deploy: 05e875f

Ziaeemehr · Aug 17, 2024 · 4d969fa · 4d969fa
commit 4d969fa
Show file tree

Hide file tree

Showing 86 changed files with 12,935 additions and 0 deletions.
diff --git a/.buildinfo b/.buildinfo
@@ -0,0 +1,4 @@
+# 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: 1da370696df4484fc42cb415bdbdc7c9
+tags: 645f666f9bcd5a90fca523b33c5a78b7
diff --git a/.doctrees/environment.pickle b/.doctrees/environment.pickle
diff --git a/.doctrees/examples/chap_03.doctree b/.doctrees/examples/chap_03.doctree
diff --git a/.doctrees/examples/chap_04.doctree b/.doctrees/examples/chap_04.doctree
diff --git a/.doctrees/examples/chap_05.doctree b/.doctrees/examples/chap_05.doctree
diff --git a/.doctrees/examples/chap_06.doctree b/.doctrees/examples/chap_06.doctree
diff --git a/.doctrees/index.doctree b/.doctrees/index.doctree
diff --git a/.doctrees/nbsphinx/examples/chap_03.ipynb b/.doctrees/nbsphinx/examples/chap_03.ipynb
diff --git a/.doctrees/nbsphinx/examples/chap_04.ipynb b/.doctrees/nbsphinx/examples/chap_04.ipynb
diff --git a/.doctrees/nbsphinx/examples/chap_05.ipynb b/.doctrees/nbsphinx/examples/chap_05.ipynb
diff --git a/.doctrees/nbsphinx/examples/chap_06.ipynb b/.doctrees/nbsphinx/examples/chap_06.ipynb
diff --git a/.doctrees/nbsphinx/examples_chap_03_12_3.png b/.doctrees/nbsphinx/examples_chap_03_12_3.png
diff --git a/.doctrees/nbsphinx/examples_chap_03_15_0.png b/.doctrees/nbsphinx/examples_chap_03_15_0.png
diff --git a/.doctrees/nbsphinx/examples_chap_03_9_3.png b/.doctrees/nbsphinx/examples_chap_03_9_3.png
diff --git a/.doctrees/nbsphinx/examples_chap_04_11_0.png b/.doctrees/nbsphinx/examples_chap_04_11_0.png
diff --git a/.doctrees/nbsphinx/examples_chap_04_9_0.png b/.doctrees/nbsphinx/examples_chap_04_9_0.png
diff --git a/.doctrees/nbsphinx/examples_chap_05_13_0.png b/.doctrees/nbsphinx/examples_chap_05_13_0.png
diff --git a/.doctrees/nbsphinx/examples_chap_05_6_0.png b/.doctrees/nbsphinx/examples_chap_05_6_0.png
diff --git a/.doctrees/nbsphinx/examples_chap_05_6_1.png b/.doctrees/nbsphinx/examples_chap_05_6_1.png
diff --git a/.doctrees/nbsphinx/examples_chap_05_9_0.png b/.doctrees/nbsphinx/examples_chap_05_9_0.png
diff --git a/.doctrees/nbsphinx/examples_chap_06_10_0.png b/.doctrees/nbsphinx/examples_chap_06_10_0.png
diff --git a/.doctrees/nbsphinx/examples_chap_06_12_0.png b/.doctrees/nbsphinx/examples_chap_06_12_0.png
diff --git a/.doctrees/nbsphinx/examples_chap_06_17_1.png b/.doctrees/nbsphinx/examples_chap_06_17_1.png
diff --git a/.doctrees/nbsphinx/examples_chap_06_18_1.png b/.doctrees/nbsphinx/examples_chap_06_18_1.png
diff --git a/.doctrees/nbsphinx/examples_chap_06_18_3.png b/.doctrees/nbsphinx/examples_chap_06_18_3.png
diff --git a/.doctrees/nbsphinx/examples_chap_06_21_1.png b/.doctrees/nbsphinx/examples_chap_06_21_1.png
diff --git a/.doctrees/nbsphinx/examples_chap_06_21_3.png b/.doctrees/nbsphinx/examples_chap_06_21_3.png
diff --git a/.doctrees/nbsphinx/examples_chap_06_24_1.png b/.doctrees/nbsphinx/examples_chap_06_24_1.png
diff --git a/.doctrees/nbsphinx/examples_chap_06_25_0.png b/.doctrees/nbsphinx/examples_chap_06_25_0.png
diff --git a/.doctrees/nbsphinx/examples_chap_06_6_0.png b/.doctrees/nbsphinx/examples_chap_06_6_0.png
diff --git a/.doctrees/nbsphinx/examples_chap_06_8_0.png b/.doctrees/nbsphinx/examples_chap_06_8_0.png
diff --git a/.nojekyll b/.nojekyll
diff --git a/_images/examples_chap_03_12_3.png b/_images/examples_chap_03_12_3.png
diff --git a/_images/examples_chap_03_15_0.png b/_images/examples_chap_03_15_0.png
diff --git a/_images/examples_chap_03_9_3.png b/_images/examples_chap_03_9_3.png
diff --git a/_images/examples_chap_04_11_0.png b/_images/examples_chap_04_11_0.png
diff --git a/_images/examples_chap_04_9_0.png b/_images/examples_chap_04_9_0.png
diff --git a/_images/examples_chap_05_13_0.png b/_images/examples_chap_05_13_0.png
diff --git a/_images/examples_chap_05_6_1.png b/_images/examples_chap_05_6_1.png
diff --git a/_images/examples_chap_05_9_0.png b/_images/examples_chap_05_9_0.png
diff --git a/_images/examples_chap_06_10_0.png b/_images/examples_chap_06_10_0.png
diff --git a/_images/examples_chap_06_12_0.png b/_images/examples_chap_06_12_0.png
diff --git a/_images/examples_chap_06_21_3.png b/_images/examples_chap_06_21_3.png
diff --git a/_images/examples_chap_06_24_1.png b/_images/examples_chap_06_24_1.png
diff --git a/_images/examples_chap_06_25_0.png b/_images/examples_chap_06_25_0.png
diff --git a/_images/examples_chap_06_6_0.png b/_images/examples_chap_06_6_0.png
diff --git a/_images/examples_chap_06_8_0.png b/_images/examples_chap_06_8_0.png
diff --git a/_modules/index.html b/_modules/index.html
@@ -0,0 +1,81 @@
+<!DOCTYPE html>
+
+<html lang="en" data-content_root="../">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>Overview: module code &#8212; spikes 0.1.dev1+g05e875f documentation</title>
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=82a976d7" />
+    <link rel="stylesheet" type="text/css" href="../_static/nature.css?v=0f882399" />
+    <link rel="stylesheet" type="text/css" href="../_static/graphviz.css?v=fd3f3429" />
+    <script src="../_static/documentation_options.js?v=cfd37796"></script>
+    <script src="../_static/doctools.js?v=9a2dae69"></script>
+    <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
+    <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
+    <link rel="index" title="Index" href="../genindex.html" />
+    <link rel="search" title="Search" href="../search.html" /> 
+  </head><body>
+    <div class="related" role="navigation" aria-label="Related">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../genindex.html" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="right" >
+          <a href="../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../index.html">spikes 0.1.dev1+g05e875f documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Overview: module code</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+
+  <h1>All modules for which code is available</h1>
+<ul><li><a href="spikes/plot.html">spikes.plot</a></li>
+<li><a href="spikes/solver.html">spikes.solver</a></li>
+<li><a href="spikes/utils.html">spikes.utils</a></li>
+</ul>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="Main">
+        <div class="sphinxsidebarwrapper">
+<search 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" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
+      <input type="submit" value="Go" />
+    </form>
+    </div>
+</search>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+        </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related" role="navigation" aria-label="Related">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../index.html">spikes 0.1.dev1+g05e875f documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Overview: module code</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+    &#169; Copyright 2024, Abolfazl Ziaeemehr.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.4.7.
+    </div>
+  </body>
+</html>
diff --git a/_modules/spikes/plot.html b/_modules/spikes/plot.html
diff --git a/_modules/spikes/solver.html b/_modules/spikes/solver.html
diff --git a/_modules/spikes/utils.html b/_modules/spikes/utils.html
@@ -0,0 +1,158 @@
+<!DOCTYPE html>
+
+<html lang="en" data-content_root="../../">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>spikes.utils &#8212; spikes 0.1.dev1+g05e875f documentation</title>
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=82a976d7" />
+    <link rel="stylesheet" type="text/css" href="../../_static/nature.css?v=0f882399" />
+    <link rel="stylesheet" type="text/css" href="../../_static/graphviz.css?v=fd3f3429" />
+    <script src="../../_static/documentation_options.js?v=cfd37796"></script>
+    <script src="../../_static/doctools.js?v=9a2dae69"></script>
+    <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
+    <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
+    <link rel="index" title="Index" href="../../genindex.html" />
+    <link rel="search" title="Search" href="../../search.html" /> 
+  </head><body>
+    <div class="related" role="navigation" aria-label="Related">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../genindex.html" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="right" >
+          <a href="../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../index.html">spikes 0.1.dev1+g05e875f documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../index.html" accesskey="U">Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">spikes.utils</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+
+  <h1>Source code for spikes.utils</h1><div class="highlight"><pre>
+<span></span><span class="kn">import</span> <span class="nn">spikes</span> 
+<span class="kn">import</span> <span class="nn">sympy</span>
+
+<div class="viewcode-block" id="characteristic_polynomial">
+<a class="viewcode-back" href="../../index.html#spikes.utils.characteristic_polynomial">[docs]</a>
+<span class="k">def</span> <span class="nf">characteristic_polynomial</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Computes the characteristic polynomial of a given matrix.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    matrix: (list of lists) </span>
+<span class="sd">        A 2D list representing the matrix.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    sympy.Poly: </span>
+<span class="sd">        The characteristic polynomial of the matrix.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="c1"># Define the symbolic variable</span>
+    <span class="n">x</span> <span class="o">=</span> <span class="n">sympy</span><span class="o">.</span><span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;x&#39;</span><span class="p">)</span>
+
+    <span class="c1"># Convert the input matrix to a sympy.Matrix</span>
+    <span class="n">A</span> <span class="o">=</span> <span class="n">sympy</span><span class="o">.</span><span class="n">Matrix</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
+
+    <span class="c1"># Compute the characteristic polynomial</span>
+    <span class="n">char_poly</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">charpoly</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+
+    <span class="c1"># Get the polynomial coefficients</span>
+    <span class="n">coefficients</span> <span class="o">=</span> <span class="n">char_poly</span><span class="o">.</span><span class="n">all_coeffs</span><span class="p">()</span>
+
+    <span class="c1"># Create the polynomial using sympy.Poly</span>
+    <span class="n">p</span> <span class="o">=</span> <span class="n">sympy</span><span class="o">.</span><span class="n">Poly</span><span class="p">(</span><span class="n">coefficients</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">p</span></div>
+
+
+
+<div class="viewcode-block" id="routh">
+<a class="viewcode-back" href="../../index.html#spikes.utils.routh">[docs]</a>
+<span class="k">def</span> <span class="nf">routh</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot; Construct the Routh-Hurwitz array given a polynomial in s</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    p: sympy.Poly</span>
+<span class="sd">        The characteristic polynomial of coefficient matrix</span>
+<span class="sd">    </span>
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    value: sympy.Matrix</span>
+<span class="sd">        The Routh-Hurwitz array</span>
+<span class="sd">    </span>
+<span class="sd">    References https://github.com/alchemyst/Dynamics-and-Control/blob/master/tbcontrol/symbolic.py</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">coefficients</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">all_coeffs</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">coefficients</span><span class="p">)</span>
+    <span class="n">M</span> <span class="o">=</span> <span class="n">sympy</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">N</span><span class="p">,</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="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+
+    <span class="n">r1</span> <span class="o">=</span> <span class="n">coefficients</span><span class="p">[</span><span class="mi">0</span><span class="p">::</span><span class="mi">2</span><span class="p">]</span>
+    <span class="n">r2</span> <span class="o">=</span> <span class="n">coefficients</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="n">M</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:</span><span class="nb">len</span><span class="p">(</span><span class="n">r1</span><span class="p">)]</span> <span class="o">=</span> <span class="p">[</span><span class="n">r1</span><span class="p">]</span>
+    <span class="n">M</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:</span><span class="nb">len</span><span class="p">(</span><span class="n">r2</span><span class="p">)]</span> <span class="o">=</span> <span class="p">[</span><span class="n">r2</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="mi">2</span><span class="p">,</span> <span class="n">N</span><span class="p">):</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">N</span><span class="o">//</span><span class="mi">2</span><span class="p">):</span>
+            <span class="n">S</span> <span class="o">=</span> <span class="n">M</span><span class="p">[[</span><span class="n">i</span><span class="o">-</span><span class="mi">2</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="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]]</span>
+            <span class="n">M</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">sympy</span><span class="o">.</span><span class="n">simplify</span><span class="p">(</span><span class="o">-</span><span class="n">S</span><span class="o">.</span><span class="n">det</span><span class="p">()</span><span class="o">/</span><span class="n">M</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="mi">0</span><span class="p">])</span>
+        <span class="c1"># If a row of the routh table becomes zero,Take the derivative of the previous row and substitute it instead</span>
+        <span class="c1"># Ref: Norman S. Nise, Control Systems Engineering, 8th Edition, Chapter 6, Section 3</span>
+        <span class="k">if</span> <span class="n">M</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:]</span> <span class="o">==</span> <span class="n">sympy</span><span class="o">.</span><span class="n">Matrix</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">M</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">])]):</span>
+            <span class="c1"># Find the coefficients on taking the derivative of the Auxiliary polynomial</span>
+            <span class="n">diff_arr</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="o">-</span><span class="n">i</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">2</span><span class="p">))</span>
+            <span class="n">diff_arr</span><span class="o">.</span><span class="n">extend</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">M</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="nb">len</span><span class="p">(</span><span class="n">diff_arr</span><span class="p">)))</span>
+            <span class="n">diff_arr</span> <span class="o">=</span> <span class="n">sympy</span><span class="o">.</span><span class="n">Matrix</span><span class="p">([</span><span class="n">diff_arr</span><span class="p">])</span>
+            <span class="c1"># Multiply the coefficients with the value in previous row</span>
+            <span class="n">M</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">sympy</span><span class="o">.</span><span class="n">matrix_multiply_elementwise</span><span class="p">(</span><span class="n">diff_arr</span><span class="p">,</span> <span class="n">M</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="p">:])</span>
+    <span class="k">return</span> <span class="n">M</span><span class="p">[:,</span> <span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span></div>
+
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="Main">
+        <div class="sphinxsidebarwrapper">
+<search 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" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
+      <input type="submit" value="Go" />
+    </form>
+    </div>
+</search>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+        </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related" role="navigation" aria-label="Related">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../index.html">spikes 0.1.dev1+g05e875f documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">spikes.utils</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+    &#169; Copyright 2024, Abolfazl Ziaeemehr.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.4.7.
+    </div>
+  </body>
+</html>