add transformation function

docs/build/html/_modules/function.html

@@ -37,7 +37,7 @@
 <span class="c1"># -*- coding: utf-8 -*-</span>
 <span class="sd">&quot;&quot;&quot;Mathematical equations.</span>
 
-<span class="sd">:Date: 2019-11-02</span>
+<span class="sd">:Date: 2019-11-04</span>
 
 <span class="sd">.. module:: function</span>
 <span class="sd">  :platform: *nix, Windows</span>
@@ -48,6 +48,50 @@
 <span class="kn">import</span> <span class="nn">math</span>
 <span class="kn">from</span> <span class="nn">pylib.mathematics</span> <span class="k">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">&quot;&quot;&quot;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: &quot;a&quot; 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: &quot;b&quot; 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: &quot;c&quot; 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: &quot;d&quot; 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">  &quot;&quot;&quot;</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">function_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">function_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">&quot;&quot;&quot;A sine wave or sinusoid is a mathematical curve that describes a</span>
 <span class="sd">  smooth periodic oscillation.</span>

docs/build/html/function.html

@@ -37,7 +37,7 @@
 <p>Mathematical equations.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Date</dt>
-<dd class="field-odd"><p>2019-11-02</p>
+<dd class="field-odd"><p>2019-11-04</p>
 </dd>
 </dl>
 <span class="target" id="module-function"></span><dl class="function">
@@ -232,6 +232,35 @@ linear speed.</p>
 </div>
 </dd></dl>
 
+<dl class="function">
+<dt id="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>
+<dd><p>Transform functions.</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 or list of functions</p></li>
+<li><p><strong>scale_vertical</strong> – “a” scale factor in vertical direction (default
+= 1)</p></li>
+<li><p><strong>scale_horizontal</strong> – “b” scale factor in horizontal direction
+(default = 1)</p></li>
+<li><p><strong>shift_horizontal</strong> – “c” shift factor in horizontal direction
+(default = 0)</p></li>
+<li><p><strong>shift_vertical</strong> – “d” shift factor in vertical direction (default
+= 0)</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p>transformed function or list of transformed functions</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>function or list</p>
+</dd>
+</dl>
+<div class="math notranslate nohighlight">
+\[y = a \, f(b\,(x-c)) + d\]</div>
+</dd></dl>
+
 </div>
 
 

docs/build/html/genindex.html

@@ -319,6 +319,8 @@
       <li><a href="time_of_day.html#module-time_of_day">time_of_day (module)</a>, <a href="time_of_day.html#module-time_of_day">[1]</a>
 </li>
       <li><a href="time_of_day.html#time_of_day.transform">transform() (in module time_of_day)</a>
+</li>
+      <li><a href="function.html#function.transformation">transformation() (in module function)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>

pylib/function.py

@@ -2,7 +2,7 @@
 # -*- coding: utf-8 -*-
 """Mathematical equations.
 
-:Date: 2019-11-02
+:Date: 2019-11-04
 
 .. module:: function
   :platform: *nix, Windows
@@ -13,6 +13,50 @@
 import math
 from pylib.mathematics import lcm
 
+def transformation(f, scale_vertical=1, scale_horizontal=1,
+                   shift_horizontal=0, shift_vertical=0):
+  r"""Transform functions.
+
+  :param f: function or list of functions
+  :type f: function or list
+  :param scale_vertical: "a" scale factor in vertical direction (default
+    = 1)
+  :type height: float
+  :param scale_horizontal: "b" scale factor in horizontal direction
+    (default = 1)
+  :type height: float
+  :param shift_horizontal: "c" shift factor in horizontal direction
+    (default = 0)
+  :type height: float
+  :param shift_vertical: "d" shift factor in vertical direction (default
+    = 0)
+  :type height: float
+
+  :returns: transformed function or list of transformed functions
+  :rtype: function or list
+
+  .. math::
+    y = a \, f(b\,(x-c)) + d
+  """
+  # shorter variables
+  a = scale_vertical
+  b = scale_horizontal
+  c = shift_horizontal
+  d = shift_vertical
+
+  # check if f is a function than put it in a list and return only
+  # the function, not the one element list
+  if callable(f):
+    return function_transformation(
+      [f], scale_vertical=a, scale_horizontal=b, shift_horizontal=c, shift_vertical=d)[0]
+
+  # otherwise assume list of functions
+  if not f:  # if f is empty. End of the recursive fucntion
+    return []
+  return [lambda x, t: a*f[0](b*(x-c), t)+d] +\
+    function_transformation(
+      f[1:], scale_vertical=a, scale_horizontal=b, shift_horizontal=c, shift_vertical=d)
+
 def sine_wave(A=1, k=1, f=1, phi=0, D=0, degree=False):
   r"""A sine wave or sinusoid is a mathematical curve that describes a
   smooth periodic oscillation.