<span class="target" id="module-data"></span><dl class="function">
|
||||||
<dt id="data.fold_list">
|
<dt id="pylib.data.fold_list">
|
||||||
<code class="sig-name descname">fold_list</code><span class="sig-paren">(</span><em class="sig-param">lst</em>, <em class="sig-param">n</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/data.html#fold_list"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#data.fold_list" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">fold_list</code><span class="sig-paren">(</span><em class="sig-param">lst</em>, <em class="sig-param">n</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/data.html#fold_list"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.data.fold_list" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Convert one-dimensional kx1 array (list) to two-dimensional mxn
|
<dd><p>Convert one-dimensional kx1 array (list) to two-dimensional mxn
|
||||||
array. m = k / n</p>
|
array. m = k / n</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
@@ -62,8 +64,8 @@ array. m = k / n</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="data.get_id">
|
<dt id="pylib.data.get_id">
|
||||||
<code class="sig-name descname">get_id</code><span class="sig-paren">(</span><em class="sig-param">ids</em>, <em class="sig-param">uide</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/data.html#get_id"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#data.get_id" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">get_id</code><span class="sig-paren">(</span><em class="sig-param">ids</em>, <em class="sig-param">uide</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/data.html#get_id"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.data.get_id" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Get full id from unique id ending.</p>
|
<dd><p>Get full id from unique id ending.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -82,8 +84,8 @@ array. m = k / n</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="data.load">
|
<dt id="pylib.data.load">
|
||||||
<code class="sig-name descname">load</code><span class="sig-paren">(</span><em class="sig-param">file_name</em>, <em class="sig-param">default=None</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/data.html#load"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#data.load" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">load</code><span class="sig-paren">(</span><em class="sig-param">file_name</em>, <em class="sig-param">default=None</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/data.html#load"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.data.load" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Load stored program objects from binary file.</p>
|
<dd><p>Load stored program objects from binary file.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -103,8 +105,8 @@ array. m = k / n</p>
|
|||||||
</dd></dl>
|
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|
||||||
|
|
||||||
<dl class="function">
|
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|
||||||
<dt id="data.read">
|
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|
||||||
<code class="sig-name descname">read</code><span class="sig-paren">(</span><em class="sig-param">file_name</em>, <em class="sig-param">x_column</em>, <em class="sig-param">y_column</em>, <em class="sig-param">default=None</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/data.html#read"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#data.read" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">read</code><span class="sig-paren">(</span><em class="sig-param">file_name</em>, <em class="sig-param">x_column</em>, <em class="sig-param">y_column</em>, <em class="sig-param">default=None</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/data.html#read"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.data.read" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Read ascii data file.</p>
|
<dd><p>Read ascii data file.</p>
|
||||||
<dl class="field-list simple">
|
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|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -126,8 +128,8 @@ array. m = k / n</p>
|
|||||||
</dd></dl>
|
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||||||
|
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||||||
<dl class="function">
|
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|
||||||
<dt id="data.seq">
|
<dt id="pylib.data.seq">
|
||||||
<code class="sig-name descname">seq</code><span class="sig-paren">(</span><em class="sig-param">start</em>, <em class="sig-param">stop=None</em>, <em class="sig-param">step=1</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/data.html#seq"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#data.seq" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">seq</code><span class="sig-paren">(</span><em class="sig-param">start</em>, <em class="sig-param">stop=None</em>, <em class="sig-param">step=1</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/data.html#seq"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.data.seq" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Create an arithmetic bounded sequence.</p>
|
<dd><p>Create an arithmetic bounded sequence.</p>
|
||||||
<p>The sequence is one of the following;</p>
|
<p>The sequence is one of the following;</p>
|
||||||
<ul class="simple">
|
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|
||||||
@@ -155,8 +157,8 @@ between consecutive terms).</p></li>
|
|||||||
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|
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||||||
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||||||
<dl class="function">
|
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||||||
<dt id="data.store">
|
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|
||||||
<code class="sig-name descname">store</code><span class="sig-paren">(</span><em class="sig-param">file_name</em>, <em class="sig-param">object_data</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/data.html#store"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#data.store" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">store</code><span class="sig-paren">(</span><em class="sig-param">file_name</em>, <em class="sig-param">object_data</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/data.html#store"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.data.store" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Store program objects to binary file.</p>
|
<dd><p>Store program objects to binary file.</p>
|
||||||
<dl class="field-list simple">
|
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|
||||||
<dt class="field-odd">Parameters</dt>
|
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|
||||||
@@ -169,8 +171,8 @@ between consecutive terms).</p></li>
|
|||||||
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||||||
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||||||
<dt id="data.unique_ending">
|
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|
||||||
<code class="sig-name descname">unique_ending</code><span class="sig-paren">(</span><em class="sig-param">ids</em>, <em class="sig-param">n=1</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/data.html#unique_ending"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#data.unique_ending" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">unique_ending</code><span class="sig-paren">(</span><em class="sig-param">ids</em>, <em class="sig-param">n=1</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/data.html#unique_ending"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.data.unique_ending" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>From id list get list with unique ending.</p>
|
<dd><p>From id list get list with unique ending.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -189,8 +191,8 @@ between consecutive terms).</p></li>
|
|||||||
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|
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||||||
|
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||||||
<dl class="function">
|
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|
||||||
<dt id="data.write">
|
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||||||
<code class="sig-name descname">write</code><span class="sig-paren">(</span><em class="sig-param">file_name</em>, <em class="sig-param">data</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/data.html#write"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#data.write" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">write</code><span class="sig-paren">(</span><em class="sig-param">file_name</em>, <em class="sig-param">data</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/data.html#write"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.data.write" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Write ascii file.</p>
|
<dd><p>Write ascii file.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -221,11 +223,24 @@ between consecutive terms).</p></li>
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|||||||
|
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||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
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|
<ul class="current">
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|
<li class="toctree-l1 current"><a class="reference internal" href="modules.html">pylib</a><ul class="current">
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<li class="toctree-l2 current"><a class="reference internal" href="pylib.html">pylib package</a></li>
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||||||
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</ul>
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||||||
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<div class="relations">
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||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
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<ul>
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<ul>
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<li><a href="index.html">Documentation overview</a><ul>
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<li><a href="index.html">Documentation overview</a><ul>
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|
<li><a href="modules.html">pylib</a><ul>
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<li><a href="pylib.html">pylib package</a><ul>
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<li>Previous: <a href="pylib.numerical.ode_model.html" title="previous chapter">pylib.numerical.ode_model module</a></li>
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<li>Next: <a href="pylib.date.html" title="next chapter">pylib.date module</a></li>
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@@ -259,7 +274,7 @@ between consecutive terms).</p></li>
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|||||||
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
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& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
||||||
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<a href="_sources/data.rst.txt"
|
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rel="nofollow">Page source</a>
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<head>
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|
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<meta charset="utf-8" />
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<title>date module — pylib 2019.5.19 documentation</title>
|
<title>pylib.date module — pylib 2019.12.21 documentation</title>
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<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
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||||||
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|
|||||||
<script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
|
<script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
|
||||||
<link rel="index" title="Index" href="genindex.html" />
|
<link rel="index" title="Index" href="genindex.html" />
|
||||||
<link rel="search" title="Search" href="search.html" />
|
<link rel="search" title="Search" href="search.html" />
|
||||||
|
<link rel="next" title="pylib.drawblock module" href="pylib.drawblock.html" />
|
||||||
|
<link rel="prev" title="pylib.data module" href="pylib.data.html" />
|
||||||
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||||||
<link rel="stylesheet" href="_static/custom.css" type="text/css" />
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|
|||||||
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||||||
<div class="body" role="main">
|
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|
||||||
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|
||||||
<div class="section" id="module-date">
|
<div class="section" id="module-pylib.date">
|
||||||
<span id="date-module"></span><h1>date module<a class="headerlink" href="#module-date" title="Permalink to this headline">¶</a></h1>
|
<span id="pylib-date-module"></span><h1>pylib.date module<a class="headerlink" href="#module-pylib.date" title="Permalink to this headline">¶</a></h1>
|
||||||
<p>Calculate spacial dates.</p>
|
<p>Calculate spacial dates.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Date</dt>
|
<dt class="field-odd">Date</dt>
|
||||||
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|
|||||||
</dd>
|
</dd>
|
||||||
</dl>
|
</dl>
|
||||||
<span class="target" id="module-date"></span><dl class="function">
|
<span class="target" id="module-date"></span><dl class="function">
|
||||||
<dt id="date.ascension_of_jesus">
|
<dt id="pylib.date.ascension_of_jesus">
|
||||||
<code class="sig-name descname">ascension_of_jesus</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/date.html#ascension_of_jesus"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#date.ascension_of_jesus" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">ascension_of_jesus</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/date.html#ascension_of_jesus"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.date.ascension_of_jesus" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Ascension of Jesus.</p>
|
<dd><p>Ascension of Jesus.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -58,8 +60,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="date.easter_friday">
|
<dt id="pylib.date.easter_friday">
|
||||||
<code class="sig-name descname">easter_friday</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/date.html#easter_friday"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#date.easter_friday" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">easter_friday</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/date.html#easter_friday"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.date.easter_friday" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Easter Friday.</p>
|
<dd><p>Easter Friday.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -75,8 +77,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="date.easter_monday">
|
<dt id="pylib.date.easter_monday">
|
||||||
<code class="sig-name descname">easter_monday</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/date.html#easter_monday"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#date.easter_monday" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">easter_monday</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/date.html#easter_monday"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.date.easter_monday" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Easter Monday.</p>
|
<dd><p>Easter Monday.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -92,8 +94,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="date.easter_sunday">
|
<dt id="pylib.date.easter_sunday">
|
||||||
<code class="sig-name descname">easter_sunday</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/date.html#easter_sunday"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#date.easter_sunday" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">easter_sunday</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/date.html#easter_sunday"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.date.easter_sunday" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Easter Sunday.</p>
|
<dd><p>Easter Sunday.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -109,8 +111,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="date.gaußsche_osterformel">
|
<dt id="pylib.date.gaußsche_osterformel">
|
||||||
<code class="sig-name descname">gaußsche_osterformel</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/date.html#gaußsche_osterformel"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#date.gaußsche_osterformel" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">gaußsche_osterformel</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/date.html#gaußsche_osterformel"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.date.gaußsche_osterformel" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Gaußsche Osterformel.</p>
|
<dd><p>Gaußsche Osterformel.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -143,8 +145,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="date.pentecost">
|
<dt id="pylib.date.pentecost">
|
||||||
<code class="sig-name descname">pentecost</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/date.html#pentecost"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#date.pentecost" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">pentecost</code><span class="sig-paren">(</span><em class="sig-param">year</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/date.html#pentecost"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.date.pentecost" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Pentecost.</p>
|
<dd><p>Pentecost.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -178,11 +180,24 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul class="current">
|
||||||
|
<li class="toctree-l1 current"><a class="reference internal" href="modules.html">pylib</a><ul class="current">
|
||||||
|
<li class="toctree-l2 current"><a class="reference internal" href="pylib.html">pylib package</a></li>
|
||||||
|
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|
||||||
|
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|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
<ul>
|
<ul>
|
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<li><a href="index.html">Documentation overview</a><ul>
|
<li><a href="index.html">Documentation overview</a><ul>
|
||||||
|
<li><a href="modules.html">pylib</a><ul>
|
||||||
|
<li><a href="pylib.html">pylib package</a><ul>
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|
<li>Previous: <a href="pylib.data.html" title="previous chapter">pylib.data module</a></li>
|
||||||
|
<li>Next: <a href="pylib.drawblock.html" title="next chapter">pylib.drawblock module</a></li>
|
||||||
|
</ul></li>
|
||||||
|
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|
||||||
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|
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||||||
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|
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||||||
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|
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|
||||||
@@ -216,7 +231,7 @@
|
|||||||
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
||||||
|
|
||||||
|
|
|
|
||||||
<a href="_sources/date.rst.txt"
|
<a href="_sources/pylib.date.rst.txt"
|
||||||
rel="nofollow">Page source</a>
|
rel="nofollow">Page source</a>
|
||||||
</div>
|
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|
||||||
|
|
||||||
145
docs/build/html/pylib.drawblock.html
vendored
Normal file
145
docs/build/html/pylib.drawblock.html
vendored
Normal file
@@ -0,0 +1,145 @@
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|
||||||
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|
||||||
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|
||||||
|
<title>pylib.drawblock module — pylib 2019.12.21 documentation</title>
|
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|
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|
<link rel="prev" title="pylib.date module" href="pylib.date.html" />
|
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|
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||||||
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||||||
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|
||||||
|
<div class="section" id="module-pylib.drawblock">
|
||||||
|
<span id="pylib-drawblock-module"></span><h1>pylib.drawblock module<a class="headerlink" href="#module-pylib.drawblock" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>Draw with block characters.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Date</dt>
|
||||||
|
<dd class="field-odd"><p>2019-11-15</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
<span class="target" id="module-drawblock"></span><dl class="function">
|
||||||
|
<dt id="pylib.drawblock.histogram">
|
||||||
|
<code class="sig-name descname">histogram</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/drawblock.html#histogram"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.drawblock.histogram" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Histogram chart with block symbols.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>dots
|
||||||
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,_,
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||||||
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|1|
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||||||
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```
|
||||||
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▁▂▃▄▅▆▇█
|
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12345678
|
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<h3>Navigation</h3>
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<p class="caption"><span class="caption-text">Contents:</span></p>
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<ul>
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<li><a href="modules.html">pylib</a><ul>
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<li><a href="pylib.html">pylib package</a><ul>
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<li>Next: <a href="pylib.function.html" title="next chapter">pylib.function module</a></li>
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©2019, Daniel Weschke.
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& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
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@@ -4,7 +4,7 @@
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<html xmlns="http://www.w3.org/1999/xhtml">
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<title>function module — pylib 2019.5.19 documentation</title>
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<title>pylib.function module — pylib 2019.12.21 documentation</title>
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<div class="body" role="main">
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<div class="body" role="main">
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<div class="section" id="module-function">
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<div class="section" id="module-pylib.function">
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||||||
<span id="function-module"></span><h1>function module<a class="headerlink" href="#module-function" title="Permalink to this headline">¶</a></h1>
|
<span id="pylib-function-module"></span><h1>pylib.function module<a class="headerlink" href="#module-pylib.function" title="Permalink to this headline">¶</a></h1>
|
||||||
<p>Mathematical equations.</p>
|
<p>Mathematical equations.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
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||||||
<dt class="field-odd">Date</dt>
|
<dt class="field-odd">Date</dt>
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||||||
@@ -41,8 +43,8 @@
|
|||||||
</dd>
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</dd>
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||||||
</dl>
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</dl>
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||||||
<span class="target" id="module-function"></span><dl class="function">
|
<span class="target" id="module-function"></span><dl class="function">
|
||||||
<dt id="function.cosine_wave">
|
<dt id="pylib.function.cosine_wave">
|
||||||
<code class="sig-name descname">cosine_wave</code><span class="sig-paren">(</span><em class="sig-param">A=1</em>, <em class="sig-param">k=1</em>, <em class="sig-param">f=1</em>, <em class="sig-param">phi=0</em>, <em class="sig-param">D=0</em>, <em class="sig-param">degree=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/function.html#cosine_wave"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#function.cosine_wave" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">cosine_wave</code><span class="sig-paren">(</span><em class="sig-param">A=1</em>, <em class="sig-param">k=1</em>, <em class="sig-param">f=1</em>, <em class="sig-param">phi=0</em>, <em class="sig-param">D=0</em>, <em class="sig-param">degree=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/function.html#cosine_wave"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.function.cosine_wave" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>A cosine wave is said to be sinusoidal, because,
|
<dd><p>A cosine wave is said to be sinusoidal, because,
|
||||||
<span class="math notranslate nohighlight">\(\cos(x) = \sin(x + \pi/2)\)</span>, which is also a sine wave with a
|
<span class="math notranslate nohighlight">\(\cos(x) = \sin(x + \pi/2)\)</span>, which is also a sine wave with a
|
||||||
phase-shift of π/2 radians. Because of this head start, it is often
|
phase-shift of π/2 radians. Because of this head start, it is often
|
||||||
@@ -68,13 +70,13 @@ time t</p>
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|||||||
</dl>
|
</dl>
|
||||||
<div class="admonition seealso">
|
<div class="admonition seealso">
|
||||||
<p class="admonition-title">See also</p>
|
<p class="admonition-title">See also</p>
|
||||||
<p><a class="reference internal" href="#function.sine_wave" title="function.sine_wave"><code class="xref py py-meth docutils literal notranslate"><span class="pre">sine_wave()</span></code></a></p>
|
<p><a class="reference internal" href="#pylib.function.sine_wave" title="pylib.function.sine_wave"><code class="xref py py-meth docutils literal notranslate"><span class="pre">sine_wave()</span></code></a></p>
|
||||||
</div>
|
</div>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
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|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="function.epitrochoid">
|
<dt id="pylib.function.epitrochoid">
|
||||||
<code class="sig-name descname">epitrochoid</code><span class="sig-paren">(</span><em class="sig-param">R</em>, <em class="sig-param">r</em>, <em class="sig-param">d</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/function.html#epitrochoid"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#function.epitrochoid" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">epitrochoid</code><span class="sig-paren">(</span><em class="sig-param">R</em>, <em class="sig-param">r</em>, <em class="sig-param">d</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/function.html#epitrochoid"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.function.epitrochoid" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Epitrochoid</p>
|
<dd><p>Epitrochoid</p>
|
||||||
<p>A point is attached with a distance d from the center of a circle
|
<p>A point is attached with a distance d from the center of a circle
|
||||||
of radius r. The circle is rolling around the outside of a fixed
|
of radius r. The circle is rolling around the outside of a fixed
|
||||||
@@ -122,8 +124,8 @@ y(\theta) = (R + r)\sin\theta - d\sin\left(\frac{R+r}{r}\theta\right) \\
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
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|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="function.hypotrochoid">
|
<dt id="pylib.function.hypotrochoid">
|
||||||
<code class="sig-name descname">hypotrochoid</code><span class="sig-paren">(</span><em class="sig-param">R</em>, <em class="sig-param">r</em>, <em class="sig-param">d</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/function.html#hypotrochoid"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#function.hypotrochoid" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">hypotrochoid</code><span class="sig-paren">(</span><em class="sig-param">R</em>, <em class="sig-param">r</em>, <em class="sig-param">d</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/function.html#hypotrochoid"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.function.hypotrochoid" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Hypotrochoid</p>
|
<dd><p>Hypotrochoid</p>
|
||||||
<p>A point is attached with a distance d from the center of a circle
|
<p>A point is attached with a distance d from the center of a circle
|
||||||
of radius r. The circle is rolling around the inside of a fixed
|
of radius r. The circle is rolling around the inside of a fixed
|
||||||
@@ -170,13 +172,13 @@ y(\theta) = (R - r)\sin\theta - d\sin\left(\frac{R-r}{r}\theta\right) \\
|
|||||||
</div>
|
</div>
|
||||||
<div class="admonition seealso">
|
<div class="admonition seealso">
|
||||||
<p class="admonition-title">See also</p>
|
<p class="admonition-title">See also</p>
|
||||||
<p><a class="reference internal" href="mathematics.html#mathematics.lcm" title="mathematics.lcm"><code class="xref py py-meth docutils literal notranslate"><span class="pre">mathematics.lcm()</span></code></a></p>
|
<p><code class="xref py py-meth docutils literal notranslate"><span class="pre">mathematics.lcm()</span></code></p>
|
||||||
</div>
|
</div>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="function.sine_wave">
|
<dt id="pylib.function.sine_wave">
|
||||||
<code class="sig-name descname">sine_wave</code><span class="sig-paren">(</span><em class="sig-param">A=1</em>, <em class="sig-param">k=1</em>, <em class="sig-param">f=1</em>, <em class="sig-param">phi=0</em>, <em class="sig-param">D=0</em>, <em class="sig-param">degree=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/function.html#sine_wave"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#function.sine_wave" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">sine_wave</code><span class="sig-paren">(</span><em class="sig-param">A=1</em>, <em class="sig-param">k=1</em>, <em class="sig-param">f=1</em>, <em class="sig-param">phi=0</em>, <em class="sig-param">D=0</em>, <em class="sig-param">degree=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/function.html#sine_wave"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.function.sine_wave" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>A sine wave or sinusoid is a mathematical curve that describes a
|
<dd><p>A sine wave or sinusoid is a mathematical curve that describes a
|
||||||
smooth periodic oscillation.</p>
|
smooth periodic oscillation.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
@@ -228,13 +230,13 @@ angular frequency ω and the linear speed (speed of propagation)
|
|||||||
linear speed.</p>
|
linear speed.</p>
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||||||
<div class="admonition seealso">
|
<div class="admonition seealso">
|
||||||
<p class="admonition-title">See also</p>
|
<p class="admonition-title">See also</p>
|
||||||
<p><a class="reference internal" href="#function.cosine_wave" title="function.cosine_wave"><code class="xref py py-meth docutils literal notranslate"><span class="pre">cosine_wave()</span></code></a></p>
|
<p><a class="reference internal" href="#pylib.function.cosine_wave" title="pylib.function.cosine_wave"><code class="xref py py-meth docutils literal notranslate"><span class="pre">cosine_wave()</span></code></a></p>
|
||||||
</div>
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||||||
</dd></dl>
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</dd></dl>
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||||||
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||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="function.to_str">
|
<dt id="pylib.function.to_str">
|
||||||
<code class="sig-name descname">to_str</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x=None</em>, <em class="sig-param">x_0=0</em>, <em class="sig-param">x_1=1</em>, <em class="sig-param">t=None</em>, <em class="sig-param">h=10</em>, <em class="sig-param">w=80</em>, <em class="sig-param">density=1</em>, <em class="sig-param">char_set='line'</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/function.html#to_str"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#function.to_str" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">to_str</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x=None</em>, <em class="sig-param">x_0=0</em>, <em class="sig-param">x_1=1</em>, <em class="sig-param">t=None</em>, <em class="sig-param">h=10</em>, <em class="sig-param">w=80</em>, <em class="sig-param">density=1</em>, <em class="sig-param">char_set='line'</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/function.html#to_str"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.function.to_str" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Represent functions as string frame with a specific character set.
|
<dd><p>Represent functions as string frame with a specific character set.
|
||||||
which are normed to the range of [0, 1] to</p>
|
which are normed to the range of [0, 1] to</p>
|
||||||
<dl class="field-list simple">
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|
||||||
@@ -245,9 +247,9 @@ which are normed to the range of [0, 1] to</p>
|
|||||||
<li><p><strong>w</strong> (<em>int</em>) – number of chars in horizontal direction</p></li>
|
<li><p><strong>w</strong> (<em>int</em>) – number of chars in horizontal direction</p></li>
|
||||||
<li><p><strong>char_set</strong> (<em>str</em>) – either “braille” or “block”. “braille” uses Unicode
|
<li><p><strong>char_set</strong> (<em>str</em>) – either “braille” or “block”. “braille” uses Unicode
|
||||||
Characters in the Braille Patterns Block (fisrt index U+2800, last
|
Characters in the Braille Patterns Block (fisrt index U+2800, last
|
||||||
index U+28FF <a class="reference internal" href="pylib.html#cudb" id="id1"><span>[CUDB]</span></a>) and the “block” uses part of the Unicode
|
index U+28FF <a class="reference internal" href="#cudb" id="id1"><span>[CUDB]</span></a>) and the “block” uses part of the Unicode
|
||||||
Characters in the Block Elements Block (fisrt index U+2580, last
|
Characters in the Block Elements Block (fisrt index U+2580, last
|
||||||
index U+259F <a class="reference internal" href="pylib.html#cudb" id="id2"><span>[CUDB]</span></a>). Alias for braille is line and alias for
|
index U+259F <a class="reference internal" href="#cudb" id="id2"><span>[CUDB]</span></a>). Alias for braille is line and alias for
|
||||||
block is histogram</p></li>
|
block is histogram</p></li>
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||||||
</ul>
|
</ul>
|
||||||
</dd>
|
</dd>
|
||||||
@@ -357,13 +359,13 @@ Example of 3 columns and 3 rows (upside down view of ‘normal’ braille/drawil
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</dl>
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</dl>
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||||||
<div class="admonition seealso">
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<div class="admonition seealso">
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||||||
<p class="admonition-title">See also</p>
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<p class="admonition-title">See also</p>
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||||||
<p><a class="reference internal" href="pylib.html#pylib.function.transformation" title="pylib.function.transformation"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pylib.function.transformation()</span></code></a></p>
|
<p><a class="reference internal" href="#pylib.function.transformation" title="pylib.function.transformation"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pylib.function.transformation()</span></code></a></p>
|
||||||
</div>
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||||||
</dd></dl>
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||||||
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||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="function.transformation">
|
<dt id="pylib.function.transformation">
|
||||||
<code class="sig-name descname">transformation</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">scale_vertical=1</em>, <em class="sig-param">scale_horizontal=1</em>, <em class="sig-param">shift_horizontal=0</em>, <em class="sig-param">shift_vertical=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/function.html#transformation"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#function.transformation" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">transformation</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">scale_vertical=1</em>, <em class="sig-param">scale_horizontal=1</em>, <em class="sig-param">shift_horizontal=0</em>, <em class="sig-param">shift_vertical=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/function.html#transformation"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.function.transformation" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Transform functions.</p>
|
<dd><p>Transform functions.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -409,11 +411,24 @@ Example of 3 columns and 3 rows (upside down view of ‘normal’ braille/drawil
|
|||||||
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||||||
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||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
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||||||
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<p class="caption"><span class="caption-text">Contents:</span></p>
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||||||
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<ul class="current">
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<li class="toctree-l1 current"><a class="reference internal" href="modules.html">pylib</a><ul class="current">
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<li class="toctree-l2 current"><a class="reference internal" href="pylib.html">pylib package</a></li>
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</ul>
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</li>
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||||||
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</ul>
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||||||
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|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="index.html">Documentation overview</a><ul>
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<li><a href="index.html">Documentation overview</a><ul>
|
||||||
|
<li><a href="modules.html">pylib</a><ul>
|
||||||
|
<li><a href="pylib.html">pylib package</a><ul>
|
||||||
|
<li>Previous: <a href="pylib.drawblock.html" title="previous chapter">pylib.drawblock module</a></li>
|
||||||
|
<li>Next: <a href="pylib.geometry.html" title="next chapter">pylib.geometry module</a></li>
|
||||||
|
</ul></li>
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||||||
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</ul></li>
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||||||
</ul></li>
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||||||
</ul>
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</div>
|
</div>
|
||||||
@@ -447,7 +462,7 @@ Example of 3 columns and 3 rows (upside down view of ‘normal’ braille/drawil
|
|||||||
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
||||||
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|
||||||
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|
||||||
<a href="_sources/function.rst.txt"
|
<a href="_sources/pylib.function.rst.txt"
|
||||||
rel="nofollow">Page source</a>
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rel="nofollow">Page source</a>
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</div>
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||||||
307
docs/build/html/pylib.geometry.html
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307
docs/build/html/pylib.geometry.html
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<title>pylib.geometry module — pylib 2019.12.21 documentation</title>
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<link rel="index" title="Index" href="genindex.html" />
|
||||||
|
<link rel="search" title="Search" href="search.html" />
|
||||||
|
<link rel="next" title="pylib.geometry2d module" href="pylib.geometry2d.html" />
|
||||||
|
<link rel="prev" title="pylib.function module" href="pylib.function.html" />
|
||||||
|
|
||||||
|
<link rel="stylesheet" href="_static/custom.css" type="text/css" />
|
||||||
|
|
||||||
|
|
||||||
|
<meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
|
||||||
|
|
||||||
|
</head><body>
|
||||||
|
|
||||||
|
|
||||||
|
<div class="document">
|
||||||
|
<div class="documentwrapper">
|
||||||
|
<div class="bodywrapper">
|
||||||
|
|
||||||
|
|
||||||
|
<div class="body" role="main">
|
||||||
|
|
||||||
|
<div class="section" id="module-pylib.geometry">
|
||||||
|
<span id="pylib-geometry-module"></span><h1>pylib.geometry module<a class="headerlink" href="#module-pylib.geometry" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>2D geometry objects.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Date</dt>
|
||||||
|
<dd class="field-odd"><p>2019-12-21</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
<span class="target" id="module-geometry"></span><dl class="class">
|
||||||
|
<dt id="pylib.geometry.CS">
|
||||||
|
<em class="property">class </em><code class="sig-name descname">CS</code><span class="sig-paren">(</span><em class="sig-param">x=[1, 0, 0], y=[0, 1, 0], z=[0, 0, 1]</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#CS"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.CS" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">mathematics.matrix</span></code></p>
|
||||||
|
<p>Coordinate system</p>
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.CS.get_coordinates">
|
||||||
|
<code class="sig-name descname">get_coordinates</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#CS.get_coordinates"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.CS.get_coordinates" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Get coordinates in 3d space</p>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.CS.x90">
|
||||||
|
<em class="property">static </em><code class="sig-name descname">x90</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#CS.x90"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.CS.x90" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.CS.xm90">
|
||||||
|
<em class="property">static </em><code class="sig-name descname">xm90</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#CS.xm90"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.CS.xm90" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.CS.y90">
|
||||||
|
<em class="property">static </em><code class="sig-name descname">y90</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#CS.y90"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.CS.y90" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.CS.ym90">
|
||||||
|
<em class="property">static </em><code class="sig-name descname">ym90</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#CS.ym90"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.CS.ym90" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="class">
|
||||||
|
<dt id="pylib.geometry.Circle">
|
||||||
|
<em class="property">class </em><code class="sig-name descname">Circle</code><span class="sig-paren">(</span><em class="sig-param">radius=1</em>, <em class="sig-param">n=10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Circle"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Circle" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Bases: <a class="reference internal" href="#pylib.geometry.Polygon" title="pylib.geometry.Polygon"><code class="xref py py-class docutils literal notranslate"><span class="pre">pylib.geometry.Polygon</span></code></a></p>
|
||||||
|
<p>Circle a closed wireframe object in local coordinate system</p>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="class">
|
||||||
|
<dt id="pylib.geometry.Direction">
|
||||||
|
<em class="property">class </em><code class="sig-name descname">Direction</code><span class="sig-paren">(</span><em class="sig-param">x=1</em>, <em class="sig-param">y=0</em>, <em class="sig-param">z=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Direction"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Direction" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">mathematics.vector</span></code></p>
|
||||||
|
<p>Direction in local coordinate system</p>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="class">
|
||||||
|
<dt id="pylib.geometry.Line">
|
||||||
|
<em class="property">class </em><code class="sig-name descname">Line</code><span class="sig-paren">(</span><em class="sig-param">point1=vector([-1</em>, <em class="sig-param">0</em>, <em class="sig-param">0])</em>, <em class="sig-param">point2=vector([1</em>, <em class="sig-param">0</em>, <em class="sig-param">0])</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Line"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Line" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Bases: <a class="reference internal" href="#pylib.geometry.Wireframe" title="pylib.geometry.Wireframe"><code class="xref py py-class docutils literal notranslate"><span class="pre">pylib.geometry.Wireframe</span></code></a></p>
|
||||||
|
<p>Line a open wireframe object in local coordinate system</p>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="class">
|
||||||
|
<dt id="pylib.geometry.Point">
|
||||||
|
<em class="property">class </em><code class="sig-name descname">Point</code><span class="sig-paren">(</span><em class="sig-param">x=0</em>, <em class="sig-param">y=0</em>, <em class="sig-param">z=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Point"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Point" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">mathematics.vector</span></code></p>
|
||||||
|
<p>Point in local coordinate system</p>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="class">
|
||||||
|
<dt id="pylib.geometry.Polygon">
|
||||||
|
<em class="property">class </em><code class="sig-name descname">Polygon</code><span class="sig-paren">(</span><em class="sig-param">*points</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Polygon"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Polygon" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Bases: <a class="reference internal" href="#pylib.geometry.Wireframe" title="pylib.geometry.Wireframe"><code class="xref py py-class docutils literal notranslate"><span class="pre">pylib.geometry.Wireframe</span></code></a></p>
|
||||||
|
<p>Polygon as closed wireframe object in local coordinate system</p>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="class">
|
||||||
|
<dt id="pylib.geometry.Wireframe">
|
||||||
|
<em class="property">class </em><code class="sig-name descname">Wireframe</code><span class="sig-paren">(</span><em class="sig-param">*points</em>, <em class="sig-param">closed=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
|
||||||
|
<p>Open and closed wireframe object in local coordinate system</p>
|
||||||
|
<p>This class create its own points (copy).</p>
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.Wireframe.ch_cs">
|
||||||
|
<code class="sig-name descname">ch_cs</code><span class="sig-paren">(</span><em class="sig-param">cs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.ch_cs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.ch_cs" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.Wireframe.points">
|
||||||
|
<code class="sig-name descname">points</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.points"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.points" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Get coordinates in 3d space</p>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.Wireframe.rotate_x">
|
||||||
|
<code class="sig-name descname">rotate_x</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.rotate_x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.rotate_x" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.Wireframe.rotate_y">
|
||||||
|
<code class="sig-name descname">rotate_y</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.rotate_y"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.rotate_y" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.Wireframe.rotate_z">
|
||||||
|
<code class="sig-name descname">rotate_z</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.rotate_z"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.rotate_z" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.Wireframe.scale">
|
||||||
|
<code class="sig-name descname">scale</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.scale" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.Wireframe.translate">
|
||||||
|
<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.translate" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.Wireframe.xyz">
|
||||||
|
<code class="sig-name descname">xyz</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#Wireframe.xyz"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.Wireframe.xyz" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="class">
|
||||||
|
<dt id="pylib.geometry.World">
|
||||||
|
<em class="property">class </em><code class="sig-name descname">World</code><a class="reference internal" href="_modules/pylib/geometry.html#World"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
|
||||||
|
<p>World-space with world-space coordinates</p>
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.World.add">
|
||||||
|
<code class="sig-name descname">add</code><span class="sig-paren">(</span><em class="sig-param">*objects</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.add"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.add" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.World.bounding_box">
|
||||||
|
<code class="sig-name descname">bounding_box</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.bounding_box"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.bounding_box" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.World.center">
|
||||||
|
<code class="sig-name descname">center</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.center"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.center" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.World.ch_cs">
|
||||||
|
<code class="sig-name descname">ch_cs</code><span class="sig-paren">(</span><em class="sig-param">cs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.ch_cs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.ch_cs" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.World.cs">
|
||||||
|
<code class="sig-name descname">cs</code><span class="sig-paren">(</span><em class="sig-param">cs=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.cs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.cs" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.World.objects">
|
||||||
|
<code class="sig-name descname">objects</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.objects"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.objects" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.World.rotate_x">
|
||||||
|
<code class="sig-name descname">rotate_x</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.rotate_x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.rotate_x" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.World.rotate_y">
|
||||||
|
<code class="sig-name descname">rotate_y</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.rotate_y"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.rotate_y" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.World.rotate_z">
|
||||||
|
<code class="sig-name descname">rotate_z</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.rotate_z"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.rotate_z" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd></dd></dl>
|
||||||
|
|
||||||
|
<dl class="method">
|
||||||
|
<dt id="pylib.geometry.World.scale">
|
||||||
|
<code class="sig-name descname">scale</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.scale" title="Permalink to this definition">¶</a></dt>
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||||||
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<dd></dd></dl>
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||||||
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<dl class="method">
|
||||||
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<dt id="pylib.geometry.World.space_diagonal">
|
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<code class="sig-name descname">space_diagonal</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.space_diagonal"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.space_diagonal" title="Permalink to this definition">¶</a></dt>
|
||||||
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<dd></dd></dl>
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<dl class="method">
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||||||
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<dt id="pylib.geometry.World.translate">
|
||||||
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<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry.html#World.translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry.World.translate" title="Permalink to this definition">¶</a></dt>
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||||||
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<dd></dd></dl>
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<li>Next: <a href="pylib.geometry2d.html" title="next chapter">pylib.geometry2d module</a></li>
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©2019, Daniel Weschke.
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@@ -4,7 +4,7 @@
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<html xmlns="http://www.w3.org/1999/xhtml">
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<html xmlns="http://www.w3.org/1999/xhtml">
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||||||
<head>
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<head>
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||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
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||||||
<title>geometry module — pylib 2019.5.19 documentation</title>
|
<title>pylib.geometry2d module — pylib 2019.12.21 documentation</title>
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||||||
<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
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|||||||
<script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
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<script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
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<link rel="prev" title="pylib.geometry module" href="pylib.geometry.html" />
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<link rel="stylesheet" href="_static/custom.css" type="text/css" />
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@@ -32,17 +34,17 @@
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|||||||
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||||||
<div class="body" role="main">
|
<div class="body" role="main">
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||||||
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|
||||||
<div class="section" id="module-geometry">
|
<div class="section" id="module-pylib.geometry2d">
|
||||||
<span id="geometry-module"></span><h1>geometry module<a class="headerlink" href="#module-geometry" title="Permalink to this headline">¶</a></h1>
|
<span id="pylib-geometry2d-module"></span><h1>pylib.geometry2d module<a class="headerlink" href="#module-pylib.geometry2d" title="Permalink to this headline">¶</a></h1>
|
||||||
<p>2D geometry objects.</p>
|
<p>2D geometry objects.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Date</dt>
|
<dt class="field-odd">Date</dt>
|
||||||
<dd class="field-odd"><p>2019-08-28</p>
|
<dd class="field-odd"><p>2019-08-28</p>
|
||||||
</dd>
|
</dd>
|
||||||
</dl>
|
</dl>
|
||||||
<span class="target" id="module-geometry"></span><dl class="function">
|
<span class="target" id="module-geometry2d"></span><dl class="function">
|
||||||
<dt id="geometry.angle">
|
<dt id="pylib.geometry2d.angle">
|
||||||
<code class="sig-name descname">angle</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">point2=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#angle"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.angle" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">angle</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">point2=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#angle"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.angle" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Angle of point or between two points.</p>
|
<dd><p>Angle of point or between two points.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -61,8 +63,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.cubic">
|
<dt id="pylib.geometry2d.cubic">
|
||||||
<code class="sig-name descname">cubic</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">angle1</em>, <em class="sig-param">point2</em>, <em class="sig-param">angle2</em>, <em class="sig-param">samples=10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#cubic"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.cubic" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">cubic</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">angle1</em>, <em class="sig-param">point2</em>, <em class="sig-param">angle2</em>, <em class="sig-param">samples=10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#cubic"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.cubic" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Cubic line defined by two end points and the rotation in radians
|
<dd><p>Cubic line defined by two end points and the rotation in radians
|
||||||
at the points.</p>
|
at the points.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
@@ -86,8 +88,8 @@ at the points.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.cubic_deg">
|
<dt id="pylib.geometry2d.cubic_deg">
|
||||||
<code class="sig-name descname">cubic_deg</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">angle1</em>, <em class="sig-param">point2</em>, <em class="sig-param">angle2</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#cubic_deg"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.cubic_deg" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">cubic_deg</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">angle1</em>, <em class="sig-param">point2</em>, <em class="sig-param">angle2</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#cubic_deg"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.cubic_deg" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Cubic line defined by two end points and the roation in degree
|
<dd><p>Cubic line defined by two end points and the roation in degree
|
||||||
at the points.</p>
|
at the points.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
@@ -109,13 +111,13 @@ at the points.</p>
|
|||||||
</dl>
|
</dl>
|
||||||
<div class="admonition seealso">
|
<div class="admonition seealso">
|
||||||
<p class="admonition-title">See also</p>
|
<p class="admonition-title">See also</p>
|
||||||
<p><a class="reference internal" href="#geometry.cubic" title="geometry.cubic"><code class="xref py py-meth docutils literal notranslate"><span class="pre">cubic()</span></code></a></p>
|
<p><a class="reference internal" href="#pylib.geometry2d.cubic" title="pylib.geometry2d.cubic"><code class="xref py py-meth docutils literal notranslate"><span class="pre">cubic()</span></code></a></p>
|
||||||
</div>
|
</div>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.cubics">
|
<dt id="pylib.geometry2d.cubics">
|
||||||
<code class="sig-name descname">cubics</code><span class="sig-paren">(</span><em class="sig-param">pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#cubics"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.cubics" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">cubics</code><span class="sig-paren">(</span><em class="sig-param">pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#cubics"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.cubics" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Cubic lines defined by a list of two end points. The deformation
|
<dd><p>Cubic lines defined by a list of two end points. The deformation
|
||||||
as displacement and rotation (radians) is defined element wise as
|
as displacement and rotation (radians) is defined element wise as
|
||||||
keyword argument deformation or global node wise as
|
keyword argument deformation or global node wise as
|
||||||
@@ -162,8 +164,8 @@ decides what the left and the right end point of the line is.</p></li>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.distance">
|
<dt id="pylib.geometry2d.distance">
|
||||||
<code class="sig-name descname">distance</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">point2</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#distance"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.distance" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">distance</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">point2</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#distance"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.distance" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Distance between two points (or length of a straight line).</p>
|
<dd><p>Distance between two points (or length of a straight line).</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -182,8 +184,8 @@ decides what the left and the right end point of the line is.</p></li>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.interpolate_hermite">
|
<dt id="pylib.geometry2d.interpolate_hermite">
|
||||||
<code class="sig-name descname">interpolate_hermite</code><span class="sig-paren">(</span><em class="sig-param">lvd</em>, <em class="sig-param">lr</em>, <em class="sig-param">rvd</em>, <em class="sig-param">rr</em>, <em class="sig-param">lhd=0</em>, <em class="sig-param">rhd=0</em>, <em class="sig-param">scale_x=1</em>, <em class="sig-param">scale_y=1</em>, <em class="sig-param">samples=10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#interpolate_hermite"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.interpolate_hermite" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">interpolate_hermite</code><span class="sig-paren">(</span><em class="sig-param">lvd</em>, <em class="sig-param">lr</em>, <em class="sig-param">rvd</em>, <em class="sig-param">rr</em>, <em class="sig-param">lhd=0</em>, <em class="sig-param">rhd=0</em>, <em class="sig-param">scale_x=1</em>, <em class="sig-param">scale_y=1</em>, <em class="sig-param">samples=10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#interpolate_hermite"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.interpolate_hermite" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Interpolate cubic line with hermite boundary conditions.</p>
|
<dd><p>Interpolate cubic line with hermite boundary conditions.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -207,8 +209,8 @@ x = s\,L + x_1\end{split}\]</div>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.line">
|
<dt id="pylib.geometry2d.line">
|
||||||
<code class="sig-name descname">line</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">point2</em>, <em class="sig-param">samples=2</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#line"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.line" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">line</code><span class="sig-paren">(</span><em class="sig-param">point1</em>, <em class="sig-param">point2</em>, <em class="sig-param">samples=2</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#line"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.line" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Line defined by two end points.</p>
|
<dd><p>Line defined by two end points.</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
\[y = \frac{y_2-y_1}{x_2-x_1}(x-x_1) + y_1\]</div>
|
\[y = \frac{y_2-y_1}{x_2-x_1}(x-x_1) + y_1\]</div>
|
||||||
@@ -239,8 +241,8 @@ x = s\,L + x_1\end{split}\]</div>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.lines">
|
<dt id="pylib.geometry2d.lines">
|
||||||
<code class="sig-name descname">lines</code><span class="sig-paren">(</span><em class="sig-param">pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#lines"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.lines" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">lines</code><span class="sig-paren">(</span><em class="sig-param">pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#lines"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.lines" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Lines defined by a list of end points.</p>
|
<dd><p>Lines defined by a list of end points.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -274,14 +276,14 @@ decides what the left and the right end point of the line is.</p></li>
|
|||||||
</dl>
|
</dl>
|
||||||
<div class="admonition seealso">
|
<div class="admonition seealso">
|
||||||
<p class="admonition-title">See also</p>
|
<p class="admonition-title">See also</p>
|
||||||
<p><a class="reference internal" href="geometry_plot.html#geometry_plot.plot_lines" title="geometry_plot.plot_lines"><code class="xref py py-meth docutils literal notranslate"><span class="pre">plot_lines()</span></code></a> of the <a class="reference internal" href="pylib.html#module-geometry_plot" title="geometry_plot: Geometry plotting. (*nix, Windows)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">geometry_plot</span></code></a>
|
<p><code class="xref py py-meth docutils literal notranslate"><span class="pre">plot_lines()</span></code> of the <code class="xref py py-mod docutils literal notranslate"><span class="pre">geometry_plot</span></code>
|
||||||
module to plot the lines</p>
|
module to plot the lines</p>
|
||||||
</div>
|
</div>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.rectangle">
|
<dt id="pylib.geometry2d.rectangle">
|
||||||
<code class="sig-name descname">rectangle</code><span class="sig-paren">(</span><em class="sig-param">width</em>, <em class="sig-param">height</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#rectangle"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.rectangle" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">rectangle</code><span class="sig-paren">(</span><em class="sig-param">width</em>, <em class="sig-param">height</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#rectangle"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.rectangle" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><dl class="field-list simple">
|
<dd><dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
<dd class="field-odd"><ul class="simple">
|
<dd class="field-odd"><ul class="simple">
|
||||||
@@ -299,8 +301,8 @@ module to plot the lines</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.rotate">
|
<dt id="pylib.geometry2d.rotate">
|
||||||
<code class="sig-name descname">rotate</code><span class="sig-paren">(</span><em class="sig-param">origin</em>, <em class="sig-param">angle</em>, <em class="sig-param">*pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#rotate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.rotate" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">rotate</code><span class="sig-paren">(</span><em class="sig-param">origin</em>, <em class="sig-param">angle</em>, <em class="sig-param">*pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#rotate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.rotate" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotate a point or polygon counterclockwise by a given angle
|
<dd><p>Rotate a point or polygon counterclockwise by a given angle
|
||||||
around a given origin. The angle should be given in radians.</p>
|
around a given origin. The angle should be given in radians.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
@@ -321,13 +323,13 @@ around a given origin. The angle should be given in radians.</p>
|
|||||||
</dl>
|
</dl>
|
||||||
<div class="admonition seealso">
|
<div class="admonition seealso">
|
||||||
<p class="admonition-title">See also</p>
|
<p class="admonition-title">See also</p>
|
||||||
<p><a class="reference internal" href="#geometry.rotate_xy" title="geometry.rotate_xy"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rotate_xy()</span></code></a></p>
|
<p><a class="reference internal" href="#pylib.geometry2d.rotate_xy" title="pylib.geometry2d.rotate_xy"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rotate_xy()</span></code></a></p>
|
||||||
</div>
|
</div>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.rotate_deg">
|
<dt id="pylib.geometry2d.rotate_deg">
|
||||||
<code class="sig-name descname">rotate_deg</code><span class="sig-paren">(</span><em class="sig-param">origin</em>, <em class="sig-param">angle</em>, <em class="sig-param">*pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#rotate_deg"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.rotate_deg" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">rotate_deg</code><span class="sig-paren">(</span><em class="sig-param">origin</em>, <em class="sig-param">angle</em>, <em class="sig-param">*pts</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#rotate_deg"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.rotate_deg" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotate a point or polygon counterclockwise by a given angle
|
<dd><p>Rotate a point or polygon counterclockwise by a given angle
|
||||||
around a given origin. The angle should be given in degrees.</p>
|
around a given origin. The angle should be given in degrees.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
@@ -348,13 +350,13 @@ around a given origin. The angle should be given in degrees.</p>
|
|||||||
</dl>
|
</dl>
|
||||||
<div class="admonition seealso">
|
<div class="admonition seealso">
|
||||||
<p class="admonition-title">See also</p>
|
<p class="admonition-title">See also</p>
|
||||||
<p><a class="reference internal" href="#geometry.rotate" title="geometry.rotate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rotate()</span></code></a></p>
|
<p><a class="reference internal" href="#pylib.geometry2d.rotate" title="pylib.geometry2d.rotate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rotate()</span></code></a></p>
|
||||||
</div>
|
</div>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.rotate_xy">
|
<dt id="pylib.geometry2d.rotate_xy">
|
||||||
<code class="sig-name descname">rotate_xy</code><span class="sig-paren">(</span><em class="sig-param">origin</em>, <em class="sig-param">angle</em>, <em class="sig-param">x</em>, <em class="sig-param">y</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#rotate_xy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.rotate_xy" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">rotate_xy</code><span class="sig-paren">(</span><em class="sig-param">origin</em>, <em class="sig-param">angle</em>, <em class="sig-param">x</em>, <em class="sig-param">y</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#rotate_xy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.rotate_xy" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotate x and y coordinates counterclockwise by a given angle
|
<dd><p>Rotate x and y coordinates counterclockwise by a given angle
|
||||||
around a given origin. The angle should be given in radians.</p>
|
around a given origin. The angle should be given in radians.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
@@ -370,13 +372,13 @@ around a given origin. The angle should be given in radians.</p>
|
|||||||
</dl>
|
</dl>
|
||||||
<div class="admonition seealso">
|
<div class="admonition seealso">
|
||||||
<p class="admonition-title">See also</p>
|
<p class="admonition-title">See also</p>
|
||||||
<p><a class="reference internal" href="#geometry.rotate" title="geometry.rotate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rotate()</span></code></a></p>
|
<p><a class="reference internal" href="#pylib.geometry2d.rotate" title="pylib.geometry2d.rotate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rotate()</span></code></a></p>
|
||||||
</div>
|
</div>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.square">
|
<dt id="pylib.geometry2d.square">
|
||||||
<code class="sig-name descname">square</code><span class="sig-paren">(</span><em class="sig-param">width</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#square"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.square" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">square</code><span class="sig-paren">(</span><em class="sig-param">width</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#square"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.square" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><dl class="field-list simple">
|
<dd><dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
<dd class="field-odd"><p><strong>width</strong> (<em>int</em><em> or </em><em>float</em>) – the edge size of the square</p>
|
<dd class="field-odd"><p><strong>width</strong> (<em>int</em><em> or </em><em>float</em>) – the edge size of the square</p>
|
||||||
@@ -390,13 +392,13 @@ around a given origin. The angle should be given in radians.</p>
|
|||||||
</dl>
|
</dl>
|
||||||
<div class="admonition seealso">
|
<div class="admonition seealso">
|
||||||
<p class="admonition-title">See also</p>
|
<p class="admonition-title">See also</p>
|
||||||
<p><a class="reference internal" href="#geometry.rectangle" title="geometry.rectangle"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rectangle()</span></code></a></p>
|
<p><a class="reference internal" href="#pylib.geometry2d.rectangle" title="pylib.geometry2d.rectangle"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rectangle()</span></code></a></p>
|
||||||
</div>
|
</div>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.translate">
|
<dt id="pylib.geometry2d.translate">
|
||||||
<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">vec</em>, <em class="sig-param">*pts</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.translate" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">vec</em>, <em class="sig-param">*pts</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.translate" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Translate a point or polygon by a given vector.</p>
|
<dd><p>Translate a point or polygon by a given vector.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -414,13 +416,13 @@ around a given origin. The angle should be given in radians.</p>
|
|||||||
</dl>
|
</dl>
|
||||||
<div class="admonition seealso">
|
<div class="admonition seealso">
|
||||||
<p class="admonition-title">See also</p>
|
<p class="admonition-title">See also</p>
|
||||||
<p><a class="reference internal" href="#geometry.translate_xy" title="geometry.translate_xy"><code class="xref py py-meth docutils literal notranslate"><span class="pre">translate_xy()</span></code></a></p>
|
<p><a class="reference internal" href="#pylib.geometry2d.translate_xy" title="pylib.geometry2d.translate_xy"><code class="xref py py-meth docutils literal notranslate"><span class="pre">translate_xy()</span></code></a></p>
|
||||||
</div>
|
</div>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry.translate_xy">
|
<dt id="pylib.geometry2d.translate_xy">
|
||||||
<code class="sig-name descname">translate_xy</code><span class="sig-paren">(</span><em class="sig-param">vec</em>, <em class="sig-param">x</em>, <em class="sig-param">y</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry.html#translate_xy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry.translate_xy" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">translate_xy</code><span class="sig-paren">(</span><em class="sig-param">vec</em>, <em class="sig-param">x</em>, <em class="sig-param">y</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d.html#translate_xy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d.translate_xy" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Translate a point or polygon by a given vector.</p>
|
<dd><p>Translate a point or polygon by a given vector.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -439,7 +441,7 @@ around a given origin. The angle should be given in radians.</p>
|
|||||||
</dl>
|
</dl>
|
||||||
<div class="admonition seealso">
|
<div class="admonition seealso">
|
||||||
<p class="admonition-title">See also</p>
|
<p class="admonition-title">See also</p>
|
||||||
<p><a class="reference internal" href="#geometry.translate" title="geometry.translate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">translate()</span></code></a></p>
|
<p><a class="reference internal" href="#pylib.geometry2d.translate" title="pylib.geometry2d.translate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">translate()</span></code></a></p>
|
||||||
</div>
|
</div>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
@@ -462,11 +464,24 @@ around a given origin. The angle should be given in radians.</p>
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
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|
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|
<li class="toctree-l1 current"><a class="reference internal" href="modules.html">pylib</a><ul class="current">
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<li class="toctree-l2 current"><a class="reference internal" href="pylib.html">pylib package</a></li>
|
||||||
|
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|
||||||
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|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
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<h3>Related Topics</h3>
|
||||||
<ul>
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<ul>
|
||||||
<li><a href="index.html">Documentation overview</a><ul>
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<li><a href="index.html">Documentation overview</a><ul>
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||||||
|
<li><a href="modules.html">pylib</a><ul>
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||||||
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<li><a href="pylib.html">pylib package</a><ul>
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||||||
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<li>Previous: <a href="pylib.geometry.html" title="previous chapter">pylib.geometry module</a></li>
|
||||||
|
<li>Next: <a href="pylib.geometry2d_plot.html" title="next chapter">pylib.geometry2d_plot module</a></li>
|
||||||
|
</ul></li>
|
||||||
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|
||||||
</ul></li>
|
</ul></li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
@@ -500,7 +515,7 @@ around a given origin. The angle should be given in radians.</p>
|
|||||||
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
||||||
|
|
||||||
|
|
|
|
||||||
<a href="_sources/geometry.rst.txt"
|
<a href="_sources/pylib.geometry2d.rst.txt"
|
||||||
rel="nofollow">Page source</a>
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rel="nofollow">Page source</a>
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||||||
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|
||||||
|
|
||||||
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>geometry_plot module — pylib 2019.5.19 documentation</title>
|
<title>pylib.geometry2d_plot module — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
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@@ -16,6 +16,8 @@
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<link rel="stylesheet" href="_static/custom.css" type="text/css" />
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||||||
@@ -32,22 +34,22 @@
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|||||||
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|
||||||
<div class="body" role="main">
|
<div class="body" role="main">
|
||||||
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|
||||||
<div class="section" id="module-geometry_plot">
|
<div class="section" id="module-pylib.geometry2d_plot">
|
||||||
<span id="geometry-plot-module"></span><h1>geometry_plot module<a class="headerlink" href="#module-geometry_plot" title="Permalink to this headline">¶</a></h1>
|
<span id="pylib-geometry2d-plot-module"></span><h1>pylib.geometry2d_plot module<a class="headerlink" href="#module-pylib.geometry2d_plot" title="Permalink to this headline">¶</a></h1>
|
||||||
<p>2D geometry plotter using matplotlib (pylab).</p>
|
<p>2D geometry plotter using matplotlib (pylab).</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Date</dt>
|
<dt class="field-odd">Date</dt>
|
||||||
<dd class="field-odd"><p>2019-08-20</p>
|
<dd class="field-odd"><p>2019-08-20</p>
|
||||||
</dd>
|
</dd>
|
||||||
</dl>
|
</dl>
|
||||||
<span class="target" id="module-geometry_plot"></span><dl class="function">
|
<span class="target" id="module-geometry2d_plot"></span><dl class="function">
|
||||||
<dt id="geometry_plot.plot_cubic_lines">
|
<dt id="pylib.geometry2d_plot.plot_cubic_lines">
|
||||||
<code class="sig-name descname">plot_cubic_lines</code><span class="sig-paren">(</span><em class="sig-param">lns</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry_plot.html#plot_cubic_lines"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry_plot.plot_cubic_lines" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">plot_cubic_lines</code><span class="sig-paren">(</span><em class="sig-param">lns</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d_plot.html#plot_cubic_lines"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d_plot.plot_cubic_lines" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd></dd></dl>
|
<dd></dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="geometry_plot.plot_lines">
|
<dt id="pylib.geometry2d_plot.plot_lines">
|
||||||
<code class="sig-name descname">plot_lines</code><span class="sig-paren">(</span><em class="sig-param">lns</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/geometry_plot.html#plot_lines"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#geometry_plot.plot_lines" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">plot_lines</code><span class="sig-paren">(</span><em class="sig-param">lns</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/geometry2d_plot.html#plot_lines"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.geometry2d_plot.plot_lines" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd></dd></dl>
|
<dd></dd></dl>
|
||||||
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|
||||||
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|
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||||||
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|||||||
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||||||
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|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
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|
||||||
|
<li class="toctree-l1 current"><a class="reference internal" href="modules.html">pylib</a><ul class="current">
|
||||||
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<li class="toctree-l2 current"><a class="reference internal" href="pylib.html">pylib package</a></li>
|
||||||
|
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|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="index.html">Documentation overview</a><ul>
|
<li><a href="index.html">Documentation overview</a><ul>
|
||||||
|
<li><a href="modules.html">pylib</a><ul>
|
||||||
|
<li><a href="pylib.html">pylib package</a><ul>
|
||||||
|
<li>Previous: <a href="pylib.geometry2d.html" title="previous chapter">pylib.geometry2d module</a></li>
|
||||||
|
<li>Next: <a href="pylib.mathematics.html" title="next chapter">pylib.mathematics module</a></li>
|
||||||
|
</ul></li>
|
||||||
|
</ul></li>
|
||||||
</ul></li>
|
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|
||||||
</ul>
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||||||
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|
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||||||
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|
|||||||
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
||||||
|
|
||||||
|
|
|
|
||||||
<a href="_sources/geometry_plot.rst.txt"
|
<a href="_sources/pylib.geometry2d_plot.rst.txt"
|
||||||
rel="nofollow">Page source</a>
|
rel="nofollow">Page source</a>
|
||||||
</div>
|
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|
||||||
|
|
||||||
1909
docs/build/html/pylib.html
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|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
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|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>mathematics module — pylib 2019.5.19 documentation</title>
|
<title>pylib.mathematics module — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
|
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|
|||||||
<script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
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<script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
|
||||||
<link rel="index" title="Index" href="genindex.html" />
|
<link rel="index" title="Index" href="genindex.html" />
|
||||||
<link rel="search" title="Search" href="search.html" />
|
<link rel="search" title="Search" href="search.html" />
|
||||||
|
<link rel="next" title="pylib.time_of_day module" href="pylib.time_of_day.html" />
|
||||||
|
<link rel="prev" title="pylib.geometry2d_plot module" href="pylib.geometry2d_plot.html" />
|
||||||
|
|
||||||
<link rel="stylesheet" href="_static/custom.css" type="text/css" />
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|
||||||
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|
||||||
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|
|||||||
|
|
||||||
<div class="body" role="main">
|
<div class="body" role="main">
|
||||||
|
|
||||||
<div class="section" id="module-mathematics">
|
<div class="section" id="module-pylib.mathematics">
|
||||||
<span id="mathematics-module"></span><h1>mathematics module<a class="headerlink" href="#module-mathematics" title="Permalink to this headline">¶</a></h1>
|
<span id="pylib-mathematics-module"></span><h1>pylib.mathematics module<a class="headerlink" href="#module-pylib.mathematics" title="Permalink to this headline">¶</a></h1>
|
||||||
<p>Mathematical functions and objects.</p>
|
<p>Mathematical functions and objects.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Date</dt>
|
<dt class="field-odd">Date</dt>
|
||||||
@@ -41,19 +43,19 @@
|
|||||||
</dd>
|
</dd>
|
||||||
</dl>
|
</dl>
|
||||||
<span class="target" id="module-mathematics"></span><dl class="function">
|
<span class="target" id="module-mathematics"></span><dl class="function">
|
||||||
<dt id="mathematics.lcm">
|
<dt id="pylib.mathematics.lcm">
|
||||||
<code class="sig-name descname">lcm</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">b</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#lcm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.lcm" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">lcm</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">b</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#lcm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.lcm" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Compute the lowest common multiple of a and b</p>
|
<dd><p>Compute the lowest common multiple of a and b</p>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="class">
|
<dl class="class">
|
||||||
<dt id="mathematics.matrix">
|
<dt id="pylib.mathematics.matrix">
|
||||||
<em class="property">class </em><code class="sig-name descname">matrix</code><a class="reference internal" href="_modules/mathematics.html#matrix"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix" title="Permalink to this definition">¶</a></dt>
|
<em class="property">class </em><code class="sig-name descname">matrix</code><a class="reference internal" href="_modules/pylib/mathematics.html#matrix"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></p>
|
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></p>
|
||||||
<p>Use/create matrix like list of lists</p>
|
<p>Use/create matrix like list of lists</p>
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.matrix.rotate_x">
|
<dt id="pylib.mathematics.matrix.rotate_x">
|
||||||
<code class="sig-name descname">rotate_x</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.rotate_x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.rotate_x" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">rotate_x</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.rotate_x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.rotate_x" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotation about the x dirction.</p>
|
<dd><p>Rotation about the x dirction.</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
\[\begin{split}\begin{bmatrix}
|
\[\begin{split}\begin{bmatrix}
|
||||||
@@ -77,8 +79,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.matrix.rotate_y">
|
<dt id="pylib.mathematics.matrix.rotate_y">
|
||||||
<code class="sig-name descname">rotate_y</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.rotate_y"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.rotate_y" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">rotate_y</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.rotate_y"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.rotate_y" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotation about the y dirction.</p>
|
<dd><p>Rotation about the y dirction.</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
\[\begin{split}\begin{bmatrix}
|
\[\begin{split}\begin{bmatrix}
|
||||||
@@ -102,8 +104,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.matrix.rotate_z">
|
<dt id="pylib.mathematics.matrix.rotate_z">
|
||||||
<code class="sig-name descname">rotate_z</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.rotate_z"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.rotate_z" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">rotate_z</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.rotate_z"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.rotate_z" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotation about the z dirction.</p>
|
<dd><p>Rotation about the z dirction.</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
\[\begin{split}\begin{bmatrix}
|
\[\begin{split}\begin{bmatrix}
|
||||||
@@ -127,8 +129,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.matrix.rx">
|
<dt id="pylib.mathematics.matrix.rx">
|
||||||
<em class="property">static </em><code class="sig-name descname">rx</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.rx"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.rx" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">rx</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.rx"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.rx" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotation matrix about the x direction.</p>
|
<dd><p>Rotation matrix about the x direction.</p>
|
||||||
<p>Rotates the coordinate system of vectors</p>
|
<p>Rotates the coordinate system of vectors</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
@@ -142,8 +144,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.matrix.ry">
|
<dt id="pylib.mathematics.matrix.ry">
|
||||||
<em class="property">static </em><code class="sig-name descname">ry</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.ry"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.ry" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">ry</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.ry"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.ry" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotation matrix about the y direction.</p>
|
<dd><p>Rotation matrix about the y direction.</p>
|
||||||
<p>Rotates the coordinate system of vectors</p>
|
<p>Rotates the coordinate system of vectors</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
@@ -157,8 +159,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.matrix.rz">
|
<dt id="pylib.mathematics.matrix.rz">
|
||||||
<em class="property">static </em><code class="sig-name descname">rz</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.rz"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.rz" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">rz</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.rz"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.rz" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotation matrix about the z direction.</p>
|
<dd><p>Rotation matrix about the z direction.</p>
|
||||||
<p>Rotates the coordinate system of vectors</p>
|
<p>Rotates the coordinate system of vectors</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
@@ -193,8 +195,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.matrix.s">
|
<dt id="pylib.mathematics.matrix.s">
|
||||||
<em class="property">static </em><code class="sig-name descname">s</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.s"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.s" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">s</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.s"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.s" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Scaling matrix</p>
|
<dd><p>Scaling matrix</p>
|
||||||
<p>uniform scaling if sx=sy=sz=s.
|
<p>uniform scaling if sx=sy=sz=s.
|
||||||
Note that scaling happens around the origin, so objects not
|
Note that scaling happens around the origin, so objects not
|
||||||
@@ -213,8 +215,8 @@ it should be.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.matrix.scale">
|
<dt id="pylib.mathematics.matrix.scale">
|
||||||
<code class="sig-name descname">scale</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.scale" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">scale</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.scale" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Scaling</p>
|
<dd><p>Scaling</p>
|
||||||
<p>uniform scaling if sx=sy=sz=s.
|
<p>uniform scaling if sx=sy=sz=s.
|
||||||
Note that scaling happens around the origin, so objects not
|
Note that scaling happens around the origin, so objects not
|
||||||
@@ -244,8 +246,8 @@ it should be.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.matrix.t">
|
<dt id="pylib.mathematics.matrix.t">
|
||||||
<em class="property">static </em><code class="sig-name descname">t</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.t"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.t" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">t</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.t"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.t" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Translation matrix</p>
|
<dd><p>Translation matrix</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
\[\begin{split}T =
|
\[\begin{split}T =
|
||||||
@@ -258,8 +260,8 @@ it should be.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.matrix.translate">
|
<dt id="pylib.mathematics.matrix.translate">
|
||||||
<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.translate" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#matrix.translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.matrix.translate" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Translation</p>
|
<dd><p>Translation</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
\[\begin{split}\begin{bmatrix}
|
\[\begin{split}\begin{bmatrix}
|
||||||
@@ -285,8 +287,8 @@ it should be.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="class">
|
<dl class="class">
|
||||||
<dt id="mathematics.vector">
|
<dt id="pylib.mathematics.vector">
|
||||||
<em class="property">class </em><code class="sig-name descname">vector</code><a class="reference internal" href="_modules/mathematics.html#vector"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector" title="Permalink to this definition">¶</a></dt>
|
<em class="property">class </em><code class="sig-name descname">vector</code><a class="reference internal" href="_modules/pylib/mathematics.html#vector"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></p>
|
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></p>
|
||||||
<p>Use/create vector like lists</p>
|
<p>Use/create vector like lists</p>
|
||||||
<ul class="simple">
|
<ul class="simple">
|
||||||
@@ -345,29 +347,29 @@ it should be.</p>
|
|||||||
</pre></div>
|
</pre></div>
|
||||||
</div>
|
</div>
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.abs">
|
<dt id="pylib.mathematics.vector.abs">
|
||||||
<em class="property">static </em><code class="sig-name descname">abs</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.abs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.abs" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">abs</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.abs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.abs" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Return modulus parts of a complex vector</p>
|
<dd><p>Return modulus parts of a complex vector</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
</dl>
|
</dl>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.ang">
|
<dt id="pylib.mathematics.vector.ang">
|
||||||
<em class="property">static </em><code class="sig-name descname">ang</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">b</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.ang"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.ang" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">ang</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">b</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.ang"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.ang" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd></dd></dl>
|
<dd></dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.arg">
|
<dt id="pylib.mathematics.vector.arg">
|
||||||
<em class="property">static </em><code class="sig-name descname">arg</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.arg"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.arg" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">arg</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.arg"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.arg" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Return phase parts of a complex vector</p>
|
<dd><p>Return phase parts of a complex vector</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
</dl>
|
</dl>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.ch_cs">
|
<dt id="pylib.mathematics.vector.ch_cs">
|
||||||
<code class="sig-name descname">ch_cs</code><span class="sig-paren">(</span><em class="sig-param">cs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.ch_cs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.ch_cs" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">ch_cs</code><span class="sig-paren">(</span><em class="sig-param">cs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.ch_cs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.ch_cs" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Transform this vector from its defined coordinate system to a
|
<dd><p>Transform this vector from its defined coordinate system to a
|
||||||
new coordinate system, defined by the given coordinate system (u,
|
new coordinate system, defined by the given coordinate system (u,
|
||||||
v and w direction vectors).</p>
|
v and w direction vectors).</p>
|
||||||
@@ -383,16 +385,16 @@ v and w direction vectors).</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.conjugate">
|
<dt id="pylib.mathematics.vector.conjugate">
|
||||||
<em class="property">static </em><code class="sig-name descname">conjugate</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.conjugate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.conjugate" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">conjugate</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.conjugate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.conjugate" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>New vector object</p>
|
<dd><p>New vector object</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
</dl>
|
</dl>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.cross">
|
<dt id="pylib.mathematics.vector.cross">
|
||||||
<em class="property">static </em><code class="sig-name descname">cross</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">b</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.cross"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.cross" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">cross</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">b</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.cross"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.cross" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Cross product</p>
|
<dd><p>Cross product</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
</dl>
|
</dl>
|
||||||
@@ -403,8 +405,8 @@ The direction of c can be found with the right-hand rule.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.full">
|
<dt id="pylib.mathematics.vector.full">
|
||||||
<em class="property">static </em><code class="sig-name descname">full</code><span class="sig-paren">(</span><em class="sig-param">length</em>, <em class="sig-param">fill_value</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.full"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.full" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">full</code><span class="sig-paren">(</span><em class="sig-param">length</em>, <em class="sig-param">fill_value</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.full"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.full" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Returns a vector of length m or matrix of size m rows, n
|
<dd><p>Returns a vector of length m or matrix of size m rows, n
|
||||||
columns filled with v.</p>
|
columns filled with v.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
@@ -428,16 +430,16 @@ columns filled with v.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.im">
|
<dt id="pylib.mathematics.vector.im">
|
||||||
<em class="property">static </em><code class="sig-name descname">im</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.im"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.im" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">im</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.im"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.im" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Return the imaginary parts of a complex vector</p>
|
<dd><p>Return the imaginary parts of a complex vector</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
</dl>
|
</dl>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.normalize">
|
<dt id="pylib.mathematics.vector.normalize">
|
||||||
<em class="property">static </em><code class="sig-name descname">normalize</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.normalize"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.normalize" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">normalize</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.normalize"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.normalize" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Normalize a vector (i. e. the vector has a length of 1)</p>
|
<dd><p>Normalize a vector (i. e. the vector has a length of 1)</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
</dl>
|
</dl>
|
||||||
@@ -450,8 +452,8 @@ columns filled with v.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.ones">
|
<dt id="pylib.mathematics.vector.ones">
|
||||||
<em class="property">static </em><code class="sig-name descname">ones</code><span class="sig-paren">(</span><em class="sig-param">length</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.ones"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.ones" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">ones</code><span class="sig-paren">(</span><em class="sig-param">length</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.ones"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.ones" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Returns a vector of length m or matrix of size rows, n
|
<dd><p>Returns a vector of length m or matrix of size rows, n
|
||||||
columns filled with ones.</p>
|
columns filled with ones.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
@@ -469,8 +471,8 @@ columns filled with ones.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.random">
|
<dt id="pylib.mathematics.vector.random">
|
||||||
<em class="property">static </em><code class="sig-name descname">random</code><span class="sig-paren">(</span><em class="sig-param">shape</em>, <em class="sig-param">lmin=0.0</em>, <em class="sig-param">lmax=1.0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.random"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.random" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">random</code><span class="sig-paren">(</span><em class="sig-param">shape</em>, <em class="sig-param">lmin=0.0</em>, <em class="sig-param">lmax=1.0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.random"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.random" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Returns a random vector of length n or matrix of size m rows, n
|
<dd><p>Returns a random vector of length n or matrix of size m rows, n
|
||||||
columns filled with random numbers.</p>
|
columns filled with random numbers.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
@@ -488,16 +490,16 @@ columns filled with random numbers.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.re">
|
<dt id="pylib.mathematics.vector.re">
|
||||||
<em class="property">static </em><code class="sig-name descname">re</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.re"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.re" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">re</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.re"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.re" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Return the real parts of a complex vector</p>
|
<dd><p>Return the real parts of a complex vector</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
</dl>
|
</dl>
|
||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.rotate_x">
|
<dt id="pylib.mathematics.vector.rotate_x">
|
||||||
<code class="sig-name descname">rotate_x</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.rotate_x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.rotate_x" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">rotate_x</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.rotate_x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.rotate_x" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotation about the x dirction.</p>
|
<dd><p>Rotation about the x dirction.</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
|
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
|
||||||
@@ -511,8 +513,8 @@ columns filled with random numbers.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.rotate_y">
|
<dt id="pylib.mathematics.vector.rotate_y">
|
||||||
<code class="sig-name descname">rotate_y</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.rotate_y"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.rotate_y" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">rotate_y</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.rotate_y"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.rotate_y" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotation about the y dirction.</p>
|
<dd><p>Rotation about the y dirction.</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
|
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
|
||||||
@@ -526,8 +528,8 @@ columns filled with random numbers.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.rotate_z">
|
<dt id="pylib.mathematics.vector.rotate_z">
|
||||||
<code class="sig-name descname">rotate_z</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.rotate_z"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.rotate_z" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">rotate_z</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.rotate_z"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.rotate_z" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Rotation about the z dirction.</p>
|
<dd><p>Rotation about the z dirction.</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
|
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
|
||||||
@@ -541,8 +543,8 @@ columns filled with random numbers.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.scale">
|
<dt id="pylib.mathematics.vector.scale">
|
||||||
<code class="sig-name descname">scale</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.scale" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">scale</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.scale" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Scaling</p>
|
<dd><p>Scaling</p>
|
||||||
<p>uniform scaling if sx=sy=sz=s.
|
<p>uniform scaling if sx=sy=sz=s.
|
||||||
Note that scaling happens around the origin, so objects not
|
Note that scaling happens around the origin, so objects not
|
||||||
@@ -562,8 +564,8 @@ it should be.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.translate">
|
<dt id="pylib.mathematics.vector.translate">
|
||||||
<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.translate" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.translate" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Translation</p>
|
<dd><p>Translation</p>
|
||||||
<div class="math notranslate nohighlight">
|
<div class="math notranslate nohighlight">
|
||||||
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
|
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
|
||||||
@@ -577,13 +579,13 @@ it should be.</p>
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.xyz">
|
<dt id="pylib.mathematics.vector.xyz">
|
||||||
<code class="sig-name descname">xyz</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.xyz"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.xyz" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">xyz</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.xyz"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.xyz" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd></dd></dl>
|
<dd></dd></dl>
|
||||||
|
|
||||||
<dl class="method">
|
<dl class="method">
|
||||||
<dt id="mathematics.vector.zeros">
|
<dt id="pylib.mathematics.vector.zeros">
|
||||||
<em class="property">static </em><code class="sig-name descname">zeros</code><span class="sig-paren">(</span><em class="sig-param">length</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.zeros"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.zeros" title="Permalink to this definition">¶</a></dt>
|
<em class="property">static </em><code class="sig-name descname">zeros</code><span class="sig-paren">(</span><em class="sig-param">length</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/mathematics.html#vector.zeros"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.mathematics.vector.zeros" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Returns a zero vector of length m or matrix of size rows, n
|
<dd><p>Returns a zero vector of length m or matrix of size rows, n
|
||||||
columns filled with zeros.</p>
|
columns filled with zeros.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
@@ -621,11 +623,24 @@ columns filled with zeros.</p>
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul class="current">
|
||||||
|
<li class="toctree-l1 current"><a class="reference internal" href="modules.html">pylib</a><ul class="current">
|
||||||
|
<li class="toctree-l2 current"><a class="reference internal" href="pylib.html">pylib package</a></li>
|
||||||
|
</ul>
|
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|
</li>
|
||||||
|
</ul>
|
||||||
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|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
<ul>
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<ul>
|
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<li><a href="index.html">Documentation overview</a><ul>
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<li><a href="index.html">Documentation overview</a><ul>
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<li><a href="modules.html">pylib</a><ul>
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<li><a href="pylib.html">pylib package</a><ul>
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<li>Previous: <a href="pylib.geometry2d_plot.html" title="previous chapter">pylib.geometry2d_plot module</a></li>
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<li>Next: <a href="pylib.time_of_day.html" title="next chapter">pylib.time_of_day module</a></li>
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|
</ul></li>
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|
||||||
</ul></li>
|
</ul></li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
@@ -659,7 +674,7 @@ columns filled with zeros.</p>
|
|||||||
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
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||||||
|
|
||||||
|
|
|
|
||||||
<a href="_sources/mathematics.rst.txt"
|
<a href="_sources/pylib.mathematics.rst.txt"
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rel="nofollow">Page source</a>
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rel="nofollow">Page source</a>
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</div>
|
</div>
|
||||||
|
|
||||||
189
docs/build/html/pylib.numerical.fit.html
vendored
Normal file
189
docs/build/html/pylib.numerical.fit.html
vendored
Normal file
@@ -0,0 +1,189 @@
|
|||||||
|
|
||||||
|
<!DOCTYPE html>
|
||||||
|
|
||||||
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
|
<head>
|
||||||
|
<meta charset="utf-8" />
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|
<title>pylib.numerical.fit module — pylib 2019.12.21 documentation</title>
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<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
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<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
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<div class="document">
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<div class="documentwrapper">
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<div class="bodywrapper">
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<div class="body" role="main">
|
||||||
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|
||||||
|
<div class="section" id="module-pylib.numerical.fit">
|
||||||
|
<span id="pylib-numerical-fit-module"></span><h1>pylib.numerical.fit module<a class="headerlink" href="#module-pylib.numerical.fit" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>Function and approximation.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Date</dt>
|
||||||
|
<dd class="field-odd"><p>2019-10-15</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
<span class="target" id="module-fit"></span><dl class="function">
|
||||||
|
<dt id="pylib.numerical.fit.gauss">
|
||||||
|
<code class="sig-name descname">gauss</code><span class="sig-paren">(</span><em class="sig-param">x</em>, <em class="sig-param">*p</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/fit.html#gauss"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.fit.gauss" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Gauss distribution function.</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[f(x)=ae^{-(x-b)^{2}/(2c^{2})}\]</div>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>x</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – positions where the gauss function will be calculated</p></li>
|
||||||
|
<li><p><strong>p</strong> (<em>list</em>) – <p>gauss parameters [a, b, c, d]:</p>
|
||||||
|
<ul>
|
||||||
|
<li><p>a – amplitude (<span class="math notranslate nohighlight">\(\int y \,\mathrm{d}x=1 \Leftrightarrow a=1/(c\sqrt{2\pi})\)</span> )</p></li>
|
||||||
|
<li><p>b – expected value <span class="math notranslate nohighlight">\(\mu\)</span> (position of maximum, default = 0)</p></li>
|
||||||
|
<li><p>c – standard deviation <span class="math notranslate nohighlight">\(\sigma\)</span> (variance <span class="math notranslate nohighlight">\(\sigma^2=c^2\)</span>)</p></li>
|
||||||
|
<li><p>d – vertical offset (default = 0)</p></li>
|
||||||
|
</ul>
|
||||||
|
</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
<dt class="field-even">Returns</dt>
|
||||||
|
<dd class="field-even"><p>gauss values at given positions x</p>
|
||||||
|
</dd>
|
||||||
|
<dt class="field-odd">Return type</dt>
|
||||||
|
<dd class="field-odd"><p>numpy.ndarray</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="function">
|
||||||
|
<dt id="pylib.numerical.fit.gauss_fit">
|
||||||
|
<code class="sig-name descname">gauss_fit</code><span class="sig-paren">(</span><em class="sig-param">x</em>, <em class="sig-param">y</em>, <em class="sig-param">e=None</em>, <em class="sig-param">x_fit=None</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/fit.html#gauss_fit"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.fit.gauss_fit" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Fit Gauss distribution function to data.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>x</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – positions</p></li>
|
||||||
|
<li><p><strong>y</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – values</p></li>
|
||||||
|
<li><p><strong>e</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – error values (default = None)</p></li>
|
||||||
|
<li><p><strong>x_fit</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – positions of fitted function (default = None, if None then x
|
||||||
|
is used)</p></li>
|
||||||
|
<li><p><strong>verbose</strong> (<em>bool</em>) – verbose information (default = False)</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
<dt class="field-even">Returns</dt>
|
||||||
|
<dd class="field-even"><p><ul class="simple">
|
||||||
|
<li><p>numpy.ndarray – fitted values (y_fit)</p></li>
|
||||||
|
<li><p>numpy.ndarray – parameters of gauss distribution function (popt:
|
||||||
|
amplitude a, expected value <span class="math notranslate nohighlight">\(\mu\)</span>, standard deviation
|
||||||
|
<span class="math notranslate nohighlight">\(\sigma\)</span>, vertical offset d)</p></li>
|
||||||
|
<li><p>numpy.float64 – full width at half maximum (FWHM)</p></li>
|
||||||
|
</ul>
|
||||||
|
</p>
|
||||||
|
</dd>
|
||||||
|
<dt class="field-odd">Return type</dt>
|
||||||
|
<dd class="field-odd"><p>tuple</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
<div class="admonition seealso">
|
||||||
|
<p class="admonition-title">See also</p>
|
||||||
|
<p><a class="reference internal" href="#pylib.numerical.fit.gauss" title="pylib.numerical.fit.gauss"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gauss()</span></code></a></p>
|
||||||
|
</div>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
|
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507
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<title>pylib.numerical package — pylib 2019.5.19 documentation</title>
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<title>pylib.numerical package — pylib 2019.12.21 documentation</title>
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<div class="body" role="main">
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<div class="section" id="pylib-numerical-package">
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<h1>pylib.numerical package<a class="headerlink" href="#pylib-numerical-package" title="Permalink to this headline">¶</a></h1>
|
<span id="pylib-numerical-package"></span><h1>pylib.numerical package<a class="headerlink" href="#module-pylib.numerical" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="submodules">
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<div class="section" id="submodules">
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<h2>Submodules<a class="headerlink" href="#submodules" title="Permalink to this headline">¶</a></h2>
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<h2>Submodules<a class="headerlink" href="#submodules" title="Permalink to this headline">¶</a></h2>
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</div>
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<div class="section" id="module-pylib.numerical.fit">
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<span id="pylib-numerical-fit-module"></span><h2>pylib.numerical.fit module<a class="headerlink" href="#module-pylib.numerical.fit" title="Permalink to this headline">¶</a></h2>
|
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||||||
<p>Function and approximation.</p>
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||||||
<dl class="field-list simple">
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||||||
<dt class="field-odd">Date</dt>
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||||||
<dd class="field-odd"><p>2019-10-15</p>
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||||||
</dd>
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||||||
</dl>
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<span class="target" id="module-fit"></span><dl class="function">
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||||||
<dt id="pylib.numerical.fit.gauss">
|
|
||||||
<code class="sig-name descname">gauss</code><span class="sig-paren">(</span><em class="sig-param">x</em>, <em class="sig-param">*p</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/fit.html#gauss"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.fit.gauss" title="Permalink to this definition">¶</a></dt>
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||||||
<dd><p>Gauss distribution function.</p>
|
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||||||
<div class="math notranslate nohighlight">
|
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||||||
\[f(x)=ae^{-(x-b)^{2}/(2c^{2})}\]</div>
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||||||
<dl class="field-list simple">
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||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
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||||||
<li><p><strong>x</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – positions where the gauss function will be calculated</p></li>
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||||||
<li><p><strong>p</strong> (<em>list</em>) – <p>gauss parameters [a, b, c, d]:</p>
|
|
||||||
<ul>
|
<ul>
|
||||||
<li><p>a – amplitude (<span class="math notranslate nohighlight">\(\int y \,\mathrm{d}x=1 \Leftrightarrow a=1/(c\sqrt{2\pi})\)</span> )</p></li>
|
<li class="toctree-l1"><a class="reference internal" href="pylib.numerical.fit.html">pylib.numerical.fit module</a></li>
|
||||||
<li><p>b – expected value <span class="math notranslate nohighlight">\(\mu\)</span> (position of maximum, default = 0)</p></li>
|
<li class="toctree-l1"><a class="reference internal" href="pylib.numerical.integration.html">pylib.numerical.integration module</a></li>
|
||||||
<li><p>c – standard deviation <span class="math notranslate nohighlight">\(\sigma\)</span> (variance <span class="math notranslate nohighlight">\(\sigma^2=c^2\)</span>)</p></li>
|
<li class="toctree-l1"><a class="reference internal" href="pylib.numerical.ode.html">pylib.numerical.ode module</a></li>
|
||||||
<li><p>d – vertical offset (default = 0)</p></li>
|
<li class="toctree-l1"><a class="reference internal" href="pylib.numerical.ode_model.html">pylib.numerical.ode_model module</a></li>
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</ul>
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</p></li>
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</ul>
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</dd>
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|
||||||
<dt class="field-even">Returns</dt>
|
|
||||||
<dd class="field-even"><p>gauss values at given positions x</p>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-odd">Return type</dt>
|
|
||||||
<dd class="field-odd"><p>numpy.ndarray</p>
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</dd>
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</dl>
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||||||
</dd></dl>
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||||||
<dl class="function">
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||||||
<dt id="pylib.numerical.fit.gauss_fit">
|
|
||||||
<code class="sig-name descname">gauss_fit</code><span class="sig-paren">(</span><em class="sig-param">x</em>, <em class="sig-param">y</em>, <em class="sig-param">e=None</em>, <em class="sig-param">x_fit=None</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/fit.html#gauss_fit"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.fit.gauss_fit" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Fit Gauss distribution function to data.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>x</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – positions</p></li>
|
|
||||||
<li><p><strong>y</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – values</p></li>
|
|
||||||
<li><p><strong>e</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – error values (default = None)</p></li>
|
|
||||||
<li><p><strong>x_fit</strong> (<em>int</em><em> or </em><em>float</em><em> or </em><em>list</em><em> or </em><em>numpy.ndarray</em>) – positions of fitted function (default = None, if None then x
|
|
||||||
is used)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – verbose information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-even">Returns</dt>
|
|
||||||
<dd class="field-even"><p><ul class="simple">
|
|
||||||
<li><p>numpy.ndarray – fitted values (y_fit)</p></li>
|
|
||||||
<li><p>numpy.ndarray – parameters of gauss distribution function (popt:
|
|
||||||
amplitude a, expected value <span class="math notranslate nohighlight">\(\mu\)</span>, standard deviation
|
|
||||||
<span class="math notranslate nohighlight">\(\sigma\)</span>, vertical offset d)</p></li>
|
|
||||||
<li><p>numpy.float64 – full width at half maximum (FWHM)</p></li>
|
|
||||||
</ul>
|
|
||||||
</p>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-odd">Return type</dt>
|
|
||||||
<dd class="field-odd"><p>tuple</p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<div class="admonition seealso">
|
|
||||||
<p class="admonition-title">See also</p>
|
|
||||||
<p><a class="reference internal" href="#pylib.numerical.fit.gauss" title="pylib.numerical.fit.gauss"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gauss()</span></code></a></p>
|
|
||||||
</div>
|
</div>
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
<div class="section" id="module-pylib.numerical.integration">
|
|
||||||
<span id="pylib-numerical-integration-module"></span><h2>pylib.numerical.integration module<a class="headerlink" href="#module-pylib.numerical.integration" title="Permalink to this headline">¶</a></h2>
|
|
||||||
<p>Numerical integration, numerical quadrature.</p>
|
|
||||||
<p>de: numerische Integration, numerische Quadratur.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Date</dt>
|
|
||||||
<dd class="field-odd"><p>2015-10-15</p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<span class="target" id="module-integration"></span><dl class="function">
|
|
||||||
<dt id="pylib.numerical.integration.trapez">
|
|
||||||
<code class="sig-name descname">trapez</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">a=0</em>, <em class="sig-param">b=1</em>, <em class="sig-param">N=10</em>, <em class="sig-param">x=None</em>, <em class="sig-param">verbose=False</em>, <em class="sig-param">save_values=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/integration.html#trapez"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.integration.trapez" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Integration of <span class="math notranslate nohighlight">\(f(x)\)</span> using the trapezoidal rule
|
|
||||||
(Simpson’s rule, Kepler’s rule).</p>
|
|
||||||
<p>de: Trapezregel, Simpsonregel (Thomas Simpson), Keplersche
|
|
||||||
Fassregel (Johannes Kepler)</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em><em> or </em><em>list</em>) – function to integrate.</p></li>
|
|
||||||
<li><p><strong>a</strong> (<em>float</em>) – lower limit of integration (default = 0).</p></li>
|
|
||||||
<li><p><strong>b</strong> (<em>float</em>) – upper limit of integration (default = 1).</p></li>
|
|
||||||
<li><p><strong>N</strong> (<em>int</em>) – specify the number of subintervals.</p></li>
|
|
||||||
<li><p><strong>x</strong> (<em>list</em>) – variable of integration, necessary if f is a list
|
|
||||||
(default = None).</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-even">Returns</dt>
|
|
||||||
<dd class="field-even"><p>the definite integral as approximated by trapezoidal
|
|
||||||
rule.</p>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-odd">Return type</dt>
|
|
||||||
<dd class="field-odd"><p>float</p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<p>The trapezoidal rule approximates the integral by the area of a
|
|
||||||
trapezoid with base h=b-a and sides equal to the values of the
|
|
||||||
integrand at the two end points.</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[f_n(x) = f(a)+\frac{f(b)-f(a)}{b-a}(x-a)\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}I &= \int\limits_a^b f(x) \,\mathrm{d}x \\
|
|
||||||
I &\approx \int\limits_a^b f_n(x) \,\mathrm{d}x \\
|
|
||||||
&= \int\limits_a^b
|
|
||||||
\left( f(a)+\frac{f(b)-f(a)}{b-a}(x-a) \right)
|
|
||||||
\mathrm{d}x \\
|
|
||||||
&= \left.\left( f(a)-a\frac{f(b)-f(a)}{b-a} \right)
|
|
||||||
x \right\vert_a^b +
|
|
||||||
\left. \frac{f(b)-f(a)}{b-a} \frac{x^2}{2}
|
|
||||||
\right\vert_a^b \\
|
|
||||||
&= \frac{b-a}{2}\left[f(a)+f(b)\right]\end{split}\]</div>
|
|
||||||
<p>The composite trapezium rule. If the interval is divided into n
|
|
||||||
segments (not necessarily equal)</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[a = x_0 \leq x_1 \leq x_2 \leq \ldots \leq x_n = b\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}I &\approx \sum\limits_{i=0}^{n-1} \frac{1}{2} (x_{i+1}-x_i)
|
|
||||||
\left[f(x_{i+1})+f(x_i)\right] \\\end{split}\]</div>
|
|
||||||
<p>Special Case (Equaliy spaced base points)</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[x_{i+1}-x_i = h \quad \forall i\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[I \approx h \left\{ \frac{1}{2} \left[f(x_0)+f(x_n)\right] +
|
|
||||||
\sum\limits_{i=1}^{n-1} f(x_i) \right\}\]</div>
|
|
||||||
<p class="rubric">Example</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}I &= \int\limits_a^b f(x) \,\mathrm{d}x \\
|
|
||||||
f(x) &= x^2 \\
|
|
||||||
a &= 0 \\
|
|
||||||
b &= 1\end{split}\]</div>
|
|
||||||
<p>analytical solution</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[I = \int\limits_{0}^{1} x^2 \,\mathrm{d}x
|
|
||||||
= \left. \frac{1}{3} x^3 \right\vert_0^1
|
|
||||||
= \frac{1}{3}\]</div>
|
|
||||||
<p>numerical solution</p>
|
|
||||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">f</span> <span class="o">=</span> <span class="k">lambda</span><span class="p">(</span><span class="n">x</span><span class="p">):</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span>
|
|
||||||
<span class="gp">>>> </span><span class="n">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
|
||||||
<span class="go">0.5</span>
|
|
||||||
<span class="gp">>>> </span><span class="n">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
|
|
||||||
<span class="go">0.3350000000000001</span>
|
|
||||||
<span class="gp">>>> </span><span class="n">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
|
|
||||||
<span class="go">0.33335000000000004</span>
|
|
||||||
</pre></div>
|
|
||||||
</div>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
<div class="section" id="module-pylib.numerical.ode">
|
|
||||||
<span id="pylib-numerical-ode-module"></span><h2>pylib.numerical.ode module<a class="headerlink" href="#module-pylib.numerical.ode" title="Permalink to this headline">¶</a></h2>
|
|
||||||
<p>Numerical solver of ordinary differential equations.</p>
|
|
||||||
<p>Solves the initial value problem for systems of first order
|
|
||||||
ordinary differential equations.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Date</dt>
|
|
||||||
<dd class="field-odd"><p>2015-09-21</p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<span class="target" id="module-ode"></span><dl class="function">
|
|
||||||
<dt id="pylib.numerical.ode.e1">
|
|
||||||
<code class="sig-name descname">e1</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#e1"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.e1" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Explicit first-order method /
|
|
||||||
(standard, or forward) Euler method /
|
|
||||||
Runge-Kutta 1st order method.</p>
|
|
||||||
<p>de:
|
|
||||||
Euler’sche Polygonzugverfahren / explizite Euler-Verfahren /
|
|
||||||
Euler-Cauchy-Verfahren / Euler-vorwärts-Verfahren</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<p>Approximate the solution of the initial value problem</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}\dot{x} &= f(t,x) \\
|
|
||||||
x(t_0) &= x_0\end{split}\]</div>
|
|
||||||
<p>Choose a value h for the size of every step and set</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[t_i = t_0 + i h ~,\quad i=1,2,\ldots,n\]</div>
|
|
||||||
<p>The derivative of the solution is approximated as the forward
|
|
||||||
difference equation</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\dot{x}_i = f(t_i, x_i) = \frac{x_{i+1} - x_i}{t_{i+1}-t_i}\]</div>
|
|
||||||
<p>Therefore one step <span class="math notranslate nohighlight">\(h\)</span> of the Euler method from
|
|
||||||
<span class="math notranslate nohighlight">\(t_i\)</span> to <span class="math notranslate nohighlight">\(t_{i+1}\)</span> is</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}x_{i+1} &= x_i + (t_{i+1}-t_i) f(t_i, x_i) \\
|
|
||||||
x_{i+1} &= x_i + h f(t_i, x_i) \\\end{split}\]</div>
|
|
||||||
<p>Example 1:</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}m\ddot{u} + d\dot{u} + ku = f(t) \\
|
|
||||||
\ddot{u} = m^{-1}(f(t) - d\dot{u} - ku) \\\end{split}\]</div>
|
|
||||||
<p>with</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}x_1 &= u &\quad \dot{x}_1 = \dot{u} = x_2 \\
|
|
||||||
x_2 &= \dot{u} &\quad \dot{x}_2 = \ddot{u} \\\end{split}\]</div>
|
|
||||||
<p>becomes</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}\dot{x}_1 &= x_2 \\
|
|
||||||
\dot{x}_2 &= m^{-1}(f(t) - d x_2 - k x_1) \\\end{split}\]</div>
|
|
||||||
<p>or</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}\dot{x} &= f(t,x) \\
|
|
||||||
\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} &=
|
|
||||||
\begin{bmatrix} x_2 \\ m^{-1}(f(t) - d x_2 - k x_1)
|
|
||||||
\end{bmatrix} \\
|
|
||||||
&=
|
|
||||||
\begin{bmatrix} 0 \\ m^{-1} f(t) \end{bmatrix} +
|
|
||||||
\begin{bmatrix} 0 & 1 \\ -m^{-1} k & -m^{-1} d \end{bmatrix}
|
|
||||||
\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\end{split}\]</div>
|
|
||||||
<p>Example 2:</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}m(u)\ddot{u} + d(u,\dot{u})\dot{u} + k(u)u = f(t) \\
|
|
||||||
\ddot{u} = m^{-1}(u)(f(t) - d(u,\dot{u})\dot{u} - k(u)u) \\\end{split}\]</div>
|
|
||||||
<p>with</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}x_1 &= u &\quad \dot{x}_1 = \dot{u} = x_2 \\
|
|
||||||
x_2 &= \dot{u} &\quad \dot{x}_2 = \ddot{u} \\\end{split}\]</div>
|
|
||||||
<p>becomes</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}\dot{x}_1 &= x_2 \\
|
|
||||||
\dot{x}_2 &=
|
|
||||||
m^{-1}(x_1)(f(t) - d(x_1,x_2) x_2 - k(x_1) x_1) \\\end{split}\]</div>
|
|
||||||
<p>or</p>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\begin{split}\dot{x} &= f(t,x) \\
|
|
||||||
\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} &=
|
|
||||||
\begin{bmatrix}
|
|
||||||
x_2 \\ m^{-1}(x_1)(f(t) - d(x_1,x_2) x_2 - k(x_1) x_1)
|
|
||||||
\end{bmatrix} \\
|
|
||||||
&=
|
|
||||||
\begin{bmatrix} 0 \\ m^{-1}(x_1) f(t) \end{bmatrix} +
|
|
||||||
\begin{bmatrix}
|
|
||||||
0 & 1 \\ -m^{-1}(x_1) k(x_1) & -m^{-1} d(x_1,x_2)
|
|
||||||
\end{bmatrix}
|
|
||||||
\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\end{split}\]</div>
|
|
||||||
<p>The Euler method is a first-order method, which means that the
|
|
||||||
local error (error per step) is proportional to the square of
|
|
||||||
the step size, and the global error (error at a given time) is
|
|
||||||
proportional to the step size.</p>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="pylib.numerical.ode.e2">
|
|
||||||
<code class="sig-name descname">e2</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#e2"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.e2" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Explicit second-order method / Runge-Kutta 2nd order method.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="pylib.numerical.ode.e4">
|
|
||||||
<code class="sig-name descname">e4</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#e4"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.e4" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Explicit fourth-order method / Runge-Kutta 4th order method.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="pylib.numerical.ode.fpi">
|
|
||||||
<code class="sig-name descname">fpi</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">xi</em>, <em class="sig-param">ti</em>, <em class="sig-param">ti1</em>, <em class="sig-param">*p</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#fpi"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.fpi" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Fixed-point iteration.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to iterate <span class="math notranslate nohighlight">\(f = \dot{x}(x,t)\)</span></p></li>
|
|
||||||
<li><p><strong>xi</strong> (<em>list</em>) – initial condition <span class="math notranslate nohighlight">\(x_i\)</span></p></li>
|
|
||||||
<li><p><strong>ti</strong> (<em>float</em>) – time <span class="math notranslate nohighlight">\(t_i\)</span></p></li>
|
|
||||||
<li><p><strong>ti1</strong> (<em>float</em>) – time <span class="math notranslate nohighlight">\(t_{i+1}\)</span></p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
|
||||||
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum <span class="math notranslate nohighlight">\(\varepsilon\)</span>
|
|
||||||
(default = 1e-9)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
<dt class="field-even">Returns</dt>
|
|
||||||
<dd class="field-even"><p><span class="math notranslate nohighlight">\(x_{i}\)</span></p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[x_{i,j=0} = x_{i}\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[x_{i,j+1} = x_i + \dot{x}(x_{i,j}, t_{i+1})\cdot(t_{i+1}-t_i)\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[\text{residuum} = \frac{\lVert x_{i,j+1}-x_{i,j}\rVert}
|
|
||||||
{\lVert x_{i,j+1} \rVert} < \varepsilon\]</div>
|
|
||||||
<div class="math notranslate nohighlight">
|
|
||||||
\[x_{i} = x_{i,j=\text{end}}\]</div>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="pylib.numerical.ode.i1">
|
|
||||||
<code class="sig-name descname">i1</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#i1"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.i1" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Implicite first-order method / backward Euler method.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
|
||||||
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum (default = 1e-9)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<p>The backward Euler method has order one and is A-stable.</p>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="pylib.numerical.ode.newmark_newtonraphson">
|
|
||||||
<code class="sig-name descname">newmark_newtonraphson</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">xp0</em>, <em class="sig-param">xpp0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">gamma=0.5</em>, <em class="sig-param">beta=0.25</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#newmark_newtonraphson"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.newmark_newtonraphson" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Newmark method.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>xp0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>xpp0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>gamma</strong> (<em>float</em>) – newmark parameter for velocity (default = 0.5)</p></li>
|
|
||||||
<li><p><strong>beta</strong> (<em>float</em>) – newmark parameter for displacement (default = 0.25)</p></li>
|
|
||||||
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
|
||||||
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum (default = 1e-9)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="pylib.numerical.ode.newmark_newtonraphson_rdk">
|
|
||||||
<code class="sig-name descname">newmark_newtonraphson_rdk</code><span class="sig-paren">(</span><em class="sig-param">fnm</em>, <em class="sig-param">x0</em>, <em class="sig-param">xp0</em>, <em class="sig-param">xpp0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">gamma=0.5</em>, <em class="sig-param">beta=0.25</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#newmark_newtonraphson_rdk"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.newmark_newtonraphson_rdk" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Newmark method.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
|
||||||
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>xp0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>xpp0</strong> (<em>list</em>) – initial condition</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
|
||||||
…)</p></li>
|
|
||||||
<li><p><strong>gamma</strong> (<em>float</em>) – newmark parameter for velocity (default = 0.5)</p></li>
|
|
||||||
<li><p><strong>beta</strong> (<em>float</em>) – newmark parameter for displacement (default = 0.25)</p></li>
|
|
||||||
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
|
||||||
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum (default = 1e-9)</p></li>
|
|
||||||
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
<div class="section" id="module-pylib.numerical.ode_model">
|
|
||||||
<span id="pylib-numerical-ode-model-module"></span><h2>pylib.numerical.ode_model module<a class="headerlink" href="#module-pylib.numerical.ode_model" title="Permalink to this headline">¶</a></h2>
|
|
||||||
<p>Mathmatical models governed by ordinary differential equations.</p>
|
|
||||||
<p>Describes initial value problems as systems of first order ordinary differential
|
|
||||||
equations.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Date</dt>
|
|
||||||
<dd class="field-odd"><p>2019-05-25</p>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
<span class="target" id="module-ode_model"></span><dl class="function">
|
|
||||||
<dt id="pylib.numerical.ode_model.disk">
|
|
||||||
<code class="sig-name descname">disk</code><span class="sig-paren">(</span><em class="sig-param">x</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode_model.html#disk"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode_model.disk" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Rotation of an eccentric disk.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>x</strong> (<em>list</em>) – values of the function</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – <p>parameters of the function</p>
|
|
||||||
<ul>
|
|
||||||
<li><p>diameter</p></li>
|
|
||||||
<li><p>eccentricity</p></li>
|
|
||||||
<li><p>torque</p></li>
|
|
||||||
</ul>
|
|
||||||
</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="pylib.numerical.ode_model.disk_nm">
|
|
||||||
<code class="sig-name descname">disk_nm</code><span class="sig-paren">(</span><em class="sig-param">xn</em>, <em class="sig-param">xpn</em>, <em class="sig-param">xppn</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode_model.html#disk_nm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode_model.disk_nm" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Rotation of an eccentric disk.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>xn</strong> (<em>list</em>) – values of the function</p></li>
|
|
||||||
<li><p><strong>xpn</strong> (<em>list</em>) – first derivative values of the function</p></li>
|
|
||||||
<li><p><strong>xppn</strong> (<em>list</em>) – second derivative values of the function</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – <p>parameters of the function</p>
|
|
||||||
<ul>
|
|
||||||
<li><p>diameter</p></li>
|
|
||||||
<li><p>eccentricity</p></li>
|
|
||||||
<li><p>torque</p></li>
|
|
||||||
</ul>
|
|
||||||
</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
<dl class="function">
|
|
||||||
<dt id="pylib.numerical.ode_model.disk_nmmdk">
|
|
||||||
<code class="sig-name descname">disk_nmmdk</code><span class="sig-paren">(</span><em class="sig-param">xn</em>, <em class="sig-param">xpn</em>, <em class="sig-param">xppn</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode_model.html#disk_nmmdk"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode_model.disk_nmmdk" title="Permalink to this definition">¶</a></dt>
|
|
||||||
<dd><p>Rotation of an eccentric disk.</p>
|
|
||||||
<dl class="field-list simple">
|
|
||||||
<dt class="field-odd">Parameters</dt>
|
|
||||||
<dd class="field-odd"><ul class="simple">
|
|
||||||
<li><p><strong>xn</strong> (<em>list</em>) – values of the function</p></li>
|
|
||||||
<li><p><strong>xpn</strong> (<em>list</em>) – derivative values of the function</p></li>
|
|
||||||
<li><p><strong>xppn</strong> (<em>list</em>) – second derivative values of the function</p></li>
|
|
||||||
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
|
||||||
<li><p><strong>*p</strong> – <p>parameters of the function</p>
|
|
||||||
<ul>
|
|
||||||
<li><p>diameter</p></li>
|
|
||||||
<li><p>eccentricity</p></li>
|
|
||||||
<li><p>torque</p></li>
|
|
||||||
</ul>
|
|
||||||
</p></li>
|
|
||||||
</ul>
|
|
||||||
</dd>
|
|
||||||
</dl>
|
|
||||||
</dd></dl>
|
|
||||||
|
|
||||||
</div>
|
|
||||||
<div class="section" id="module-pylib.numerical">
|
|
||||||
<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-pylib.numerical" title="Permalink to this headline">¶</a></h2>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@@ -540,11 +66,24 @@ equations.</p>
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul class="current">
|
||||||
|
<li class="toctree-l1 current"><a class="reference internal" href="modules.html">pylib</a><ul class="current">
|
||||||
|
<li class="toctree-l2 current"><a class="reference internal" href="pylib.html">pylib package</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="index.html">Documentation overview</a><ul>
|
<li><a href="index.html">Documentation overview</a><ul>
|
||||||
|
<li><a href="modules.html">pylib</a><ul>
|
||||||
|
<li><a href="pylib.html">pylib package</a><ul>
|
||||||
|
<li>Previous: <a href="pylib.html" title="previous chapter">pylib package</a></li>
|
||||||
|
<li>Next: <a href="pylib.numerical.fit.html" title="next chapter">pylib.numerical.fit module</a></li>
|
||||||
|
</ul></li>
|
||||||
|
</ul></li>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
|
|||||||
205
docs/build/html/pylib.numerical.integration.html
vendored
Normal file
205
docs/build/html/pylib.numerical.integration.html
vendored
Normal file
@@ -0,0 +1,205 @@
|
|||||||
|
|
||||||
|
<!DOCTYPE html>
|
||||||
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<html xmlns="http://www.w3.org/1999/xhtml">
|
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<head>
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<meta charset="utf-8" />
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<title>pylib.numerical.integration module — pylib 2019.12.21 documentation</title>
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<div class="document">
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<div class="documentwrapper">
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<div class="bodywrapper">
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|
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|
<div class="body" role="main">
|
||||||
|
|
||||||
|
<div class="section" id="module-pylib.numerical.integration">
|
||||||
|
<span id="pylib-numerical-integration-module"></span><h1>pylib.numerical.integration module<a class="headerlink" href="#module-pylib.numerical.integration" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>Numerical integration, numerical quadrature.</p>
|
||||||
|
<p>de: numerische Integration, numerische Quadratur.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Date</dt>
|
||||||
|
<dd class="field-odd"><p>2015-10-15</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
<span class="target" id="module-integration"></span><dl class="function">
|
||||||
|
<dt id="pylib.numerical.integration.trapez">
|
||||||
|
<code class="sig-name descname">trapez</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">a=0</em>, <em class="sig-param">b=1</em>, <em class="sig-param">N=10</em>, <em class="sig-param">x=None</em>, <em class="sig-param">verbose=False</em>, <em class="sig-param">save_values=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/integration.html#trapez"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.integration.trapez" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Integration of <span class="math notranslate nohighlight">\(f(x)\)</span> using the trapezoidal rule
|
||||||
|
(Simpson’s rule, Kepler’s rule).</p>
|
||||||
|
<p>de: Trapezregel, Simpsonregel (Thomas Simpson), Keplersche
|
||||||
|
Fassregel (Johannes Kepler)</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>f</strong> (<em>function</em><em> or </em><em>list</em>) – function to integrate.</p></li>
|
||||||
|
<li><p><strong>a</strong> (<em>float</em>) – lower limit of integration (default = 0).</p></li>
|
||||||
|
<li><p><strong>b</strong> (<em>float</em>) – upper limit of integration (default = 1).</p></li>
|
||||||
|
<li><p><strong>N</strong> (<em>int</em>) – specify the number of subintervals.</p></li>
|
||||||
|
<li><p><strong>x</strong> (<em>list</em>) – variable of integration, necessary if f is a list
|
||||||
|
(default = None).</p></li>
|
||||||
|
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
<dt class="field-even">Returns</dt>
|
||||||
|
<dd class="field-even"><p>the definite integral as approximated by trapezoidal
|
||||||
|
rule.</p>
|
||||||
|
</dd>
|
||||||
|
<dt class="field-odd">Return type</dt>
|
||||||
|
<dd class="field-odd"><p>float</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
<p>The trapezoidal rule approximates the integral by the area of a
|
||||||
|
trapezoid with base h=b-a and sides equal to the values of the
|
||||||
|
integrand at the two end points.</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[f_n(x) = f(a)+\frac{f(b)-f(a)}{b-a}(x-a)\]</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}I &= \int\limits_a^b f(x) \,\mathrm{d}x \\
|
||||||
|
I &\approx \int\limits_a^b f_n(x) \,\mathrm{d}x \\
|
||||||
|
&= \int\limits_a^b
|
||||||
|
\left( f(a)+\frac{f(b)-f(a)}{b-a}(x-a) \right)
|
||||||
|
\mathrm{d}x \\
|
||||||
|
&= \left.\left( f(a)-a\frac{f(b)-f(a)}{b-a} \right)
|
||||||
|
x \right\vert_a^b +
|
||||||
|
\left. \frac{f(b)-f(a)}{b-a} \frac{x^2}{2}
|
||||||
|
\right\vert_a^b \\
|
||||||
|
&= \frac{b-a}{2}\left[f(a)+f(b)\right]\end{split}\]</div>
|
||||||
|
<p>The composite trapezium rule. If the interval is divided into n
|
||||||
|
segments (not necessarily equal)</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[a = x_0 \leq x_1 \leq x_2 \leq \ldots \leq x_n = b\]</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}I &\approx \sum\limits_{i=0}^{n-1} \frac{1}{2} (x_{i+1}-x_i)
|
||||||
|
\left[f(x_{i+1})+f(x_i)\right] \\\end{split}\]</div>
|
||||||
|
<p>Special Case (Equaliy spaced base points)</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[x_{i+1}-x_i = h \quad \forall i\]</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[I \approx h \left\{ \frac{1}{2} \left[f(x_0)+f(x_n)\right] +
|
||||||
|
\sum\limits_{i=1}^{n-1} f(x_i) \right\}\]</div>
|
||||||
|
<p class="rubric">Example</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}I &= \int\limits_a^b f(x) \,\mathrm{d}x \\
|
||||||
|
f(x) &= x^2 \\
|
||||||
|
a &= 0 \\
|
||||||
|
b &= 1\end{split}\]</div>
|
||||||
|
<p>analytical solution</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[I = \int\limits_{0}^{1} x^2 \,\mathrm{d}x
|
||||||
|
= \left. \frac{1}{3} x^3 \right\vert_0^1
|
||||||
|
= \frac{1}{3}\]</div>
|
||||||
|
<p>numerical solution</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">f</span> <span class="o">=</span> <span class="k">lambda</span><span class="p">(</span><span class="n">x</span><span class="p">):</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span>
|
||||||
|
<span class="gp">>>> </span><span class="n">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="go">0.5</span>
|
||||||
|
<span class="gp">>>> </span><span class="n">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
|
||||||
|
<span class="go">0.3350000000000001</span>
|
||||||
|
<span class="gp">>>> </span><span class="n">trapez</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
|
||||||
|
<span class="go">0.33335000000000004</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</dd></dl>
|
||||||
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||||||
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|
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<li>Next: <a href="pylib.numerical.ode.html" title="next chapter">pylib.numerical.ode module</a></li>
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357
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vendored
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<div class="section" id="module-pylib.numerical.ode">
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<span id="pylib-numerical-ode-module"></span><h1>pylib.numerical.ode module<a class="headerlink" href="#module-pylib.numerical.ode" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>Numerical solver of ordinary differential equations.</p>
|
||||||
|
<p>Solves the initial value problem for systems of first order
|
||||||
|
ordinary differential equations.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Date</dt>
|
||||||
|
<dd class="field-odd"><p>2015-09-21</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
<span class="target" id="module-ode"></span><dl class="function">
|
||||||
|
<dt id="pylib.numerical.ode.e1">
|
||||||
|
<code class="sig-name descname">e1</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#e1"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.e1" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Explicit first-order method /
|
||||||
|
(standard, or forward) Euler method /
|
||||||
|
Runge-Kutta 1st order method.</p>
|
||||||
|
<p>de:
|
||||||
|
Euler’sche Polygonzugverfahren / explizite Euler-Verfahren /
|
||||||
|
Euler-Cauchy-Verfahren / Euler-vorwärts-Verfahren</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
||||||
|
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
||||||
|
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
||||||
|
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
||||||
|
…)</p></li>
|
||||||
|
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
<p>Approximate the solution of the initial value problem</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}\dot{x} &= f(t,x) \\
|
||||||
|
x(t_0) &= x_0\end{split}\]</div>
|
||||||
|
<p>Choose a value h for the size of every step and set</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[t_i = t_0 + i h ~,\quad i=1,2,\ldots,n\]</div>
|
||||||
|
<p>The derivative of the solution is approximated as the forward
|
||||||
|
difference equation</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\dot{x}_i = f(t_i, x_i) = \frac{x_{i+1} - x_i}{t_{i+1}-t_i}\]</div>
|
||||||
|
<p>Therefore one step <span class="math notranslate nohighlight">\(h\)</span> of the Euler method from
|
||||||
|
<span class="math notranslate nohighlight">\(t_i\)</span> to <span class="math notranslate nohighlight">\(t_{i+1}\)</span> is</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}x_{i+1} &= x_i + (t_{i+1}-t_i) f(t_i, x_i) \\
|
||||||
|
x_{i+1} &= x_i + h f(t_i, x_i) \\\end{split}\]</div>
|
||||||
|
<p>Example 1:</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}m\ddot{u} + d\dot{u} + ku = f(t) \\
|
||||||
|
\ddot{u} = m^{-1}(f(t) - d\dot{u} - ku) \\\end{split}\]</div>
|
||||||
|
<p>with</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}x_1 &= u &\quad \dot{x}_1 = \dot{u} = x_2 \\
|
||||||
|
x_2 &= \dot{u} &\quad \dot{x}_2 = \ddot{u} \\\end{split}\]</div>
|
||||||
|
<p>becomes</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}\dot{x}_1 &= x_2 \\
|
||||||
|
\dot{x}_2 &= m^{-1}(f(t) - d x_2 - k x_1) \\\end{split}\]</div>
|
||||||
|
<p>or</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}\dot{x} &= f(t,x) \\
|
||||||
|
\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} &=
|
||||||
|
\begin{bmatrix} x_2 \\ m^{-1}(f(t) - d x_2 - k x_1)
|
||||||
|
\end{bmatrix} \\
|
||||||
|
&=
|
||||||
|
\begin{bmatrix} 0 \\ m^{-1} f(t) \end{bmatrix} +
|
||||||
|
\begin{bmatrix} 0 & 1 \\ -m^{-1} k & -m^{-1} d \end{bmatrix}
|
||||||
|
\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\end{split}\]</div>
|
||||||
|
<p>Example 2:</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}m(u)\ddot{u} + d(u,\dot{u})\dot{u} + k(u)u = f(t) \\
|
||||||
|
\ddot{u} = m^{-1}(u)(f(t) - d(u,\dot{u})\dot{u} - k(u)u) \\\end{split}\]</div>
|
||||||
|
<p>with</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}x_1 &= u &\quad \dot{x}_1 = \dot{u} = x_2 \\
|
||||||
|
x_2 &= \dot{u} &\quad \dot{x}_2 = \ddot{u} \\\end{split}\]</div>
|
||||||
|
<p>becomes</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}\dot{x}_1 &= x_2 \\
|
||||||
|
\dot{x}_2 &=
|
||||||
|
m^{-1}(x_1)(f(t) - d(x_1,x_2) x_2 - k(x_1) x_1) \\\end{split}\]</div>
|
||||||
|
<p>or</p>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\begin{split}\dot{x} &= f(t,x) \\
|
||||||
|
\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} &=
|
||||||
|
\begin{bmatrix}
|
||||||
|
x_2 \\ m^{-1}(x_1)(f(t) - d(x_1,x_2) x_2 - k(x_1) x_1)
|
||||||
|
\end{bmatrix} \\
|
||||||
|
&=
|
||||||
|
\begin{bmatrix} 0 \\ m^{-1}(x_1) f(t) \end{bmatrix} +
|
||||||
|
\begin{bmatrix}
|
||||||
|
0 & 1 \\ -m^{-1}(x_1) k(x_1) & -m^{-1} d(x_1,x_2)
|
||||||
|
\end{bmatrix}
|
||||||
|
\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\end{split}\]</div>
|
||||||
|
<p>The Euler method is a first-order method, which means that the
|
||||||
|
local error (error per step) is proportional to the square of
|
||||||
|
the step size, and the global error (error at a given time) is
|
||||||
|
proportional to the step size.</p>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="function">
|
||||||
|
<dt id="pylib.numerical.ode.e2">
|
||||||
|
<code class="sig-name descname">e2</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#e2"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.e2" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Explicit second-order method / Runge-Kutta 2nd order method.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
||||||
|
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
||||||
|
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
||||||
|
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
||||||
|
…)</p></li>
|
||||||
|
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="function">
|
||||||
|
<dt id="pylib.numerical.ode.e4">
|
||||||
|
<code class="sig-name descname">e4</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#e4"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.e4" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Explicit fourth-order method / Runge-Kutta 4th order method.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
||||||
|
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
||||||
|
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
||||||
|
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
||||||
|
…)</p></li>
|
||||||
|
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="function">
|
||||||
|
<dt id="pylib.numerical.ode.fpi">
|
||||||
|
<code class="sig-name descname">fpi</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">xi</em>, <em class="sig-param">ti</em>, <em class="sig-param">ti1</em>, <em class="sig-param">*p</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#fpi"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.fpi" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Fixed-point iteration.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>f</strong> (<em>function</em>) – the function to iterate <span class="math notranslate nohighlight">\(f = \dot{x}(x,t)\)</span></p></li>
|
||||||
|
<li><p><strong>xi</strong> (<em>list</em>) – initial condition <span class="math notranslate nohighlight">\(x_i\)</span></p></li>
|
||||||
|
<li><p><strong>ti</strong> (<em>float</em>) – time <span class="math notranslate nohighlight">\(t_i\)</span></p></li>
|
||||||
|
<li><p><strong>ti1</strong> (<em>float</em>) – time <span class="math notranslate nohighlight">\(t_{i+1}\)</span></p></li>
|
||||||
|
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
||||||
|
…)</p></li>
|
||||||
|
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
||||||
|
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum <span class="math notranslate nohighlight">\(\varepsilon\)</span>
|
||||||
|
(default = 1e-9)</p></li>
|
||||||
|
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
<dt class="field-even">Returns</dt>
|
||||||
|
<dd class="field-even"><p><span class="math notranslate nohighlight">\(x_{i}\)</span></p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[x_{i,j=0} = x_{i}\]</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[x_{i,j+1} = x_i + \dot{x}(x_{i,j}, t_{i+1})\cdot(t_{i+1}-t_i)\]</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\text{residuum} = \frac{\lVert x_{i,j+1}-x_{i,j}\rVert}
|
||||||
|
{\lVert x_{i,j+1} \rVert} < \varepsilon\]</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[x_{i} = x_{i,j=\text{end}}\]</div>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="function">
|
||||||
|
<dt id="pylib.numerical.ode.i1">
|
||||||
|
<code class="sig-name descname">i1</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#i1"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.i1" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Implicite first-order method / backward Euler method.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
||||||
|
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
||||||
|
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
||||||
|
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
||||||
|
…)</p></li>
|
||||||
|
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
||||||
|
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum (default = 1e-9)</p></li>
|
||||||
|
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
<p>The backward Euler method has order one and is A-stable.</p>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="function">
|
||||||
|
<dt id="pylib.numerical.ode.newmark_newtonraphson">
|
||||||
|
<code class="sig-name descname">newmark_newtonraphson</code><span class="sig-paren">(</span><em class="sig-param">f</em>, <em class="sig-param">x0</em>, <em class="sig-param">xp0</em>, <em class="sig-param">xpp0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">gamma=0.5</em>, <em class="sig-param">beta=0.25</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#newmark_newtonraphson"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.newmark_newtonraphson" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Newmark method.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
||||||
|
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
||||||
|
<li><p><strong>xp0</strong> (<em>list</em>) – initial condition</p></li>
|
||||||
|
<li><p><strong>xpp0</strong> (<em>list</em>) – initial condition</p></li>
|
||||||
|
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
||||||
|
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
||||||
|
…)</p></li>
|
||||||
|
<li><p><strong>gamma</strong> (<em>float</em>) – newmark parameter for velocity (default = 0.5)</p></li>
|
||||||
|
<li><p><strong>beta</strong> (<em>float</em>) – newmark parameter for displacement (default = 0.25)</p></li>
|
||||||
|
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
||||||
|
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum (default = 1e-9)</p></li>
|
||||||
|
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="function">
|
||||||
|
<dt id="pylib.numerical.ode.newmark_newtonraphson_rdk">
|
||||||
|
<code class="sig-name descname">newmark_newtonraphson_rdk</code><span class="sig-paren">(</span><em class="sig-param">fnm</em>, <em class="sig-param">x0</em>, <em class="sig-param">xp0</em>, <em class="sig-param">xpp0</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em>, <em class="sig-param">gamma=0.5</em>, <em class="sig-param">beta=0.25</em>, <em class="sig-param">max_iterations=1000</em>, <em class="sig-param">tol=1e-09</em>, <em class="sig-param">verbose=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode.html#newmark_newtonraphson_rdk"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode.newmark_newtonraphson_rdk" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Newmark method.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>f</strong> (<em>function</em>) – the function to solve</p></li>
|
||||||
|
<li><p><strong>x0</strong> (<em>list</em>) – initial condition</p></li>
|
||||||
|
<li><p><strong>xp0</strong> (<em>list</em>) – initial condition</p></li>
|
||||||
|
<li><p><strong>xpp0</strong> (<em>list</em>) – initial condition</p></li>
|
||||||
|
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
||||||
|
<li><p><strong>*p</strong> – parameters of the function (thickness, diameter,
|
||||||
|
…)</p></li>
|
||||||
|
<li><p><strong>gamma</strong> (<em>float</em>) – newmark parameter for velocity (default = 0.5)</p></li>
|
||||||
|
<li><p><strong>beta</strong> (<em>float</em>) – newmark parameter for displacement (default = 0.25)</p></li>
|
||||||
|
<li><p><strong>max_iterations</strong> (<em>int</em>) – maximum number of iterations</p></li>
|
||||||
|
<li><p><strong>tol</strong> (<em>float</em>) – tolerance against residuum (default = 1e-9)</p></li>
|
||||||
|
<li><p><strong>verbose</strong> (<em>bool</em>) – print information (default = False)</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
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|
||||||
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||||||
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<li>Next: <a href="pylib.numerical.ode_model.html" title="next chapter">pylib.numerical.ode_model module</a></li>
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194
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<div class="section" id="module-pylib.numerical.ode_model">
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<span id="pylib-numerical-ode-model-module"></span><h1>pylib.numerical.ode_model module<a class="headerlink" href="#module-pylib.numerical.ode_model" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>Mathmatical models governed by ordinary differential equations.</p>
|
||||||
|
<p>Describes initial value problems as systems of first order ordinary differential
|
||||||
|
equations.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Date</dt>
|
||||||
|
<dd class="field-odd"><p>2019-05-25</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
<span class="target" id="module-ode_model"></span><dl class="function">
|
||||||
|
<dt id="pylib.numerical.ode_model.disk">
|
||||||
|
<code class="sig-name descname">disk</code><span class="sig-paren">(</span><em class="sig-param">x</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode_model.html#disk"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode_model.disk" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Rotation of an eccentric disk.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>x</strong> (<em>list</em>) – values of the function</p></li>
|
||||||
|
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
||||||
|
<li><p><strong>*p</strong> – <p>parameters of the function</p>
|
||||||
|
<ul>
|
||||||
|
<li><p>diameter</p></li>
|
||||||
|
<li><p>eccentricity</p></li>
|
||||||
|
<li><p>torque</p></li>
|
||||||
|
</ul>
|
||||||
|
</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="function">
|
||||||
|
<dt id="pylib.numerical.ode_model.disk_nm">
|
||||||
|
<code class="sig-name descname">disk_nm</code><span class="sig-paren">(</span><em class="sig-param">xn</em>, <em class="sig-param">xpn</em>, <em class="sig-param">xppn</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode_model.html#disk_nm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode_model.disk_nm" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Rotation of an eccentric disk.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>xn</strong> (<em>list</em>) – values of the function</p></li>
|
||||||
|
<li><p><strong>xpn</strong> (<em>list</em>) – first derivative values of the function</p></li>
|
||||||
|
<li><p><strong>xppn</strong> (<em>list</em>) – second derivative values of the function</p></li>
|
||||||
|
<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
|
||||||
|
<li><p><strong>*p</strong> – <p>parameters of the function</p>
|
||||||
|
<ul>
|
||||||
|
<li><p>diameter</p></li>
|
||||||
|
<li><p>eccentricity</p></li>
|
||||||
|
<li><p>torque</p></li>
|
||||||
|
</ul>
|
||||||
|
</p></li>
|
||||||
|
</ul>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
</dd></dl>
|
||||||
|
|
||||||
|
<dl class="function">
|
||||||
|
<dt id="pylib.numerical.ode_model.disk_nmmdk">
|
||||||
|
<code class="sig-name descname">disk_nmmdk</code><span class="sig-paren">(</span><em class="sig-param">xn</em>, <em class="sig-param">xpn</em>, <em class="sig-param">xppn</em>, <em class="sig-param">t</em>, <em class="sig-param">*p</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/numerical/ode_model.html#disk_nmmdk"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.numerical.ode_model.disk_nmmdk" title="Permalink to this definition">¶</a></dt>
|
||||||
|
<dd><p>Rotation of an eccentric disk.</p>
|
||||||
|
<dl class="field-list simple">
|
||||||
|
<dt class="field-odd">Parameters</dt>
|
||||||
|
<dd class="field-odd"><ul class="simple">
|
||||||
|
<li><p><strong>xn</strong> (<em>list</em>) – values of the function</p></li>
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<li><p><strong>xpn</strong> (<em>list</em>) – derivative values of the function</p></li>
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<li><p><strong>xppn</strong> (<em>list</em>) – second derivative values of the function</p></li>
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<li><p><strong>t</strong> (<em>list</em>) – time</p></li>
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<li><p><strong>*p</strong> – <p>parameters of the function</p>
|
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<ul>
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<li><p>diameter</p></li>
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<li><p>eccentricity</p></li>
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<title>time_of_day module — pylib 2019.5.19 documentation</title>
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<title>pylib.time_of_day module — pylib 2019.12.21 documentation</title>
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<div class="body" role="main">
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<div class="section" id="module-time_of_day">
|
<div class="section" id="module-pylib.time_of_day">
|
||||||
<span id="time-of-day-module"></span><h1>time_of_day module<a class="headerlink" href="#module-time_of_day" title="Permalink to this headline">¶</a></h1>
|
<span id="pylib-time-of-day-module"></span><h1>pylib.time_of_day module<a class="headerlink" href="#module-pylib.time_of_day" title="Permalink to this headline">¶</a></h1>
|
||||||
<p>Calculate time.</p>
|
<p>Calculate time.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Date</dt>
|
<dt class="field-odd">Date</dt>
|
||||||
@@ -41,8 +42,8 @@
|
|||||||
</dd>
|
</dd>
|
||||||
</dl>
|
</dl>
|
||||||
<span class="target" id="module-time_of_day"></span><dl class="function">
|
<span class="target" id="module-time_of_day"></span><dl class="function">
|
||||||
<dt id="time_of_day.days">
|
<dt id="pylib.time_of_day.days">
|
||||||
<code class="sig-name descname">days</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/time_of_day.html#days"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#time_of_day.days" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">days</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/time_of_day.html#days"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.time_of_day.days" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>The days of the time (year).</p>
|
<dd><p>The days of the time (year).</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -58,8 +59,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="time_of_day.days_norm">
|
<dt id="pylib.time_of_day.days_norm">
|
||||||
<code class="sig-name descname">days_norm</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/time_of_day.html#days_norm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#time_of_day.days_norm" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">days_norm</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/time_of_day.html#days_norm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.time_of_day.days_norm" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>The days normalized to 365.2425 (Gregorian, on average) days.</p>
|
<dd><p>The days normalized to 365.2425 (Gregorian, on average) days.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -75,8 +76,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="time_of_day.hours">
|
<dt id="pylib.time_of_day.hours">
|
||||||
<code class="sig-name descname">hours</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/time_of_day.html#hours"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#time_of_day.hours" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">hours</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/time_of_day.html#hours"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.time_of_day.hours" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>The hours of the time.</p>
|
<dd><p>The hours of the time.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -92,8 +93,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="time_of_day.hours_norm">
|
<dt id="pylib.time_of_day.hours_norm">
|
||||||
<code class="sig-name descname">hours_norm</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/time_of_day.html#hours_norm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#time_of_day.hours_norm" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">hours_norm</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/time_of_day.html#hours_norm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.time_of_day.hours_norm" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>The hours normalized to 24 hours.</p>
|
<dd><p>The hours normalized to 24 hours.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -109,8 +110,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="time_of_day.in_seconds">
|
<dt id="pylib.time_of_day.in_seconds">
|
||||||
<code class="sig-name descname">in_seconds</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/time_of_day.html#in_seconds"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#time_of_day.in_seconds" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">in_seconds</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/time_of_day.html#in_seconds"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.time_of_day.in_seconds" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>If time is <cite>time.struct_time</cite> convert to float seconds.</p>
|
<dd><p>If time is <cite>time.struct_time</cite> convert to float seconds.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -126,8 +127,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="time_of_day.minutes">
|
<dt id="pylib.time_of_day.minutes">
|
||||||
<code class="sig-name descname">minutes</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/time_of_day.html#minutes"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#time_of_day.minutes" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">minutes</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/time_of_day.html#minutes"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.time_of_day.minutes" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>The minutes of the time.</p>
|
<dd><p>The minutes of the time.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -143,8 +144,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="time_of_day.minutes_norm">
|
<dt id="pylib.time_of_day.minutes_norm">
|
||||||
<code class="sig-name descname">minutes_norm</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/time_of_day.html#minutes_norm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#time_of_day.minutes_norm" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">minutes_norm</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/time_of_day.html#minutes_norm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.time_of_day.minutes_norm" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>The minutes normalized to 60 minutes.</p>
|
<dd><p>The minutes normalized to 60 minutes.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -160,8 +161,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="time_of_day.seconds">
|
<dt id="pylib.time_of_day.seconds">
|
||||||
<code class="sig-name descname">seconds</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/time_of_day.html#seconds"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#time_of_day.seconds" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">seconds</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/time_of_day.html#seconds"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.time_of_day.seconds" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>The seconds of the time.</p>
|
<dd><p>The seconds of the time.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -177,8 +178,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="time_of_day.seconds_norm">
|
<dt id="pylib.time_of_day.seconds_norm">
|
||||||
<code class="sig-name descname">seconds_norm</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/time_of_day.html#seconds_norm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#time_of_day.seconds_norm" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">seconds_norm</code><span class="sig-paren">(</span><em class="sig-param">time</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/time_of_day.html#seconds_norm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.time_of_day.seconds_norm" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>The seconds normalized to 60 seconds.</p>
|
<dd><p>The seconds normalized to 60 seconds.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -194,8 +195,8 @@
|
|||||||
</dd></dl>
|
</dd></dl>
|
||||||
|
|
||||||
<dl class="function">
|
<dl class="function">
|
||||||
<dt id="time_of_day.transform">
|
<dt id="pylib.time_of_day.transform">
|
||||||
<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">time_norm</em>, <em class="sig-param">length</em>, <em class="sig-param">offset=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/time_of_day.html#transform"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#time_of_day.transform" title="Permalink to this definition">¶</a></dt>
|
<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">time_norm</em>, <em class="sig-param">length</em>, <em class="sig-param">offset=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pylib/time_of_day.html#transform"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pylib.time_of_day.transform" title="Permalink to this definition">¶</a></dt>
|
||||||
<dd><p>Transform normalized time value to new length.</p>
|
<dd><p>Transform normalized time value to new length.</p>
|
||||||
<dl class="field-list simple">
|
<dl class="field-list simple">
|
||||||
<dt class="field-odd">Parameters</dt>
|
<dt class="field-odd">Parameters</dt>
|
||||||
@@ -233,11 +234,23 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul class="current">
|
||||||
|
<li class="toctree-l1 current"><a class="reference internal" href="modules.html">pylib</a><ul class="current">
|
||||||
|
<li class="toctree-l2 current"><a class="reference internal" href="pylib.html">pylib package</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="index.html">Documentation overview</a><ul>
|
<li><a href="index.html">Documentation overview</a><ul>
|
||||||
|
<li><a href="modules.html">pylib</a><ul>
|
||||||
|
<li><a href="pylib.html">pylib package</a><ul>
|
||||||
|
<li>Previous: <a href="pylib.mathematics.html" title="previous chapter">pylib.mathematics module</a></li>
|
||||||
|
</ul></li>
|
||||||
|
</ul></li>
|
||||||
</ul></li>
|
</ul></li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
@@ -271,7 +284,7 @@
|
|||||||
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>
|
||||||
|
|
||||||
|
|
|
|
||||||
<a href="_sources/time_of_day.rst.txt"
|
<a href="_sources/pylib.time_of_day.rst.txt"
|
||||||
rel="nofollow">Page source</a>
|
rel="nofollow">Page source</a>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
6
docs/build/html/search.html
vendored
6
docs/build/html/search.html
vendored
@@ -4,7 +4,7 @@
|
|||||||
<html xmlns="http://www.w3.org/1999/xhtml">
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
||||||
<head>
|
<head>
|
||||||
<meta charset="utf-8" />
|
<meta charset="utf-8" />
|
||||||
<title>Search — pylib 2019.5.19 documentation</title>
|
<title>Search — pylib 2019.12.21 documentation</title>
|
||||||
<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
|
<link rel="stylesheet" href="_static/alabaster.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
|
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
|
||||||
<link rel="stylesheet" href="_static/custom.css" type="text/css" />
|
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|
||||||
@@ -77,6 +77,10 @@
|
|||||||
|
|
||||||
|
|
||||||
<h3>Navigation</h3>
|
<h3>Navigation</h3>
|
||||||
|
<p class="caption"><span class="caption-text">Contents:</span></p>
|
||||||
|
<ul>
|
||||||
|
<li class="toctree-l1"><a class="reference internal" href="modules.html">pylib</a></li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
<div class="relations">
|
<div class="relations">
|
||||||
<h3>Related Topics</h3>
|
<h3>Related Topics</h3>
|
||||||
|
|||||||
2
docs/build/html/searchindex.js
vendored
2
docs/build/html/searchindex.js
vendored
File diff suppressed because one or more lines are too long
@@ -25,7 +25,7 @@ copyright = '2019, Daniel Weschke'
|
|||||||
author = 'Daniel Weschke'
|
author = 'Daniel Weschke'
|
||||||
|
|
||||||
# The full version, including alpha/beta/rc tags
|
# The full version, including alpha/beta/rc tags
|
||||||
release = '2019.5.19'
|
release = '2019.12.21'
|
||||||
|
|
||||||
|
|
||||||
# -- General configuration ---------------------------------------------------
|
# -- General configuration ---------------------------------------------------
|
||||||
|
|||||||
@@ -1,7 +0,0 @@
|
|||||||
data module
|
|
||||||
===========
|
|
||||||
|
|
||||||
.. automodule:: data
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
@@ -1,7 +0,0 @@
|
|||||||
date module
|
|
||||||
===========
|
|
||||||
|
|
||||||
.. automodule:: date
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
@@ -1,7 +0,0 @@
|
|||||||
function module
|
|
||||||
===============
|
|
||||||
|
|
||||||
.. automodule:: function
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
@@ -1,7 +0,0 @@
|
|||||||
geometry module
|
|
||||||
===============
|
|
||||||
|
|
||||||
.. automodule:: geometry
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
@@ -10,6 +10,8 @@ Welcome to pylib's documentation!
|
|||||||
:maxdepth: 2
|
:maxdepth: 2
|
||||||
:caption: Contents:
|
:caption: Contents:
|
||||||
|
|
||||||
|
modules
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
Indices and tables
|
Indices and tables
|
||||||
|
|||||||
@@ -1,7 +0,0 @@
|
|||||||
mathematics module
|
|
||||||
==================
|
|
||||||
|
|
||||||
.. automodule:: mathematics
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
@@ -1,46 +0,0 @@
|
|||||||
numerical package
|
|
||||||
=================
|
|
||||||
|
|
||||||
Submodules
|
|
||||||
----------
|
|
||||||
|
|
||||||
numerical.fit module
|
|
||||||
--------------------
|
|
||||||
|
|
||||||
.. automodule:: numerical.fit
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
numerical.integration module
|
|
||||||
----------------------------
|
|
||||||
|
|
||||||
.. automodule:: numerical.integration
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
numerical.ode module
|
|
||||||
--------------------
|
|
||||||
|
|
||||||
.. automodule:: numerical.ode
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
numerical.ode\_model module
|
|
||||||
---------------------------
|
|
||||||
|
|
||||||
.. automodule:: numerical.ode_model
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
|
|
||||||
Module contents
|
|
||||||
---------------
|
|
||||||
|
|
||||||
.. automodule:: numerical
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
7
docs/source/pylib.data.rst
Normal file
7
docs/source/pylib.data.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.data module
|
||||||
|
=================
|
||||||
|
|
||||||
|
.. automodule:: pylib.data
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/source/pylib.date.rst
Normal file
7
docs/source/pylib.date.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.date module
|
||||||
|
=================
|
||||||
|
|
||||||
|
.. automodule:: pylib.date
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/source/pylib.drawblock.rst
Normal file
7
docs/source/pylib.drawblock.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.drawblock module
|
||||||
|
======================
|
||||||
|
|
||||||
|
.. automodule:: pylib.drawblock
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/source/pylib.function.rst
Normal file
7
docs/source/pylib.function.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.function module
|
||||||
|
=====================
|
||||||
|
|
||||||
|
.. automodule:: pylib.function
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/source/pylib.geometry.rst
Normal file
7
docs/source/pylib.geometry.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.geometry module
|
||||||
|
=====================
|
||||||
|
|
||||||
|
.. automodule:: pylib.geometry
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/source/pylib.geometry2d.rst
Normal file
7
docs/source/pylib.geometry2d.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.geometry2d module
|
||||||
|
=======================
|
||||||
|
|
||||||
|
.. automodule:: pylib.geometry2d
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/source/pylib.geometry2d_plot.rst
Normal file
7
docs/source/pylib.geometry2d_plot.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.geometry2d\_plot module
|
||||||
|
=============================
|
||||||
|
|
||||||
|
.. automodule:: pylib.geometry2d_plot
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/source/pylib.mathematics.rst
Normal file
7
docs/source/pylib.mathematics.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.mathematics module
|
||||||
|
========================
|
||||||
|
|
||||||
|
.. automodule:: pylib.mathematics
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/source/pylib.numerical.fit.rst
Normal file
7
docs/source/pylib.numerical.fit.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.numerical.fit module
|
||||||
|
==========================
|
||||||
|
|
||||||
|
.. automodule:: pylib.numerical.fit
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/source/pylib.numerical.integration.rst
Normal file
7
docs/source/pylib.numerical.integration.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.numerical.integration module
|
||||||
|
==================================
|
||||||
|
|
||||||
|
.. automodule:: pylib.numerical.integration
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/source/pylib.numerical.ode.rst
Normal file
7
docs/source/pylib.numerical.ode.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.numerical.ode module
|
||||||
|
==========================
|
||||||
|
|
||||||
|
.. automodule:: pylib.numerical.ode
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
7
docs/source/pylib.numerical.ode_model.rst
Normal file
7
docs/source/pylib.numerical.ode_model.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.numerical.ode\_model module
|
||||||
|
=================================
|
||||||
|
|
||||||
|
.. automodule:: pylib.numerical.ode_model
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
@@ -1,46 +1,17 @@
|
|||||||
pylib.numerical package
|
pylib.numerical package
|
||||||
=======================
|
=======================
|
||||||
|
|
||||||
Submodules
|
|
||||||
----------
|
|
||||||
|
|
||||||
pylib.numerical.fit module
|
|
||||||
--------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.numerical.fit
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.numerical.integration module
|
|
||||||
----------------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.numerical.integration
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.numerical.ode module
|
|
||||||
--------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.numerical.ode
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.numerical.ode\_model module
|
|
||||||
---------------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.numerical.ode_model
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
|
|
||||||
Module contents
|
|
||||||
---------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.numerical
|
.. automodule:: pylib.numerical
|
||||||
:members:
|
:members:
|
||||||
:undoc-members:
|
:undoc-members:
|
||||||
:show-inheritance:
|
:show-inheritance:
|
||||||
|
|
||||||
|
Submodules
|
||||||
|
----------
|
||||||
|
|
||||||
|
.. toctree::
|
||||||
|
|
||||||
|
pylib.numerical.fit
|
||||||
|
pylib.numerical.integration
|
||||||
|
pylib.numerical.ode
|
||||||
|
pylib.numerical.ode_model
|
||||||
|
|||||||
@@ -1,6 +1,11 @@
|
|||||||
pylib package
|
pylib package
|
||||||
=============
|
=============
|
||||||
|
|
||||||
|
.. automodule:: pylib
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
|
|
||||||
Subpackages
|
Subpackages
|
||||||
-----------
|
-----------
|
||||||
|
|
||||||
@@ -11,75 +16,14 @@ Subpackages
|
|||||||
Submodules
|
Submodules
|
||||||
----------
|
----------
|
||||||
|
|
||||||
pylib.data module
|
.. toctree::
|
||||||
-----------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.data
|
pylib.data
|
||||||
:members:
|
pylib.date
|
||||||
:undoc-members:
|
pylib.drawblock
|
||||||
:show-inheritance:
|
pylib.function
|
||||||
|
pylib.geometry
|
||||||
pylib.date module
|
pylib.geometry2d
|
||||||
-----------------
|
pylib.geometry2d_plot
|
||||||
|
pylib.mathematics
|
||||||
.. automodule:: pylib.date
|
pylib.time_of_day
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.drawblock module
|
|
||||||
----------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.drawblock
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.function module
|
|
||||||
---------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.function
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.geometry module
|
|
||||||
---------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.geometry
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.geometry\_plot module
|
|
||||||
---------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.geometry_plot
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.mathematics module
|
|
||||||
------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.mathematics
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
pylib.time\_of\_day module
|
|
||||||
--------------------------
|
|
||||||
|
|
||||||
.. automodule:: pylib.time_of_day
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|
||||||
|
|
||||||
Module contents
|
|
||||||
---------------
|
|
||||||
|
|
||||||
.. automodule:: pylib
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
|
|||||||
7
docs/source/pylib.time_of_day.rst
Normal file
7
docs/source/pylib.time_of_day.rst
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
pylib.time\_of\_day module
|
||||||
|
==========================
|
||||||
|
|
||||||
|
.. automodule:: pylib.time_of_day
|
||||||
|
:members:
|
||||||
|
:undoc-members:
|
||||||
|
:show-inheritance:
|
||||||
@@ -1,7 +0,0 @@
|
|||||||
time\_of\_day module
|
|
||||||
====================
|
|
||||||
|
|
||||||
.. automodule:: time_of_day
|
|
||||||
:members:
|
|
||||||
:undoc-members:
|
|
||||||
:show-inheritance:
|
|
||||||
@@ -1,11 +1,22 @@
|
|||||||
#!/usr/bin/env python
|
#!/usr/bin/env python
|
||||||
# -*- coding: utf-8 -*-
|
# -*- coding: utf-8 -*-
|
||||||
|
"""Draw with block characters.
|
||||||
|
|
||||||
|
:Date: 2019-11-15
|
||||||
|
|
||||||
|
.. module:: drawblock
|
||||||
|
:platform: *nix, Windows
|
||||||
|
:synopsis: Draw with block characters.
|
||||||
|
|
||||||
|
.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
|
||||||
|
"""
|
||||||
|
|
||||||
def histogram(f, x=None):
|
def histogram(f, x=None):
|
||||||
"""Histogram chart with block symbols.
|
"""Histogram chart with block symbols.
|
||||||
|
|
||||||
dots:
|
::
|
||||||
|
|
||||||
|
dots
|
||||||
,_,
|
,_,
|
||||||
|8|
|
|8|
|
||||||
|7|
|
|7|
|
||||||
|
|||||||
@@ -2,7 +2,7 @@
|
|||||||
# -*- coding: utf-8 -*-
|
# -*- coding: utf-8 -*-
|
||||||
"""2D geometry objects.
|
"""2D geometry objects.
|
||||||
|
|
||||||
:Date: 2019-08-28
|
:Date: 2019-12-21
|
||||||
|
|
||||||
.. module:: geometry
|
.. module:: geometry
|
||||||
:platform: *nix, Windows
|
:platform: *nix, Windows
|
||||||
@@ -11,501 +11,215 @@
|
|||||||
.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
|
.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
|
||||||
"""
|
"""
|
||||||
import math
|
import math
|
||||||
import numpy as np
|
import copy
|
||||||
|
from mathematics import vector, matrix
|
||||||
|
|
||||||
|
class Direction(vector):
|
||||||
|
"""Direction in local coordinate system"""
|
||||||
|
def __init__(self, x=1, y=0, z=0):
|
||||||
|
super().__init__([x, y, z, 0])
|
||||||
|
|
||||||
def distance(point1, point2):
|
def __str__(self):
|
||||||
"""Distance between two points (or length of a straight line).
|
return str(self.xyz())
|
||||||
|
|
||||||
:param point1: first point (first end point of straight line)
|
class Point(vector):
|
||||||
:type point1: tuple
|
"""Point in local coordinate system"""
|
||||||
:param point2: second point (second end point of straight line)
|
def __init__(self, x=0, y=0, z=0):
|
||||||
:type point2: tuple
|
super().__init__([x, y, z, 1])
|
||||||
|
|
||||||
:returns: distance between the two points
|
def __str__(self):
|
||||||
:rtype: float
|
return str(self.xyz())
|
||||||
|
|
||||||
|
class CS(matrix):
|
||||||
|
"""Coordinate system
|
||||||
"""
|
"""
|
||||||
return math.sqrt((point2[0]-point1[0])**2 + (point2[1]-point1[1])**2)
|
def __init__(self, x=[1, 0, 0], y=[0, 1, 0], z=[0, 0, 1]):
|
||||||
|
super().__init__([[*x, 0], [*y, 0], [*z, 0], [0, 0, 0, 1]])
|
||||||
|
|
||||||
|
def __str__(self):
|
||||||
|
return '[' + ', '.join([str(i) for i in self.get_coordinates()]) + ']'
|
||||||
|
|
||||||
def angle(point1, point2=None):
|
@staticmethod
|
||||||
"""Angle of point or between two points.
|
def x90():
|
||||||
|
return CS((1, 0, 0), (0, 0, -1), (0, 1, 0))
|
||||||
|
|
||||||
:param point1: (first) point
|
@staticmethod
|
||||||
:type point1: tuple
|
def xm90():
|
||||||
:param point2: second point (default = None)
|
return CS((1, 0, 0), (0, 0, 1), (0, -1, 0))
|
||||||
:type point2: tuple
|
|
||||||
|
|
||||||
:returns: angle of point or between two points
|
@staticmethod
|
||||||
:rtype: float
|
def y90():
|
||||||
|
return CS((0, 0, 1), (0, 1, 0), (-1, 0, 0))
|
||||||
|
|
||||||
|
@staticmethod
|
||||||
|
def ym90():
|
||||||
|
return CS((0, 0, -1), (0, 1, 0), (1, 0, 0))
|
||||||
|
|
||||||
|
def get_coordinates(self):
|
||||||
|
"""Get coordinates in 3d space"""
|
||||||
|
return self[:3,:3]
|
||||||
|
|
||||||
|
class World():
|
||||||
|
"""World-space with world-space coordinates
|
||||||
"""
|
"""
|
||||||
if point2 is None:
|
def __init__(self):
|
||||||
return math.atan2(point1[1], point1[0])
|
self._cs = CS() # Camera
|
||||||
return math.atan2(point2[1]-point1[1], point2[0]-point1[0])
|
self._objects = []
|
||||||
|
self._store_init()
|
||||||
|
|
||||||
|
def __iter__(self):
|
||||||
|
"""Returns the Iterator object"""
|
||||||
|
return iter(self.objects())
|
||||||
|
|
||||||
def translate(vec, *pts):
|
def _store_init(self):
|
||||||
"""Translate a point or polygon by a given vector.
|
"""Initialize or reset calculated values, because a new object was added.
|
||||||
|
|
||||||
:param vec: translation vector
|
|
||||||
:type vec: tuple
|
|
||||||
:param `*pts`: points to translate
|
|
||||||
|
|
||||||
:returns: (point_x, point_y) or (point1, point2, ...)
|
|
||||||
:rtype: tuple
|
|
||||||
|
|
||||||
.. seealso::
|
|
||||||
:meth:`translate_xy`
|
|
||||||
"""
|
"""
|
||||||
vx, vy = vec
|
self._bb = None
|
||||||
return tuple([(x+vx, y+vy) for (x, y) in pts])
|
self._sd = None
|
||||||
|
|
||||||
|
def cs(self, cs=None):
|
||||||
|
if cs:
|
||||||
|
self._cs = cs
|
||||||
|
return self._cs
|
||||||
|
|
||||||
def translate_xy(vec, x, y):
|
def ch_cs(self, cs):
|
||||||
"""Translate a point or polygon by a given vector.
|
self._cs = self._cs * cs
|
||||||
|
return self
|
||||||
|
|
||||||
:param vec: translation vector
|
def rotate_x(self, theta):
|
||||||
:type vec: tuple
|
self._cs.rotate_x(theta)
|
||||||
:param x: points to translate
|
return self
|
||||||
:type x: int or float or list
|
|
||||||
:param y: points to translate
|
|
||||||
:type y: int or float or list
|
|
||||||
|
|
||||||
:returns: (x', y')
|
def rotate_y(self, theta):
|
||||||
:rtype: tuple
|
self._cs.rotate_y(theta)
|
||||||
|
return self
|
||||||
|
|
||||||
.. seealso::
|
def rotate_z(self, theta):
|
||||||
:meth:`translate`
|
self._cs.rotate_z(theta)
|
||||||
|
return self
|
||||||
|
|
||||||
|
def translate(self, tx, ty, tz):
|
||||||
|
self._cs.translate(tx, ty, tz)
|
||||||
|
return self
|
||||||
|
|
||||||
|
def scale(self, sx, sy=None, sz=None):
|
||||||
|
self._cs.scale(sx, sy, sz)
|
||||||
|
return self
|
||||||
|
|
||||||
|
def objects(self):
|
||||||
|
return [copy.deepcopy(i).ch_cs(self._cs) for i in self._objects]
|
||||||
|
|
||||||
|
def add(self, *objects):
|
||||||
|
self._store_init() # calculated values are not correct anymore
|
||||||
|
[self._objects.append(i) for i in objects]
|
||||||
|
return self
|
||||||
|
|
||||||
|
def bounding_box(self):
|
||||||
|
if self._bb is not None:
|
||||||
|
return self._bb
|
||||||
|
|
||||||
|
xmin = math.inf
|
||||||
|
ymin = math.inf
|
||||||
|
zmin = math.inf
|
||||||
|
xmax = -math.inf
|
||||||
|
ymax = -math.inf
|
||||||
|
zmax = -math.inf
|
||||||
|
for i in self._objects:
|
||||||
|
xi, yi, zi = map(min, i.xyz())
|
||||||
|
xs, ys, zs = map(max, i.xyz())
|
||||||
|
#xmax = x if x > xmax: xmax = x
|
||||||
|
xmin = xi if xi < xmin else xmin
|
||||||
|
ymin = yi if yi < ymin else ymin
|
||||||
|
zmin = zi if zi < zmin else zmin
|
||||||
|
xmax = xs if xs > xmax else xmax
|
||||||
|
ymax = ys if ys > ymax else ymax
|
||||||
|
zmax = zs if zs > zmax else zmax
|
||||||
|
|
||||||
|
self._bb = xmin, xmax, ymin, ymax, zmin, zmax
|
||||||
|
return self._bb
|
||||||
|
|
||||||
|
def space_diagonal(self):
|
||||||
|
if self._sd is not None:
|
||||||
|
return self._sd
|
||||||
|
|
||||||
|
bb = self.bounding_box()
|
||||||
|
a, b, c = bb[1]-bb[0], bb[3]-bb[2], bb[5]-bb[4]
|
||||||
|
return math.sqrt(a**2+b**2+c**2)
|
||||||
|
|
||||||
|
def center(self):
|
||||||
|
bb = self.bounding_box()
|
||||||
|
self.ch_cs([[1,0,0,-(bb[1]-bb[0])/2],[0,1,0,-(bb[3]-bb[2])/2],[0,0,1,-(bb[5]-bb[4])/2],[0,0,0,1]])
|
||||||
|
return self
|
||||||
|
|
||||||
|
# TODO: Wireframe(list) or Wireframe(matrix) ?
|
||||||
|
# list of Points
|
||||||
|
class Wireframe():
|
||||||
|
"""Open and closed wireframe object in local coordinate system
|
||||||
|
|
||||||
|
This class create its own points (copy).
|
||||||
"""
|
"""
|
||||||
vx, vy = vec
|
def __init__(self, *points, closed=False):
|
||||||
|
self._points = [copy.copy(i) for i in points]
|
||||||
if not hasattr(x, "__len__"):
|
self.closed = closed
|
||||||
x = [x]
|
|
||||||
|
def __str__(self):
|
||||||
if not hasattr(y, "__len__"):
|
return '[' + ', '.join([str(point) for point in self._points]) + ']'
|
||||||
y = [y]
|
|
||||||
|
def __iter__(self):
|
||||||
xp = [xi+vx for xi in x]
|
"""Returns the Iterator object"""
|
||||||
yp = [yi+vy for yi in y]
|
return iter(self.points())
|
||||||
|
|
||||||
# no list if it is only one value
|
def points(self):
|
||||||
if len(xp) == 1:
|
"""Get coordinates in 3d space"""
|
||||||
return xp[0], yp[0]
|
result = [i for i in self._points]
|
||||||
|
return result if not self.closed else result + [result[0]]
|
||||||
return xp, yp
|
|
||||||
|
def xyz(self):
|
||||||
|
return zip(*[i.xyz() for i in self.points()])
|
||||||
def rotate(origin, angle, *pts, **kwargs):
|
|
||||||
"""Rotate a point or polygon counterclockwise by a given angle
|
def rotate_x(self, theta):
|
||||||
around a given origin. The angle should be given in radians.
|
self._points = [point.rotate_x(theta) for point in self._points]
|
||||||
|
return self
|
||||||
:param origin: the center of rotation
|
|
||||||
:type origin: tuple
|
def rotate_y(self, theta):
|
||||||
:param angle: the rotation angle
|
self._points = [point.rotate_y(theta) for point in self._points]
|
||||||
:type angle: int or float
|
return self
|
||||||
:param `*pts`: points to rotate
|
|
||||||
:param `**kwargs`: options
|
def rotate_z(self, theta):
|
||||||
|
self._points = [point.rotate_z(theta) for point in self._points]
|
||||||
:returns: (point_x, point_y) or (point1, point2, ...)
|
return self
|
||||||
:rtype: tuple
|
|
||||||
|
def translate(self, tx, ty, tz):
|
||||||
.. seealso::
|
self._points = [point.translate(tx, ty, tz) for point in self._points]
|
||||||
:meth:`rotate_xy`
|
return self
|
||||||
"""
|
|
||||||
ox, oy = origin
|
def scale(self, sx, sy=None, sz=None):
|
||||||
|
if not sy:
|
||||||
# add first point to the end
|
sy = sx
|
||||||
if "closed" in kwargs and kwargs["closed"] is True:
|
sz = sx
|
||||||
pts += (pts[0],)
|
self._points = [point.scale(sx, sy, sz) for point in self._points]
|
||||||
|
return self
|
||||||
result = tuple([(ox + math.cos(angle) * (px - ox) - math.sin(angle) * (py - oy),
|
|
||||||
oy + math.sin(angle) * (px - ox) + math.cos(angle) * (py - oy))
|
def ch_cs(self, cs):
|
||||||
for (px, py) in pts])
|
self._points = [point.ch_cs(cs) for point in self._points]
|
||||||
|
return self
|
||||||
# no tuple in tuple if it is only one point
|
|
||||||
if len(pts) == 1:
|
class Line(Wireframe):
|
||||||
return result[0][0], result[0][1]
|
"""Line a open wireframe object in local coordinate system"""
|
||||||
|
def __init__(self, point1=Point(-1, 0, 0), point2=Point(1, 0, 0)):
|
||||||
return result
|
super().__init__(point1, point2)
|
||||||
|
|
||||||
|
class Polygon(Wireframe):
|
||||||
def rotate_deg(origin, angle, *pts, **kwargs):
|
"""Polygon as closed wireframe object in local coordinate system"""
|
||||||
"""Rotate a point or polygon counterclockwise by a given angle
|
def __init__(self, *points):
|
||||||
around a given origin. The angle should be given in degrees.
|
super().__init__(*points, closed=True)
|
||||||
|
|
||||||
:param origin: the center of rotation
|
class Circle(Polygon):
|
||||||
:type origin: tuple
|
"""Circle a closed wireframe object in local coordinate system"""
|
||||||
:param angle: the rotation angle
|
def __init__(self, radius=1, n=10):
|
||||||
:type angle: int or float
|
points = []
|
||||||
:param `*pts`: points to rotate
|
for i in range(n):
|
||||||
:param `**kwargs`: options
|
x = radius * math.sin(i*2*math.pi/n)
|
||||||
|
y = radius * math.cos(i*2*math.pi/n)
|
||||||
:returns: (point_x, point_y) or (point1, point2, ...)
|
points.append(Point(x, y, 0))
|
||||||
:rtype: tuple
|
super().__init__(*points)
|
||||||
|
|
||||||
.. seealso::
|
|
||||||
:meth:`rotate`
|
|
||||||
"""
|
|
||||||
return rotate(origin, angle*math.pi/180, *pts, **kwargs)
|
|
||||||
|
|
||||||
|
|
||||||
def rotate_xy(origin, angle, x, y, **kwargs):
|
|
||||||
"""Rotate x and y coordinates counterclockwise by a given angle
|
|
||||||
around a given origin. The angle should be given in radians.
|
|
||||||
|
|
||||||
:param origin: the center of rotation
|
|
||||||
:type origin: tuple
|
|
||||||
:param angle: the rotation angle
|
|
||||||
:type angle: int or float
|
|
||||||
:param x: x coordinates
|
|
||||||
:type x: int or float or list
|
|
||||||
:param y: y coordinates
|
|
||||||
:type y: int or float or list
|
|
||||||
:param `**kwargs`: options
|
|
||||||
|
|
||||||
.. seealso::
|
|
||||||
:meth:`rotate`
|
|
||||||
"""
|
|
||||||
ox, oy = origin
|
|
||||||
|
|
||||||
if not hasattr(x, "__len__"):
|
|
||||||
x = [x]
|
|
||||||
|
|
||||||
if not hasattr(y, "__len__"):
|
|
||||||
y = [y]
|
|
||||||
|
|
||||||
# add first point to the end
|
|
||||||
if "closed" in kwargs and kwargs["closed"] is True:
|
|
||||||
x.append(x[0])
|
|
||||||
y.append(y[0])
|
|
||||||
|
|
||||||
x_result = [ox + math.cos(angle) * (xi - ox) - math.sin(angle) * (yi - oy)
|
|
||||||
for xi, yi in zip(x, y)]
|
|
||||||
|
|
||||||
y_result = [oy + math.sin(angle) * (xi - ox) + math.cos(angle) * (yi - oy)
|
|
||||||
for xi, yi in zip(x, y)]
|
|
||||||
|
|
||||||
# no list if it is only one value
|
|
||||||
if len(x_result) == 1:
|
|
||||||
return x_result[0], y_result[0]
|
|
||||||
|
|
||||||
return x_result, y_result
|
|
||||||
|
|
||||||
|
|
||||||
def rectangle(width, height):
|
|
||||||
"""\
|
|
||||||
:param width: the width of the rectangle
|
|
||||||
:type width: int or float
|
|
||||||
:param height: the height of the rectangle
|
|
||||||
:type height: int or float
|
|
||||||
|
|
||||||
:returns: (point1, point2, point3, point4)
|
|
||||||
:rtype: tuple
|
|
||||||
"""
|
|
||||||
pt1 = (-width/2, -height/2)
|
|
||||||
pt2 = (width/2, -height/2)
|
|
||||||
pt3 = (width/2, height/2)
|
|
||||||
pt4 = (-width/2, height/2)
|
|
||||||
return pt1, pt2, pt3, pt4, pt1
|
|
||||||
|
|
||||||
|
|
||||||
def square(width):
|
|
||||||
"""\
|
|
||||||
:param width: the edge size of the square
|
|
||||||
:type width: int or float
|
|
||||||
|
|
||||||
:returns: (point1, point2, point3, point4)
|
|
||||||
:rtype: tuple
|
|
||||||
|
|
||||||
.. seealso::
|
|
||||||
:meth:`rectangle`
|
|
||||||
"""
|
|
||||||
return rectangle(width, width)
|
|
||||||
|
|
||||||
|
|
||||||
def lines(pts, **kwargs):
|
|
||||||
"""Lines defined by a list of end points.
|
|
||||||
|
|
||||||
:param pts: list of points in absolute global coordinate system. If
|
|
||||||
keyword inc is given than the inc decides what the left and the
|
|
||||||
right end point of the line is, otherwise it is assumed that the
|
|
||||||
points build a solid line, that is lines between the given points
|
|
||||||
in given order.
|
|
||||||
:type pts: list
|
|
||||||
|
|
||||||
:param `**kwargs`: options:
|
|
||||||
|
|
||||||
* deformation -- list of points. Additional deformation
|
|
||||||
(translation) at point.
|
|
||||||
* factor -- factor of the deformation (default = 1).
|
|
||||||
* inc -- the incidence table, a list of 2 element lists. The inc
|
|
||||||
decides what the left and the right end point of the line is.
|
|
||||||
* index_offset -- starting index of lists (default = 0).
|
|
||||||
|
|
||||||
:returns: list of endpoints for each line;
|
|
||||||
[((point1_x, point1_y), (point2_x, point2_y)),
|
|
||||||
(p1, p2),
|
|
||||||
...]
|
|
||||||
:rtype: list
|
|
||||||
|
|
||||||
.. seealso::
|
|
||||||
:meth:`~geometry_plot.plot_lines` of the :mod:`geometry_plot`
|
|
||||||
module to plot the lines
|
|
||||||
"""
|
|
||||||
if 'index_offset' not in kwargs:
|
|
||||||
kwargs['index_offset'] = 0
|
|
||||||
if 'deformation' in kwargs:
|
|
||||||
if 'factor' not in kwargs:
|
|
||||||
kwargs['factor'] = 1
|
|
||||||
pts = [(p[0]+d[0]*kwargs['factor'], p[1]+d[1]*kwargs['factor']) for
|
|
||||||
p, d in zip(pts, kwargs['deformation'])]
|
|
||||||
if 'inc' in kwargs:
|
|
||||||
return [(pts[l-kwargs['index_offset']],
|
|
||||||
pts[r-kwargs['index_offset']]) for l, r in kwargs['inc']]
|
|
||||||
return list(zip(pts[:-1], pts[1:]))
|
|
||||||
|
|
||||||
|
|
||||||
def cubics(pts, **kwargs):
|
|
||||||
"""Cubic lines defined by a list of two end points. The deformation
|
|
||||||
as displacement and rotation (radians) is defined element wise as
|
|
||||||
keyword argument deformation or global node wise as
|
|
||||||
global_deformation. The global coordinate system is xy. x in the
|
|
||||||
right direction and y in the top direction.
|
|
||||||
|
|
||||||
:param pts: list of points in absolute global coordinate system. If
|
|
||||||
keyword inc is given than the inc decides what the left and the
|
|
||||||
right end point of the line is, otherwise it is assumed that the
|
|
||||||
points build a solid line, that is lines between the given points
|
|
||||||
in given order.
|
|
||||||
:type pts_rot: list
|
|
||||||
|
|
||||||
:param `**kwargs`: options:
|
|
||||||
|
|
||||||
* deformation -- list of deformation element wise. Additional
|
|
||||||
deformation (translation and rotation in radians) at element
|
|
||||||
left and right node.
|
|
||||||
* rotation_plane -- rotation plane of the element wise
|
|
||||||
deformation defined by a string; either 'xy' or 'xz' (default
|
|
||||||
= 'xy'). x in the right direction and y in the top direction
|
|
||||||
or z in the bottom direction.
|
|
||||||
* global_deformation -- list of deformation global node wise.
|
|
||||||
Additional deformation (horizontal translation, vertical
|
|
||||||
translation and rotation in radians) at node.
|
|
||||||
* factor -- factor of the derformation (default = 1).
|
|
||||||
* inc -- the incidence table, a list of 2 element lists. The inc
|
|
||||||
decides what the left and the right end point of the line is.
|
|
||||||
* index_offset -- starting index of lists (default = 0).
|
|
||||||
|
|
||||||
:returns: list of endpoints for each line;
|
|
||||||
[(((point1_x, point1_y) angle1), ((point2_x, point2_y), angle2),
|
|
||||||
(p1, angle1, p2, angle2),
|
|
||||||
...]
|
|
||||||
:rtype: list
|
|
||||||
"""
|
|
||||||
if 'index_offset' not in kwargs:
|
|
||||||
kwargs['index_offset'] = 0
|
|
||||||
if 'deformation' in kwargs or 'global_deformation' in kwargs:
|
|
||||||
if 'factor' not in kwargs:
|
|
||||||
kwargs['factor'] = 1
|
|
||||||
if 'inc' in kwargs:
|
|
||||||
if 'global_deformation' in kwargs:
|
|
||||||
lr = [(pts[l-kwargs['index_offset']],
|
|
||||||
pts[r-kwargs['index_offset']]) for l, r in kwargs['inc']]
|
|
||||||
ang = [angle(l, r) for l, r in lr]
|
|
||||||
# system deformation
|
|
||||||
U = kwargs['global_deformation']
|
|
||||||
if 'rotation_plane' in kwargs and 'xz' == kwargs['rotation_plane']:
|
|
||||||
# system deformation left X Z RY right X Z RY element wise
|
|
||||||
# Z downwards -> convert to X Y RZ
|
|
||||||
Ue = [[ U[(l-kwargs['index_offset'])][0],
|
|
||||||
-U[(l-kwargs['index_offset'])][1],
|
|
||||||
U[(l-kwargs['index_offset'])][2],
|
|
||||||
U[(r-kwargs['index_offset'])][0],
|
|
||||||
-U[(r-kwargs['index_offset'])][1],
|
|
||||||
U[(r-kwargs['index_offset'])][2]] for l, r in kwargs['inc']]
|
|
||||||
else:
|
|
||||||
# system deformation left X Y RZ right X Y RZ element wise
|
|
||||||
Ue = [[U[(l-kwargs['index_offset'])][0],
|
|
||||||
U[(l-kwargs['index_offset'])][1],
|
|
||||||
U[(l-kwargs['index_offset'])][2],
|
|
||||||
U[(r-kwargs['index_offset'])][0],
|
|
||||||
U[(r-kwargs['index_offset'])][1],
|
|
||||||
U[(r-kwargs['index_offset'])][2]] for l, r in kwargs['inc']]
|
|
||||||
# element deformation, X Y RZ to x r rz
|
|
||||||
# back transformation T^T = [[c, s, 0], [-s, c, 0], [0, 0, 1]]
|
|
||||||
u = [[( math.cos(angi)*Uei[0]+math.sin(angi)*Uei[1])*kwargs['factor'],
|
|
||||||
(-math.sin(angi)*Uei[0]+math.cos(angi)*Uei[1])*kwargs['factor'],
|
|
||||||
Uei[2] *kwargs['factor'],
|
|
||||||
( math.cos(angi)*Uei[3]+math.sin(angi)*Uei[4])*kwargs['factor'],
|
|
||||||
(-math.sin(angi)*Uei[3]+math.cos(angi)*Uei[4])*kwargs['factor'],
|
|
||||||
Uei[5] *kwargs['factor']]
|
|
||||||
for Uei, angi in zip(Ue, ang)]
|
|
||||||
else: # deformation
|
|
||||||
# the deformation is in element coordinate system, therefore the angle is needed
|
|
||||||
if 'rotation_plane' in kwargs and 'xz' == kwargs['rotation_plane']:
|
|
||||||
u = [[ ue[0]*kwargs['factor'],
|
|
||||||
-ue[1]*kwargs['factor'],
|
|
||||||
ue[2]*kwargs['factor'],
|
|
||||||
ue[3]*kwargs['factor'],
|
|
||||||
-ue[4]*kwargs['factor'],
|
|
||||||
ue[5]*kwargs['factor']] for ue in kwargs['deformation']]
|
|
||||||
else:
|
|
||||||
u = [[ui*kwargs['factor'] for ui in ue] for ue in kwargs['deformation']]
|
|
||||||
return [(pts[l-kwargs['index_offset']],
|
|
||||||
pts[r-kwargs['index_offset']],
|
|
||||||
d) for (l, r), d in zip(kwargs['inc'], u)]
|
|
||||||
return list(zip(pts[:-1], pts[1:]))
|
|
||||||
|
|
||||||
|
|
||||||
def interpolate_hermite(lvd, lr, rvd, rr, lhd=0, rhd=0, scale_x=1, scale_y=1, samples=10):
|
|
||||||
r"""Interpolate cubic line with hermite boundary conditions.
|
|
||||||
|
|
||||||
:param lvd: left vertcal deflection
|
|
||||||
:type lvd: int or float
|
|
||||||
:param lr: left rotation
|
|
||||||
:type lr: int or float
|
|
||||||
:param rvd: right vertical deflection
|
|
||||||
:type rvd: int or float
|
|
||||||
:param rr: right rotation
|
|
||||||
:type rr: int or float
|
|
||||||
:param lhd: left horizontal deformation (default = 0)
|
|
||||||
:type lhd: int or float
|
|
||||||
:param rhd: right horizontal deformation (default = 0)
|
|
||||||
:type rhd: int or float
|
|
||||||
:param scale_x: length of element (default = 1)
|
|
||||||
:type scale_x: int or float
|
|
||||||
:param scale_y: factor of the deformation (default = 1).
|
|
||||||
This does not change the length.
|
|
||||||
:type scale_y: int or float
|
|
||||||
:param samples: number of sampling points (default = 10)
|
|
||||||
:type samples: int
|
|
||||||
|
|
||||||
.. math::
|
|
||||||
s = \frac{x - x_1}{L} \\
|
|
||||||
x = s\,L + x_1
|
|
||||||
|
|
||||||
"""
|
|
||||||
L = scale_x
|
|
||||||
Lp = L + rhd - lhd
|
|
||||||
|
|
||||||
# x=[0,1] in non-dimensional coordinates
|
|
||||||
x = np.linspace(0, 1, num=samples)
|
|
||||||
N1 = 1 - 3*x**2 + 2*x**3
|
|
||||||
N2 = ( x - 2*x**2 + x**3)*Lp
|
|
||||||
N3 = 3*x**2 - 2*x**3
|
|
||||||
N4 = ( - x**2 + x**3)*Lp
|
|
||||||
x = x*Lp
|
|
||||||
|
|
||||||
|
|
||||||
# x=[0,L] in global coordinates
|
|
||||||
x = np.linspace(0, Lp, num=samples)
|
|
||||||
N1 = 1 - 3*x**2/Lp**2 + 2*x**3/Lp**3
|
|
||||||
N2 = x - 2*x**2/Lp + x**3/Lp**2
|
|
||||||
N3 = 3*x**2/Lp**2 - 2*x**3/Lp**3
|
|
||||||
N4 = - x**2/Lp + x**3/Lp**2
|
|
||||||
|
|
||||||
|
|
||||||
v = N1*lvd + N2*lr + N3*rvd + N4*rr
|
|
||||||
x = x + lhd
|
|
||||||
y = v*scale_y
|
|
||||||
|
|
||||||
return x, y
|
|
||||||
|
|
||||||
|
|
||||||
#
|
|
||||||
# matplotlib format, return lists for x and y
|
|
||||||
#
|
|
||||||
|
|
||||||
def line(point1, point2, samples=2):
|
|
||||||
"""Line defined by two end points.
|
|
||||||
|
|
||||||
.. math::
|
|
||||||
y = \\frac{y_2-y_1}{x_2-x_1}(x-x_1) + y_1
|
|
||||||
|
|
||||||
:param point1: one end point
|
|
||||||
:type point1: tuple
|
|
||||||
:param point2: other end point
|
|
||||||
:type point2: tuple
|
|
||||||
:param samples: number of sampling points (default = 2)
|
|
||||||
:type samples: int
|
|
||||||
|
|
||||||
:returns: ((point1_x, point2_x), (points1_y, point2_y)) or
|
|
||||||
([sample_point1_x, sample_point2_x, ...],
|
|
||||||
[sample_points1_y, sample_point2_y, ...])
|
|
||||||
:rtype: tuple
|
|
||||||
|
|
||||||
:Example:
|
|
||||||
|
|
||||||
>>> x, y = line((0, 0), (1, 0))
|
|
||||||
>>> print(x, y)
|
|
||||||
((0, 1), (0, 0))
|
|
||||||
"""
|
|
||||||
p1x, p1y = point1
|
|
||||||
p2x, p2y = point2
|
|
||||||
|
|
||||||
denominator = (p1x - p2x)
|
|
||||||
|
|
||||||
if samples > 2 and denominator > 0:
|
|
||||||
x = np.linspace(p1x, p2x, samples)
|
|
||||||
a = (p1y - p2y) / denominator
|
|
||||||
b = (p1x*p2y - p2x*p1y) / denominator
|
|
||||||
y = a*x + b
|
|
||||||
return x, y
|
|
||||||
return (p1x, p2x), (p1y, p2y) # matplotlib format
|
|
||||||
|
|
||||||
|
|
||||||
def cubic(point1, angle1, point2, angle2, samples=10):
|
|
||||||
"""Cubic line defined by two end points and the rotation in radians
|
|
||||||
at the points.
|
|
||||||
|
|
||||||
:param point1: one end point
|
|
||||||
:type point1: tuple
|
|
||||||
:param angle1: the slope at the one end point
|
|
||||||
:type angle1: int or float
|
|
||||||
:param point2: other end point
|
|
||||||
:type point2: tuple
|
|
||||||
:param angle2: the slope at the other end point
|
|
||||||
:type angle2: int or float
|
|
||||||
:param samples: number of sampling points (default = 10)
|
|
||||||
:type samples: int
|
|
||||||
|
|
||||||
:returns: ([sample_point1_x, sample_point2_x, ...],
|
|
||||||
[sample_points1_y, sample_point2_y, ...])
|
|
||||||
:rtype: tuple
|
|
||||||
"""
|
|
||||||
p1x, p1y = point1
|
|
||||||
p2x, p2y = point2
|
|
||||||
|
|
||||||
x = np.linspace(p1x, p2x, num=samples)
|
|
||||||
|
|
||||||
p1ys = math.tan(angle1)
|
|
||||||
p2ys = math.tan(angle2)
|
|
||||||
a = (p1x*p1ys + p1x*p2ys - p2x*p1ys - p2x*p2ys - 2*p1y + 2*p2y)/(p1x**3 - 3*p1x**2*p2x + 3*p1x*p2x**2 - p2x**3)
|
|
||||||
b = (- p1x**2*p1ys - 2*p1x**2*p2ys - p1x*p2x*p1ys + p1x*p2x*p2ys + 3*p1x*p1y - 3*p1x*p2y + 2*p2x**2*p1ys + p2x**2*p2ys + 3*p2x*p1y - 3*p2x*p2y)/(p1x**3 - 3*p1x**2*p2x + 3*p1x*p2x**2 - p2x**3)
|
|
||||||
c = (p1x**3*p2ys + 2*p1x**2*p2x*p1ys + p1x**2*p2x*p2ys - p1x*p2x**2*p1ys - 2*p1x*p2x**2*p2ys - 6*p1x*p2x*p1y + 6*p1x*p2x*p2y - p2x**3*p1ys)/(p1x**3 - 3*p1x**2*p2x + 3*p1x*p2x**2 - p2x**3)
|
|
||||||
d = (- p1x**3*p2x*p2ys + p1x**3*p2y - p1x**2*p2x**2*p1ys + p1x**2*p2x**2*p2ys - 3*p1x**2*p2x*p2y + p1x*p2x**3*p1ys + 3*p1x*p2x**2*p1y - p2x**3*p1y)/(p1x**3 - 3*p1x**2*p2x + 3*p1x*p2x**2 - p2x**3)
|
|
||||||
y = a*x**3 + b*x**2 + c*x + d
|
|
||||||
return x, y
|
|
||||||
|
|
||||||
|
|
||||||
def cubic_deg(point1, angle1, point2, angle2):
|
|
||||||
"""Cubic line defined by two end points and the roation in degree
|
|
||||||
at the points.
|
|
||||||
|
|
||||||
:param point1: one end point
|
|
||||||
:type point1: tuple
|
|
||||||
:param angle1: the slope at the one end point
|
|
||||||
:type angle1: int or float
|
|
||||||
:param point2: other end point
|
|
||||||
:type point2: tuple
|
|
||||||
:param angle2: the slope at the other end point
|
|
||||||
:type angle2: int or float
|
|
||||||
|
|
||||||
:returns: ([sample_point1_x, sample_point2_x, ...],
|
|
||||||
[sample_points1_y, sample_point2_y, ...])
|
|
||||||
:rtype: tuple
|
|
||||||
|
|
||||||
.. seealso::
|
|
||||||
:meth:`cubic`
|
|
||||||
"""
|
|
||||||
return cubic(point1, angle1 * math.pi/180, point2, angle2 * math.pi/180)
|
|
||||||
|
|||||||
511
pylib/geometry2d.py
Normal file
511
pylib/geometry2d.py
Normal file
@@ -0,0 +1,511 @@
|
|||||||
|
#!/usr/bin/env python
|
||||||
|
# -*- coding: utf-8 -*-
|
||||||
|
"""2D geometry objects.
|
||||||
|
|
||||||
|
:Date: 2019-08-28
|
||||||
|
|
||||||
|
.. module:: geometry2d
|
||||||
|
:platform: *nix, Windows
|
||||||
|
:synopsis: 2D geometry objects.
|
||||||
|
|
||||||
|
.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
|
||||||
|
"""
|
||||||
|
import math
|
||||||
|
import numpy as np
|
||||||
|
|
||||||
|
|
||||||
|
def distance(point1, point2):
|
||||||
|
"""Distance between two points (or length of a straight line).
|
||||||
|
|
||||||
|
:param point1: first point (first end point of straight line)
|
||||||
|
:type point1: tuple
|
||||||
|
:param point2: second point (second end point of straight line)
|
||||||
|
:type point2: tuple
|
||||||
|
|
||||||
|
:returns: distance between the two points
|
||||||
|
:rtype: float
|
||||||
|
"""
|
||||||
|
return math.sqrt((point2[0]-point1[0])**2 + (point2[1]-point1[1])**2)
|
||||||
|
|
||||||
|
|
||||||
|
def angle(point1, point2=None):
|
||||||
|
"""Angle of point or between two points.
|
||||||
|
|
||||||
|
:param point1: (first) point
|
||||||
|
:type point1: tuple
|
||||||
|
:param point2: second point (default = None)
|
||||||
|
:type point2: tuple
|
||||||
|
|
||||||
|
:returns: angle of point or between two points
|
||||||
|
:rtype: float
|
||||||
|
"""
|
||||||
|
if point2 is None:
|
||||||
|
return math.atan2(point1[1], point1[0])
|
||||||
|
return math.atan2(point2[1]-point1[1], point2[0]-point1[0])
|
||||||
|
|
||||||
|
|
||||||
|
def translate(vec, *pts):
|
||||||
|
"""Translate a point or polygon by a given vector.
|
||||||
|
|
||||||
|
:param vec: translation vector
|
||||||
|
:type vec: tuple
|
||||||
|
:param `*pts`: points to translate
|
||||||
|
|
||||||
|
:returns: (point_x, point_y) or (point1, point2, ...)
|
||||||
|
:rtype: tuple
|
||||||
|
|
||||||
|
.. seealso::
|
||||||
|
:meth:`translate_xy`
|
||||||
|
"""
|
||||||
|
vx, vy = vec
|
||||||
|
return tuple([(x+vx, y+vy) for (x, y) in pts])
|
||||||
|
|
||||||
|
|
||||||
|
def translate_xy(vec, x, y):
|
||||||
|
"""Translate a point or polygon by a given vector.
|
||||||
|
|
||||||
|
:param vec: translation vector
|
||||||
|
:type vec: tuple
|
||||||
|
:param x: points to translate
|
||||||
|
:type x: int or float or list
|
||||||
|
:param y: points to translate
|
||||||
|
:type y: int or float or list
|
||||||
|
|
||||||
|
:returns: (x', y')
|
||||||
|
:rtype: tuple
|
||||||
|
|
||||||
|
.. seealso::
|
||||||
|
:meth:`translate`
|
||||||
|
"""
|
||||||
|
vx, vy = vec
|
||||||
|
|
||||||
|
if not hasattr(x, "__len__"):
|
||||||
|
x = [x]
|
||||||
|
|
||||||
|
if not hasattr(y, "__len__"):
|
||||||
|
y = [y]
|
||||||
|
|
||||||
|
xp = [xi+vx for xi in x]
|
||||||
|
yp = [yi+vy for yi in y]
|
||||||
|
|
||||||
|
# no list if it is only one value
|
||||||
|
if len(xp) == 1:
|
||||||
|
return xp[0], yp[0]
|
||||||
|
|
||||||
|
return xp, yp
|
||||||
|
|
||||||
|
|
||||||
|
def rotate(origin, angle, *pts, **kwargs):
|
||||||
|
"""Rotate a point or polygon counterclockwise by a given angle
|
||||||
|
around a given origin. The angle should be given in radians.
|
||||||
|
|
||||||
|
:param origin: the center of rotation
|
||||||
|
:type origin: tuple
|
||||||
|
:param angle: the rotation angle
|
||||||
|
:type angle: int or float
|
||||||
|
:param `*pts`: points to rotate
|
||||||
|
:param `**kwargs`: options
|
||||||
|
|
||||||
|
:returns: (point_x, point_y) or (point1, point2, ...)
|
||||||
|
:rtype: tuple
|
||||||
|
|
||||||
|
.. seealso::
|
||||||
|
:meth:`rotate_xy`
|
||||||
|
"""
|
||||||
|
ox, oy = origin
|
||||||
|
|
||||||
|
# add first point to the end
|
||||||
|
if "closed" in kwargs and kwargs["closed"] is True:
|
||||||
|
pts += (pts[0],)
|
||||||
|
|
||||||
|
result = tuple([(ox + math.cos(angle) * (px - ox) - math.sin(angle) * (py - oy),
|
||||||
|
oy + math.sin(angle) * (px - ox) + math.cos(angle) * (py - oy))
|
||||||
|
for (px, py) in pts])
|
||||||
|
|
||||||
|
# no tuple in tuple if it is only one point
|
||||||
|
if len(pts) == 1:
|
||||||
|
return result[0][0], result[0][1]
|
||||||
|
|
||||||
|
return result
|
||||||
|
|
||||||
|
|
||||||
|
def rotate_deg(origin, angle, *pts, **kwargs):
|
||||||
|
"""Rotate a point or polygon counterclockwise by a given angle
|
||||||
|
around a given origin. The angle should be given in degrees.
|
||||||
|
|
||||||
|
:param origin: the center of rotation
|
||||||
|
:type origin: tuple
|
||||||
|
:param angle: the rotation angle
|
||||||
|
:type angle: int or float
|
||||||
|
:param `*pts`: points to rotate
|
||||||
|
:param `**kwargs`: options
|
||||||
|
|
||||||
|
:returns: (point_x, point_y) or (point1, point2, ...)
|
||||||
|
:rtype: tuple
|
||||||
|
|
||||||
|
.. seealso::
|
||||||
|
:meth:`rotate`
|
||||||
|
"""
|
||||||
|
return rotate(origin, angle*math.pi/180, *pts, **kwargs)
|
||||||
|
|
||||||
|
|
||||||
|
def rotate_xy(origin, angle, x, y, **kwargs):
|
||||||
|
"""Rotate x and y coordinates counterclockwise by a given angle
|
||||||
|
around a given origin. The angle should be given in radians.
|
||||||
|
|
||||||
|
:param origin: the center of rotation
|
||||||
|
:type origin: tuple
|
||||||
|
:param angle: the rotation angle
|
||||||
|
:type angle: int or float
|
||||||
|
:param x: x coordinates
|
||||||
|
:type x: int or float or list
|
||||||
|
:param y: y coordinates
|
||||||
|
:type y: int or float or list
|
||||||
|
:param `**kwargs`: options
|
||||||
|
|
||||||
|
.. seealso::
|
||||||
|
:meth:`rotate`
|
||||||
|
"""
|
||||||
|
ox, oy = origin
|
||||||
|
|
||||||
|
if not hasattr(x, "__len__"):
|
||||||
|
x = [x]
|
||||||
|
|
||||||
|
if not hasattr(y, "__len__"):
|
||||||
|
y = [y]
|
||||||
|
|
||||||
|
# add first point to the end
|
||||||
|
if "closed" in kwargs and kwargs["closed"] is True:
|
||||||
|
x.append(x[0])
|
||||||
|
y.append(y[0])
|
||||||
|
|
||||||
|
x_result = [ox + math.cos(angle) * (xi - ox) - math.sin(angle) * (yi - oy)
|
||||||
|
for xi, yi in zip(x, y)]
|
||||||
|
|
||||||
|
y_result = [oy + math.sin(angle) * (xi - ox) + math.cos(angle) * (yi - oy)
|
||||||
|
for xi, yi in zip(x, y)]
|
||||||
|
|
||||||
|
# no list if it is only one value
|
||||||
|
if len(x_result) == 1:
|
||||||
|
return x_result[0], y_result[0]
|
||||||
|
|
||||||
|
return x_result, y_result
|
||||||
|
|
||||||
|
|
||||||
|
def rectangle(width, height):
|
||||||
|
"""\
|
||||||
|
:param width: the width of the rectangle
|
||||||
|
:type width: int or float
|
||||||
|
:param height: the height of the rectangle
|
||||||
|
:type height: int or float
|
||||||
|
|
||||||
|
:returns: (point1, point2, point3, point4)
|
||||||
|
:rtype: tuple
|
||||||
|
"""
|
||||||
|
pt1 = (-width/2, -height/2)
|
||||||
|
pt2 = (width/2, -height/2)
|
||||||
|
pt3 = (width/2, height/2)
|
||||||
|
pt4 = (-width/2, height/2)
|
||||||
|
return pt1, pt2, pt3, pt4, pt1
|
||||||
|
|
||||||
|
|
||||||
|
def square(width):
|
||||||
|
"""\
|
||||||
|
:param width: the edge size of the square
|
||||||
|
:type width: int or float
|
||||||
|
|
||||||
|
:returns: (point1, point2, point3, point4)
|
||||||
|
:rtype: tuple
|
||||||
|
|
||||||
|
.. seealso::
|
||||||
|
:meth:`rectangle`
|
||||||
|
"""
|
||||||
|
return rectangle(width, width)
|
||||||
|
|
||||||
|
|
||||||
|
def lines(pts, **kwargs):
|
||||||
|
"""Lines defined by a list of end points.
|
||||||
|
|
||||||
|
:param pts: list of points in absolute global coordinate system. If
|
||||||
|
keyword inc is given than the inc decides what the left and the
|
||||||
|
right end point of the line is, otherwise it is assumed that the
|
||||||
|
points build a solid line, that is lines between the given points
|
||||||
|
in given order.
|
||||||
|
:type pts: list
|
||||||
|
|
||||||
|
:param `**kwargs`: options:
|
||||||
|
|
||||||
|
* deformation -- list of points. Additional deformation
|
||||||
|
(translation) at point.
|
||||||
|
* factor -- factor of the deformation (default = 1).
|
||||||
|
* inc -- the incidence table, a list of 2 element lists. The inc
|
||||||
|
decides what the left and the right end point of the line is.
|
||||||
|
* index_offset -- starting index of lists (default = 0).
|
||||||
|
|
||||||
|
:returns: list of endpoints for each line;
|
||||||
|
[((point1_x, point1_y), (point2_x, point2_y)),
|
||||||
|
(p1, p2),
|
||||||
|
...]
|
||||||
|
:rtype: list
|
||||||
|
|
||||||
|
.. seealso::
|
||||||
|
:meth:`~geometry_plot.plot_lines` of the :mod:`geometry_plot`
|
||||||
|
module to plot the lines
|
||||||
|
"""
|
||||||
|
if 'index_offset' not in kwargs:
|
||||||
|
kwargs['index_offset'] = 0
|
||||||
|
if 'deformation' in kwargs:
|
||||||
|
if 'factor' not in kwargs:
|
||||||
|
kwargs['factor'] = 1
|
||||||
|
pts = [(p[0]+d[0]*kwargs['factor'], p[1]+d[1]*kwargs['factor']) for
|
||||||
|
p, d in zip(pts, kwargs['deformation'])]
|
||||||
|
if 'inc' in kwargs:
|
||||||
|
return [(pts[l-kwargs['index_offset']],
|
||||||
|
pts[r-kwargs['index_offset']]) for l, r in kwargs['inc']]
|
||||||
|
return list(zip(pts[:-1], pts[1:]))
|
||||||
|
|
||||||
|
|
||||||
|
def cubics(pts, **kwargs):
|
||||||
|
"""Cubic lines defined by a list of two end points. The deformation
|
||||||
|
as displacement and rotation (radians) is defined element wise as
|
||||||
|
keyword argument deformation or global node wise as
|
||||||
|
global_deformation. The global coordinate system is xy. x in the
|
||||||
|
right direction and y in the top direction.
|
||||||
|
|
||||||
|
:param pts: list of points in absolute global coordinate system. If
|
||||||
|
keyword inc is given than the inc decides what the left and the
|
||||||
|
right end point of the line is, otherwise it is assumed that the
|
||||||
|
points build a solid line, that is lines between the given points
|
||||||
|
in given order.
|
||||||
|
:type pts_rot: list
|
||||||
|
|
||||||
|
:param `**kwargs`: options:
|
||||||
|
|
||||||
|
* deformation -- list of deformation element wise. Additional
|
||||||
|
deformation (translation and rotation in radians) at element
|
||||||
|
left and right node.
|
||||||
|
* rotation_plane -- rotation plane of the element wise
|
||||||
|
deformation defined by a string; either 'xy' or 'xz' (default
|
||||||
|
= 'xy'). x in the right direction and y in the top direction
|
||||||
|
or z in the bottom direction.
|
||||||
|
* global_deformation -- list of deformation global node wise.
|
||||||
|
Additional deformation (horizontal translation, vertical
|
||||||
|
translation and rotation in radians) at node.
|
||||||
|
* factor -- factor of the derformation (default = 1).
|
||||||
|
* inc -- the incidence table, a list of 2 element lists. The inc
|
||||||
|
decides what the left and the right end point of the line is.
|
||||||
|
* index_offset -- starting index of lists (default = 0).
|
||||||
|
|
||||||
|
:returns: list of endpoints for each line;
|
||||||
|
[(((point1_x, point1_y) angle1), ((point2_x, point2_y), angle2),
|
||||||
|
(p1, angle1, p2, angle2),
|
||||||
|
...]
|
||||||
|
:rtype: list
|
||||||
|
"""
|
||||||
|
if 'index_offset' not in kwargs:
|
||||||
|
kwargs['index_offset'] = 0
|
||||||
|
if 'deformation' in kwargs or 'global_deformation' in kwargs:
|
||||||
|
if 'factor' not in kwargs:
|
||||||
|
kwargs['factor'] = 1
|
||||||
|
if 'inc' in kwargs:
|
||||||
|
if 'global_deformation' in kwargs:
|
||||||
|
lr = [(pts[l-kwargs['index_offset']],
|
||||||
|
pts[r-kwargs['index_offset']]) for l, r in kwargs['inc']]
|
||||||
|
ang = [angle(l, r) for l, r in lr]
|
||||||
|
# system deformation
|
||||||
|
U = kwargs['global_deformation']
|
||||||
|
if 'rotation_plane' in kwargs and 'xz' == kwargs['rotation_plane']:
|
||||||
|
# system deformation left X Z RY right X Z RY element wise
|
||||||
|
# Z downwards -> convert to X Y RZ
|
||||||
|
Ue = [[ U[(l-kwargs['index_offset'])][0],
|
||||||
|
-U[(l-kwargs['index_offset'])][1],
|
||||||
|
U[(l-kwargs['index_offset'])][2],
|
||||||
|
U[(r-kwargs['index_offset'])][0],
|
||||||
|
-U[(r-kwargs['index_offset'])][1],
|
||||||
|
U[(r-kwargs['index_offset'])][2]] for l, r in kwargs['inc']]
|
||||||
|
else:
|
||||||
|
# system deformation left X Y RZ right X Y RZ element wise
|
||||||
|
Ue = [[U[(l-kwargs['index_offset'])][0],
|
||||||
|
U[(l-kwargs['index_offset'])][1],
|
||||||
|
U[(l-kwargs['index_offset'])][2],
|
||||||
|
U[(r-kwargs['index_offset'])][0],
|
||||||
|
U[(r-kwargs['index_offset'])][1],
|
||||||
|
U[(r-kwargs['index_offset'])][2]] for l, r in kwargs['inc']]
|
||||||
|
# element deformation, X Y RZ to x r rz
|
||||||
|
# back transformation T^T = [[c, s, 0], [-s, c, 0], [0, 0, 1]]
|
||||||
|
u = [[( math.cos(angi)*Uei[0]+math.sin(angi)*Uei[1])*kwargs['factor'],
|
||||||
|
(-math.sin(angi)*Uei[0]+math.cos(angi)*Uei[1])*kwargs['factor'],
|
||||||
|
Uei[2] *kwargs['factor'],
|
||||||
|
( math.cos(angi)*Uei[3]+math.sin(angi)*Uei[4])*kwargs['factor'],
|
||||||
|
(-math.sin(angi)*Uei[3]+math.cos(angi)*Uei[4])*kwargs['factor'],
|
||||||
|
Uei[5] *kwargs['factor']]
|
||||||
|
for Uei, angi in zip(Ue, ang)]
|
||||||
|
else: # deformation
|
||||||
|
# the deformation is in element coordinate system, therefore the angle is needed
|
||||||
|
if 'rotation_plane' in kwargs and 'xz' == kwargs['rotation_plane']:
|
||||||
|
u = [[ ue[0]*kwargs['factor'],
|
||||||
|
-ue[1]*kwargs['factor'],
|
||||||
|
ue[2]*kwargs['factor'],
|
||||||
|
ue[3]*kwargs['factor'],
|
||||||
|
-ue[4]*kwargs['factor'],
|
||||||
|
ue[5]*kwargs['factor']] for ue in kwargs['deformation']]
|
||||||
|
else:
|
||||||
|
u = [[ui*kwargs['factor'] for ui in ue] for ue in kwargs['deformation']]
|
||||||
|
return [(pts[l-kwargs['index_offset']],
|
||||||
|
pts[r-kwargs['index_offset']],
|
||||||
|
d) for (l, r), d in zip(kwargs['inc'], u)]
|
||||||
|
return list(zip(pts[:-1], pts[1:]))
|
||||||
|
|
||||||
|
|
||||||
|
def interpolate_hermite(lvd, lr, rvd, rr, lhd=0, rhd=0, scale_x=1, scale_y=1, samples=10):
|
||||||
|
r"""Interpolate cubic line with hermite boundary conditions.
|
||||||
|
|
||||||
|
:param lvd: left vertcal deflection
|
||||||
|
:type lvd: int or float
|
||||||
|
:param lr: left rotation
|
||||||
|
:type lr: int or float
|
||||||
|
:param rvd: right vertical deflection
|
||||||
|
:type rvd: int or float
|
||||||
|
:param rr: right rotation
|
||||||
|
:type rr: int or float
|
||||||
|
:param lhd: left horizontal deformation (default = 0)
|
||||||
|
:type lhd: int or float
|
||||||
|
:param rhd: right horizontal deformation (default = 0)
|
||||||
|
:type rhd: int or float
|
||||||
|
:param scale_x: length of element (default = 1)
|
||||||
|
:type scale_x: int or float
|
||||||
|
:param scale_y: factor of the deformation (default = 1).
|
||||||
|
This does not change the length.
|
||||||
|
:type scale_y: int or float
|
||||||
|
:param samples: number of sampling points (default = 10)
|
||||||
|
:type samples: int
|
||||||
|
|
||||||
|
.. math::
|
||||||
|
s = \frac{x - x_1}{L} \\
|
||||||
|
x = s\,L + x_1
|
||||||
|
|
||||||
|
"""
|
||||||
|
L = scale_x
|
||||||
|
Lp = L + rhd - lhd
|
||||||
|
|
||||||
|
# x=[0,1] in non-dimensional coordinates
|
||||||
|
x = np.linspace(0, 1, num=samples)
|
||||||
|
N1 = 1 - 3*x**2 + 2*x**3
|
||||||
|
N2 = ( x - 2*x**2 + x**3)*Lp
|
||||||
|
N3 = 3*x**2 - 2*x**3
|
||||||
|
N4 = ( - x**2 + x**3)*Lp
|
||||||
|
x = x*Lp
|
||||||
|
|
||||||
|
|
||||||
|
# x=[0,L] in global coordinates
|
||||||
|
x = np.linspace(0, Lp, num=samples)
|
||||||
|
N1 = 1 - 3*x**2/Lp**2 + 2*x**3/Lp**3
|
||||||
|
N2 = x - 2*x**2/Lp + x**3/Lp**2
|
||||||
|
N3 = 3*x**2/Lp**2 - 2*x**3/Lp**3
|
||||||
|
N4 = - x**2/Lp + x**3/Lp**2
|
||||||
|
|
||||||
|
|
||||||
|
v = N1*lvd + N2*lr + N3*rvd + N4*rr
|
||||||
|
x = x + lhd
|
||||||
|
y = v*scale_y
|
||||||
|
|
||||||
|
return x, y
|
||||||
|
|
||||||
|
|
||||||
|
#
|
||||||
|
# matplotlib format, return lists for x and y
|
||||||
|
#
|
||||||
|
|
||||||
|
def line(point1, point2, samples=2):
|
||||||
|
"""Line defined by two end points.
|
||||||
|
|
||||||
|
.. math::
|
||||||
|
y = \\frac{y_2-y_1}{x_2-x_1}(x-x_1) + y_1
|
||||||
|
|
||||||
|
:param point1: one end point
|
||||||
|
:type point1: tuple
|
||||||
|
:param point2: other end point
|
||||||
|
:type point2: tuple
|
||||||
|
:param samples: number of sampling points (default = 2)
|
||||||
|
:type samples: int
|
||||||
|
|
||||||
|
:returns: ((point1_x, point2_x), (points1_y, point2_y)) or
|
||||||
|
([sample_point1_x, sample_point2_x, ...],
|
||||||
|
[sample_points1_y, sample_point2_y, ...])
|
||||||
|
:rtype: tuple
|
||||||
|
|
||||||
|
:Example:
|
||||||
|
|
||||||
|
>>> x, y = line((0, 0), (1, 0))
|
||||||
|
>>> print(x, y)
|
||||||
|
((0, 1), (0, 0))
|
||||||
|
"""
|
||||||
|
p1x, p1y = point1
|
||||||
|
p2x, p2y = point2
|
||||||
|
|
||||||
|
denominator = (p1x - p2x)
|
||||||
|
|
||||||
|
if samples > 2 and denominator > 0:
|
||||||
|
x = np.linspace(p1x, p2x, samples)
|
||||||
|
a = (p1y - p2y) / denominator
|
||||||
|
b = (p1x*p2y - p2x*p1y) / denominator
|
||||||
|
y = a*x + b
|
||||||
|
return x, y
|
||||||
|
return (p1x, p2x), (p1y, p2y) # matplotlib format
|
||||||
|
|
||||||
|
|
||||||
|
def cubic(point1, angle1, point2, angle2, samples=10):
|
||||||
|
"""Cubic line defined by two end points and the rotation in radians
|
||||||
|
at the points.
|
||||||
|
|
||||||
|
:param point1: one end point
|
||||||
|
:type point1: tuple
|
||||||
|
:param angle1: the slope at the one end point
|
||||||
|
:type angle1: int or float
|
||||||
|
:param point2: other end point
|
||||||
|
:type point2: tuple
|
||||||
|
:param angle2: the slope at the other end point
|
||||||
|
:type angle2: int or float
|
||||||
|
:param samples: number of sampling points (default = 10)
|
||||||
|
:type samples: int
|
||||||
|
|
||||||
|
:returns: ([sample_point1_x, sample_point2_x, ...],
|
||||||
|
[sample_points1_y, sample_point2_y, ...])
|
||||||
|
:rtype: tuple
|
||||||
|
"""
|
||||||
|
p1x, p1y = point1
|
||||||
|
p2x, p2y = point2
|
||||||
|
|
||||||
|
x = np.linspace(p1x, p2x, num=samples)
|
||||||
|
|
||||||
|
p1ys = math.tan(angle1)
|
||||||
|
p2ys = math.tan(angle2)
|
||||||
|
a = (p1x*p1ys + p1x*p2ys - p2x*p1ys - p2x*p2ys - 2*p1y + 2*p2y)/(p1x**3 - 3*p1x**2*p2x + 3*p1x*p2x**2 - p2x**3)
|
||||||
|
b = (- p1x**2*p1ys - 2*p1x**2*p2ys - p1x*p2x*p1ys + p1x*p2x*p2ys + 3*p1x*p1y - 3*p1x*p2y + 2*p2x**2*p1ys + p2x**2*p2ys + 3*p2x*p1y - 3*p2x*p2y)/(p1x**3 - 3*p1x**2*p2x + 3*p1x*p2x**2 - p2x**3)
|
||||||
|
c = (p1x**3*p2ys + 2*p1x**2*p2x*p1ys + p1x**2*p2x*p2ys - p1x*p2x**2*p1ys - 2*p1x*p2x**2*p2ys - 6*p1x*p2x*p1y + 6*p1x*p2x*p2y - p2x**3*p1ys)/(p1x**3 - 3*p1x**2*p2x + 3*p1x*p2x**2 - p2x**3)
|
||||||
|
d = (- p1x**3*p2x*p2ys + p1x**3*p2y - p1x**2*p2x**2*p1ys + p1x**2*p2x**2*p2ys - 3*p1x**2*p2x*p2y + p1x*p2x**3*p1ys + 3*p1x*p2x**2*p1y - p2x**3*p1y)/(p1x**3 - 3*p1x**2*p2x + 3*p1x*p2x**2 - p2x**3)
|
||||||
|
y = a*x**3 + b*x**2 + c*x + d
|
||||||
|
return x, y
|
||||||
|
|
||||||
|
|
||||||
|
def cubic_deg(point1, angle1, point2, angle2):
|
||||||
|
"""Cubic line defined by two end points and the roation in degree
|
||||||
|
at the points.
|
||||||
|
|
||||||
|
:param point1: one end point
|
||||||
|
:type point1: tuple
|
||||||
|
:param angle1: the slope at the one end point
|
||||||
|
:type angle1: int or float
|
||||||
|
:param point2: other end point
|
||||||
|
:type point2: tuple
|
||||||
|
:param angle2: the slope at the other end point
|
||||||
|
:type angle2: int or float
|
||||||
|
|
||||||
|
:returns: ([sample_point1_x, sample_point2_x, ...],
|
||||||
|
[sample_points1_y, sample_point2_y, ...])
|
||||||
|
:rtype: tuple
|
||||||
|
|
||||||
|
.. seealso::
|
||||||
|
:meth:`cubic`
|
||||||
|
"""
|
||||||
|
return cubic(point1, angle1 * math.pi/180, point2, angle2 * math.pi/180)
|
||||||
@@ -4,15 +4,14 @@
|
|||||||
|
|
||||||
:Date: 2019-08-20
|
:Date: 2019-08-20
|
||||||
|
|
||||||
.. module:: geometry_plot
|
.. module:: geometry2d_plot
|
||||||
:platform: *nix, Windows
|
:platform: *nix, Windows
|
||||||
:synopsis: Geometry plotting.
|
:synopsis: 2D geometry plotting.
|
||||||
|
|
||||||
.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
|
.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
|
||||||
"""
|
"""
|
||||||
import math
|
|
||||||
import pylab
|
import pylab
|
||||||
from geometry import (
|
from geometry2d import (
|
||||||
distance, angle, line, interpolate_hermite, rotate_xy, translate_xy
|
distance, angle, line, interpolate_hermite, rotate_xy, translate_xy
|
||||||
)
|
)
|
||||||
|
|
||||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user