Merge pull request #94 from TeaspoonTDA/lizliz/issue88

Adding starting code for magnitude function
TeaspoonTDA · Mar 1, 2024 · 23e6e5d · 23e6e5d
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diff --git a/doc_source/TDA.rst b/doc_source/TDA.rst
@@ -10,4 +10,5 @@ This branch of the documentation covers tool used for topological data analysis.
    Distances <distances.rst>
    Drawing <drawing.rst>
    Persistence <persistence.rst>
-   Zero Dimensional Sublevel Set Persistence (SLSP) Module <sublevel_set_persistence.rst>
+   Zero Dimensional Sublevel Set Persistence (SLSP) Module <sublevel_set_persistence.rst>
+   Magnitude <magnitude.rst>
diff --git a/doc_source/magnitude.rst b/doc_source/magnitude.rst
@@ -0,0 +1,31 @@
+Magnitude
+=========
+
+This module is related to calculation of the magnitude. Some relevant links and references are below. 
+
+- `Magnitude in ncatlab <https://ncatlab.org/nlab/show/magnitude+of+an+enriched+category>`_.
+- Tom Leinster, The magnitude of metric spaces. Doc. Math. 18 (2013), pp. 857-905. doi: `10.4171/DM/415 <https://doi.org/10.4171/DM/415>`_. 
+- Miguel O'Malley, Sara Kalisnik, Nina Otter. Alpha magnitude. Journal of Pure and Applied Algebra, Volume 227, Issue 11,2023, doi: `10.1016/j.jpaa.2023.107396 <https://doi.org/10.1016/j.jpaa.2023.107396>`_.
+
+
+
+Magnitude function
+****************************************
+
+
+.. automodule:: teaspoon.TDA.Magnitude
+    :members: MagnitudeFunction
+    :noindex:
+
+
+.. This function calculates the magnitude function, ``t \\mapsto |tX|``, of an input distance matrix assumed to be calculated from a finite metric space ``X``, on the interval defined by `t_range` at `t_n` locations.
+
+.. - Given a finite metric space ``(X,d)`` and for matrix purposes, fix an order on the points ``x_1,\\cdots,x_n``.
+.. - Denote the distance matrix by ``D=[d(x_i,x_j)]_{ij}=[D_{ij}]_{ij}``
+.. - Denote the similarity matrix ``Z=Z_X`` to have entries ``Z_{ij}=e^{-D_{ij}}``
+.. - We'll also be interested in the scaled version for some ``t \\in (0,\\infty)``, where ``tZ`` is the matrix for metric space ``tX`` and ``tZ_{ij}=e^{-tD_{ij}}``
+.. - The magnitude of ``|tX|`` is 
+..   `` |tX| = \\sum_{i,j} ((tZ)^{-1})_{ij} ``
+.. where ``(tZ)^{-1}`` is the inverse of the matrix ``tZ``, assuming it exists. 
+.. - The magnitude function is 
+..   ``M: t \\mapsto |tX|`` 
diff --git a/docs/.buildinfo b/docs/.buildinfo
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diff --git a/docs/AC.html b/docs/AC.html
@@ -1,23 +1,24 @@
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   <title>2.1.2. Auto-correlation for time delay (tau). &mdash; teaspoon 1.3.7 documentation</title>
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@@ -31,12 +32,16 @@
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@@ -85,6 +90,7 @@
 <li class="toctree-l3"><a class="reference internal" href="drawing.html">2.3.3. Drawing</a></li>
 <li class="toctree-l3"><a class="reference internal" href="persistence.html">2.3.4. Persistence</a></li>
 <li class="toctree-l3"><a class="reference internal" href="sublevel_set_persistence.html">2.3.5. Zero Dimensional Sublevel Set Persistence (SLSP) Module</a></li>
+<li class="toctree-l3"><a class="reference internal" href="magnitude.html">2.3.6. Magnitude</a></li>
 </ul>
 </li>
 <li class="toctree-l2"><a class="reference internal" href="SP.html">2.4. Signal Processing (SP) Module</a><ul>
@@ -123,7 +129,7 @@
         <div class="rst-content style-external-links">
           <div role="navigation" aria-label="Page navigation">
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           <li class="breadcrumb-item"><a href="modules.html"><span class="section-number">2. </span>Table of Contents</a></li>
           <li class="breadcrumb-item"><a href="parameter_selection.html"><span class="section-number">2.1. </span>Parameter selection module documentation</a></li>
       <li class="breadcrumb-item active"><span class="section-number">2.1.2. </span>Auto-correlation for time delay (tau).</li>
@@ -136,43 +142,19 @@
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-<span class="target" id="module-teaspoon.parameter_selection.autocorrelation"></span><section id="auto-correlation-for-time-delay-tau">
-<h1><span class="section-number">2.1.2. </span>Auto-correlation for time delay (tau).<a class="headerlink" href="#auto-correlation-for-time-delay-tau" title="Permalink to this heading"></a></h1>
+  <section id="auto-correlation-for-time-delay-tau">
+<span id="module-teaspoon.parameter_selection.autocorrelation"></span><h1><span class="section-number">2.1.2. </span>Auto-correlation for time delay (tau).<a class="headerlink" href="#auto-correlation-for-time-delay-tau" title="Link to this heading"></a></h1>
 <p>This function implements Auto-Correlation (AC) for the selection of the delay tau for permutation entropy.
 Additionally, it only requires a single time series and has a fast computation time.
 However, this method is only designed for linear system.</p>
 </section>
 <dl class="py function">
 <dt class="sig sig-object py" id="teaspoon.parameter_selection.autocorrelation.autoCorrelation_tau">
-<span class="sig-prename descclassname"><span class="pre">teaspoon.parameter_selection.autocorrelation.</span></span><span class="sig-name descname"><span class="pre">autoCorrelation_tau</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ts</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cutoff</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.36788</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">AC_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'spearman'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plotting</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/teaspoon/parameter_selection/autocorrelation.html#autoCorrelation_tau"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#teaspoon.parameter_selection.autocorrelation.autoCorrelation_tau" title="Permalink to this definition"></a></dt>
+<span class="sig-prename descclassname"><span class="pre">teaspoon.parameter_selection.autocorrelation.</span></span><span class="sig-name descname"><span class="pre">autoCorrelation_tau</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ts</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cutoff</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.36788</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">AC_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'spearman'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plotting</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/teaspoon/parameter_selection/autocorrelation.html#autoCorrelation_tau"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#teaspoon.parameter_selection.autocorrelation.autoCorrelation_tau" title="Link to this definition"></a></dt>
 <dd><p>This function takes a time series and uses AC to find the optimum
 delay based on the correlation being less than a specified cutoff (default  is 1/e, which is approximately 0.36788).</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>ts</strong> (<em>array</em>) – Time series (1d).</p></li>
 <li><p><strong>cutoff</strong> (<em>float</em>) – value for which correlation is considered insignificant (default is 1/e).</p></li>
@@ -185,10 +167,10 @@ <h1><span class="section-number">2.1.2. </span>Auto-correlation for time delay (
 </dd>
 </dl>
 <dl class="field-list simple">
-<dt class="field-odd">Returns</dt>
+<dt class="field-odd">Returns<span class="colon">:</span></dt>
 <dd class="field-odd"><p>tau, The embedding delay for permutation formation.</p>
 </dd>
-<dt class="field-even">Return type</dt>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
 <dd class="field-even"><p>(int)</p>
 </dd>
 </dl>