Merge pull request #111 from stanweer1/test_release

Stochastic Bifurcation Code and Documentation
TeaspoonTDA · May 20, 2024 · 8ceb571 · 8ceb571
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diff --git a/doc_source/SP.rst b/doc_source/SP.rst
@@ -13,3 +13,4 @@ The signal processing module include various methods of analyzing a time series.
    Information Module <information.rst>
    Miscellaneous <misc.rst>
    Texture Analysis <texture_analysis.rst>
+   Stochastic P-Bifurcation Detection <stoch_bif.md>
diff --git a/doc_source/conf.py b/doc_source/conf.py
@@ -13,14 +13,17 @@
 from unittest import mock
 sys.modules['ripser'] = mock.Mock()
 
-
 # -- Project information -----------------------------------------------------
 
 project = 'teaspoon'
 copyright = '2020, Munch'
 author = 'Elizabeth Munch'
-release = '1.3.7'
+release = '1.5.3'
 
+source_suffix = {
+    '.rst': 'restructuredtext',
+    '.md': 'markdown',
+}
 
 # -- General configuration ---------------------------------------------------
 extensions = ['sphinx.ext.autodoc',
@@ -40,8 +43,11 @@
               'sphinxcontrib.bibtex',
               'sphinx-prompt',
               'nbsphinx',
-              'IPython.sphinxext.ipython_console_highlighting']
+              'IPython.sphinxext.ipython_console_highlighting',
+              'myst_parser']
+
 # Add any paths that contain templates here, relative to this directory.
+myst_heading_anchors = 5
 templates_path = ['_templates']
 exclude_patterns = []
 bibtex_bibfiles = ['references.bib']

diff --git a/doc_source/figures/analytical_homological_plot.png b/doc_source/figures/analytical_homological_plot.png
diff --git a/doc_source/stoch_bif.md b/doc_source/stoch_bif.md
@@ -0,0 +1,41 @@
+# Stochastic P-Bifurcation Detection
+
+Stochastic P-bifurcations are points of topological changes in the joint probability density function (PDF) of a stochastic system. Please cite the papers [“A topological framework for identifying phenomenological bifurcations in stochastic dynamical systems”](https://doi.org/10.1007/s11071-024-09289-1) and [“Topological Detection of Phenomenological Bifurcations with Unreliable Kernel Densities”](https://doi.org/10.48550/arXiv.2401.16563) when using these functions. These modules can be used to detect P-bifurcation given
+
+- [Analytical Densities](#analytical-density)
+
+## Analytical Density
+
+Given the analytical PDFs, the homological bifurcation plot can be generated with the module below
+
+```{eval-rst}
+.. automodule:: teaspoon.SP.StochasticP
+   :members: analytical_homological_bifurcation_plot
+```
+
+### Example
+
+The following example plots an analytical bifurcation plot for a set of PDFs where the system shifts from a monostability to a limit cycle:
+
+```python
+import numpy as np
+from teaspoon.SP.StochasticP import analytical_homological_bifurcation_plot
+X, Y = np.meshgrid(np.linspace(-3,3,100), np.linspace(-3,3,100))
+factors = np.linspace(-1,1,20)
+
+PDFs = []
+for h in factors:
+
+    p = np.exp(-0.5*((X**2+Y**2)**2 + h*(X**2 + Y**2)))
+    PDFs.append(p)
+
+M = analytical_homological_bifurcation_plot(PDFs, bifurcation_parameters=factors, dimensions=[1], filter=0.02, maxEps=1, numStops=100, plotting=True)
+```
+
+The output for this example is
+
+```{image} figures/analytical_homological_plot.png
+:alt: Analytical Homological Plot
+:width: 300px
+:align: left
+```
diff --git a/docs/.doctrees/AC.doctree b/docs/.doctrees/AC.doctree
diff --git a/docs/.doctrees/CL.doctree b/docs/.doctrees/CL.doctree
diff --git a/docs/.doctrees/CL_CC.doctree b/docs/.doctrees/CL_CC.doctree
diff --git a/docs/.doctrees/CL_KM.doctree b/docs/.doctrees/CL_KM.doctree
diff --git a/docs/.doctrees/CL_PI.doctree b/docs/.doctrees/CL_PI.doctree
diff --git a/docs/.doctrees/CL_PL.doctree b/docs/.doctrees/CL_PL.doctree
diff --git a/docs/.doctrees/CL_PS.doctree b/docs/.doctrees/CL_PS.doctree
diff --git a/docs/.doctrees/CL_TF.doctree b/docs/.doctrees/CL_TF.doctree
diff --git a/docs/.doctrees/DS.doctree b/docs/.doctrees/DS.doctree
diff --git a/docs/.doctrees/DynSysLib.doctree b/docs/.doctrees/DynSysLib.doctree
diff --git a/docs/.doctrees/FNN.doctree b/docs/.doctrees/FNN.doctree
diff --git a/docs/.doctrees/FSA.doctree b/docs/.doctrees/FSA.doctree
diff --git a/docs/.doctrees/F_PD.doctree b/docs/.doctrees/F_PD.doctree
diff --git a/docs/.doctrees/MI.doctree b/docs/.doctrees/MI.doctree
diff --git a/docs/.doctrees/ML.doctree b/docs/.doctrees/ML.doctree
diff --git a/docs/.doctrees/MakeData.doctree b/docs/.doctrees/MakeData.doctree
diff --git a/docs/.doctrees/MsPE.doctree b/docs/.doctrees/MsPE.doctree
diff --git a/docs/.doctrees/PAMI.doctree b/docs/.doctrees/PAMI.doctree
diff --git a/docs/.doctrees/PHN.doctree b/docs/.doctrees/PHN.doctree
diff --git a/docs/.doctrees/PointCloud.doctree b/docs/.doctrees/PointCloud.doctree
diff --git a/docs/.doctrees/SP.doctree b/docs/.doctrees/SP.doctree
diff --git a/docs/.doctrees/TDA.doctree b/docs/.doctrees/TDA.doctree
diff --git a/docs/.doctrees/citing.doctree b/docs/.doctrees/citing.doctree
diff --git a/docs/.doctrees/contributing.doctree b/docs/.doctrees/contributing.doctree
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diff --git a/docs/.doctrees/drawing.doctree b/docs/.doctrees/drawing.doctree
diff --git a/docs/.doctrees/environment.pickle b/docs/.doctrees/environment.pickle
diff --git a/docs/.doctrees/index.doctree b/docs/.doctrees/index.doctree
diff --git a/docs/.doctrees/information.doctree b/docs/.doctrees/information.doctree
diff --git a/docs/.doctrees/installation.doctree b/docs/.doctrees/installation.doctree
diff --git a/docs/.doctrees/license.doctree b/docs/.doctrees/license.doctree
diff --git a/docs/.doctrees/magnitude.doctree b/docs/.doctrees/magnitude.doctree
diff --git a/docs/.doctrees/misc.doctree b/docs/.doctrees/misc.doctree
diff --git a/docs/.doctrees/modules.doctree b/docs/.doctrees/modules.doctree
diff --git a/docs/.doctrees/nbsphinx/notebooks/distance.ipynb b/docs/.doctrees/nbsphinx/notebooks/distance.ipynb
diff --git a/docs/.doctrees/network.doctree b/docs/.doctrees/network.doctree
diff --git a/docs/.doctrees/parameter_selection.doctree b/docs/.doctrees/parameter_selection.doctree
diff --git a/docs/.doctrees/persistence.doctree b/docs/.doctrees/persistence.doctree
diff --git a/docs/.doctrees/sample_md.doctree b/docs/.doctrees/sample_md.doctree
diff --git a/docs/.doctrees/stoch_bif.doctree b/docs/.doctrees/stoch_bif.doctree
diff --git a/docs/.doctrees/stochastic_bifurcation.doctree b/docs/.doctrees/stochastic_bifurcation.doctree
diff --git a/docs/.doctrees/sublevel_set_persistence.doctree b/docs/.doctrees/sublevel_set_persistence.doctree
diff --git a/docs/.doctrees/texture_analysis.doctree b/docs/.doctrees/texture_analysis.doctree
diff --git a/docs/.doctrees/tsa.doctree b/docs/.doctrees/tsa.doctree
diff --git a/docs/SP.html b/docs/SP.html
@@ -1,47 +1,40 @@
 <!DOCTYPE html>
-<html class="writer-html5" lang="en" data-content_root="./">
+<html class="writer-html5" lang="en" >
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-
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+  <title>2.2. Signal Processing (SP) Module Documentation &mdash; teaspoon 1.3.7 documentation</title>
+      <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
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+        <script>window.MathJax = {"tex": {"inlineMath": [["$", "$"], ["\\(", "\\)"]], "processEscapes": true}, "options": {"ignoreHtmlClass": "tex2jax_ignore|mathjax_ignore|document", "processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
+        <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
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+    <link rel="next" title="2.2.1. Time Series Analysis (TSA) Tools" href="tsa.html" />
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@@ -77,33 +70,18 @@
 <li class="toctree-l3"><a class="reference internal" href="FNN.html#teaspoon.parameter_selection.FNN_n.FNN_n"><code class="docutils literal notranslate"><span class="pre">FNN_n()</span></code></a></li>
 </ul>
 </li>
-<li class="toctree-l2"><a class="reference internal" href="ML.html">2.2. Machine Learning (ML) Module</a><ul>
-<li class="toctree-l3"><a class="reference internal" href="DS.html">2.2.1. Datasets</a></li>
-<li class="toctree-l3"><a class="reference internal" href="F_PD.html">2.2.2. Featurization</a></li>
-<li class="toctree-l3"><a class="reference internal" href="CL.html">2.2.3. Classification</a></li>
-<li class="toctree-l3"><a class="reference internal" href="ML.html#references">2.2.4. References</a></li>
-</ul>
-</li>
-<li class="toctree-l2"><a class="reference internal" href="TDA.html">2.3. Topological Data Analaysis (TDA) Module</a><ul>
-<li class="toctree-l3"><a class="reference internal" href="PHN.html">2.3.1. Persistent Homology of Networks (PHN) Module</a></li>
-<li class="toctree-l3"><a class="reference internal" href="distances.html">2.3.2. Distances</a></li>
-<li class="toctree-l3"><a class="reference internal" href="drawing.html">2.3.3. Drawing</a></li>
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-<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 current"><a class="current reference internal" href="#">2.4. Signal Processing (SP) Module</a><ul>
-<li class="toctree-l3"><a class="reference internal" href="tsa.html">2.4.1. Time Series Analysis (TSA) Tools</a></li>
-<li class="toctree-l3"><a class="reference internal" href="network.html">2.4.2. Network Representation of Time Series</a></li>
-<li class="toctree-l3"><a class="reference internal" href="information.html">2.4.3. Information Module</a></li>
-<li class="toctree-l3"><a class="reference internal" href="misc.html">2.4.4. Miscellaneous</a></li>
-<li class="toctree-l3"><a class="reference internal" href="texture_analysis.html">2.4.5. Texture Analysis</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">2.2. Signal Processing (SP) Module</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="tsa.html">2.2.1. Time Series Analysis (TSA) Tools</a></li>
+<li class="toctree-l3"><a class="reference internal" href="network.html">2.2.2. Network Representation of Time Series</a></li>
+<li class="toctree-l3"><a class="reference internal" href="information.html">2.2.3. Information Module</a></li>
+<li class="toctree-l3"><a class="reference internal" href="misc.html">2.2.4. Miscellaneous</a></li>
+<li class="toctree-l3"><a class="reference internal" href="texture_analysis.html">2.2.5. Texture Analysis</a></li>
+<li class="toctree-l3"><a class="reference internal" href="stoch_bif.html">2.2.6. Stochastic P-Bifurcation Detection</a></li>
 </ul>
 </li>
-<li class="toctree-l2"><a class="reference internal" href="MakeData.html">2.5. Make Data (MakeData) Module</a><ul>
-<li class="toctree-l3"><a class="reference internal" href="PointCloud.html">2.5.1. Point Cloud Data Generation (PointCloud) Module</a></li>
-<li class="toctree-l3"><a class="reference internal" href="DynSysLib.html">2.5.2. Dynamic Systems Library (DynSysLib) Module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="MakeData.html">2.3. Make Data (MakeData) Module</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="PointCloud.html">2.3.1. Point Cloud Data Generation (PointCloud) Module</a></li>
+<li class="toctree-l3"><a class="reference internal" href="DynSysLib.html">2.3.2. Dynamic Systems Library (DynSysLib) Module</a></li>
 </ul>
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@@ -129,9 +107,9 @@
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           <div role="navigation" aria-label="Page navigation">
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+      <li><a href="index.html" class="icon icon-home"></a></li>
           <li class="breadcrumb-item"><a href="modules.html"><span class="section-number">2. </span>Table of Contents</a></li>
-      <li class="breadcrumb-item active"><span class="section-number">2.4. </span>Signal Processing (SP) Module Documentation</li>
+      <li class="breadcrumb-item active"><span class="section-number">2.2. </span>Signal Processing (SP) Module Documentation</li>
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@@ -141,16 +119,41 @@
           <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
            <div itemprop="articleBody">
 
-  <section id="signal-processing-sp-module-documentation">
-<span id="sp"></span><h1><span class="section-number">2.4. </span>Signal Processing (SP) Module Documentation<a class="headerlink" href="#signal-processing-sp-module-documentation" title="Link to this heading"></a></h1>
+
+<style>
+/* CSS overrides for sphinx_rtd_theme */
+
+/* 24px margin */
+.nbinput.nblast.container,
+.nboutput.nblast.container {
+    margin-bottom: 19px;  /* padding has already 5px */
+}
+
+/* ... except between code cells! */
+.nblast.container + .nbinput.container {
+    margin-top: -19px;
+}
+
+.admonition > p:before {
+    margin-right: 4px;  /* make room for the exclamation icon */
+}
+
+/* Fix math alignment, see https://github.com/rtfd/sphinx_rtd_theme/pull/686 */
+.math {
+    text-align: unset;
+}
+</style>
+<section id="signal-processing-sp-module-documentation">
+<span id="sp"></span><h1><span class="section-number">2.2. </span>Signal Processing (SP) Module Documentation<a class="headerlink" href="#signal-processing-sp-module-documentation" title="Link to this heading"></a></h1>
 <p>The signal processing module include various methods of analyzing a time series. The included modules are in the table of contents below. More description of each module is available at each sub-modules page.</p>
 <div class="toctree-wrapper compound">
 <ul>
-<li class="toctree-l1"><a class="reference internal" href="tsa.html">2.4.1. Time Series Analysis (TSA) Tools</a></li>
-<li class="toctree-l1"><a class="reference internal" href="network.html">2.4.2. Network Representation of Time Series</a></li>
-<li class="toctree-l1"><a class="reference internal" href="information.html">2.4.3. Information Module</a></li>
-<li class="toctree-l1"><a class="reference internal" href="misc.html">2.4.4. Miscellaneous</a></li>
-<li class="toctree-l1"><a class="reference internal" href="texture_analysis.html">2.4.5. Texture Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="tsa.html">2.2.1. Time Series Analysis (TSA) Tools</a></li>
+<li class="toctree-l1"><a class="reference internal" href="network.html">2.2.2. Network Representation of Time Series</a></li>
+<li class="toctree-l1"><a class="reference internal" href="information.html">2.2.3. Information Module</a></li>
+<li class="toctree-l1"><a class="reference internal" href="misc.html">2.2.4. Miscellaneous</a></li>
+<li class="toctree-l1"><a class="reference internal" href="texture_analysis.html">2.2.5. Texture Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="stoch_bif.html">2.2.6. Stochastic P-Bifurcation Detection</a></li>
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@@ -159,8 +162,8 @@
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diff --git a/docs/_images/analytical_homological_plot.png b/docs/_images/analytical_homological_plot.png