add ode solver, tests and update docs

This commit is contained in:
2019-05-26 21:54:58 +02:00
parent 184e80269b
commit d0873a36da
33 changed files with 1821 additions and 396 deletions

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# Sphinx build info version 1
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
config: 09cf9ce4470e7ee74b6ce2abe5e4453a
config: 94375f4299332632f508e2242b7c30d8
tags: 645f666f9bcd5a90fca523b33c5a78b7

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date
fit
geometry
solver
solver_model

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solver module
=============
.. automodule:: solver
:members:
:undoc-members:
:show-inheritance:

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solver\_model module
====================
.. automodule:: solver_model
:members:
:undoc-members:
:show-inheritance:

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src package
===========
Submodules
----------
src.data module
---------------
.. automodule:: src.data
:members:
:undoc-members:
:show-inheritance:
src.date module
---------------
.. automodule:: src.date
:members:
:undoc-members:
:show-inheritance:
src.fit module
--------------
.. automodule:: src.fit
:members:
:undoc-members:
:show-inheritance:
src.geometry module
-------------------
.. automodule:: src.geometry
:members:
:undoc-members:
:show-inheritance:
Module contents
---------------
.. automodule:: src
:members:
:undoc-members:
:show-inheritance:

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@@ -310,8 +310,8 @@ div.hint {
}
div.seealso {
background-color: #EEE;
border: 1px solid #CCC;
background-color: #3c3c3c;
border: 1px solid #2C2C2C;
}
div.topic {

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<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="_static/language_data.js"></script>
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<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
@@ -33,28 +34,67 @@
<div class="section" id="module-data">
<span id="data-module"></span><h1>data module<a class="headerlink" href="#module-data" title="Permalink to this headline"></a></h1>
<dl class="function">
<p>Read and write data to or from file.</p>
<span class="target" id="module-data"></span><dl class="function">
<dt id="data.data_load">
<code class="descname">data_load</code><span class="sig-paren">(</span><em>file_name</em>, <em>verbose=False</em><span class="sig-paren">)</span><a class="headerlink" href="#data.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">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>file_name</strong> (<em>str</em>) file to load</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>loaded data</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>object</p>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="data.data_read">
<code class="descname">data_read</code><span class="sig-paren">(</span><em>file_name</em>, <em>x_column</em>, <em>y_column</em><span class="sig-paren">)</span><a class="headerlink" href="#data.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">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>filename</strong> (<em>str</em>) file to read</p></li>
<li><p><strong>x_column</strong> (<em>int</em>) column index for the x data (first column is 0)</p></li>
<li><p><strong>y_column</strong> (<em>int</em>) column index for the y data (first column is 0)</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>x and y</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>tuple(list, list)</p>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="data.data_store">
<code class="descname">data_store</code><span class="sig-paren">(</span><em>file_name</em>, <em>object_data</em><span class="sig-paren">)</span><a class="headerlink" href="#data.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">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>file_name</strong> (<em>str</em>) file to store</p></li>
<li><p><strong>object_data</strong> (<em>object</em>) data to store</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="data.main">
<code class="descname">main</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#data.main" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dd><p>Main function.</p>
</dd></dl>
</div>

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<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="_static/language_data.js"></script>
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<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
@@ -33,15 +34,25 @@
<div class="section" id="module-date">
<span id="date-module"></span><h1>date module<a class="headerlink" href="#module-date" title="Permalink to this headline"></a></h1>
<p>Created on Mon Jan 15 21:52:34 2018</p>
<p>&#64;author: Daniel Weschke</p>
<dl class="function">
<p>Calculate spacial dates.</p>
<dl class="field-list simple">
<dt class="field-odd">Date</dt>
<dd class="field-odd"><p>2018-01-15</p>
</dd>
</dl>
<span class="target" id="module-date"></span><dl class="function">
<dt id="date.ascension_of_jesus">
<code class="descname">ascension_of_jesus</code><span class="sig-paren">(</span><em>year</em><span class="sig-paren">)</span><a class="headerlink" href="#date.ascension_of_jesus" title="Permalink to this definition"></a></dt>
<dd><p>Ascension of Jesus.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>datetime.date the day of ascension of Jesus</p>
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>year</strong> (<em>int</em>) the year to calculate the ascension of Jesus</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>the day of ascension of Jesus</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>datetime.date</p>
</dd>
</dl>
</dd></dl>
@@ -51,8 +62,14 @@
<code class="descname">easter_friday</code><span class="sig-paren">(</span><em>year</em><span class="sig-paren">)</span><a class="headerlink" href="#date.easter_friday" title="Permalink to this definition"></a></dt>
<dd><p>Easter Friday.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>datetime.date the day of Easter Friday</p>
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>year</strong> (<em>int</em>) the year to calculate the Easter Friday</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>the day of Easter Friday</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>datetime.date</p>
</dd>
</dl>
</dd></dl>
@@ -62,8 +79,14 @@
<code class="descname">easter_monday</code><span class="sig-paren">(</span><em>year</em><span class="sig-paren">)</span><a class="headerlink" href="#date.easter_monday" title="Permalink to this definition"></a></dt>
<dd><p>Easter Monday.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>datetime.date the day of Easter Monday</p>
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>year</strong> (<em>int</em>) the year to calculate the Easter Monday</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>the day of Easter Monday</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>datetime.date</p>
</dd>
</dl>
</dd></dl>
@@ -73,8 +96,14 @@
<code class="descname">easter_sunday</code><span class="sig-paren">(</span><em>year</em><span class="sig-paren">)</span><a class="headerlink" href="#date.easter_sunday" title="Permalink to this definition"></a></dt>
<dd><p>Easter Sunday.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>datetime.date the day of Easter Sunday</p>
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>year</strong> (<em>int</em>) the year to calculate the Easter Sunday</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>the day of Easter Sunday</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>datetime.date</p>
</dd>
</dl>
</dd></dl>
@@ -84,24 +113,32 @@
<code class="descname">gaußsche_osterformel</code><span class="sig-paren">(</span><em>year</em><span class="sig-paren">)</span><a class="headerlink" href="#date.gaußsche_osterformel" title="Permalink to this definition"></a></dt>
<dd><p>Gaußsche Osterformel.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>int the day of Easter Sunday as a day in march.</p>
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>year</strong> (<em>int</em>) the year to calculate the Easter Sunday</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>the day of Easter Sunday as a day in march.</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>int</p>
</dd>
<dt class="field-even">Variables</dt>
<dd class="field-even"><ul class="simple">
<li><p><strong>X</strong> (<em>int</em>) Das Jahr / year</p></li>
<li><p><strong>K</strong><strong>(</strong><strong>X</strong><strong>)</strong> (<em>int</em>) Die Säkularzahl</p></li>
<li><p><strong>M</strong><strong>(</strong><strong>X</strong><strong>)</strong> (<em>int</em>) Die säkulare Mondschaltung</p></li>
<li><p><strong>S</strong><strong>(</strong><strong>K</strong><strong>)</strong> (<em>int</em>) Die säkulare Sonnenschaltung</p></li>
<li><p><strong>A</strong><strong>(</strong><strong>X</strong><strong>)</strong> (<em>int</em>) Den Mondparameter</p></li>
<li><p><strong>D</strong><strong>(</strong><strong>A</strong><strong>,</strong><strong>M</strong><strong>)</strong> (<em>int</em>) Den Keim für den ersten Vollmond im Frühling</p></li>
<li><p><strong>R</strong><strong>(</strong><strong>D</strong><strong>,</strong><strong>A</strong><strong>)</strong> (<em>int</em>) Die kalendarische Korrekturgröße</p></li>
<li><p><strong>OG</strong><strong>(</strong><strong>D</strong><strong>,</strong><strong>R</strong><strong>)</strong> (<em>int</em>) Die Ostergrenze</p></li>
<li><p><strong>SZ</strong><strong>(</strong><strong>X</strong><strong>,</strong><strong>S</strong><strong>)</strong> (<em>int</em>) Den ersten Sonntag im März</p></li>
<li><p><strong>OE</strong><strong>(</strong><strong>OG</strong><strong>,</strong><strong>SZ</strong><strong>)</strong> (<em>int</em>) Die Entfernung des Ostersonntags von der Ostergrenze (Osterentfernung in Tagen)</p></li>
<li><p><strong>OS</strong><strong>(</strong><strong>OG</strong><strong>,</strong><strong>OE</strong><strong>)</strong> (<em>int</em>) Das Datum des Ostersonntags als Märzdatum (32. März = 1. April usw.)</p></li>
</ul>
</dd>
</dl>
<p>Algorithmus gilt für den Gregorianischen Kalender.</p>
<ul class="simple">
<li><p>X Das Jahr / year</p></li>
<li><p>K(X) Die Säkularzahl</p></li>
<li><p>M(K) Die säkulare Mondschaltung</p></li>
<li><p>S(K) Die säkulare Sonnenschaltung</p></li>
<li><p>A(X) Den Mondparameter</p></li>
<li><p>D(A,M) Den Keim für den ersten Vollmond im Frühling</p></li>
<li><p>R(D,A) Die kalendarische Korrekturgröße</p></li>
<li><p>OG(D,R) Die Ostergrenze</p></li>
<li><p>SZ(X,S) Den ersten Sonntag im März</p></li>
<li><p>OE(OG,SZ) Die Entfernung des Ostersonntags von der Ostergrenze (Osterentfernung in Tagen)</p></li>
<li><p>OS(OG,OE) Das Datum des Ostersonntags als Märzdatum (32. März = 1. April usw.)</p></li>
</ul>
<p>source: <a class="reference external" href="https://de.wikipedia.org/wiki/Gau%C3%9Fsche_Osterformel">https://de.wikipedia.org/wiki/Gau%C3%9Fsche_Osterformel</a></p>
</dd></dl>
@@ -110,8 +147,14 @@
<code class="descname">pentecost</code><span class="sig-paren">(</span><em>year</em><span class="sig-paren">)</span><a class="headerlink" href="#date.pentecost" title="Permalink to this definition"></a></dt>
<dd><p>Pentecost.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>datetime.date the day of Pentecost</p>
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>year</strong> (<em>int</em>) the year to calculate the Pentecost</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>the day of Pentecost</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>datetime.date</p>
</dd>
</dl>
</dd></dl>

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@@ -13,6 +13,7 @@
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="_static/language_data.js"></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="search" title="Search" href="search.html" />
@@ -33,26 +34,32 @@
<div class="section" id="module-fit">
<span id="fit-module"></span><h1>fit module<a class="headerlink" href="#module-fit" title="Permalink to this headline"></a></h1>
<dl class="function">
<p>Function and approximation.</p>
<span class="target" id="module-fit"></span><dl class="function">
<dt id="fit.gauss">
<code class="descname">gauss</code><span class="sig-paren">(</span><em>x</em>, <em>*p</em><span class="sig-paren">)</span><a class="headerlink" href="#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> positions where the gauss function will be calculated</p></li>
<li><p><strong>p</strong> <p>gauss parameters [a, b, c, d]:</p>
<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 (integral = 1 if a = 1/(c*sqrt(2*pi)))</p></li>
<li><p>b expected value mu (position of maximum, default = 0)</p></li>
<li><p>c standard deviation sigma (variance sigma**2 = c**2)</p></li>
<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>array gauss values at given positions x</p>
<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>
@@ -64,22 +71,32 @@
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> positions</p></li>
<li><p><strong>y</strong> values</p></li>
<li><p><strong>e</strong> error values</p></li>
<li><p><strong>x_fit</strong> positions of fitted function (default steps is 3*len(x) but min 150)</p></li>
<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>y_fit values</p></li>
<li><p>popt parameters of gauss distribution function (amplitude a, expected
value mu, standard deviation sigma, vertical offset d)</p></li>
<li><p>FWHM full width at half maximum</p></li>
<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="#fit.gauss" title="fit.gauss"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gauss()</span></code></a></p>
</div>
</dd></dl>
<dl class="function">

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@@ -14,6 +14,7 @@
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="_static/language_data.js"></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="#" />
<link rel="search" title="Search" href="search.html" />
@@ -42,8 +43,10 @@
| <a href="#E"><strong>E</strong></a>
| <a href="#F"><strong>F</strong></a>
| <a href="#G"><strong>G</strong></a>
| <a href="#I"><strong>I</strong></a>
| <a href="#L"><strong>L</strong></a>
| <a href="#M"><strong>M</strong></a>
| <a href="#N"><strong>N</strong></a>
| <a href="#P"><strong>P</strong></a>
| <a href="#R"><strong>R</strong></a>
| <a href="#S"><strong>S</strong></a>
@@ -73,17 +76,23 @@
<h2 id="D">D</h2>
<table style="width: 100%" class="indextable genindextable"><tr>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="data.html#module-data">data (module)</a>
<li><a href="data.html#module-data">data (module)</a>, <a href="data.html#module-data">[1]</a>
</li>
<li><a href="data.html#data.data_load">data_load() (in module data)</a>
</li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="data.html#data.data_read">data_read() (in module data)</a>
</li>
<li><a href="data.html#data.data_store">data_store() (in module data)</a>
</li>
<li><a href="date.html#module-date">date (module)</a>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="date.html#module-date">date (module)</a>, <a href="date.html#module-date">[1]</a>
</li>
<li><a href="solver_model.html#solver_model.disk">disk() (in module solver_model)</a>
</li>
<li><a href="solver_model.html#solver_model.disk_nm">disk_nm() (in module solver_model)</a>
</li>
<li><a href="solver_model.html#solver_model.disk_nmmdk">disk_nmmdk() (in module solver_model)</a>
</li>
</ul></td>
</tr></table>
@@ -91,10 +100,16 @@
<h2 id="E">E</h2>
<table style="width: 100%" class="indextable genindextable"><tr>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="date.html#date.easter_friday">easter_friday() (in module date)</a>
<li><a href="solver.html#solver.e1">e1() (in module solver)</a>
</li>
<li><a href="solver.html#solver.e2">e2() (in module solver)</a>
</li>
<li><a href="solver.html#solver.e4">e4() (in module solver)</a>
</li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="date.html#date.easter_friday">easter_friday() (in module date)</a>
</li>
<li><a href="date.html#date.easter_monday">easter_monday() (in module date)</a>
</li>
<li><a href="date.html#date.easter_sunday">easter_sunday() (in module date)</a>
@@ -105,7 +120,7 @@
<h2 id="F">F</h2>
<table style="width: 100%" class="indextable genindextable"><tr>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="fit.html#module-fit">fit (module)</a>
<li><a href="fit.html#module-fit">fit (module)</a>, <a href="fit.html#module-fit">[1]</a>
</li>
</ul></td>
</tr></table>
@@ -121,7 +136,15 @@
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="date.html#date.gaußsche_osterformel">gaußsche_osterformel() (in module date)</a>
</li>
<li><a href="geometry.html#module-geometry">geometry (module)</a>
<li><a href="geometry.html#module-geometry">geometry (module)</a>, <a href="geometry.html#module-geometry">[1]</a>
</li>
</ul></td>
</tr></table>
<h2 id="I">I</h2>
<table style="width: 100%" class="indextable genindextable"><tr>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="solver.html#solver.i1">i1() (in module solver)</a>
</li>
</ul></td>
</tr></table>
@@ -146,6 +169,18 @@
</ul></td>
</tr></table>
<h2 id="N">N</h2>
<table style="width: 100%" class="indextable genindextable"><tr>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="solver.html#solver.newmark_newtonraphson">newmark_newtonraphson() (in module solver)</a>
</li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="solver.html#solver.newmark_newtonraphson_rdk">newmark_newtonraphson_rdk() (in module solver)</a>
</li>
</ul></td>
</tr></table>
<h2 id="P">P</h2>
<table style="width: 100%" class="indextable genindextable"><tr>
<td style="width: 33%; vertical-align: top;"><ul>
@@ -175,6 +210,12 @@
<h2 id="S">S</h2>
<table style="width: 100%" class="indextable genindextable"><tr>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="solver.html#module-solver">solver (module)</a>, <a href="solver.html#module-solver">[1]</a>
</li>
</ul></td>
<td style="width: 33%; vertical-align: top;"><ul>
<li><a href="solver_model.html#module-solver_model">solver_model (module)</a>, <a href="solver_model.html#module-solver_model">[1]</a>
</li>
<li><a href="geometry.html#geometry.square">square() (in module geometry)</a>
</li>
</ul></td>

View File

@@ -13,6 +13,7 @@
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="_static/language_data.js"></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="search" title="Search" href="search.html" />
@@ -33,32 +34,81 @@
<div class="section" id="module-geometry">
<span id="geometry-module"></span><h1>geometry module<a class="headerlink" href="#module-geometry" title="Permalink to this headline"></a></h1>
<p>2D</p>
<p>&#64;date: 2019-03-21
&#64;author: Daniel Weschke</p>
<dl class="function">
<p>2D geometry objects.</p>
<dl class="field-list simple">
<dt class="field-odd">Date</dt>
<dd class="field-odd"><p>2019-03-21</p>
</dd>
</dl>
<span class="target" id="module-geometry"></span><dl class="function">
<dt id="geometry.cubic">
<code class="descname">cubic</code><span class="sig-paren">(</span><em>point1</em>, <em>angle1</em>, <em>point2</em>, <em>angle2</em>, <em>samples=50</em><span class="sig-paren">)</span><a class="headerlink" href="#geometry.cubic" title="Permalink to this definition"></a></dt>
<dd><p>returns
([sample_point1_x, sample_point2_x, …], [sample_points1_y, sample_point2_y, …])</p>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>point1</strong> (<em>tuple</em>) one end point</p></li>
<li><p><strong>angle1</strong> (<em>int</em><em> or </em><em>float</em>) the slope at the one end point</p></li>
<li><p><strong>point2</strong> (<em>tuple</em>) other end point</p></li>
<li><p><strong>angle2</strong> (<em>int</em><em> or </em><em>float</em>) the slope at the other end point</p></li>
<li><p><strong>samples</strong> (<em>int</em>) number of sampling points</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>([sample_point1_x, sample_point2_x, …],
[sample_points1_y, sample_point2_y, …])</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>tuple</p>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="geometry.cubic_deg">
<code class="descname">cubic_deg</code><span class="sig-paren">(</span><em>point1</em>, <em>angle1</em>, <em>point2</em>, <em>angle2</em><span class="sig-paren">)</span><a class="headerlink" href="#geometry.cubic_deg" title="Permalink to this definition"></a></dt>
<dd><p>returns
([sample_point1_x, sample_point2_x, …], [sample_points1_y, sample_point2_y, …])</p>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>point1</strong> (<em>tuple</em>) one end point</p></li>
<li><p><strong>angle1</strong> (<em>int</em><em> or </em><em>float</em>) the slope at the one end point</p></li>
<li><p><strong>point2</strong> (<em>tuple</em>) other end point</p></li>
<li><p><strong>angle2</strong> (<em>int</em><em> or </em><em>float</em>) the slope at the other end point</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>([sample_point1_x, sample_point2_x, …],
[sample_points1_y, sample_point2_y, …])</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="#geometry.cubic" title="geometry.cubic"><code class="xref py py-meth docutils literal notranslate"><span class="pre">cubic()</span></code></a></p>
</div>
</dd></dl>
<dl class="function">
<dt id="geometry.line">
<code class="descname">line</code><span class="sig-paren">(</span><em>point1</em>, <em>point2</em>, <em>samples=2</em><span class="sig-paren">)</span><a class="headerlink" href="#geometry.line" title="Permalink to this definition"></a></dt>
<dd><p>samples: number of sampling points</p>
<p>y = (y2-y1)/(x2-x1)*(x-x1) + y1</p>
<dl class="simple">
<dt>returns</dt><dd><p>((point1_x, point2_x), (points1_y, point2_y))
or
([sample_point1_x, sample_point2_x, …], [sample_points1_y, sample_point2_y, …])</p>
<dd><div class="math notranslate nohighlight">
\[y = \frac{y_2-y_1}{x_2-x_1}(x-x_1) + y_1\]</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>point1</strong> (<em>tuple</em>) one end point</p></li>
<li><p><strong>point2</strong> (<em>tuple</em>) other end point</p></li>
<li><p><strong>samples</strong> (<em>int</em>) number of sampling points</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>((point1_x, point2_x), (points1_y, point2_y)) or
([sample_point1_x, sample_point2_x, …],
[sample_points1_y, sample_point2_y, …])</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>tuple</p>
</dd>
</dl>
</dd></dl>
@@ -66,26 +116,57 @@ or
<dl class="function">
<dt id="geometry.points">
<code class="descname">points</code><span class="sig-paren">(</span><em>*pts</em><span class="sig-paren">)</span><a class="headerlink" href="#geometry.points" title="Permalink to this definition"></a></dt>
<dd><p>returns
((point1_x, point2_x), (point1_y, point2_y), …)</p>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>*pts</strong> points to rearrange</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>((point1_x, point2_x), (point1_y, point2_y), …)</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>tuple</p>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="geometry.rectangle">
<code class="descname">rectangle</code><span class="sig-paren">(</span><em>width</em>, <em>height</em><span class="sig-paren">)</span><a class="headerlink" href="#geometry.rectangle" title="Permalink to this definition"></a></dt>
<dd><p>returns
(point1, point2, point3, point4)</p>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>width</strong> (<em>int</em><em> or </em><em>float</em>) the width of the rectangle</p></li>
<li><p><strong>height</strong> (<em>int</em><em> or </em><em>float</em>) the height of the rectangle</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>(point1, point2, point3, point4)</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>tuple</p>
</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="geometry.rotate">
<code class="descname">rotate</code><span class="sig-paren">(</span><em>origin</em>, <em>angle</em>, <em>*pts</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#geometry.rotate" title="Permalink to this definition"></a></dt>
<dd><p>Rotate a point or polygon counterclockwise by a given angle around a given origin.</p>
<p>The angle should be given in radians.</p>
<dl class="simple">
<dt>returns</dt><dd><p>(point_x, point_y)
or
(point1, point2, …)</p>
<dd><p>Rotate a point or polygon counterclockwise by a given angle around a given
origin. The angle should be given in radians.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>origin</strong> (<em>tuple</em>) the center of rotation</p></li>
<li><p><strong>angle</strong> (<em>int</em><em> or </em><em>float</em>) the rotation angle</p></li>
<li><p><strong>*pts</strong> points to rotate</p></li>
<li><p><strong>**kwargs</strong> options</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>(point_x, point_y) or (point1, point2, …)</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>tuple</p>
</dd>
</dl>
</dd></dl>
@@ -93,31 +174,66 @@ or
<dl class="function">
<dt id="geometry.rotate_deg">
<code class="descname">rotate_deg</code><span class="sig-paren">(</span><em>origin</em>, <em>angle</em>, <em>*pts</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#geometry.rotate_deg" title="Permalink to this definition"></a></dt>
<dd><p>Rotate a point or polygon counterclockwise by a given angle around a given origin.</p>
<p>The angle should be given in degrees.</p>
<dl class="simple">
<dt>returns</dt><dd><p>(point_x, point_y)
or
(point1, point2, …)</p>
<dd><p>Rotate a point or polygon counterclockwise by a given angle around a given
origin. The angle should be given in degrees.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>origin</strong> (<em>tuple</em>) the center of rotation</p></li>
<li><p><strong>angle</strong> (<em>int</em><em> or </em><em>float</em>) the rotation angle</p></li>
<li><p><strong>*pts</strong> points to rotate</p></li>
<li><p><strong>**kwargs</strong> options</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>(point_x, point_y) or (point1, point2, …)</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="#geometry.rotate" title="geometry.rotate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rotate()</span></code></a></p>
</div>
</dd></dl>
<dl class="function">
<dt id="geometry.square">
<code class="descname">square</code><span class="sig-paren">(</span><em>width</em><span class="sig-paren">)</span><a class="headerlink" href="#geometry.square" title="Permalink to this definition"></a></dt>
<dd><p>returns
(point1, point2, point3, point4)</p>
<dd><dl class="field-list simple">
<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>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>(point1, point2, point3, point4)</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="#geometry.rectangle" title="geometry.rectangle"><code class="xref py py-meth docutils literal notranslate"><span class="pre">rectangle()</span></code></a></p>
</div>
</dd></dl>
<dl class="function">
<dt id="geometry.translate">
<code class="descname">translate</code><span class="sig-paren">(</span><em>vec</em>, <em>*pts</em><span class="sig-paren">)</span><a class="headerlink" href="#geometry.translate" title="Permalink to this definition"></a></dt>
<dd><p>Translate a point or polygon by a given vector.</p>
<dl class="simple">
<dt>returns</dt><dd><p>(point_x, point_y)
or
(point1, point2, …)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>vec</strong> (<em>tuple</em>) translation vector</p></li>
<li><p><strong>*pts</strong> points to translate</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>(point_x, point_y) or (point1, point2, …)</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>tuple</p>
</dd>
</dl>
</dd></dl>

View File

@@ -13,6 +13,7 @@
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="_static/language_data.js"></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="search" title="Search" href="search.html" />

View File

@@ -13,6 +13,7 @@
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="_static/language_data.js"></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="search" title="Search" href="search.html" />
@@ -39,6 +40,8 @@
<li class="toctree-l1"><a class="reference internal" href="date.html">date module</a></li>
<li class="toctree-l1"><a class="reference internal" href="fit.html">fit module</a></li>
<li class="toctree-l1"><a class="reference internal" href="geometry.html">geometry module</a></li>
<li class="toctree-l1"><a class="reference internal" href="solver.html">solver module</a></li>
<li class="toctree-l1"><a class="reference internal" href="solver_model.html">solver_model module</a></li>
</ul>
</div>
</div>

View File

@@ -2,9 +2,10 @@
# Project: pylib
# Version:
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<EFBFBD><EFBFBD><EFBFBD><EFBFBD>т]Q<><59><D0A4>
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5<EFBFBD>H<EFBFBD>;<07>U<><55>ȷ<EFBFBD><C8B7>^ZCn2E<32>:<3A>F<EFBFBD>[<07><59>F<EFBFBD>|7<><37><1B>3<EFBFBD>`0<>P<EFBFBD>ү<EFBFBD>.<2E><>t<EFBFBD>C<0F><>N
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View File

@@ -13,6 +13,7 @@
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="_static/language_data.js"></script>
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<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
@@ -44,7 +45,8 @@
<div class="modindex-jumpbox">
<a href="#cap-d"><strong>d</strong></a> |
<a href="#cap-f"><strong>f</strong></a> |
<a href="#cap-g"><strong>g</strong></a>
<a href="#cap-g"><strong>g</strong></a> |
<a href="#cap-s"><strong>s</strong></a>
</div>
<table class="indextable modindextable">
@@ -54,29 +56,42 @@
<tr>
<td></td>
<td>
<a href="data.html#module-data"><code class="xref">data</code></a></td><td>
<em></em></td></tr>
<a href="data.html#module-data"><code class="xref">data</code></a> <em>(*nix, Windows)</em></td><td>
<em>Handle data files.</em></td></tr>
<tr>
<td></td>
<td>
<a href="date.html#module-date"><code class="xref">date</code></a></td><td>
<em></em></td></tr>
<a href="date.html#module-date"><code class="xref">date</code></a> <em>(*nix, Windows)</em></td><td>
<em>Special dates.</em></td></tr>
<tr class="pcap"><td></td><td>&#160;</td><td></td></tr>
<tr class="cap" id="cap-f"><td></td><td>
<strong>f</strong></td><td></td></tr>
<tr>
<td></td>
<td>
<a href="fit.html#module-fit"><code class="xref">fit</code></a></td><td>
<em></em></td></tr>
<a href="fit.html#module-fit"><code class="xref">fit</code></a> <em>(*nix, Windows)</em></td><td>
<em>Function and approximation.</em></td></tr>
<tr class="pcap"><td></td><td>&#160;</td><td></td></tr>
<tr class="cap" id="cap-g"><td></td><td>
<strong>g</strong></td><td></td></tr>
<tr>
<td></td>
<td>
<a href="geometry.html#module-geometry"><code class="xref">geometry</code></a></td><td>
<em></em></td></tr>
<a href="geometry.html#module-geometry"><code class="xref">geometry</code></a> <em>(*nix, Windows)</em></td><td>
<em>Geometry objects.</em></td></tr>
<tr class="pcap"><td></td><td>&#160;</td><td></td></tr>
<tr class="cap" id="cap-s"><td></td><td>
<strong>s</strong></td><td></td></tr>
<tr>
<td></td>
<td>
<a href="solver.html#module-solver"><code class="xref">solver</code></a> <em>(*nix, Windows)</em></td><td>
<em>Numerical solver.</em></td></tr>
<tr>
<td></td>
<td>
<a href="solver_model.html#module-solver_model"><code class="xref">solver_model</code></a> <em>(*nix, Windows)</em></td><td>
<em>Mechanical models.</em></td></tr>
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<div class="section" id="module-solver">
<span id="solver-module"></span><h1>solver module<a class="headerlink" href="#module-solver" 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-solver"></span><dl class="function">
<dt id="solver.e1">
<code class="descname">e1</code><span class="sig-paren">(</span><em>f</em>, <em>x0</em>, <em>t</em>, <em>*p</em>, <em>verbose=False</em><span class="sig-paren">)</span><a class="headerlink" href="#solver.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:
Eulersche 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">
\[\begin{split}\dot{x} &amp;= f(t,x) \\
x(t_0) &amp;= x_0\end{split}\]</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>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">
\[\begin{split}x_{i+1} &amp;= x_i + (t_{i+1}-t_i) f(t_i, x_i) \\
x_{i+1} &amp;= x_i + h f(t_i, x_i) \\\end{split}\]</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">
\[\begin{split}x_1 &amp;= u &amp;\quad \dot{x}_1 = \dot{u} = x_2 \\
x_2 &amp;= \dot{u} &amp;\quad \dot{x}_2 = \ddot{u} \\\end{split}\]</div>
<p>becomes</p>
<div class="math notranslate nohighlight">
\[\begin{split}\dot{x}_1 &amp;= x_2 \\
\dot{x}_2 &amp;= m^{-1}(f(t) - d x_2 - k x_1) \\\end{split}\]</div>
<p>or</p>
<div class="math notranslate nohighlight">
\[\begin{split}\dot{x} &amp;= f(t,x) \\
\begin{bmatrix} \dot{x}_1 \\ \dot{x}_1 \end{bmatrix} &amp;=
\begin{bmatrix} x_2 \\ m^{-1}(f(t) - d x_2 - k x_1) \end{bmatrix} \\
&amp;=
\begin{bmatrix} 0 \\ m^{-1} f(t) \end{bmatrix} +
\begin{bmatrix} 0 &amp; 1 \\ -m^{-1} k &amp; -m^{-1} d \end{bmatrix}
\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\end{split}\]</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">
\[\begin{split}x_1 &amp;= u &amp;\quad \dot{x}_1 = \dot{u} = x_2 \\
x_2 &amp;= \dot{u} &amp;\quad \dot{x}_2 = \ddot{u} \\\end{split}\]</div>
<p>becomes</p>
<div class="math notranslate nohighlight">
\[\begin{split}\dot{x}_1 &amp;= x_2 \\
\dot{x}_2 &amp;= m^{-1}(x_1)(f(t) - d(x_1,x_2) x_2 - k(x_1) x_1) \\\end{split}\]</div>
<p>or</p>
<div class="math notranslate nohighlight">
\[\begin{split}\dot{x} &amp;= f(t,x) \\
\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} &amp;=
\begin{bmatrix} x_2 \\ m^{-1}(x_1)(f(t) - d(x_1,x_2) x_2 - k(x_1) x_1) \end{bmatrix} \\
&amp;=
\begin{bmatrix} 0 \\ m^{-1}(x_1) f(t) \end{bmatrix} +
\begin{bmatrix} 0 &amp; 1 \\ -m^{-1}(x_1) k(x_1) &amp; -m^{-1} d(x_1,x_2) \end{bmatrix}
\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\end{split}\]</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="solver.e2">
<code class="descname">e2</code><span class="sig-paren">(</span><em>f</em>, <em>x0</em>, <em>t</em>, <em>*p</em>, <em>verbose=False</em><span class="sig-paren">)</span><a class="headerlink" href="#solver.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="solver.e4">
<code class="descname">e4</code><span class="sig-paren">(</span><em>f</em>, <em>x0</em>, <em>t</em>, <em>*p</em>, <em>verbose=False</em><span class="sig-paren">)</span><a class="headerlink" href="#solver.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="solver.i1">
<code class="descname">i1</code><span class="sig-paren">(</span><em>f</em>, <em>x0</em>, <em>t</em>, <em>*p</em>, <em>max_iterations=1000</em>, <em>tol=1e-09</em>, <em>verbose=False</em><span class="sig-paren">)</span><a class="headerlink" href="#solver.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="solver.newmark_newtonraphson">
<code class="descname">newmark_newtonraphson</code><span class="sig-paren">(</span><em>f</em>, <em>x0</em>, <em>xp0</em>, <em>xpp0</em>, <em>t</em>, <em>*p</em>, <em>gamma=0.5</em>, <em>beta=0.25</em>, <em>max_iterations=1000</em>, <em>tol=1e-09</em>, <em>verbose=False</em><span class="sig-paren">)</span><a class="headerlink" href="#solver.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="solver.newmark_newtonraphson_rdk">
<code class="descname">newmark_newtonraphson_rdk</code><span class="sig-paren">(</span><em>fnm</em>, <em>x0</em>, <em>xp0</em>, <em>xpp0</em>, <em>t</em>, <em>*p</em>, <em>gamma=0.5</em>, <em>beta=0.25</em>, <em>maxIterations=1000</em>, <em>tol=1e-09</em>, <em>verbose=False</em><span class="sig-paren">)</span><a class="headerlink" href="#solver.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>
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<div class="section" id="module-solver_model">
<span id="solver-model-module"></span><h1>solver_model module<a class="headerlink" href="#module-solver_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-solver_model"></span><dl class="function">
<dt id="solver_model.disk">
<code class="descname">disk</code><span class="sig-paren">(</span><em>x</em>, <em>t</em>, <em>*p</em><span class="sig-paren">)</span><a class="headerlink" href="#solver_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="solver_model.disk_nm">
<code class="descname">disk_nm</code><span class="sig-paren">(</span><em>xn</em>, <em>xpn</em>, <em>xppn</em>, <em>t</em>, <em>*p</em><span class="sig-paren">)</span><a class="headerlink" href="#solver_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="solver_model.disk_nmmdk">
<code class="descname">disk_nmmdk</code><span class="sig-paren">(</span><em>xn</em>, <em>xpn</em>, <em>xppn</em>, <em>t</em>, <em>*p</em><span class="sig-paren">)</span><a class="headerlink" href="#solver_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>
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'highlight_bg': '#444F65',
'xref_bg': 'transparent',
'xref_border': 'transparent',
'seealso_bg': '#3c3c3c',
'seealso_border': '#2C2C2C',
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date
fit
geometry
solver
solver_model

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docs/source/solver.rst Normal file
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solver module
=============
.. automodule:: solver
:members:
:undoc-members:
:show-inheritance:

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solver\_model module
====================
.. automodule:: solver_model
:members:
:undoc-members:
:show-inheritance:

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src package
===========
Submodules
----------
src.data module
---------------
.. automodule:: src.data
:members:
:undoc-members:
:show-inheritance:
src.date module
---------------
.. automodule:: src.date
:members:
:undoc-members:
:show-inheritance:
src.fit module
--------------
.. automodule:: src.fit
:members:
:undoc-members:
:show-inheritance:
src.geometry module
-------------------
.. automodule:: src.geometry
:members:
:undoc-members:
:show-inheritance:
Module contents
---------------
.. automodule:: src
:members:
:undoc-members:
:show-inheritance: