пре 3 година · 0e900f565e
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				+      <h1 class="site-logo" id="site-title">State Space Models: A Modern Approach</h1>
			
 
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				+   State Space Models: A Modern Approach
			
 
				+  </a>
			
 
				+ </li>
			
 
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				+<ul class="nav bd-sidenav">
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/scratch.html">
			
 
				+   Scratchpad
			
 
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				+ </li>
			
 
				+ <li class="toctree-l1 has-children">
			
 
				+  <a class="reference internal" href="chapters/ssm/ssm_index.html">
			
 
				+   Introduction
			
 
				+  </a>
			
 
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				+  </label>
			
 
				+  <ul>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/ssm/hmm.html">
			
 
				+     Hidden Markov Models
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/ssm/hsmm.html">
			
 
				+     Hidden Semi-Markov Models
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/ssm/lgssm.html">
			
 
				+     Linear Gaussian SSMs
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/ssm/nonlin.html">
			
 
				+     Non-Linear Gaussian SSMs
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/ssm/nongauss.html">
			
 
				+     Non-Gaussian SSMs
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/ssm/switching.html">
			
 
				+     Switching SSMs
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/ssm/deep.html">
			
 
				+     Deep SSMs
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/ssm/rnn.html">
			
 
				+     Recurrent Neural Networks
			
 
				+    </a>
			
 
				+   </li>
			
 
				+  </ul>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1 has-children">
			
 
				+  <a class="reference internal" href="chapters/hmm/hmm_index.html">
			
 
				+   Inference in discrete SSMs
			
 
				+  </a>
			
 
				+  <input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/>
			
 
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				+  <ul>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/hmm/hmm_filter.html">
			
 
				+     HMM filtering (forwards algorithm)
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/hmm/hmm_smoother.html">
			
 
				+     HMM smoothing (forwards-backwards algorithm)
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/hmm/hmm_viterbi.html">
			
 
				+     Viterbi algorithm
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/hmm/hmm_parallel.html">
			
 
				+     Parallel HMM  smoothing
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/hmm/hmm_sampling.html">
			
 
				+     Forwards-filtering backwards-sampling algorithm
			
 
				+    </a>
			
 
				+   </li>
			
 
				+  </ul>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1 has-children">
			
 
				+  <a class="reference internal" href="chapters/lgssm/lgssm_index.html">
			
 
				+   Inference in linear-Gaussian SSMs
			
 
				+  </a>
			
 
				+  <input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/>
			
 
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				+  <ul>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/lgssm/kalman_filter.html">
			
 
				+     Kalman filtering
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/lgssm/kalman_smoother.html">
			
 
				+     Kalman (RTS) smoother
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/lgssm/kalman_parallel.html">
			
 
				+     Parallel Kalman Smoother
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/lgssm/kalman_sampling.html">
			
 
				+     Forwards-filtering backwards sampling
			
 
				+    </a>
			
 
				+   </li>
			
 
				+  </ul>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1 has-children">
			
 
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				+   Extended (linearized) methods
			
 
				+  </a>
			
 
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				+   <li class="toctree-l2">
			
 
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				+     Extended Kalman filtering
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/extended/extended_smoother.html">
			
 
				+     Extended Kalman smoother
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/extended/extended_parallel.html">
			
 
				+     Parallel extended Kalman smoothing
			
 
				+    </a>
			
 
				+   </li>
			
 
				+  </ul>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1 has-children">
			
 
				+  <a class="reference internal" href="chapters/unscented/unscented_index.html">
			
 
				+   Unscented methods
			
 
				+  </a>
			
 
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				+  <ul>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/unscented/unscented_filter.html">
			
 
				+     Unscented filtering
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/unscented/unscented_smoother.html">
			
 
				+     Unscented smoothing
			
 
				+    </a>
			
 
				+   </li>
			
 
				+  </ul>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/quadrature/quadrature_index.html">
			
 
				+   Quadrature and cubature methods
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/postlin/postlin_index.html">
			
 
				+   Posterior linearization
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/adf/adf_index.html">
			
 
				+   Assumed Density Filtering
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/vi/vi_index.html">
			
 
				+   Variational inference
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/pf/pf_index.html">
			
 
				+   Particle filtering
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/smc/smc_index.html">
			
 
				+   Sequential Monte Carlo
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1 has-children">
			
 
				+  <a class="reference internal" href="chapters/learning/learning_index.html">
			
 
				+   Offline parameter estimation (learning)
			
 
				+  </a>
			
 
				+  <input class="toctree-checkbox" id="toctree-checkbox-6" name="toctree-checkbox-6" type="checkbox"/>
			
 
				+  <label for="toctree-checkbox-6">
			
 
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				+  <ul>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/learning/em.html">
			
 
				+     Expectation Maximization (EM)
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/learning/sgd.html">
			
 
				+     Stochastic Gradient Descent (SGD)
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/learning/vb.html">
			
 
				+     Variational Bayes (VB)
			
 
				+    </a>
			
 
				+   </li>
			
 
				+   <li class="toctree-l2">
			
 
				+    <a class="reference internal" href="chapters/learning/mcmc.html">
			
 
				+     Markov Chain Monte Carlo (MCMC)
			
 
				+    </a>
			
 
				+   </li>
			
 
				+  </ul>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/tracking/tracking_index.html">
			
 
				+   Multi-target tracking
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/ensemble/ensemble_index.html">
			
 
				+   Data assimilation using Ensemble Kalman filter
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/bnp/bnp_index.html">
			
 
				+   Bayesian non-parametric SSMs
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/changepoint/changepoint_index.html">
			
 
				+   Changepoint detection
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/timeseries/timeseries_index.html">
			
 
				+   Timeseries forecasting
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/gp/gp_index.html">
			
 
				+   Markovian Gaussian processes
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/ode/ode_index.html">
			
 
				+   Differential equations and SSMs
			
 
				+  </a>
			
 
				+ </li>
			
 
				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="chapters/control/control_index.html">
			
 
				+   Optimal control
			
 
				+  </a>
			
 
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				+ <li class="toctree-l1">
			
 
				+  <a class="reference internal" href="bib.html">
			
 
				+   Bibliography
			
 
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				+                <h1>ssm-book</h1>
			
 
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				+                <div id="print-main-content">
			
 
				+                    <div id="jb-print-toc">
			
 
				+                        
			
 
				+                    </div>
			
 
				+                </div>
			
 
				+            </div>
			
 
				+            
			
 
				+              <div>
			
 
				+                
			
 
				+  <div class="tex2jax_ignore mathjax_ignore section" id="ssm-book">
			
 
				+<h1>ssm-book<a class="headerlink" href="#ssm-book" title="Permalink to this headline">¶</a></h1>
			
 
				+<p>Interactive textbook on state-space models.
			
 
				+The rendered content can be found at <a class="reference external" href="https://probml.github.io/ssm-book/root.html">https://probml.github.io/ssm-book/root.html</a>.</p>
			
 
				+</div>
			
 
				+
			
 
				+    <script type="text/x-thebe-config">
			
 
				+    {
			
 
				+        requestKernel: true,
			
 
				+        binderOptions: {
			
 
				+            repo: "binder-examples/jupyter-stacks-datascience",
			
 
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				+            theme: "abcdef",
			
 
				+            mode: "python"
			
 
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				+    </script>
			
 
				+    <script>kernelName = 'python3'</script>
			
 
				+
			
 
				+              </div>
			
 
				+              
			
 
				+            
			
 
				+                <!-- Previous / next buttons -->
			
 
				+<div class='prev-next-area'>
			
 
				+</div>
			
 
				+            
			
 
				+        </div>
			
 
				+    </div>
			
 
				+    <footer class="footer">
			
 
				+  <p>
			
 
				+    
			
 
				+      By Kevin Murphy, Scott Linderman, et al.<br/>
			
 
				+    
			
 
				+        &copy; Copyright 2021.<br/>
			
 
				+  </p>
			
 
				+</footer>
			
 
				+</main>
			
 
				+
			
 
				+
			
 
				+      </div>
			
 
				+    </div>
			
 
				+  
			
 
				+  <script src="_static/js/index.be7d3bbb2ef33a8344ce.js"></script>
			
 
				+
			
 
				+  </body>
			
 
				+</html>
			
--- a/_images/casino.png
+++ b/_images/casino.png
--- a/_images/cat_dog.jpg
+++ b/_images/cat_dog.jpg
--- a/_images/scratch_2_0.png
+++ b/_images/scratch_2_0.png
--- a/_panels_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css
+++ b/_panels_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css
--- a/_panels_static/panels-variables.06eb56fa6e07937060861dad626602ad.css
+++ b/_panels_static/panels-variables.06eb56fa6e07937060861dad626602ad.css
@@ -0,0 +1,7 @@
 
				+:root {
			
 
				+--tabs-color-label-active: hsla(231, 99%, 66%, 1);
			
 
				+--tabs-color-label-inactive: rgba(178, 206, 245, 0.62);
			
 
				+--tabs-color-overline: rgb(207, 236, 238);
			
 
				+--tabs-color-underline: rgb(207, 236, 238);
			
 
				+--tabs-size-label: 1rem;
			
 
				+}
			
--- a/_sources/README.md
+++ b/_sources/README.md
@@ -0,0 +1,3 @@
 
				+# ssm-book
			
 
				+Interactive textbook on state-space models.
			
 
				+The rendered content can be found at [https://probml.github.io/ssm-book/root.html](https://probml.github.io/ssm-book/root.html).
			
--- a/_sources/bib.md
+++ b/_sources/bib.md
@@ -0,0 +1,5 @@
 
				+# Bibliography
			
 
				+
			
 
				+
			
 
				+```{bibliography}
			
 
				+```
			
--- a/_sources/chapters/adf/adf_index.md
+++ b/_sources/chapters/adf/adf_index.md
@@ -0,0 +1,13 @@
 
				+
			
 
				+
			
 
				+(ch:ADF)=
			
 
				+# Assumed Density Filtering
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/blank.ipynb
+++ b/_sources/chapters/blank.ipynb
@@ -0,0 +1,39 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "(chap:my-chap)=\n",
			
 
				+    "# Chapter title\n",
			
 
				+    "\n"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": []
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/bnp/bnp_index.md
+++ b/_sources/chapters/bnp/bnp_index.md
@@ -0,0 +1,9 @@
 
				+
			
 
				+
			
 
				+(ch:BNP)=
			
 
				+# Bayesian non-parametric SSMs
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/changepoint/changepoint_index.md
+++ b/_sources/chapters/changepoint/changepoint_index.md
@@ -0,0 +1,14 @@
 
				+
			
 
				+
			
 
				+(ch:changepoint)=
			
 
				+# Changepoint detection
			
 
				+
			
 
				+
			
 
				+
			
 
				+{cite}`Agudelo-Espana2020`, {cite}`Adams2007`, {cite}`Fearnhead04`, {cite}`Fearnhead06`, {cite}`Fearnhead07`, 
			
 
				+{cite}`Fearnhead11`
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/control/control_index.md
+++ b/_sources/chapters/control/control_index.md
@@ -0,0 +1,19 @@
 
				+
			
 
				+
			
 
				+(ch:control)=
			
 
				+# Optimal control
			
 
				+
			
 
				+
			
 
				+{cite}`Botvinick2012`, {cite}`Kappen2012`, {cite}`Rawlik2012`
			
 
				+
			
 
				+## LQR
			
 
				+
			
 
				+## MPC
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/ensemble/ensemble_index.md
+++ b/_sources/chapters/ensemble/ensemble_index.md
@@ -0,0 +1,10 @@
 
				+
			
 
				+
			
 
				+(ch:ensemble)=
			
 
				+# Data assimilation using Ensemble Kalman filter
			
 
				+
			
 
				+
			
 
				+{cite}`Evensen2009`, {cite}`Roth2017enkf`
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/extended/extended_filter.ipynb
+++ b/_sources/chapters/extended/extended_filter.ipynb
@@ -0,0 +1,32 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Extended Kalman filtering"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/extended/extended_index.md
+++ b/_sources/chapters/extended/extended_index.md
@@ -0,0 +1,7 @@
 
				+
			
 
				+
			
 
				+(ch:extended)=
			
 
				+# Extended (linearized) methods 
			
 
				+
			
 
				+```{tableofcontents}
			
 
				+```
			
--- a/_sources/chapters/extended/extended_parallel.ipynb
+++ b/_sources/chapters/extended/extended_parallel.ipynb
@@ -0,0 +1,34 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Parallel extended Kalman smoothing\n",
			
 
				+    "\n",
			
 
				+    "{cite}`Sarkka2020icassp`\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/extended/extended_smoother.ipynb
+++ b/_sources/chapters/extended/extended_smoother.ipynb
@@ -0,0 +1,32 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Extended Kalman smoother"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/gp/gp_index.md
+++ b/_sources/chapters/gp/gp_index.md
@@ -0,0 +1,13 @@
 
				+
			
 
				+
			
 
				+(ch:GP)=
			
 
				+# Markovian Gaussian processes
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/hmm/hmm_filter.ipynb
+++ b/_sources/chapters/hmm/hmm_filter.ipynb
@@ -0,0 +1,32 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# HMM filtering (forwards algorithm)\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/hmm/hmm_index.md
+++ b/_sources/chapters/hmm/hmm_index.md
@@ -0,0 +1,10 @@
 
				+(ch:hmm)=
			
 
				+# Inference in discrete SSMs 
			
 
				+
			
 
				+This chapter covers inference in HMMs.
			
 
				+
			
 
				+
			
 
				+```{tableofcontents}
			
 
				+```
			
 
				+
			
 
				+See (sec:casino-ex).
			
--- a/_sources/chapters/hmm/hmm_parallel.ipynb
+++ b/_sources/chapters/hmm/hmm_parallel.ipynb
@@ -0,0 +1,36 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Parallel HMM  smoothing\n",
			
 
				+    "\n",
			
 
				+    "{cite}`Hassan2021`\n",
			
 
				+    "\n",
			
 
				+    "\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/hmm/hmm_sampling.ipynb
+++ b/_sources/chapters/hmm/hmm_sampling.ipynb
@@ -0,0 +1,32 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Forwards-filtering backwards-sampling algorithm\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/hmm/hmm_smoother.ipynb
+++ b/_sources/chapters/hmm/hmm_smoother.ipynb
@@ -0,0 +1,51 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# HMM smoothing (forwards-backwards algorithm)\n"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "## Forwards filter, backwards smoother algorithm"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "## Two-filter algorithm"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": []
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/hmm/hmm_viterbi.ipynb
+++ b/_sources/chapters/hmm/hmm_viterbi.ipynb
@@ -0,0 +1,32 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Viterbi algorithm\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/learning/em.ipynb
+++ b/_sources/chapters/learning/em.ipynb
@@ -0,0 +1,35 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "(sec:em)=\n",
			
 
				+    "# Expectation Maximization (EM)\n",
			
 
				+    "\n",
			
 
				+    "{cite}`Ghahramani96a`\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.8"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/learning/learning_index.md
+++ b/_sources/chapters/learning/learning_index.md
@@ -0,0 +1,7 @@
 
				+
			
 
				+
			
 
				+(ch:learning)=
			
 
				+# Offline parameter estimation (learning)
			
 
				+
			
 
				+```{tableofcontents}
			
 
				+```
			
--- a/_sources/chapters/learning/mcmc.ipynb
+++ b/_sources/chapters/learning/mcmc.ipynb
@@ -0,0 +1,34 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "(sec:mcmc)=\n",
			
 
				+    "# Markov Chain Monte Carlo (MCMC)\n",
			
 
				+    "\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.8"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/learning/sgd.ipynb
+++ b/_sources/chapters/learning/sgd.ipynb
@@ -0,0 +1,34 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "(sec:sgd)=\n",
			
 
				+    "# Stochastic Gradient Descent (SGD)\n",
			
 
				+    "\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.8"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/learning/vb.ipynb
+++ b/_sources/chapters/learning/vb.ipynb
@@ -0,0 +1,35 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "\n",
			
 
				+    "(sec:VB)=\n",
			
 
				+    "# Variational Bayes (VB)\n",
			
 
				+    "\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.8"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/lgssm/kalman_filter.ipynb
+++ b/_sources/chapters/lgssm/kalman_filter.ipynb
@@ -0,0 +1,32 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Kalman filtering"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/lgssm/kalman_parallel.ipynb
+++ b/_sources/chapters/lgssm/kalman_parallel.ipynb
@@ -0,0 +1,37 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Parallel Kalman Smoother\n",
			
 
				+    "\n",
			
 
				+    "{cite}`Sarkka2021`\n",
			
 
				+    "\n",
			
 
				+    "\n",
			
 
				+    "\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/lgssm/kalman_sampling.ipynb
+++ b/_sources/chapters/lgssm/kalman_sampling.ipynb
@@ -0,0 +1,32 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Forwards-filtering backwards sampling"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/lgssm/kalman_smoother.ipynb
+++ b/_sources/chapters/lgssm/kalman_smoother.ipynb
@@ -0,0 +1,32 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Kalman (RTS) smoother"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/lgssm/lgssm_index.md
+++ b/_sources/chapters/lgssm/lgssm_index.md
@@ -0,0 +1,7 @@
 
				+
			
 
				+
			
 
				+(ch:lgssm)=
			
 
				+# Inference in linear-Gaussian SSMs
			
 
				+
			
 
				+```{tableofcontents}
			
 
				+```
			
--- a/_sources/chapters/ode/ode_index.md
+++ b/_sources/chapters/ode/ode_index.md
@@ -0,0 +1,12 @@
 
				+
			
 
				+
			
 
				+(ch:ODE)=
			
 
				+# Differential equations and SSMs
			
 
				+
			
 
				+
			
 
				+{cite}`Tronarp2019`, {cite}`Sarkka2019book`, {cite}`HennigBook`
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/pf/pf_index.md
+++ b/_sources/chapters/pf/pf_index.md
@@ -0,0 +1,10 @@
 
				+
			
 
				+
			
 
				+(ch:PF)=
			
 
				+# Particle filtering
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/postlin/postlin_index.md
+++ b/_sources/chapters/postlin/postlin_index.md
@@ -0,0 +1,12 @@
 
				+
			
 
				+
			
 
				+(ch:postlin)=
			
 
				+# Posterior linearization
			
 
				+
			
 
				+
			
 
				+{cite}`Garcia-Fernandez2017`, {cite}`Tronarp2018`, {cite}`Garcia-Fernandez2019`
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/quadrature/quadrature_index.md
+++ b/_sources/chapters/quadrature/quadrature_index.md
@@ -0,0 +1,12 @@
 
				+
			
 
				+
			
 
				+(ch:quadrature)=
			
 
				+# Quadrature and cubature methods
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/scratch.ipynb
+++ b/_sources/chapters/scratch.ipynb
--- a/_sources/chapters/scratch.md
+++ b/_sources/chapters/scratch.md
@@ -0,0 +1,116 @@
 
				+---
			
 
				+jupytext:
			
 
				+  cell_metadata_filter: -all
			
 
				+  formats: md:myst
			
 
				+  text_representation:
			
 
				+    extension: .md
			
 
				+    format_name: myst
			
 
				+kernelspec:
			
 
				+  display_name: Python 3
			
 
				+  language: python
			
 
				+  name: python3
			
 
				+---
			
 
				+
			
 
				+(ch:intro)=
			
 
				+# Scratchpad
			
 
				+
			
 
				+
			
 
				+In this chapter, we do blah.
			
 
				+Specifically
			
 
				+
			
 
				+- foo
			
 
				+- bar.
			
 
				+- baz
			
 
				+
			
 
				+For more details, see 
			
 
				+{ref}`ch:hmm` and  {cite}`Sarkka13`.
			
 
				+
			
 
				+
			
 
				+## Python
			
 
				+
			
 
				+We\'re now ready to start coding.
			
 
				+
			
 
				+```{code-cell}
			
 
				+from matplotlib import rcParams, cycler
			
 
				+import matplotlib.pyplot as plt
			
 
				+import numpy as np
			
 
				+plt.ion()
			
 
				+```
			
 
				+
			
 
				+```{code-cell}
			
 
				+# Fixing random state for reproducibility
			
 
				+np.random.seed(19680801)
			
 
				+
			
 
				+N = 10
			
 
				+data = [np.logspace(0, 1, 100) + np.random.randn(100) + ii for ii in range(N)]
			
 
				+data = np.array(data).T
			
 
				+cmap = plt.cm.coolwarm
			
 
				+rcParams['axes.prop_cycle'] = cycler(color=cmap(np.linspace(0, 1, N)))
			
 
				+
			
 
				+
			
 
				+from matplotlib.lines import Line2D
			
 
				+custom_lines = [Line2D([0], [0], color=cmap(0.), lw=4),
			
 
				+                Line2D([0], [0], color=cmap(.5), lw=4),
			
 
				+                Line2D([0], [0], color=cmap(1.), lw=4)]
			
 
				+
			
 
				+fig, ax = plt.subplots(figsize=(10, 5))
			
 
				+lines = ax.plot(data)
			
 
				+ax.legend(custom_lines, ['Cold', 'Medium', 'Hot']);
			
 
				+```
			
 
				+
			
 
				+```{code-cell}
			
 
				+import matplotlib.pyplot as plt
			
 
				+import numpy as np
			
 
				+import jax
			
 
				+import jax.numpy as jnp
			
 
				+
			
 
				+print(jax.devices())
			
 
				+```
			
 
				+
			
 
				+## Images
			
 
				+
			
 
				+
			
 
				+<!---
			
 
				+![](https://myst-parser.readthedocs.io/en/latest/_static/logo-wide.svg)
			
 
				+
			
 
				+
			
 
				+<img src="https://github.com/probml/probml-notebooks/blob/main/images/cat_dog.jpg"
			
 
				+style="height:200">
			
 
				+-->
			
 
				+
			
 
				+```{figure} /figures/cat_dog.jpg
			
 
				+:scale: 50%
			
 
				+:name: cat_dog
			
 
				+
			
 
				+A photo of a cat and a dog.
			
 
				+```
			
 
				+
			
 
				+```{figure} /figures/cat_dog.jpg
			
 
				+:scale: 50%
			
 
				+:name: cat_dog2
			
 
				+
			
 
				+Another photo of a cat and a dog.
			
 
				+```
			
 
				+
			
 
				+In {numref}`Figure %s <cat_dog>` we show catdog.
			
 
				+In {numref}`Figure %s <cat_dog2>` we show catdog2, its twin.
			
 
				+
			
 
				+
			
 
				+## Math
			
 
				+
			
 
				+We have $E= mc^2$, and also
			
 
				+
			
 
				+```{math}
			
 
				+:label: foo
			
 
				+a x^2 + bx+ c = 0
			
 
				+```
			
 
				+
			
 
				+From {eq}`foo`, it follows that
			
 
				+
			
 
				+$$
			
 
				+\begin{align}
			
 
				+0 &= a x^2 + bx+ c \\
			
 
				+0 &= a x^2 + bx+ c 
			
 
				+\end{align}
			
 
				+$$
			
 
				+
			
--- a/_sources/chapters/smc/smc_index.md
+++ b/_sources/chapters/smc/smc_index.md
@@ -0,0 +1,14 @@
 
				+
			
 
				+
			
 
				+(ch:SMC)=
			
 
				+# Sequential Monte Carlo
			
 
				+
			
 
				+{cite}`Chopin2020`
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/ssm/deep.ipynb
+++ b/_sources/chapters/ssm/deep.ipynb
@@ -0,0 +1,37 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Deep SSMs\n"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": []
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/ssm/hmm.ipynb
+++ b/_sources/chapters/ssm/hmm.ipynb
@@ -0,0 +1,612 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "(sec:hmm-ex)=\n",
			
 
				+    "# Hidden Markov Models\n",
			
 
				+    "\n",
			
 
				+    "In this section, we introduce Hidden Markov Models (HMMs)."
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "## Boilerplate"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 1,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [
			
 
				+    {
			
 
				+     "name": "stdout",
			
 
				+     "output_type": "stream",
			
 
				+     "text": [
			
 
				+      "Collecting jax[cpu]\n",
			
 
				+      "  Downloading jax-0.3.5.tar.gz (946 kB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 946 kB 2.7 MB/s eta 0:00:01\n",
			
 
				+      "\u001b[?25hCollecting absl-py\n",
			
 
				+      "  Downloading absl_py-1.0.0-py3-none-any.whl (126 kB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 126 kB 47.7 MB/s eta 0:00:01\n",
			
 
				+      "\u001b[?25hCollecting numpy>=1.19\n",
			
 
				+      "  Downloading numpy-1.22.3-cp38-cp38-macosx_10_14_x86_64.whl (17.6 MB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 17.6 MB 47.5 MB/s eta 0:00:01\n",
			
 
				+      "\u001b[?25hCollecting opt_einsum\n",
			
 
				+      "  Using cached opt_einsum-3.3.0-py3-none-any.whl (65 kB)\n",
			
 
				+      "Collecting scipy>=1.2.1\n",
			
 
				+      "  Downloading scipy-1.8.0-cp38-cp38-macosx_12_0_universal2.macosx_10_9_x86_64.whl (55.3 MB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 55.3 MB 73.1 MB/s eta 0:00:01\n",
			
 
				+      "\u001b[?25hCollecting typing_extensions\n",
			
 
				+      "  Using cached typing_extensions-4.1.1-py3-none-any.whl (26 kB)\n",
			
 
				+      "Collecting jaxlib==0.3.5\n",
			
 
				+      "  Downloading jaxlib-0.3.5-cp38-none-macosx_10_9_x86_64.whl (70.5 MB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 70.5 MB 723 kB/s  eta 0:00:01\n",
			
 
				+      "\u001b[?25hCollecting flatbuffers<3.0,>=1.12\n",
			
 
				+      "  Using cached flatbuffers-2.0-py2.py3-none-any.whl (26 kB)\n",
			
 
				+      "Requirement already satisfied: six in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from absl-py->jax[cpu]) (1.16.0)\n",
			
 
				+      "Building wheels for collected packages: jax\n",
			
 
				+      "  Building wheel for jax (setup.py) ... \u001b[?25ldone\n",
			
 
				+      "\u001b[?25h  Created wheel for jax: filename=jax-0.3.5-py3-none-any.whl size=1095861 sha256=6886baa70817bbac3b5797b3720dcb81e49097f61cee7d2e1255823ea32ccad8\n",
			
 
				+      "  Stored in directory: /Users/kpmurphy/Library/Caches/pip/wheels/05/30/aa/908988293721511b4b29e0aadf9b5d133d0f14f6c0a188e764\n",
			
 
				+      "Successfully built jax\n",
			
 
				+      "Installing collected packages: numpy, typing-extensions, scipy, opt-einsum, flatbuffers, absl-py, jaxlib, jax\n",
			
 
				+      "Successfully installed absl-py-1.0.0 flatbuffers-2.0 jax-0.3.5 jaxlib-0.3.5 numpy-1.22.3 opt-einsum-3.3.0 scipy-1.8.0 typing-extensions-4.1.1\n",
			
 
				+      "Note: you may need to restart the kernel to use updated packages.\n",
			
 
				+      "Collecting git+https://github.com/probml/jsl\n",
			
 
				+      "  Cloning https://github.com/probml/jsl to /private/var/folders/mn/vt7cgfsx6zs9vblhvbbk7pf8003xtr/T/pip-req-build-i8seqdiw\n",
			
 
				+      "  Running command git clone -q https://github.com/probml/jsl /private/var/folders/mn/vt7cgfsx6zs9vblhvbbk7pf8003xtr/T/pip-req-build-i8seqdiw\n",
			
 
				+      "Collecting chex\n",
			
 
				+      "  Downloading chex-0.1.2-py3-none-any.whl (72 kB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 72 kB 1.3 MB/s eta 0:00:011\n",
			
 
				+      "\u001b[?25hCollecting dataclasses\n",
			
 
				+      "  Using cached dataclasses-0.6-py3-none-any.whl (14 kB)\n",
			
 
				+      "Requirement already satisfied: jaxlib in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from jsl==0.0.0) (0.3.5)\n",
			
 
				+      "Requirement already satisfied: jax in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from jsl==0.0.0) (0.3.5)\n",
			
 
				+      "Collecting matplotlib\n",
			
 
				+      "  Downloading matplotlib-3.5.1-cp38-cp38-macosx_10_9_x86_64.whl (7.3 MB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 7.3 MB 3.9 MB/s eta 0:00:01\n",
			
 
				+      "\u001b[?25hCollecting tensorflow_probability\n",
			
 
				+      "  Using cached tensorflow_probability-0.16.0-py2.py3-none-any.whl (6.3 MB)\n",
			
 
				+      "Collecting dm-tree>=0.1.5\n",
			
 
				+      "  Using cached dm_tree-0.1.6-cp38-cp38-macosx_10_14_x86_64.whl (95 kB)\n",
			
 
				+      "Requirement already satisfied: absl-py>=0.9.0 in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from chex->jsl==0.0.0) (1.0.0)\n",
			
 
				+      "Requirement already satisfied: numpy>=1.18.0 in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from chex->jsl==0.0.0) (1.22.3)\n",
			
 
				+      "Collecting toolz>=0.9.0\n",
			
 
				+      "  Downloading toolz-0.11.2-py3-none-any.whl (55 kB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 55 kB 11.3 MB/s eta 0:00:01\n",
			
 
				+      "\u001b[?25hRequirement already satisfied: six in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from absl-py>=0.9.0->chex->jsl==0.0.0) (1.16.0)\n",
			
 
				+      "Requirement already satisfied: typing-extensions in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from jax->jsl==0.0.0) (4.1.1)\n",
			
 
				+      "Requirement already satisfied: scipy>=1.2.1 in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from jax->jsl==0.0.0) (1.8.0)\n",
			
 
				+      "Requirement already satisfied: opt-einsum in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from jax->jsl==0.0.0) (3.3.0)\n",
			
 
				+      "Requirement already satisfied: flatbuffers<3.0,>=1.12 in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from jaxlib->jsl==0.0.0) (2.0)\n",
			
 
				+      "Collecting cycler>=0.10\n",
			
 
				+      "  Downloading cycler-0.11.0-py3-none-any.whl (6.4 kB)\n",
			
 
				+      "Collecting kiwisolver>=1.0.1\n",
			
 
				+      "  Downloading kiwisolver-1.4.2-cp38-cp38-macosx_10_9_x86_64.whl (65 kB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 65 kB 8.5 MB/s  eta 0:00:01\n",
			
 
				+      "\u001b[?25hCollecting fonttools>=4.22.0\n",
			
 
				+      "  Downloading fonttools-4.32.0-py3-none-any.whl (900 kB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 900 kB 35.8 MB/s eta 0:00:01\n",
			
 
				+      "\u001b[?25hRequirement already satisfied: pyparsing>=2.2.1 in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from matplotlib->jsl==0.0.0) (3.0.7)\n",
			
 
				+      "Requirement already satisfied: packaging>=20.0 in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from matplotlib->jsl==0.0.0) (21.3)\n",
			
 
				+      "Requirement already satisfied: python-dateutil>=2.7 in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from matplotlib->jsl==0.0.0) (2.8.2)\n",
			
 
				+      "Collecting pillow>=6.2.0\n",
			
 
				+      "  Downloading Pillow-9.1.0-cp38-cp38-macosx_10_9_x86_64.whl (3.1 MB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 3.1 MB 76.6 MB/s eta 0:00:01\n",
			
 
				+      "\u001b[?25hCollecting gast>=0.3.2\n",
			
 
				+      "  Downloading gast-0.5.3-py3-none-any.whl (19 kB)\n",
			
 
				+      "Requirement already satisfied: decorator in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from tensorflow_probability->jsl==0.0.0) (5.1.1)\n",
			
 
				+      "Collecting cloudpickle>=1.3\n",
			
 
				+      "  Downloading cloudpickle-2.0.0-py3-none-any.whl (25 kB)\n",
			
 
				+      "Building wheels for collected packages: jsl\n",
			
 
				+      "  Building wheel for jsl (setup.py) ... \u001b[?25ldone\n",
			
 
				+      "\u001b[?25h  Created wheel for jsl: filename=jsl-0.0.0-py3-none-any.whl size=77852 sha256=e7365293dc97e2b3e72bf42cc19db7d7e355abec312fc4d87961fa2044fa06f0\n",
			
 
				+      "  Stored in directory: /private/var/folders/mn/vt7cgfsx6zs9vblhvbbk7pf8003xtr/T/pip-ephem-wheel-cache-63vxzlng/wheels/ed/8b/bf/0105dc839fecf1fc8db14f7267a6ce5ee876324b58565b359f\n",
			
 
				+      "Successfully built jsl\n",
			
 
				+      "Installing collected packages: toolz, pillow, kiwisolver, gast, fonttools, dm-tree, cycler, cloudpickle, tensorflow-probability, matplotlib, dataclasses, chex, jsl\n",
			
 
				+      "Successfully installed chex-0.1.2 cloudpickle-2.0.0 cycler-0.11.0 dataclasses-0.6 dm-tree-0.1.6 fonttools-4.32.0 gast-0.5.3 jsl-0.0.0 kiwisolver-1.4.2 matplotlib-3.5.1 pillow-9.1.0 tensorflow-probability-0.16.0 toolz-0.11.2\n",
			
 
				+      "Note: you may need to restart the kernel to use updated packages.\n",
			
 
				+      "Collecting rich\n",
			
 
				+      "  Downloading rich-12.2.0-py3-none-any.whl (229 kB)\n",
			
 
				+      "\u001b[K     |████████████████████████████████| 229 kB 2.9 MB/s eta 0:00:01\n",
			
 
				+      "\u001b[?25hRequirement already satisfied: typing-extensions<5.0,>=4.0.0 in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from rich) (4.1.1)\n",
			
 
				+      "Requirement already satisfied: pygments<3.0.0,>=2.6.0 in /opt/anaconda3/envs/scripts/lib/python3.8/site-packages (from rich) (2.11.2)\n",
			
 
				+      "Collecting commonmark<0.10.0,>=0.9.0\n",
			
 
				+      "  Using cached commonmark-0.9.1-py2.py3-none-any.whl (51 kB)\n",
			
 
				+      "Installing collected packages: commonmark, rich\n",
			
 
				+      "Successfully installed commonmark-0.9.1 rich-12.2.0\n",
			
 
				+      "Note: you may need to restart the kernel to use updated packages.\n"
			
 
				+     ]
			
 
				+    }
			
 
				+   ],
			
 
				+   "source": [
			
 
				+    "# Install necessary libraries\n",
			
 
				+    "\n",
			
 
				+    "try:\n",
			
 
				+    "    import jax\n",
			
 
				+    "except:\n",
			
 
				+    "    # For cuda version, see https://github.com/google/jax#installation\n",
			
 
				+    "    %pip install --upgrade \"jax[cpu]\" \n",
			
 
				+    "    import jax\n",
			
 
				+    "\n",
			
 
				+    "try:\n",
			
 
				+    "    import jsl\n",
			
 
				+    "except:\n",
			
 
				+    "    %pip install git+https://github.com/probml/jsl\n",
			
 
				+    "    import jsl\n",
			
 
				+    "\n",
			
 
				+    "try:\n",
			
 
				+    "    import rich\n",
			
 
				+    "except:\n",
			
 
				+    "    %pip install rich\n",
			
 
				+    "    import rich\n",
			
 
				+    "\n",
			
 
				+    "\n"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 2,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [],
			
 
				+   "source": [
			
 
				+    "# Import standard libraries\n",
			
 
				+    "\n",
			
 
				+    "import abc\n",
			
 
				+    "from dataclasses import dataclass\n",
			
 
				+    "import functools\n",
			
 
				+    "import itertools\n",
			
 
				+    "\n",
			
 
				+    "from typing import Any, Callable, NamedTuple, Optional, Union, Tuple\n",
			
 
				+    "\n",
			
 
				+    "import matplotlib.pyplot as plt\n",
			
 
				+    "import numpy as np\n",
			
 
				+    "\n",
			
 
				+    "\n",
			
 
				+    "import jax\n",
			
 
				+    "import jax.numpy as jnp\n",
			
 
				+    "from jax import lax, vmap, jit, grad\n",
			
 
				+    "from jax.scipy.special import logit\n",
			
 
				+    "from jax.nn import softmax\n",
			
 
				+    "from functools import partial\n",
			
 
				+    "from jax.random import PRNGKey, split\n",
			
 
				+    "\n",
			
 
				+    "import inspect\n",
			
 
				+    "import inspect as py_inspect\n",
			
 
				+    "from rich import inspect as r_inspect\n",
			
 
				+    "from rich import print as r_print\n",
			
 
				+    "\n",
			
 
				+    "def print_source(fname):\n",
			
 
				+    "    r_print(py_inspect.getsource(fname))"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "## Utility code"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 3,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [],
			
 
				+   "source": [
			
 
				+    "\n",
			
 
				+    "\n",
			
 
				+    "def normalize(u, axis=0, eps=1e-15):\n",
			
 
				+    "    '''\n",
			
 
				+    "    Normalizes the values within the axis in a way that they sum up to 1.\n",
			
 
				+    "    Parameters\n",
			
 
				+    "    ----------\n",
			
 
				+    "    u : array\n",
			
 
				+    "    axis : int\n",
			
 
				+    "    eps : float\n",
			
 
				+    "        Threshold for the alpha values\n",
			
 
				+    "    Returns\n",
			
 
				+    "    -------\n",
			
 
				+    "    * array\n",
			
 
				+    "        Normalized version of the given matrix\n",
			
 
				+    "    * array(seq_len, n_hidden) :\n",
			
 
				+    "        The values of the normalizer\n",
			
 
				+    "    '''\n",
			
 
				+    "    u = jnp.where(u == 0, 0, jnp.where(u < eps, eps, u))\n",
			
 
				+    "    c = u.sum(axis=axis)\n",
			
 
				+    "    c = jnp.where(c == 0, 1, c)\n",
			
 
				+    "    return u / c, c"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "(sec:casino-ex)=\n",
			
 
				+    "## Example: Casino HMM\n",
			
 
				+    "\n",
			
 
				+    "We first create the \"Ocassionally dishonest casino\" model from {cite}`Durbin98`.\n",
			
 
				+    "\n",
			
 
				+    "```{figure} /figures/casino.png\n",
			
 
				+    ":scale: 50%\n",
			
 
				+    ":name: casino-fig\n",
			
 
				+    "\n",
			
 
				+    "Illustration of the casino HMM.\n",
			
 
				+    "```\n",
			
 
				+    "\n",
			
 
				+    "There are 2 hidden states, each of which emit 6 possible observations."
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 5,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [
			
 
				+    {
			
 
				+     "name": "stderr",
			
 
				+     "output_type": "stream",
			
 
				+     "text": [
			
 
				+      "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
			
 
				+     ]
			
 
				+    }
			
 
				+   ],
			
 
				+   "source": [
			
 
				+    "# state transition matrix\n",
			
 
				+    "A = np.array([\n",
			
 
				+    "    [0.95, 0.05],\n",
			
 
				+    "    [0.10, 0.90]\n",
			
 
				+    "])\n",
			
 
				+    "\n",
			
 
				+    "# observation matrix\n",
			
 
				+    "B = np.array([\n",
			
 
				+    "    [1/6, 1/6, 1/6, 1/6, 1/6, 1/6], # fair die\n",
			
 
				+    "    [1/10, 1/10, 1/10, 1/10, 1/10, 5/10] # loaded die\n",
			
 
				+    "])\n",
			
 
				+    "\n",
			
 
				+    "pi, _ = normalize(np.array([1, 1]))\n",
			
 
				+    "pi = np.array(pi)\n",
			
 
				+    "\n",
			
 
				+    "\n",
			
 
				+    "(nstates, nobs) = np.shape(B)\n"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "Let's make a little data structure to store all the parameters.\n",
			
 
				+    "We use NamedTuple rather than dataclass, since we assume these are immutable.\n",
			
 
				+    "(Also, standard python dataclass does not work well with JAX, which requires parameters to be\n",
			
 
				+    "pytrees, as discussed in https://github.com/google/jax/issues/2371)."
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 74,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [
			
 
				+    {
			
 
				+     "name": "stdout",
			
 
				+     "output_type": "stream",
			
 
				+     "text": [
			
 
				+      "HMM(trans_mat=array([[0.95, 0.05],\n",
			
 
				+      "       [0.1 , 0.9 ]]), obs_mat=array([[0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
			
 
				+      "        0.16666667],\n",
			
 
				+      "       [0.1       , 0.1       , 0.1       , 0.1       , 0.1       ,\n",
			
 
				+      "        0.5       ]]), init_dist=array([0.5, 0.5], dtype=float32))\n",
			
 
				+      "<class 'numpy.ndarray'>\n",
			
 
				+      "HMM(trans_mat=DeviceArray([[0.95, 0.05],\n",
			
 
				+      "             [0.1 , 0.9 ]], dtype=float32), obs_mat=DeviceArray([[0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
			
 
				+      "              0.16666667],\n",
			
 
				+      "             [0.1       , 0.1       , 0.1       , 0.1       , 0.1       ,\n",
			
 
				+      "              0.5       ]], dtype=float32), init_dist=DeviceArray([0.5, 0.5], dtype=float32))\n",
			
 
				+      "<class 'jaxlib.xla_extension.DeviceArray'>\n"
			
 
				+     ]
			
 
				+    }
			
 
				+   ],
			
 
				+   "source": [
			
 
				+    "Array = Union[np.array, jnp.array]\n",
			
 
				+    "\n",
			
 
				+    "class HMM(NamedTuple):\n",
			
 
				+    "    trans_mat: Array  # A : (n_states, n_states)\n",
			
 
				+    "    obs_mat: Array  # B : (n_states, n_obs)\n",
			
 
				+    "    init_dist: Array  # pi : (n_states)\n",
			
 
				+    "\n",
			
 
				+    "params_np = HMM(A, B, pi)\n",
			
 
				+    "print(params_np)\n",
			
 
				+    "print(type(params_np.trans_mat))\n",
			
 
				+    "\n",
			
 
				+    "\n",
			
 
				+    "params = jax.tree_map(lambda x: jnp.array(x), params_np)\n",
			
 
				+    "print(params)\n",
			
 
				+    "print(type(params.trans_mat))"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "## Sampling from the joint\n",
			
 
				+    "\n",
			
 
				+    "Let's write code to sample from this model. \n"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "### Numpy version\n",
			
 
				+    "\n",
			
 
				+    "First we code it in numpy using a for loop."
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 30,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [],
			
 
				+   "source": [
			
 
				+    "def hmm_sample_np(params, seq_len, random_state=0):\n",
			
 
				+    "    np.random.seed(random_state)\n",
			
 
				+    "    trans_mat, obs_mat, init_dist = params.trans_mat, params.obs_mat, params.init_dist\n",
			
 
				+    "    n_states, n_obs = obs_mat.shape\n",
			
 
				+    "    state_seq = np.zeros(seq_len, dtype=int)\n",
			
 
				+    "    obs_seq = np.zeros(seq_len, dtype=int)\n",
			
 
				+    "    for t in range(seq_len):\n",
			
 
				+    "        if t==0:\n",
			
 
				+    "            zt = np.random.choice(n_states, p=init_dist)\n",
			
 
				+    "        else:\n",
			
 
				+    "            zt = np.random.choice(n_states, p=trans_mat[zt])\n",
			
 
				+    "        yt = np.random.choice(n_obs, p=obs_mat[zt])\n",
			
 
				+    "        state_seq[t] = zt\n",
			
 
				+    "        obs_seq[t] = yt\n",
			
 
				+    "\n",
			
 
				+    "    return state_seq, obs_seq"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 75,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [
			
 
				+    {
			
 
				+     "name": "stdout",
			
 
				+     "output_type": "stream",
			
 
				+     "text": [
			
 
				+      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0\n",
			
 
				+      " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
			
 
				+      " 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
			
 
				+      "[4 1 0 2 3 4 5 4 3 1 5 4 5 0 5 2 5 3 5 4 5 5 4 2 1 4 1 0 0 4 2 2 3 3 3 0 4\n",
			
 
				+      " 0 2 4 3 2 5 5 3 5 3 1 3 3 3 2 3 5 5 0 4 4 5 0 0 1 3 5 1 5 0 1 2 4 0 0 0 4\n",
			
 
				+      " 0 5 1 4 3 5 4 5 0 2 3 5 2 4 1 2 1 0 4 3 5 0 4 5 1 5]\n"
			
 
				+     ]
			
 
				+    }
			
 
				+   ],
			
 
				+   "source": [
			
 
				+    "seq_len = 100\n",
			
 
				+    "state_seq, obs_seq = hmm_sample_np(params_np, seq_len, random_state=1)\n",
			
 
				+    "print(state_seq)\n",
			
 
				+    "print(obs_seq)"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "### JAX version\n",
			
 
				+    "\n",
			
 
				+    "Now let's write a JAX version using jax.lax.scan (for the inter-dependent states) and vmap (for the observations).\n",
			
 
				+    "This is harder to read than the numpy version, but faster."
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 91,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [],
			
 
				+   "source": [
			
 
				+    "#@partial(jit, static_argnums=(1,))\n",
			
 
				+    "def markov_chain_sample(rng_key, init_dist, trans_mat, seq_len):\n",
			
 
				+    "    n_states = len(init_dist)\n",
			
 
				+    "\n",
			
 
				+    "    def draw_state(prev_state, key):\n",
			
 
				+    "        state = jax.random.choice(key, n_states, p=trans_mat[prev_state])\n",
			
 
				+    "        return state, state\n",
			
 
				+    "\n",
			
 
				+    "    rng_key, rng_state = jax.random.split(rng_key, 2)\n",
			
 
				+    "    keys = jax.random.split(rng_state, seq_len - 1)\n",
			
 
				+    "    initial_state = jax.random.choice(rng_key, n_states, p=init_dist)\n",
			
 
				+    "    final_state, states = jax.lax.scan(draw_state, initial_state, keys)\n",
			
 
				+    "    state_seq = jnp.append(jnp.array([initial_state]), states)\n",
			
 
				+    "\n",
			
 
				+    "    return state_seq"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 90,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [],
			
 
				+   "source": [
			
 
				+    "#@partial(jit, static_argnums=(1,))\n",
			
 
				+    "def hmm_sample(rng_key, params, seq_len):\n",
			
 
				+    "\n",
			
 
				+    "    trans_mat, obs_mat, init_dist = params.trans_mat, params.obs_mat, params.init_dist\n",
			
 
				+    "    n_states, n_obs = obs_mat.shape\n",
			
 
				+    "    rng_key, rng_obs = jax.random.split(rng_key, 2)\n",
			
 
				+    "    state_seq = markov_chain_sample(rng_key, init_dist, trans_mat, seq_len)\n",
			
 
				+    "\n",
			
 
				+    "    def draw_obs(z, key):\n",
			
 
				+    "        obs = jax.random.choice(key, n_obs, p=obs_mat[z])\n",
			
 
				+    "        return obs\n",
			
 
				+    "\n",
			
 
				+    "    keys = jax.random.split(rng_obs, seq_len)\n",
			
 
				+    "    obs_seq = jax.vmap(draw_obs, in_axes=(0, 0))(state_seq, keys)\n",
			
 
				+    "    \n",
			
 
				+    "    return state_seq, obs_seq"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 70,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [],
			
 
				+   "source": [
			
 
				+    "#@partial(jit, static_argnums=(1,))\n",
			
 
				+    "def hmm_sample2(rng_key, params, seq_len):\n",
			
 
				+    "\n",
			
 
				+    "    trans_mat, obs_mat, init_dist = params.trans_mat, params.obs_mat, params.init_dist\n",
			
 
				+    "    n_states, n_obs = obs_mat.shape\n",
			
 
				+    "\n",
			
 
				+    "    def draw_state(prev_state, key):\n",
			
 
				+    "        state = jax.random.choice(key, n_states, p=trans_mat[prev_state])\n",
			
 
				+    "        return state, state\n",
			
 
				+    "\n",
			
 
				+    "    rng_key, rng_state, rng_obs = jax.random.split(rng_key, 3)\n",
			
 
				+    "    keys = jax.random.split(rng_state, seq_len - 1)\n",
			
 
				+    "    initial_state = jax.random.choice(rng_key, n_states, p=init_dist)\n",
			
 
				+    "    final_state, states = jax.lax.scan(draw_state, initial_state, keys)\n",
			
 
				+    "    state_seq = jnp.append(jnp.array([initial_state]), states)\n",
			
 
				+    "\n",
			
 
				+    "    def draw_obs(z, key):\n",
			
 
				+    "        obs = jax.random.choice(key, n_obs, p=obs_mat[z])\n",
			
 
				+    "        return obs\n",
			
 
				+    "\n",
			
 
				+    "    keys = jax.random.split(rng_obs, seq_len)\n",
			
 
				+    "    obs_seq = jax.vmap(draw_obs, in_axes=(0, 0))(state_seq, keys)\n",
			
 
				+    "\n",
			
 
				+    "    return state_seq, obs_seq"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 93,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [
			
 
				+    {
			
 
				+     "name": "stdout",
			
 
				+     "output_type": "stream",
			
 
				+     "text": [
			
 
				+      "[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
			
 
				+      " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1\n",
			
 
				+      " 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
			
 
				+      "[5 5 2 2 0 0 0 1 3 3 2 2 5 1 5 1 0 2 2 4 2 5 1 5 5 0 0 4 2 4 3 2 3 4 1 0 5\n",
			
 
				+      " 2 2 2 1 4 3 2 2 2 4 1 0 3 5 2 5 1 4 2 5 2 5 0 5 4 4 4 2 2 0 4 5 2 2 0 1 5\n",
			
 
				+      " 1 3 4 5 1 5 0 5 1 5 1 2 4 5 3 4 5 4 0 4 0 2 4 5 3 3]\n"
			
 
				+     ]
			
 
				+    }
			
 
				+   ],
			
 
				+   "source": [
			
 
				+    "\n",
			
 
				+    "key = PRNGKey(2)\n",
			
 
				+    "seq_len = 100\n",
			
 
				+    "\n",
			
 
				+    "state_seq, obs_seq = hmm_sample(key, params, seq_len)\n",
			
 
				+    "print(state_seq)\n",
			
 
				+    "print(obs_seq)"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "### Check correctness by computing empirical pairwise statistics\n",
			
 
				+    "\n",
			
 
				+    "We will compute the number of i->j transitions, and check that it is close to the true \n",
			
 
				+    "A[i,j] transition probabilites."
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": 107,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [
			
 
				+    {
			
 
				+     "name": "stdout",
			
 
				+     "output_type": "stream",
			
 
				+     "text": [
			
 
				+      "[0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1\n",
			
 
				+      " 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0\n",
			
 
				+      " 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0\n",
			
 
				+      " 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0\n",
			
 
				+      " 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0\n",
			
 
				+      " 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0\n",
			
 
				+      " 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0\n",
			
 
				+      " 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1\n",
			
 
				+      " 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1\n",
			
 
				+      " 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0\n",
			
 
				+      " 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0\n",
			
 
				+      " 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0\n",
			
 
				+      " 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1\n",
			
 
				+      " 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1]\n",
			
 
				+      "[[244.  93.]\n",
			
 
				+      " [ 92.  70.]]\n",
			
 
				+      "[[0.7240356  0.27596438]\n",
			
 
				+      " [0.56790125 0.43209878]]\n"
			
 
				+     ]
			
 
				+    }
			
 
				+   ],
			
 
				+   "source": [
			
 
				+    "import collections\n",
			
 
				+    "def compute_counts(state_seq, nstates):\n",
			
 
				+    "    wseq = np.array(state_seq)\n",
			
 
				+    "    word_pairs = [pair for pair in zip(wseq[:-1], wseq[1:])]\n",
			
 
				+    "    counter_pairs = collections.Counter(word_pairs)\n",
			
 
				+    "    counts = np.zeros((nstates, nstates))\n",
			
 
				+    "    for (k,v) in counter_pairs.items():\n",
			
 
				+    "        counts[k[0], k[1]] = v\n",
			
 
				+    "    return counts\n",
			
 
				+    "\n",
			
 
				+    "def normalize_counts(counts):\n",
			
 
				+    "    ncounts = vmap(lambda v: normalize(v)[0], in_axes=0)(counts)\n",
			
 
				+    "    return ncounts\n",
			
 
				+    "\n",
			
 
				+    "init_dist = jnp.array([1.0, 0.0])\n",
			
 
				+    "trans_mat = jnp.array([[0.7, 0.3], [0.5, 0.5]])\n",
			
 
				+    "rng_key = jax.random.PRNGKey(0)\n",
			
 
				+    "seq_len = 500\n",
			
 
				+    "state_seq = markov_chain_sample(rng_key, init_dist, trans_mat, seq_len)\n",
			
 
				+    "print(state_seq)\n",
			
 
				+    "\n",
			
 
				+    "counts = compute_counts(state_seq, nstates=2)\n",
			
 
				+    "print(counts)\n",
			
 
				+    "\n",
			
 
				+    "trans_mat_empirical = normalize_counts(counts)\n",
			
 
				+    "print(trans_mat_empirical)\n",
			
 
				+    "\n",
			
 
				+    "assert jnp.allclose(trans_mat, trans_mat_empirical, atol=1e-1)\n"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "code",
			
 
				+   "execution_count": null,
			
 
				+   "metadata": {},
			
 
				+   "outputs": [],
			
 
				+   "source": []
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.8"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/ssm/hsmm.ipynb
+++ b/_sources/chapters/ssm/hsmm.ipynb
@@ -0,0 +1,33 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Hidden Semi-Markov Models\n",
			
 
				+    "\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/ssm/lgssm.ipynb
+++ b/_sources/chapters/ssm/lgssm.ipynb
@@ -0,0 +1,37 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Linear Gaussian SSMs\n"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": []
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/ssm/nongauss.ipynb
+++ b/_sources/chapters/ssm/nongauss.ipynb
@@ -0,0 +1,37 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "#  Non-Gaussian SSMs\n"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": []
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/ssm/nonlin.ipynb
+++ b/_sources/chapters/ssm/nonlin.ipynb
@@ -0,0 +1,32 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Non-Linear Gaussian SSMs\n"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/ssm/rnn.ipynb
+++ b/_sources/chapters/ssm/rnn.ipynb
@@ -0,0 +1,37 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Recurrent Neural Networks\n"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": []
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/ssm/ssm_index.md
+++ b/_sources/chapters/ssm/ssm_index.md
@@ -0,0 +1,7 @@
 
				+
			
 
				+
			
 
				+(ch:ssm)=
			
 
				+# Introduction 
			
 
				+
			
 
				+```{tableofcontents}
			
 
				+```
			
--- a/_sources/chapters/ssm/switching.ipynb
+++ b/_sources/chapters/ssm/switching.ipynb
@@ -0,0 +1,44 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Switching SSMs\n"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "## Jump Markov Linear Dynamical Systems"
			
 
				+   ]
			
 
				+  },
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": []
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/timeseries/timeseries_index.md
+++ b/_sources/chapters/timeseries/timeseries_index.md
@@ -0,0 +1,13 @@
 
				+
			
 
				+
			
 
				+(ch:timeseries)=
			
 
				+# Timeseries forecasting
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/tracking/tracking_index.md
+++ b/_sources/chapters/tracking/tracking_index.md
@@ -0,0 +1,12 @@
 
				+
			
 
				+
			
 
				+(ch:tracking)=
			
 
				+# Multi-target tracking
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/chapters/unscented/unscented_filter.ipynb
+++ b/_sources/chapters/unscented/unscented_filter.ipynb
@@ -0,0 +1,32 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Unscented filtering"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/unscented/unscented_index.md
+++ b/_sources/chapters/unscented/unscented_index.md
@@ -0,0 +1,7 @@
 
				+
			
 
				+
			
 
				+(ch:unscented)=
			
 
				+# Unscented methods
			
 
				+
			
 
				+```{tableofcontents}
			
 
				+```
			
--- a/_sources/chapters/unscented/unscented_smoother.ipynb
+++ b/_sources/chapters/unscented/unscented_smoother.ipynb
@@ -0,0 +1,32 @@
 
				+{
			
 
				+ "cells": [
			
 
				+  {
			
 
				+   "cell_type": "markdown",
			
 
				+   "metadata": {},
			
 
				+   "source": [
			
 
				+    "# Unscented smoothing"
			
 
				+   ]
			
 
				+  }
			
 
				+ ],
			
 
				+ "metadata": {
			
 
				+  "kernelspec": {
			
 
				+   "display_name": "Python 3",
			
 
				+   "language": "python",
			
 
				+   "name": "python3"
			
 
				+  },
			
 
				+  "language_info": {
			
 
				+   "codemirror_mode": {
			
 
				+    "name": "ipython",
			
 
				+    "version": 3
			
 
				+   },
			
 
				+   "file_extension": ".py",
			
 
				+   "mimetype": "text/x-python",
			
 
				+   "name": "python",
			
 
				+   "nbconvert_exporter": "python",
			
 
				+   "pygments_lexer": "ipython3",
			
 
				+   "version": "3.8.5"
			
 
				+  }
			
 
				+ },
			
 
				+ "nbformat": 4,
			
 
				+ "nbformat_minor": 4
			
 
				+}
			
--- a/_sources/chapters/vi/vi_index.md
+++ b/_sources/chapters/vi/vi_index.md
@@ -0,0 +1,13 @@
 
				+
			
 
				+
			
 
				+(ch:VI)=
			
 
				+# Variational inference
			
 
				+
			
 
				+{cite}`BayesNewton`,
			
 
				+{cite}`Courts2020`, {cite}`Courts2021`
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
--- a/_sources/root.md
+++ b/_sources/root.md
@@ -0,0 +1,14 @@
 
				+# State Space Models: A Modern Approach
			
 
				+
			
 
				+This is an interactive textbook on state space models (SSM)
			
 
				+using the [JAX Python library](https://github.com/google/jax).
			
 
				+Some of the content is covered in other books
			
 
				+such as  {cite}`Sarkka13` and {cite}`vol2`.
			
 
				+However, we go into more detail, and focus on how to efficiently
			
 
				+implement the various algorithms in a "modern" computing environment,
			
 
				+exploiting recent progress
			
 
				+in automatic differentiation and parallel computing.
			
 
				+
			
 
				+
			
 
				+```{tableofcontents}
			
 
				+```
			
--- a/_static/__init__.py
+++ b/_static/__init__.py
--- a/_static/__pycache__/__init__.cpython-38.pyc
+++ b/_static/__pycache__/__init__.cpython-38.pyc
--- a/_static/basic.css
+++ b/_static/basic.css
@@ -0,0 +1,906 @@
 
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				+ * basic.css
			
 
				+ * ~~~~~~~~~
			
 
				+ *
			
 
				+ * Sphinx stylesheet -- basic theme.
			
 
				+ *
			
 
				+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
			
 
				+ * :license: BSD, see LICENSE for details.
			
 
				+ *
			
 
				+ */
			
 
				+
			
 
				+/* -- main layout ----------------------------------------------------------- */
			
 
				+
			
 
				+div.clearer {
			
 
				+    clear: both;
			
 
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				+
			
 
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				+
			
 
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				+
			
 
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				+    display: none;
			
 
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				+
			
 
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				+div.sphinxsidebar input {
			
 
				+    border: 1px solid #98dbcc;
			
 
				+    font-family: sans-serif;
			
 
				+    font-size: 1em;
			
 
				+}
			
 
				+
			
 
				+div.sphinxsidebar #searchbox form.search {
			
 
				+    overflow: hidden;
			
 
				+}
			
 
				+
			
 
				+div.sphinxsidebar #searchbox input[type="text"] {
			
 
				+    float: left;
			
 
				+    width: 80%;
			
 
				+    padding: 0.25em;
			
 
				+    box-sizing: border-box;
			
 
				+}
			
 
				+
			
 
				+div.sphinxsidebar #searchbox input[type="submit"] {
			
 
				+    float: left;
			
 
				+    width: 20%;
			
 
				+    border-left: none;
			
 
				+    padding: 0.25em;
			
 
				+    box-sizing: border-box;
			
 
				+}
			
 
				+
			
 
				+
			
 
				+img {
			
 
				+    border: 0;
			
 
				+    max-width: 100%;
			
 
				+}
			
 
				+
			
 
				+/* -- search page ----------------------------------------------------------- */
			
 
				+
			
 
				+ul.search {
			
 
				+    margin: 10px 0 0 20px;
			
 
				+    padding: 0;
			
 
				+}
			
 
				+
			
 
				+ul.search li {
			
 
				+    padding: 5px 0 5px 20px;
			
 
				+    background-image: url(file.png);
			
 
				+    background-repeat: no-repeat;
			
 
				+    background-position: 0 7px;
			
 
				+}
			
 
				+
			
 
				+ul.search li a {
			
 
				+    font-weight: bold;
			
 
				+}
			
 
				+
			
 
				+ul.search li p.context {
			
 
				+    color: #888;
			
 
				+    margin: 2px 0 0 30px;
			
 
				+    text-align: left;
			
 
				+}
			
 
				+
			
 
				+ul.keywordmatches li.goodmatch a {
			
 
				+    font-weight: bold;
			
 
				+}
			
 
				+
			
 
				+/* -- index page ------------------------------------------------------------ */
			
 
				+
			
 
				+table.contentstable {
			
 
				+    width: 90%;
			
 
				+    margin-left: auto;
			
 
				+    margin-right: auto;
			
 
				+}
			
 
				+
			
 
				+table.contentstable p.biglink {
			
 
				+    line-height: 150%;
			
 
				+}
			
 
				+
			
 
				+a.biglink {
			
 
				+    font-size: 1.3em;
			
 
				+}
			
 
				+
			
 
				+span.linkdescr {
			
 
				+    font-style: italic;
			
 
				+    padding-top: 5px;
			
 
				+    font-size: 90%;
			
 
				+}
			
 
				+
			
 
				+/* -- general index --------------------------------------------------------- */
			
 
				+
			
 
				+table.indextable {
			
 
				+    width: 100%;
			
 
				+}
			
 
				+
			
 
				+table.indextable td {
			
 
				+    text-align: left;
			
 
				+    vertical-align: top;
			
 
				+}
			
 
				+
			
 
				+table.indextable ul {
			
 
				+    margin-top: 0;
			
 
				+    margin-bottom: 0;
			
 
				+    list-style-type: none;
			
 
				+}
			
 
				+
			
 
				+table.indextable > tbody > tr > td > ul {
			
 
				+    padding-left: 0em;
			
 
				+}
			
 
				+
			
 
				+table.indextable tr.pcap {
			
 
				+    height: 10px;
			
 
				+}
			
 
				+
			
 
				+table.indextable tr.cap {
			
 
				+    margin-top: 10px;
			
 
				+    background-color: #f2f2f2;
			
 
				+}
			
 
				+
			
 
				+img.toggler {
			
 
				+    margin-right: 3px;
			
 
				+    margin-top: 3px;
			
 
				+    cursor: pointer;
			
 
				+}
			
 
				+
			
 
				+div.modindex-jumpbox {
			
 
				+    border-top: 1px solid #ddd;
			
 
				+    border-bottom: 1px solid #ddd;
			
 
				+    margin: 1em 0 1em 0;
			
 
				+    padding: 0.4em;
			
 
				+}
			
 
				+
			
 
				+div.genindex-jumpbox {
			
 
				+    border-top: 1px solid #ddd;
			
 
				+    border-bottom: 1px solid #ddd;
			
 
				+    margin: 1em 0 1em 0;
			
 
				+    padding: 0.4em;
			
 
				+}
			
 
				+
			
 
				+/* -- domain module index --------------------------------------------------- */
			
 
				+
			
 
				+table.modindextable td {
			
 
				+    padding: 2px;
			
 
				+    border-collapse: collapse;
			
 
				+}
			
 
				+
			
 
				+/* -- general body styles --------------------------------------------------- */
			
 
				+
			
 
				+div.body {
			
 
				+    min-width: 450px;
			
 
				+    max-width: 800px;
			
 
				+}
			
 
				+
			
 
				+div.body p, div.body dd, div.body li, div.body blockquote {
			
 
				+    -moz-hyphens: auto;
			
 
				+    -ms-hyphens: auto;
			
 
				+    -webkit-hyphens: auto;
			
 
				+    hyphens: auto;
			
 
				+}
			
 
				+
			
 
				+a.headerlink {
			
 
				+    visibility: hidden;
			
 
				+}
			
 
				+
			
 
				+a.brackets:before,
			
 
				+span.brackets > a:before{
			
 
				+    content: "[";
			
 
				+}
			
 
				+
			
 
				+a.brackets:after,
			
 
				+span.brackets > a:after {
			
 
				+    content: "]";
			
 
				+}
			
 
				+
			
 
				+h1:hover > a.headerlink,
			
 
				+h2:hover > a.headerlink,
			
 
				+h3:hover > a.headerlink,
			
 
				+h4:hover > a.headerlink,
			
 
				+h5:hover > a.headerlink,
			
 
				+h6:hover > a.headerlink,
			
 
				+dt:hover > a.headerlink,
			
 
				+caption:hover > a.headerlink,
			
 
				+p.caption:hover > a.headerlink,
			
 
				+div.code-block-caption:hover > a.headerlink {
			
 
				+    visibility: visible;
			
 
				+}
			
 
				+
			
 
				+div.body p.caption {
			
 
				+    text-align: inherit;
			
 
				+}
			
 
				+
			
 
				+div.body td {
			
 
				+    text-align: left;
			
 
				+}
			
 
				+
			
 
				+.first {
			
 
				+    margin-top: 0 !important;
			
 
				+}
			
 
				+
			
 
				+p.rubric {
			
 
				+    margin-top: 30px;
			
 
				+    font-weight: bold;
			
 
				+}
			
 
				+
			
 
				+img.align-left, figure.align-left, .figure.align-left, object.align-left {
			
 
				+    clear: left;
			
 
				+    float: left;
			
 
				+    margin-right: 1em;
			
 
				+}
			
 
				+
			
 
				+img.align-right, figure.align-right, .figure.align-right, object.align-right {
			
 
				+    clear: right;
			
 
				+    float: right;
			
 
				+    margin-left: 1em;
			
 
				+}
			
 
				+
			
 
				+img.align-center, figure.align-center, .figure.align-center, object.align-center {
			
 
				+  display: block;
			
 
				+  margin-left: auto;
			
 
				+  margin-right: auto;
			
 
				+}
			
 
				+
			
 
				+img.align-default, figure.align-default, .figure.align-default {
			
 
				+  display: block;
			
 
				+  margin-left: auto;
			
 
				+  margin-right: auto;
			
 
				+}
			
 
				+
			
 
				+.align-left {
			
 
				+    text-align: left;
			
 
				+}
			
 
				+
			
 
				+.align-center {
			
 
				+    text-align: center;
			
 
				+}
			
 
				+
			
 
				+.align-default {
			
 
				+    text-align: center;
			
 
				+}
			
 
				+
			
 
				+.align-right {
			
 
				+    text-align: right;
			
 
				+}
			
 
				+
			
 
				+/* -- sidebars -------------------------------------------------------------- */
			
 
				+
			
 
				+div.sidebar,
			
 
				+aside.sidebar {
			
 
				+    margin: 0 0 0.5em 1em;
			
 
				+    border: 1px solid #ddb;
			
 
				+    padding: 7px;
			
 
				+    background-color: #ffe;
			
 
				+    width: 40%;
			
 
				+    float: right;
			
 
				+    clear: right;
			
 
				+    overflow-x: auto;
			
 
				+}
			
 
				+
			
 
				+p.sidebar-title {
			
 
				+    font-weight: bold;
			
 
				+}
			
 
				+
			
 
				+div.admonition, div.topic, blockquote {
			
 
				+    clear: left;
			
 
				+}
			
 
				+
			
 
				+/* -- topics ---------------------------------------------------------------- */
			
 
				+
			
 
				+div.topic {
			
 
				+    border: 1px solid #ccc;
			
 
				+    padding: 7px;
			
 
				+    margin: 10px 0 10px 0;
			
 
				+}
			
 
				+
			
 
				+p.topic-title {
			
 
				+    font-size: 1.1em;
			
 
				+    font-weight: bold;
			
 
				+    margin-top: 10px;
			
 
				+}
			
 
				+
			
 
				+/* -- admonitions ----------------------------------------------------------- */
			
 
				+
			
 
				+div.admonition {
			
 
				+    margin-top: 10px;
			
 
				+    margin-bottom: 10px;
			
 
				+    padding: 7px;
			
 
				+}
			
 
				+
			
 
				+div.admonition dt {
			
 
				+    font-weight: bold;
			
 
				+}
			
 
				+
			
 
				+p.admonition-title {
			
 
				+    margin: 0px 10px 5px 0px;
			
 
				+    font-weight: bold;
			
 
				+}
			
 
				+
			
 
				+div.body p.centered {
			
 
				+    text-align: center;
			
 
				+    margin-top: 25px;
			
 
				+}
			
 
				+
			
 
				+/* -- content of sidebars/topics/admonitions -------------------------------- */
			
 
				+
			
 
				+div.sidebar > :last-child,
			
 
				+aside.sidebar > :last-child,
			
 
				+div.topic > :last-child,
			
 
				+div.admonition > :last-child {
			
 
				+    margin-bottom: 0;
			
 
				+}
			
 
				+
			
 
				+div.sidebar::after,
			
 
				+aside.sidebar::after,
			
 
				+div.topic::after,
			
 
				+div.admonition::after,
			
 
				+blockquote::after {
			
 
				+    display: block;
			
 
				+    content: '';
			
 
				+    clear: both;
			
 
				+}
			
 
				+
			
 
				+/* -- tables ---------------------------------------------------------------- */
			
 
				+
			
 
				+table.docutils {
			
 
				+    margin-top: 10px;
			
 
				+    margin-bottom: 10px;
			
 
				+    border: 0;
			
 
				+    border-collapse: collapse;
			
 
				+}
			
 
				+
			
 
				+table.align-center {
			
 
				+    margin-left: auto;
			
 
				+    margin-right: auto;
			
 
				+}
			
 
				+
			
 
				+table.align-default {
			
 
				+    margin-left: auto;
			
 
				+    margin-right: auto;
			
 
				+}
			
 
				+
			
 
				+table caption span.caption-number {
			
 
				+    font-style: italic;
			
 
				+}
			
 
				+
			
 
				+table caption span.caption-text {
			
 
				+}
			
 
				+
			
 
				+table.docutils td, table.docutils th {
			
 
				+    padding: 1px 8px 1px 5px;
			
 
				+    border-top: 0;
			
 
				+    border-left: 0;
			
 
				+    border-right: 0;
			
 
				+    border-bottom: 1px solid #aaa;
			
 
				+}
			
 
				+
			
 
				+table.footnote td, table.footnote th {
			
 
				+    border: 0 !important;
			
 
				+}
			
 
				+
			
 
				+th {
			
 
				+    text-align: left;
			
 
				+    padding-right: 5px;
			
 
				+}
			
 
				+
			
 
				+table.citation {
			
 
				+    border-left: solid 1px gray;
			
 
				+    margin-left: 1px;
			
 
				+}
			
 
				+
			
 
				+table.citation td {
			
 
				+    border-bottom: none;
			
 
				+}
			
 
				+
			
 
				+th > :first-child,
			
 
				+td > :first-child {
			
 
				+    margin-top: 0px;
			
 
				+}
			
 
				+
			
 
				+th > :last-child,
			
 
				+td > :last-child {
			
 
				+    margin-bottom: 0px;
			
 
				+}
			
 
				+
			
 
				+/* -- figures --------------------------------------------------------------- */
			
 
				+
			
 
				+div.figure, figure {
			
 
				+    margin: 0.5em;
			
 
				+    padding: 0.5em;
			
 
				+}
			
 
				+
			
 
				+div.figure p.caption, figcaption {
			
 
				+    padding: 0.3em;
			
 
				+}
			
 
				+
			
 
				+div.figure p.caption span.caption-number,
			
 
				+figcaption span.caption-number {
			
 
				+    font-style: italic;
			
 
				+}
			
 
				+
			
 
				+div.figure p.caption span.caption-text,
			
 
				+figcaption span.caption-text {
			
 
				+}
			
 
				+
			
 
				+/* -- field list styles ----------------------------------------------------- */
			
 
				+
			
 
				+table.field-list td, table.field-list th {
			
 
				+    border: 0 !important;
			
 
				+}
			
 
				+
			
 
				+.field-list ul {
			
 
				+    margin: 0;
			
 
				+    padding-left: 1em;
			
 
				+}
			
 
				+
			
 
				+.field-list p {
			
 
				+    margin: 0;
			
 
				+}
			
 
				+
			
 
				+.field-name {
			
 
				+    -moz-hyphens: manual;
			
 
				+    -ms-hyphens: manual;
			
 
				+    -webkit-hyphens: manual;
			
 
				+    hyphens: manual;
			
 
				+}
			
 
				+
			
 
				+/* -- hlist styles ---------------------------------------------------------- */
			
 
				+
			
 
				+table.hlist {
			
 
				+    margin: 1em 0;
			
 
				+}
			
 
				+
			
 
				+table.hlist td {
			
 
				+    vertical-align: top;
			
 
				+}
			
 
				+
			
 
				+/* -- object description styles --------------------------------------------- */
			
 
				+
			
 
				+.sig {
			
 
				+	font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace;
			
 
				+}
			
 
				+
			
 
				+.sig-name, code.descname {
			
 
				+    background-color: transparent;
			
 
				+    font-weight: bold;
			
 
				+}
			
 
				+
			
 
				+.sig-name {
			
 
				+	font-size: 1.1em;
			
 
				+}
			
 
				+
			
 
				+code.descname {
			
 
				+    font-size: 1.2em;
			
 
				+}
			
 
				+
			
 
				+.sig-prename, code.descclassname {
			
 
				+    background-color: transparent;
			
 
				+}
			
 
				+
			
 
				+.optional {
			
 
				+    font-size: 1.3em;
			
 
				+}
			
 
				+
			
 
				+.sig-paren {
			
 
				+    font-size: larger;
			
 
				+}
			
 
				+
			
 
				+.sig-param.n {
			
 
				+	font-style: italic;
			
 
				+}
			
 
				+
			
 
				+/* C++ specific styling */
			
 
				+
			
 
				+.sig-inline.c-texpr,
			
 
				+.sig-inline.cpp-texpr {
			
 
				+	font-family: unset;
			
 
				+}
			
 
				+
			
 
				+.sig.c   .k, .sig.c   .kt,
			
 
				+.sig.cpp .k, .sig.cpp .kt {
			
 
				+	color: #0033B3;
			
 
				+}
			
 
				+
			
 
				+.sig.c   .m,
			
 
				+.sig.cpp .m {
			
 
				+	color: #1750EB;
			
 
				+}
			
 
				+
			
 
				+.sig.c   .s, .sig.c   .sc,
			
 
				+.sig.cpp .s, .sig.cpp .sc {
			
 
				+	color: #067D17;
			
 
				+}
			
 
				+
			
 
				+
			
 
				+/* -- other body styles ----------------------------------------------------- */
			
 
				+
			
 
				+ol.arabic {
			
 
				+    list-style: decimal;
			
 
				+}
			
 
				+
			
 
				+ol.loweralpha {
			
 
				+    list-style: lower-alpha;
			
 
				+}
			
 
				+
			
 
				+ol.upperalpha {
			
 
				+    list-style: upper-alpha;
			
 
				+}
			
 
				+
			
 
				+ol.lowerroman {
			
 
				+    list-style: lower-roman;
			
 
				+}
			
 
				+
			
 
				+ol.upperroman {
			
 
				+    list-style: upper-roman;
			
 
				+}
			
 
				+
			
 
				+:not(li) > ol > li:first-child > :first-child,
			
 
				+:not(li) > ul > li:first-child > :first-child {
			
 
				+    margin-top: 0px;
			
 
				+}
			
 
				+
			
 
				+:not(li) > ol > li:last-child > :last-child,
			
 
				+:not(li) > ul > li:last-child > :last-child {
			
 
				+    margin-bottom: 0px;
			
 
				+}
			
 
				+
			
 
				+ol.simple ol p,
			
 
				+ol.simple ul p,
			
 
				+ul.simple ol p,
			
 
				+ul.simple ul p {
			
 
				+    margin-top: 0;
			
 
				+}
			
 
				+
			
 
				+ol.simple > li:not(:first-child) > p,
			
 
				+ul.simple > li:not(:first-child) > p {
			
 
				+    margin-top: 0;
			
 
				+}
			
 
				+
			
 
				+ol.simple p,
			
 
				+ul.simple p {
			
 
				+    margin-bottom: 0;
			
 
				+}
			
 
				+
			
 
				+dl.footnote > dt,
			
 
				+dl.citation > dt {
			
 
				+    float: left;
			
 
				+    margin-right: 0.5em;
			
 
				+}
			
 
				+
			
 
				+dl.footnote > dd,
			
 
				+dl.citation > dd {
			
 
				+    margin-bottom: 0em;
			
 
				+}
			
 
				+
			
 
				+dl.footnote > dd:after,
			
 
				+dl.citation > dd:after {
			
 
				+    content: "";
			
 
				+    clear: both;
			
 
				+}
			
 
				+
			
 
				+dl.field-list {
			
 
				+    display: grid;
			
 
				+    grid-template-columns: fit-content(30%) auto;
			
 
				+}
			
 
				+
			
 
				+dl.field-list > dt {
			
 
				+    font-weight: bold;
			
 
				+    word-break: break-word;
			
 
				+    padding-left: 0.5em;
			
 
				+    padding-right: 5px;
			
 
				+}
			
 
				+
			
 
				+dl.field-list > dt:after {
			
 
				+    content: ":";
			
 
				+}
			
 
				+
			
 
				+dl.field-list > dd {
			
 
				+    padding-left: 0.5em;
			
 
				+    margin-top: 0em;
			
 
				+    margin-left: 0em;
			
 
				+    margin-bottom: 0em;
			
 
				+}
			
 
				+
			
 
				+dl {
			
 
				+    margin-bottom: 15px;
			
 
				+}
			
 
				+
			
 
				+dd > :first-child {
			
 
				+    margin-top: 0px;
			
 
				+}
			
 
				+
			
 
				+dd ul, dd table {
			
 
				+    margin-bottom: 10px;
			
 
				+}
			
 
				+
			
 
				+dd {
			
 
				+    margin-top: 3px;
			
 
				+    margin-bottom: 10px;
			
 
				+    margin-left: 30px;
			
 
				+}
			
 
				+
			
 
				+dl > dd:last-child,
			
 
				+dl > dd:last-child > :last-child {
			
 
				+    margin-bottom: 0;
			
 
				+}
			
 
				+
			
 
				+dt:target, span.highlighted {
			
 
				+    background-color: #fbe54e;
			
 
				+}
			
 
				+
			
 
				+rect.highlighted {
			
 
				+    fill: #fbe54e;
			
 
				+}
			
 
				+
			
 
				+dl.glossary dt {
			
 
				+    font-weight: bold;
			
 
				+    font-size: 1.1em;
			
 
				+}
			
 
				+
			
 
				+.versionmodified {
			
 
				+    font-style: italic;
			
 
				+}
			
 
				+
			
 
				+.system-message {
			
 
				+    background-color: #fda;
			
 
				+    padding: 5px;
			
 
				+    border: 3px solid red;
			
 
				+}
			
 
				+
			
 
				+.footnote:target  {
			
 
				+    background-color: #ffa;
			
 
				+}
			
 
				+
			
 
				+.line-block {
			
 
				+    display: block;
			
 
				+    margin-top: 1em;
			
 
				+    margin-bottom: 1em;
			
 
				+}
			
 
				+
			
 
				+.line-block .line-block {
			
 
				+    margin-top: 0;
			
 
				+    margin-bottom: 0;
			
 
				+    margin-left: 1.5em;
			
 
				+}
			
 
				+
			
 
				+.guilabel, .menuselection {
			
 
				+    font-family: sans-serif;
			
 
				+}
			
 
				+
			
 
				+.accelerator {
			
 
				+    text-decoration: underline;
			
 
				+}
			
 
				+
			
 
				+.classifier {
			
 
				+    font-style: oblique;
			
 
				+}
			
 
				+
			
 
				+.classifier:before {
			
 
				+    font-style: normal;
			
 
				+    margin: 0 0.5em;
			
 
				+    content: ":";
			
 
				+    display: inline-block;
			
 
				+}
			
 
				+
			
 
				+abbr, acronym {
			
 
				+    border-bottom: dotted 1px;
			
 
				+    cursor: help;
			
 
				+}
			
 
				+
			
 
				+/* -- code displays --------------------------------------------------------- */
			
 
				+
			
 
				+pre {
			
 
				+    overflow: auto;
			
 
				+    overflow-y: hidden;  /* fixes display issues on Chrome browsers */
			
 
				+}
			
 
				+
			
 
				+pre, div[class*="highlight-"] {
			
 
				+    clear: both;
			
 
				+}
			
 
				+
			
 
				+span.pre {
			
 
				+    -moz-hyphens: none;
			
 
				+    -ms-hyphens: none;
			
 
				+    -webkit-hyphens: none;
			
 
				+    hyphens: none;
			
 
				+    white-space: nowrap;
			
 
				+}
			
 
				+
			
 
				+div[class*="highlight-"] {
			
 
				+    margin: 1em 0;
			
 
				+}
			
 
				+
			
 
				+td.linenos pre {
			
 
				+    border: 0;
			
 
				+    background-color: transparent;
			
 
				+    color: #aaa;
			
 
				+}
			
 
				+
			
 
				+table.highlighttable {
			
 
				+    display: block;
			
 
				+}
			
 
				+
			
 
				+table.highlighttable tbody {
			
 
				+    display: block;
			
 
				+}
			
 
				+
			
 
				+table.highlighttable tr {
			
 
				+    display: flex;
			
 
				+}
			
 
				+
			
 
				+table.highlighttable td {
			
 
				+    margin: 0;
			
 
				+    padding: 0;
			
 
				+}
			
 
				+
			
 
				+table.highlighttable td.linenos {
			
 
				+    padding-right: 0.5em;
			
 
				+}
			
 
				+
			
 
				+table.highlighttable td.code {
			
 
				+    flex: 1;
			
 
				+    overflow: hidden;
			
 
				+}
			
 
				+
			
 
				+.highlight .hll {
			
 
				+    display: block;
			
 
				+}
			
 
				+
			
 
				+div.highlight pre,
			
 
				+table.highlighttable pre {
			
 
				+    margin: 0;
			
 
				+}
			
 
				+
			
 
				+div.code-block-caption + div {
			
 
				+    margin-top: 0;
			
 
				+}
			
 
				+
			
 
				+div.code-block-caption {
			
 
				+    margin-top: 1em;
			
 
				+    padding: 2px 5px;
			
 
				+    font-size: small;
			
 
				+}
			
 
				+
			
 
				+div.code-block-caption code {
			
 
				+    background-color: transparent;
			
 
				+}
			
 
				+
			
 
				+table.highlighttable td.linenos,
			
 
				+span.linenos,
			
 
				+div.highlight span.gp {  /* gp: Generic.Prompt */
			
 
				+  user-select: none;
			
 
				+  -webkit-user-select: text; /* Safari fallback only */
			
 
				+  -webkit-user-select: none; /* Chrome/Safari */
			
 
				+  -moz-user-select: none; /* Firefox */
			
 
				+  -ms-user-select: none; /* IE10+ */
			
 
				+}
			
 
				+
			
 
				+div.code-block-caption span.caption-number {
			
 
				+    padding: 0.1em 0.3em;
			
 
				+    font-style: italic;
			
 
				+}
			
 
				+
			
 
				+div.code-block-caption span.caption-text {
			
 
				+}
			
 
				+
			
 
				+div.literal-block-wrapper {
			
 
				+    margin: 1em 0;
			
 
				+}
			
 
				+
			
 
				+code.xref, a code {
			
 
				+    background-color: transparent;
			
 
				+    font-weight: bold;
			
 
				+}
			
 
				+
			
 
				+h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
			
 
				+    background-color: transparent;
			
 
				+}
			
 
				+
			
 
				+.viewcode-link {
			
 
				+    float: right;
			
 
				+}
			
 
				+
			
 
				+.viewcode-back {
			
 
				+    float: right;
			
 
				+    font-family: sans-serif;
			
 
				+}
			
 
				+
			
 
				+div.viewcode-block:target {
			
 
				+    margin: -1px -10px;
			
 
				+    padding: 0 10px;
			
 
				+}
			
 
				+
			
 
				+/* -- math display ---------------------------------------------------------- */
			
 
				+
			
 
				+img.math {
			
 
				+    vertical-align: middle;
			
 
				+}
			
 
				+
			
 
				+div.body div.math p {
			
 
				+    text-align: center;
			
 
				+}
			
 
				+
			
 
				+span.eqno {
			
 
				+    float: right;
			
 
				+}
			
 
				+
			
 
				+span.eqno a.headerlink {
			
 
				+    position: absolute;
			
 
				+    z-index: 1;
			
 
				+}
			
 
				+
			
 
				+div.math:hover a.headerlink {
			
 
				+    visibility: visible;
			
 
				+}
			
 
				+
			
 
				+/* -- printout stylesheet --------------------------------------------------- */
			
 
				+
			
 
				+@media print {
			
 
				+    div.document,
			
 
				+    div.documentwrapper,
			
 
				+    div.bodywrapper {
			
 
				+        margin: 0 !important;
			
 
				+        width: 100%;
			
 
				+    }
			
 
				+
			
 
				+    div.sphinxsidebar,
			
 
				+    div.related,
			
 
				+    div.footer,
			
 
				+    #top-link {
			
 
				+        display: none;
			
 
				+    }
			
 
				+}
			
--- a/_static/check-solid.svg
+++ b/_static/check-solid.svg
@@ -0,0 +1,4 @@
 
				+<svg xmlns="http://www.w3.org/2000/svg" class="icon icon-tabler icon-tabler-check" width="44" height="44" viewBox="0 0 24 24" stroke-width="2" stroke="#22863a" fill="none" stroke-linecap="round" stroke-linejoin="round">
			
 
				+  <path stroke="none" d="M0 0h24v24H0z" fill="none"/>
			
 
				+  <path d="M5 12l5 5l10 -10" />
			
 
				+</svg>
			
--- a/_static/clipboard.min.js
+++ b/_static/clipboard.min.js
--- a/_static/copy-button.svg
+++ b/_static/copy-button.svg
@@ -0,0 +1,5 @@
 
				+<svg xmlns="http://www.w3.org/2000/svg" class="icon icon-tabler icon-tabler-copy" width="44" height="44" viewBox="0 0 24 24" stroke-width="1.5" stroke="#000000" fill="none" stroke-linecap="round" stroke-linejoin="round">
			
 
				+  <path stroke="none" d="M0 0h24v24H0z" fill="none"/>
			
 
				+  <rect x="8" y="8" width="12" height="12" rx="2" />
			
 
				+  <path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2" />
			
 
				+</svg>
			
--- a/_static/copybutton.css
+++ b/_static/copybutton.css
@@ -0,0 +1,93 @@
 
				+/* Copy buttons */
			
 
				+button.copybtn {
			
 
				+    position: absolute;
			
 
				+    display: flex;
			
 
				+    top: .3em;
			
 
				+    right: .3em;
			
 
				+    width: 1.7em;
			
 
				+    height: 1.7em;
			
 
				+	opacity: 0;
			
 
				+    transition: opacity 0.3s, border .3s, background-color .3s;
			
 
				+    user-select: none;
			
 
				+    padding: 0;
			
 
				+    border: none;
			
 
				+    outline: none;
			
 
				+    border-radius: 0.4em;
			
 
				+    /* The colors that GitHub uses */
			
 
				+    border: #1b1f2426 1px solid;
			
 
				+    background-color: #f6f8fa;
			
 
				+    color: #57606a;
			
 
				+}
			
 
				+
			
 
				+button.copybtn.success {
			
 
				+    border-color: #22863a;
			
 
				+    color: #22863a;
			
 
				+}
			
 
				+
			
 
				+button.copybtn svg {
			
 
				+    stroke: currentColor;
			
 
				+    width: 1.5em;
			
 
				+    height: 1.5em;
			
 
				+    padding: 0.1em;
			
 
				+}
			
 
				+
			
 
				+div.highlight  {
			
 
				+    position: relative;
			
 
				+}
			
 
				+
			
 
				+.highlight:hover button.copybtn {
			
 
				+	opacity: 1;
			
 
				+}
			
 
				+
			
 
				+.highlight button.copybtn:hover {
			
 
				+    background-color: rgb(235, 235, 235);
			
 
				+}
			
 
				+
			
 
				+.highlight button.copybtn:active {
			
 
				+    background-color: rgb(187, 187, 187);
			
 
				+}
			
 
				+
			
 
				+/**
			
 
				+ * A minimal CSS-only tooltip copied from:
			
 
				+ *   https://codepen.io/mildrenben/pen/rVBrpK
			
 
				+ *
			
 
				+ * To use, write HTML like the following:
			
 
				+ *
			
 
				+ * <p class="o-tooltip--left" data-tooltip="Hey">Short</p>
			
 
				+ */
			
 
				+ .o-tooltip--left {
			
 
				+  position: relative;
			
 
				+ }
			
 
				+
			
 
				+ .o-tooltip--left:after {
			
 
				+    opacity: 0;
			
 
				+    visibility: hidden;
			
 
				+    position: absolute;
			
 
				+    content: attr(data-tooltip);
			
 
				+    padding: .2em;
			
 
				+    font-size: .8em;
			
 
				+    left: -.2em;
			
 
				+    background: grey;
			
 
				+    color: white;
			
 
				+    white-space: nowrap;
			
 
				+    z-index: 2;
			
 
				+    border-radius: 2px;
			
 
				+    transform: translateX(-102%) translateY(0);
			
 
				+    transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1);
			
 
				+}
			
 
				+
			
 
				+.o-tooltip--left:hover:after {
			
 
				+    display: block;
			
 
				+    opacity: 1;
			
 
				+    visibility: visible;
			
 
				+    transform: translateX(-100%) translateY(0);
			
 
				+    transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1);
			
 
				+    transition-delay: .5s;
			
 
				+}
			
 
				+
			
 
				+/* By default the copy button shouldn't show up when printing a page */
			
 
				+@media print {
			
 
				+    button.copybtn {
			
 
				+        display: none;
			
 
				+    }
			
 
				+}
			
--- a/_static/copybutton.js
+++ b/_static/copybutton.js
@@ -0,0 +1,220 @@
 
				+// Localization support
			
 
				+const messages = {
			
 
				+  'en': {
			
 
				+    'copy': 'Copy',
			
 
				+    'copy_to_clipboard': 'Copy to clipboard',
			
 
				+    'copy_success': 'Copied!',
			
 
				+    'copy_failure': 'Failed to copy',
			
 
				+  },
			
 
				+  'es' : {
			
 
				+    'copy': 'Copiar',
			
 
				+    'copy_to_clipboard': 'Copiar al portapapeles',
			
 
				+    'copy_success': '¡Copiado!',
			
 
				+    'copy_failure': 'Error al copiar',
			
 
				+  },
			
 
				+  'de' : {
			
 
				+    'copy': 'Kopieren',
			
 
				+    'copy_to_clipboard': 'In die Zwischenablage kopieren',
			
 
				+    'copy_success': 'Kopiert!',
			
 
				+    'copy_failure': 'Fehler beim Kopieren',
			
 
				+  },
			
 
				+  'fr' : {
			
 
				+    'copy': 'Copier',
			
 
				+    'copy_to_clipboard': 'Copié dans le presse-papier',
			
 
				+    'copy_success': 'Copié !',
			
 
				+    'copy_failure': 'Échec de la copie',
			
 
				+  },
			
 
				+  'ru': {
			
 
				+    'copy': 'Скопировать',
			
 
				+    'copy_to_clipboard': 'Скопировать в буфер',
			
 
				+    'copy_success': 'Скопировано!',
			
 
				+    'copy_failure': 'Не удалось скопировать',
			
 
				+  },
			
 
				+  'zh-CN': {
			
 
				+    'copy': '复制',
			
 
				+    'copy_to_clipboard': '复制到剪贴板',
			
 
				+    'copy_success': '复制成功!',
			
 
				+    'copy_failure': '复制失败',
			
 
				+  },
			
 
				+  'it' : {
			
 
				+    'copy': 'Copiare',
			
 
				+    'copy_to_clipboard': 'Copiato negli appunti',
			
 
				+    'copy_success': 'Copiato!',
			
 
				+    'copy_failure': 'Errore durante la copia',
			
 
				+  }
			
 
				+}
			
 
				+
			
 
				+let locale = 'en'
			
 
				+if( document.documentElement.lang !== undefined
			
 
				+    && messages[document.documentElement.lang] !== undefined ) {
			
 
				+  locale = document.documentElement.lang
			
 
				+}
			
 
				+
			
 
				+let doc_url_root = DOCUMENTATION_OPTIONS.URL_ROOT;
			
 
				+if (doc_url_root == '#') {
			
 
				+    doc_url_root = '';
			
 
				+}
			
 
				+
			
 
				+/**
			
 
				+ * SVG files for our copy buttons
			
 
				+ */
			
 
				+let iconCheck = `<svg xmlns="http://www.w3.org/2000/svg" class="icon icon-tabler icon-tabler-check" width="44" height="44" viewBox="0 0 24 24" stroke-width="2" stroke="#22863a" fill="none" stroke-linecap="round" stroke-linejoin="round">
			
 
				+  <title>${messages[locale]['copy_success']}</title>
			
 
				+  <path stroke="none" d="M0 0h24v24H0z" fill="none"/>
			
 
				+  <path d="M5 12l5 5l10 -10" />
			
 
				+</svg>`
			
 
				+
			
 
				+// If the user specified their own SVG use that, otherwise use the default
			
 
				+let iconCopy = ``;
			
 
				+if (!iconCopy) {
			
 
				+  iconCopy = `<svg xmlns="http://www.w3.org/2000/svg" class="icon icon-tabler icon-tabler-copy" width="44" height="44" viewBox="0 0 24 24" stroke-width="1.5" stroke="#000000" fill="none" stroke-linecap="round" stroke-linejoin="round">
			
 
				+  <title>${messages[locale]['copy_to_clipboard']}</title>
			
 
				+  <path stroke="none" d="M0 0h24v24H0z" fill="none"/>
			
 
				+  <rect x="8" y="8" width="12" height="12" rx="2" />
			
 
				+  <path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2" />
			
 
				+</svg>`
			
 
				+}
			
 
				+
			
 
				+/**
			
 
				+ * Set up copy/paste for code blocks
			
 
				+ */
			
 
				+
			
 
				+const runWhenDOMLoaded = cb => {
			
 
				+  if (document.readyState != 'loading') {
			
 
				+    cb()
			
 
				+  } else if (document.addEventListener) {
			
 
				+    document.addEventListener('DOMContentLoaded', cb)
			
 
				+  } else {
			
 
				+    document.attachEvent('onreadystatechange', function() {
			
 
				+      if (document.readyState == 'complete') cb()
			
 
				+    })
			
 
				+  }
			
 
				+}
			
 
				+
			
 
				+const codeCellId = index => `codecell${index}`
			
 
				+
			
 
				+// Clears selected text since ClipboardJS will select the text when copying
			
 
				+const clearSelection = () => {
			
 
				+  if (window.getSelection) {
			
 
				+    window.getSelection().removeAllRanges()
			
 
				+  } else if (document.selection) {
			
 
				+    document.selection.empty()
			
 
				+  }
			
 
				+}
			
 
				+
			
 
				+// Changes tooltip text for two seconds, then changes it back
			
 
				+const temporarilyChangeTooltip = (el, oldText, newText) => {
			
 
				+  el.setAttribute('data-tooltip', newText)
			
 
				+  el.classList.add('success')
			
 
				+  setTimeout(() => el.setAttribute('data-tooltip', oldText), 2000)
			
 
				+  setTimeout(() => el.classList.remove('success'), 2000)
			
 
				+}
			
 
				+
			
 
				+// Changes the copy button icon for two seconds, then changes it back
			
 
				+const temporarilyChangeIcon = (el) => {
			
 
				+  el.innerHTML = iconCheck;
			
 
				+  setTimeout(() => {el.innerHTML = iconCopy}, 2000)
			
 
				+}
			
 
				+
			
 
				+const addCopyButtonToCodeCells = () => {
			
 
				+  // If ClipboardJS hasn't loaded, wait a bit and try again. This
			
 
				+  // happens because we load ClipboardJS asynchronously.
			
 
				+  if (window.ClipboardJS === undefined) {
			
 
				+    setTimeout(addCopyButtonToCodeCells, 250)
			
 
				+    return
			
 
				+  }
			
 
				+
			
 
				+  // Add copybuttons to all of our code cells
			
 
				+  const codeCells = document.querySelectorAll('div.highlight pre')
			
 
				+  codeCells.forEach((codeCell, index) => {
			
 
				+    const id = codeCellId(index)
			
 
				+    codeCell.setAttribute('id', id)
			
 
				+
			
 
				+    const clipboardButton = id =>
			
 
				+    `<button class="copybtn o-tooltip--left" data-tooltip="${messages[locale]['copy']}" data-clipboard-target="#${id}">
			
 
				+      ${iconCopy}
			
 
				+    </button>`
			
 
				+    codeCell.insertAdjacentHTML('afterend', clipboardButton(id))
			
 
				+  })
			
 
				+
			
 
				+function escapeRegExp(string) {
			
 
				+    return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
			
 
				+}
			
 
				+
			
 
				+// Callback when a copy button is clicked. Will be passed the node that was clicked
			
 
				+// should then grab the text and replace pieces of text that shouldn't be used in output
			
 
				+function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") {
			
 
				+
			
 
				+    var regexp;
			
 
				+    var match;
			
 
				+
			
 
				+    // Do we check for line continuation characters and "HERE-documents"?
			
 
				+    var useLineCont = !!lineContinuationChar
			
 
				+    var useHereDoc = !!hereDocDelim
			
 
				+
			
 
				+    // create regexp to capture prompt and remaining line
			
 
				+    if (isRegexp) {
			
 
				+        regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)')
			
 
				+    } else {
			
 
				+        regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)')
			
 
				+    }
			
 
				+
			
 
				+    const outputLines = [];
			
 
				+    var promptFound = false;
			
 
				+    var gotLineCont = false;
			
 
				+    var gotHereDoc = false;
			
 
				+    const lineGotPrompt = [];
			
 
				+    for (const line of textContent.split('\n')) {
			
 
				+        match = line.match(regexp)
			
 
				+        if (match || gotLineCont || gotHereDoc) {
			
 
				+            promptFound = regexp.test(line)
			
 
				+            lineGotPrompt.push(promptFound)
			
 
				+            if (removePrompts && promptFound) {
			
 
				+                outputLines.push(match[2])
			
 
				+            } else {
			
 
				+                outputLines.push(line)
			
 
				+            }
			
 
				+            gotLineCont = line.endsWith(lineContinuationChar) & useLineCont
			
 
				+            if (line.includes(hereDocDelim) & useHereDoc)
			
 
				+                gotHereDoc = !gotHereDoc
			
 
				+        } else if (!onlyCopyPromptLines) {
			
 
				+            outputLines.push(line)
			
 
				+        } else if (copyEmptyLines && line.trim() === '') {
			
 
				+            outputLines.push(line)
			
 
				+        }
			
 
				+    }
			
 
				+
			
 
				+    // If no lines with the prompt were found then just use original lines
			
 
				+    if (lineGotPrompt.some(v => v === true)) {
			
 
				+        textContent = outputLines.join('\n');
			
 
				+    }
			
 
				+
			
 
				+    // Remove a trailing newline to avoid auto-running when pasting
			
 
				+    if (textContent.endsWith("\n")) {
			
 
				+        textContent = textContent.slice(0, -1)
			
 
				+    }
			
 
				+    return textContent
			
 
				+}
			
 
				+
			
 
				+
			
 
				+var copyTargetText = (trigger) => {
			
 
				+  var target = document.querySelector(trigger.attributes['data-clipboard-target'].value);
			
 
				+  return formatCopyText(target.innerText, '', false, true, true, true, '', '')
			
 
				+}
			
 
				+
			
 
				+  // Initialize with a callback so we can modify the text before copy
			
 
				+  const clipboard = new ClipboardJS('.copybtn', {text: copyTargetText})
			
 
				+
			
 
				+  // Update UI with error/success messages
			
 
				+  clipboard.on('success', event => {
			
 
				+    clearSelection()
			
 
				+    temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_success'])
			
 
				+    temporarilyChangeIcon(event.trigger)
			
 
				+  })
			
 
				+
			
 
				+  clipboard.on('error', event => {
			
 
				+    temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_failure'])
			
 
				+  })
			
 
				+}
			
 
				+
			
 
				+runWhenDOMLoaded(addCopyButtonToCodeCells)
			
--- a/_static/copybutton_funcs.js
+++ b/_static/copybutton_funcs.js
@@ -0,0 +1,58 @@
 
				+function escapeRegExp(string) {
			
 
				+    return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
			
 
				+}
			
 
				+
			
 
				+// Callback when a copy button is clicked. Will be passed the node that was clicked
			
 
				+// should then grab the text and replace pieces of text that shouldn't be used in output
			
 
				+export function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") {
			
 
				+
			
 
				+    var regexp;
			
 
				+    var match;
			
 
				+
			
 
				+    // Do we check for line continuation characters and "HERE-documents"?
			
 
				+    var useLineCont = !!lineContinuationChar
			
 
				+    var useHereDoc = !!hereDocDelim
			
 
				+
			
 
				+    // create regexp to capture prompt and remaining line
			
 
				+    if (isRegexp) {
			
 
				+        regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)')
			
 
				+    } else {
			
 
				+        regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)')
			
 
				+    }
			
 
				+
			
 
				+    const outputLines = [];
			
 
				+    var promptFound = false;
			
 
				+    var gotLineCont = false;
			
 
				+    var gotHereDoc = false;
			
 
				+    const lineGotPrompt = [];
			
 
				+    for (const line of textContent.split('\n')) {
			
 
				+        match = line.match(regexp)
			
 
				+        if (match || gotLineCont || gotHereDoc) {
			
 
				+            promptFound = regexp.test(line)
			
 
				+            lineGotPrompt.push(promptFound)
			
 
				+            if (removePrompts && promptFound) {
			
 
				+                outputLines.push(match[2])
			
 
				+            } else {
			
 
				+                outputLines.push(line)
			
 
				+            }
			
 
				+            gotLineCont = line.endsWith(lineContinuationChar) & useLineCont
			
 
				+            if (line.includes(hereDocDelim) & useHereDoc)
			
 
				+                gotHereDoc = !gotHereDoc
			
 
				+        } else if (!onlyCopyPromptLines) {
			
 
				+            outputLines.push(line)
			
 
				+        } else if (copyEmptyLines && line.trim() === '') {
			
 
				+            outputLines.push(line)
			
 
				+        }
			
 
				+    }
			
 
				+
			
 
				+    // If no lines with the prompt were found then just use original lines
			
 
				+    if (lineGotPrompt.some(v => v === true)) {
			
 
				+        textContent = outputLines.join('\n');
			
 
				+    }
			
 
				+
			
 
				+    // Remove a trailing newline to avoid auto-running when pasting
			
 
				+    if (textContent.endsWith("\n")) {
			
 
				+        textContent = textContent.slice(0, -1)
			
 
				+    }
			
 
				+    return textContent
			
 
				+}
			
--- a/_static/css/blank.css
+++ b/_static/css/blank.css
@@ -0,0 +1,2 @@
 
				+/* This file is intentionally left blank to override the stylesheet of the
			
 
				+parent theme via theme.conf. The parent style we import directly in theme.css */
			
--- a/_static/css/index.ff1ffe594081f20da1ef19478df9384b.css
+++ b/_static/css/index.ff1ffe594081f20da1ef19478df9384b.css
--- a/_static/css/theme.css
+++ b/_static/css/theme.css
@@ -0,0 +1,120 @@
 
				+/* Provided by the Sphinx base theme template at build time */
			
 
				+@import "../basic.css";
			
 
				+
			
 
				+:root {
			
 
				+  /*****************************************************************************
			
 
				+  * Theme config
			
 
				+  **/
			
 
				+  --pst-header-height: 60px;
			
 
				+
			
 
				+  /*****************************************************************************
			
 
				+  * Font size
			
 
				+  **/
			
 
				+  --pst-font-size-base: 15px; /* base font size - applied at body / html level */
			
 
				+
			
 
				+  /* heading font sizes */
			
 
				+  --pst-font-size-h1: 36px;
			
 
				+  --pst-font-size-h2: 32px;
			
 
				+  --pst-font-size-h3: 26px;
			
 
				+  --pst-font-size-h4: 21px;
			
 
				+  --pst-font-size-h5: 18px;
			
 
				+  --pst-font-size-h6: 16px;
			
 
				+
			
 
				+  /* smaller then heading font sizes*/
			
 
				+  --pst-font-size-milli: 12px;
			
 
				+
			
 
				+  --pst-sidebar-font-size: .9em;
			
 
				+  --pst-sidebar-caption-font-size: .9em;
			
 
				+
			
 
				+  /*****************************************************************************
			
 
				+  * Font family
			
 
				+  **/
			
 
				+  /* These are adapted from https://systemfontstack.com/ */
			
 
				+  --pst-font-family-base-system: -apple-system, BlinkMacSystemFont, Segoe UI, "Helvetica Neue",
			
 
				+    Arial, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol;
			
 
				+  --pst-font-family-monospace-system: "SFMono-Regular", Menlo, Consolas, Monaco,
			
 
				+    Liberation Mono, Lucida Console, monospace;
			
 
				+
			
 
				+  --pst-font-family-base: var(--pst-font-family-base-system);
			
 
				+  --pst-font-family-heading: var(--pst-font-family-base);
			
 
				+  --pst-font-family-monospace: var(--pst-font-family-monospace-system);
			
 
				+
			
 
				+  /*****************************************************************************
			
 
				+  * Color
			
 
				+  * 
			
 
				+  * Colors are defined in rgb string way, "red, green, blue"
			
 
				+  **/
			
 
				+  --pst-color-primary: 19, 6, 84;
			
 
				+  --pst-color-success: 40, 167, 69;
			
 
				+  --pst-color-info: 0, 123, 255;  /*23, 162, 184;*/
			
 
				+  --pst-color-warning: 255, 193, 7;
			
 
				+  --pst-color-danger: 220, 53, 69;
			
 
				+  --pst-color-text-base: 51, 51, 51;
			
 
				+
			
 
				+  --pst-color-h1: var(--pst-color-primary);
			
 
				+  --pst-color-h2: var(--pst-color-primary);
			
 
				+  --pst-color-h3: var(--pst-color-text-base);
			
 
				+  --pst-color-h4: var(--pst-color-text-base);
			
 
				+  --pst-color-h5: var(--pst-color-text-base);
			
 
				+  --pst-color-h6: var(--pst-color-text-base);
			
 
				+  --pst-color-paragraph: var(--pst-color-text-base);
			
 
				+  --pst-color-link: 0, 91, 129;
			
 
				+  --pst-color-link-hover: 227, 46, 0;
			
 
				+  --pst-color-headerlink: 198, 15, 15;
			
 
				+  --pst-color-headerlink-hover: 255, 255, 255;
			
 
				+  --pst-color-preformatted-text: 34, 34, 34;
			
 
				+  --pst-color-preformatted-background: 250, 250, 250;
			
 
				+  --pst-color-inline-code: 232, 62, 140;
			
 
				+
			
 
				+  --pst-color-active-navigation: 19, 6, 84;
			
 
				+  --pst-color-navbar-link: 77, 77, 77;
			
 
				+  --pst-color-navbar-link-hover: var(--pst-color-active-navigation);
			
 
				+  --pst-color-navbar-link-active: var(--pst-color-active-navigation);
			
 
				+  --pst-color-sidebar-link: 77, 77, 77;
			
 
				+  --pst-color-sidebar-link-hover: var(--pst-color-active-navigation);
			
 
				+  --pst-color-sidebar-link-active: var(--pst-color-active-navigation);
			
 
				+  --pst-color-sidebar-expander-background-hover: 244, 244, 244;
			
 
				+  --pst-color-sidebar-caption: 77, 77, 77;
			
 
				+  --pst-color-toc-link: 119, 117, 122;
			
 
				+  --pst-color-toc-link-hover: var(--pst-color-active-navigation);
			
 
				+  --pst-color-toc-link-active: var(--pst-color-active-navigation);
			
 
				+
			
 
				+  /*****************************************************************************
			
 
				+  * Icon
			
 
				+  **/
			
 
				+
			
 
				+  /* font awesome icons*/
			
 
				+  --pst-icon-check-circle: '\f058';
			
 
				+  --pst-icon-info-circle: '\f05a';
			
 
				+  --pst-icon-exclamation-triangle: '\f071';
			
 
				+  --pst-icon-exclamation-circle: '\f06a';
			
 
				+  --pst-icon-times-circle: '\f057';
			
 
				+  --pst-icon-lightbulb: '\f0eb';
			
 
				+
			
 
				+  /*****************************************************************************
			
 
				+  * Admonitions
			
 
				+  **/
			
 
				+
			
 
				+  --pst-color-admonition-default: var(--pst-color-info);
			
 
				+  --pst-color-admonition-note: var(--pst-color-info);
			
 
				+  --pst-color-admonition-attention: var(--pst-color-warning);
			
 
				+  --pst-color-admonition-caution: var(--pst-color-warning);
			
 
				+  --pst-color-admonition-warning: var(--pst-color-warning);
			
 
				+  --pst-color-admonition-danger: var(--pst-color-danger);
			
 
				+  --pst-color-admonition-error: var(--pst-color-danger);
			
 
				+  --pst-color-admonition-hint: var(--pst-color-success);
			
 
				+  --pst-color-admonition-tip: var(--pst-color-success);
			
 
				+  --pst-color-admonition-important: var(--pst-color-success);
			
 
				+
			
 
				+  --pst-icon-admonition-default: var(--pst-icon-info-circle);
			
 
				+  --pst-icon-admonition-note: var(--pst-icon-info-circle);
			
 
				+  --pst-icon-admonition-attention: var(--pst-icon-exclamation-circle);
			
 
				+  --pst-icon-admonition-caution: var(--pst-icon-exclamation-triangle);
			
 
				+  --pst-icon-admonition-warning: var(--pst-icon-exclamation-triangle);
			
 
				+  --pst-icon-admonition-danger: var(--pst-icon-exclamation-triangle);
			
 
				+  --pst-icon-admonition-error: var(--pst-icon-times-circle);
			
 
				+  --pst-icon-admonition-hint: var(--pst-icon-lightbulb);
			
 
				+  --pst-icon-admonition-tip: var(--pst-icon-lightbulb);
			
 
				+  --pst-icon-admonition-important: var(--pst-icon-exclamation-circle);
			
 
				+
			
 
				+}
			
--- a/_static/doctools.js
+++ b/_static/doctools.js
@@ -0,0 +1,358 @@
 
				+/*
			
 
				+ * doctools.js
			
 
				+ * ~~~~~~~~~~~
			
 
				+ *
			
 
				+ * Sphinx JavaScript utilities for all documentation.
			
 
				+ *
			
 
				+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
			
 
				+ * :license: BSD, see LICENSE for details.
			
 
				+ *
			
 
				+ */
			
 
				+
			
 
				+/**
			
 
				+ * select a different prefix for underscore
			
 
				+ */
			
 
				+$u = _.noConflict();
			
 
				+
			
 
				+/**
			
 
				+ * make the code below compatible with browsers without
			
 
				+ * an installed firebug like debugger
			
 
				+if (!window.console || !console.firebug) {
			
 
				+  var names = ["log", "debug", "info", "warn", "error", "assert", "dir",
			
 
				+    "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace",
			
 
				+    "profile", "profileEnd"];
			
 
				+  window.console = {};
			
 
				+  for (var i = 0; i < names.length; ++i)
			
 
				+    window.console[names[i]] = function() {};
			
 
				+}
			
 
				+ */
			
 
				+
			
 
				+/**
			
 
				+ * small helper function to urldecode strings
			
 
				+ *
			
 
				+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL
			
 
				+ */
			
 
				+jQuery.urldecode = function(x) {
			
 
				+  if (!x) {
			
 
				+    return x
			
 
				+  }
			
 
				+  return decodeURIComponent(x.replace(/\+/g, ' '));
			
 
				+};
			
 
				+
			
 
				+/**
			
 
				+ * small helper function to urlencode strings
			
 
				+ */
			
 
				+jQuery.urlencode = encodeURIComponent;
			
 
				+
			
 
				+/**
			
 
				+ * This function returns the parsed url parameters of the
			
 
				+ * current request. Multiple values per key are supported,
			
 
				+ * it will always return arrays of strings for the value parts.
			
 
				+ */
			
 
				+jQuery.getQueryParameters = function(s) {
			
 
				+  if (typeof s === 'undefined')
			
 
				+    s = document.location.search;
			
 
				+  var parts = s.substr(s.indexOf('?') + 1).split('&');
			
 
				+  var result = {};
			
 
				+  for (var i = 0; i < parts.length; i++) {
			
 
				+    var tmp = parts[i].split('=', 2);
			
 
				+    var key = jQuery.urldecode(tmp[0]);
			
 
				+    var value = jQuery.urldecode(tmp[1]);
			
 
				+    if (key in result)
			
 
				+      result[key].push(value);
			
 
				+    else
			
 
				+      result[key] = [value];
			
 
				+  }
			
 
				+  return result;
			
 
				+};
			
 
				+
			
 
				+/**
			
 
				+ * highlight a given string on a jquery object by wrapping it in
			
 
				+ * span elements with the given class name.
			
 
				+ */
			
 
				+jQuery.fn.highlightText = function(text, className) {
			
 
				+  function highlight(node, addItems) {
			
 
				+    if (node.nodeType === 3) {
			
 
				+      var val = node.nodeValue;
			
 
				+      var pos = val.toLowerCase().indexOf(text);
			
 
				+      if (pos >= 0 &&
			
 
				+          !jQuery(node.parentNode).hasClass(className) &&
			
 
				+          !jQuery(node.parentNode).hasClass("nohighlight")) {
			
 
				+        var span;
			
 
				+        var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
			
 
				+        if (isInSVG) {
			
 
				+          span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
			
 
				+        } else {
			
 
				+          span = document.createElement("span");
			
 
				+          span.className = className;
			
 
				+        }
			
 
				+        span.appendChild(document.createTextNode(val.substr(pos, text.length)));
			
 
				+        node.parentNode.insertBefore(span, node.parentNode.insertBefore(
			
 
				+          document.createTextNode(val.substr(pos + text.length)),
			
 
				+          node.nextSibling));
			
 
				+        node.nodeValue = val.substr(0, pos);
			
 
				+        if (isInSVG) {
			
 
				+          var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
			
 
				+          var bbox = node.parentElement.getBBox();
			
 
				+          rect.x.baseVal.value = bbox.x;
			
 
				+          rect.y.baseVal.value = bbox.y;
			
 
				+          rect.width.baseVal.value = bbox.width;
			
 
				+          rect.height.baseVal.value = bbox.height;
			
 
				+          rect.setAttribute('class', className);
			
 
				+          addItems.push({
			
 
				+              "parent": node.parentNode,
			
 
				+              "target": rect});
			
 
				+        }
			
 
				+      }
			
 
				+    }
			
 
				+    else if (!jQuery(node).is("button, select, textarea")) {
			
 
				+      jQuery.each(node.childNodes, function() {
			
 
				+        highlight(this, addItems);
			
 
				+      });
			
 
				+    }
			
 
				+  }
			
 
				+  var addItems = [];
			
 
				+  var result = this.each(function() {
			
 
				+    highlight(this, addItems);
			
 
				+  });
			
 
				+  for (var i = 0; i < addItems.length; ++i) {
			
 
				+    jQuery(addItems[i].parent).before(addItems[i].target);
			
 
				+  }
			
 
				+  return result;
			
 
				+};
			
 
				+
			
 
				+/*
			
 
				+ * backward compatibility for jQuery.browser
			
 
				+ * This will be supported until firefox bug is fixed.
			
 
				+ */
			
 
				+if (!jQuery.browser) {
			
 
				+  jQuery.uaMatch = function(ua) {
			
 
				+    ua = ua.toLowerCase();
			
 
				+
			
 
				+    var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
			
 
				+      /(webkit)[ \/]([\w.]+)/.exec(ua) ||
			
 
				+      /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
			
 
				+      /(msie) ([\w.]+)/.exec(ua) ||
			
 
				+      ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
			
 
				+      [];
			
 
				+
			
 
				+    return {
			
 
				+      browser: match[ 1 ] || "",
			
 
				+      version: match[ 2 ] || "0"
			
 
				+    };
			
 
				+  };
			
 
				+  jQuery.browser = {};
			
 
				+  jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
			
 
				+}
			
 
				+
			
 
				+/**
			
 
				+ * Small JavaScript module for the documentation.
			
 
				+ */
			
 
				+var Documentation = {
			
 
				+
			
 
				+  init : function() {
			
 
				+    this.fixFirefoxAnchorBug();
			
 
				+    this.highlightSearchWords();
			
 
				+    this.initIndexTable();
			
 
				+    this.initOnKeyListeners();
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * i18n support
			
 
				+   */
			
 
				+  TRANSLATIONS : {},
			
 
				+  PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; },
			
 
				+  LOCALE : 'unknown',
			
 
				+
			
 
				+  // gettext and ngettext don't access this so that the functions
			
 
				+  // can safely bound to a different name (_ = Documentation.gettext)
			
 
				+  gettext : function(string) {
			
 
				+    var translated = Documentation.TRANSLATIONS[string];
			
 
				+    if (typeof translated === 'undefined')
			
 
				+      return string;
			
 
				+    return (typeof translated === 'string') ? translated : translated[0];
			
 
				+  },
			
 
				+
			
 
				+  ngettext : function(singular, plural, n) {
			
 
				+    var translated = Documentation.TRANSLATIONS[singular];
			
 
				+    if (typeof translated === 'undefined')
			
 
				+      return (n == 1) ? singular : plural;
			
 
				+    return translated[Documentation.PLURALEXPR(n)];
			
 
				+  },
			
 
				+
			
 
				+  addTranslations : function(catalog) {
			
 
				+    for (var key in catalog.messages)
			
 
				+      this.TRANSLATIONS[key] = catalog.messages[key];
			
 
				+    this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')');
			
 
				+    this.LOCALE = catalog.locale;
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * add context elements like header anchor links
			
 
				+   */
			
 
				+  addContextElements : function() {
			
 
				+    $('div[id] > :header:first').each(function() {
			
 
				+      $('<a class="headerlink">\u00B6</a>').
			
 
				+      attr('href', '#' + this.id).
			
 
				+      attr('title', _('Permalink to this headline')).
			
 
				+      appendTo(this);
			
 
				+    });
			
 
				+    $('dt[id]').each(function() {
			
 
				+      $('<a class="headerlink">\u00B6</a>').
			
 
				+      attr('href', '#' + this.id).
			
 
				+      attr('title', _('Permalink to this definition')).
			
 
				+      appendTo(this);
			
 
				+    });
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * workaround a firefox stupidity
			
 
				+   * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075
			
 
				+   */
			
 
				+  fixFirefoxAnchorBug : function() {
			
 
				+    if (document.location.hash && $.browser.mozilla)
			
 
				+      window.setTimeout(function() {
			
 
				+        document.location.href += '';
			
 
				+      }, 10);
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * highlight the search words provided in the url in the text
			
 
				+   */
			
 
				+  highlightSearchWords : function() {
			
 
				+    var params = $.getQueryParameters();
			
 
				+    var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : [];
			
 
				+    if (terms.length) {
			
 
				+      var body = $('div.body');
			
 
				+      if (!body.length) {
			
 
				+        body = $('body');
			
 
				+      }
			
 
				+      window.setTimeout(function() {
			
 
				+        $.each(terms, function() {
			
 
				+          body.highlightText(this.toLowerCase(), 'highlighted');
			
 
				+        });
			
 
				+      }, 10);
			
 
				+      $('<p class="highlight-link"><a href="javascript:Documentation.' +
			
 
				+        'hideSearchWords()">' + _('Hide Search Matches') + '</a></p>')
			
 
				+          .appendTo($('#searchbox'));
			
 
				+    }
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * init the domain index toggle buttons
			
 
				+   */
			
 
				+  initIndexTable : function() {
			
 
				+    var togglers = $('img.toggler').click(function() {
			
 
				+      var src = $(this).attr('src');
			
 
				+      var idnum = $(this).attr('id').substr(7);
			
 
				+      $('tr.cg-' + idnum).toggle();
			
 
				+      if (src.substr(-9) === 'minus.png')
			
 
				+        $(this).attr('src', src.substr(0, src.length-9) + 'plus.png');
			
 
				+      else
			
 
				+        $(this).attr('src', src.substr(0, src.length-8) + 'minus.png');
			
 
				+    }).css('display', '');
			
 
				+    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) {
			
 
				+        togglers.click();
			
 
				+    }
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * helper function to hide the search marks again
			
 
				+   */
			
 
				+  hideSearchWords : function() {
			
 
				+    $('#searchbox .highlight-link').fadeOut(300);
			
 
				+    $('span.highlighted').removeClass('highlighted');
			
 
				+    var url = new URL(window.location);
			
 
				+    url.searchParams.delete('highlight');
			
 
				+    window.history.replaceState({}, '', url);
			
 
				+  },
			
 
				+
			
 
				+   /**
			
 
				+   * helper function to focus on search bar
			
 
				+   */
			
 
				+  focusSearchBar : function() {
			
 
				+    $('input[name=q]').first().focus();
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * make the url absolute
			
 
				+   */
			
 
				+  makeURL : function(relativeURL) {
			
 
				+    return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL;
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * get the current relative url
			
 
				+   */
			
 
				+  getCurrentURL : function() {
			
 
				+    var path = document.location.pathname;
			
 
				+    var parts = path.split(/\//);
			
 
				+    $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() {
			
 
				+      if (this === '..')
			
 
				+        parts.pop();
			
 
				+    });
			
 
				+    var url = parts.join('/');
			
 
				+    return path.substring(url.lastIndexOf('/') + 1, path.length - 1);
			
 
				+  },
			
 
				+
			
 
				+  initOnKeyListeners: function() {
			
 
				+    // only install a listener if it is really needed
			
 
				+    if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS &&
			
 
				+        !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS)
			
 
				+        return;
			
 
				+
			
 
				+    $(document).keydown(function(event) {
			
 
				+      var activeElementType = document.activeElement.tagName;
			
 
				+      // don't navigate when in search box, textarea, dropdown or button
			
 
				+      if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT'
			
 
				+          && activeElementType !== 'BUTTON') {
			
 
				+        if (event.altKey || event.ctrlKey || event.metaKey)
			
 
				+          return;
			
 
				+
			
 
				+          if (!event.shiftKey) {
			
 
				+            switch (event.key) {
			
 
				+              case 'ArrowLeft':
			
 
				+                if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS)
			
 
				+                  break;
			
 
				+                var prevHref = $('link[rel="prev"]').prop('href');
			
 
				+                if (prevHref) {
			
 
				+                  window.location.href = prevHref;
			
 
				+                  return false;
			
 
				+                }
			
 
				+                break;
			
 
				+              case 'ArrowRight':
			
 
				+                if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS)
			
 
				+                  break;
			
 
				+                var nextHref = $('link[rel="next"]').prop('href');
			
 
				+                if (nextHref) {
			
 
				+                  window.location.href = nextHref;
			
 
				+                  return false;
			
 
				+                }
			
 
				+                break;
			
 
				+              case 'Escape':
			
 
				+                if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS)
			
 
				+                  break;
			
 
				+                Documentation.hideSearchWords();
			
 
				+                return false;
			
 
				+          }
			
 
				+        }
			
 
				+
			
 
				+        // some keyboard layouts may need Shift to get /
			
 
				+        switch (event.key) {
			
 
				+          case '/':
			
 
				+            if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS)
			
 
				+              break;
			
 
				+            Documentation.focusSearchBar();
			
 
				+            return false;
			
 
				+        }
			
 
				+      }
			
 
				+    });
			
 
				+  }
			
 
				+};
			
 
				+
			
 
				+// quick alias for translations
			
 
				+_ = Documentation.gettext;
			
 
				+
			
 
				+$(document).ready(function() {
			
 
				+  Documentation.init();
			
 
				+});
			
--- a/_static/documentation_options.js
+++ b/_static/documentation_options.js
@@ -0,0 +1,14 @@
 
				+var DOCUMENTATION_OPTIONS = {
			
 
				+    URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
			
 
				+    VERSION: '',
			
 
				+    LANGUAGE: 'None',
			
 
				+    COLLAPSE_INDEX: false,
			
 
				+    BUILDER: 'html',
			
 
				+    FILE_SUFFIX: '.html',
			
 
				+    LINK_SUFFIX: '.html',
			
 
				+    HAS_SOURCE: true,
			
 
				+    SOURCELINK_SUFFIX: '',
			
 
				+    NAVIGATION_WITH_KEYS: true,
			
 
				+    SHOW_SEARCH_SUMMARY: true,
			
 
				+    ENABLE_SEARCH_SHORTCUTS: true,
			
 
				+};
			
--- a/_static/file.png
+++ b/_static/file.png
--- a/_static/images/logo_binder.svg
+++ b/_static/images/logo_binder.svg
@@ -0,0 +1,19 @@
 
				+<?xml version="1.0" encoding="utf-8"?>
			
 
				+<!-- Generator: Adobe Illustrator 23.0.1, SVG Export Plug-In . SVG Version: 6.00 Build 0)  -->
			
 
				+<svg version="1.1" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
			
 
				+	 viewBox="0 0 44.4 44.4" style="enable-background:new 0 0 44.4 44.4;" xml:space="preserve">
			
 
				+<style type="text/css">
			
 
				+	.st0{fill:none;stroke:#F5A252;stroke-width:5;stroke-miterlimit:10;}
			
 
				+	.st1{fill:none;stroke:#579ACA;stroke-width:5;stroke-miterlimit:10;}
			
 
				+	.st2{fill:none;stroke:#E66581;stroke-width:5;stroke-miterlimit:10;}
			
 
				+</style>
			
 
				+<title>logo</title>
			
 
				+<g>
			
 
				+	<path class="st0" d="M33.9,6.4c3.6,3.9,3.4,9.9-0.5,13.5s-9.9,3.4-13.5-0.5s-3.4-9.9,0.5-13.5l0,0C24.2,2.4,30.2,2.6,33.9,6.4z"/>
			
 
				+	<path class="st1" d="M35.1,27.3c2.6,4.6,1.1,10.4-3.5,13c-4.6,2.6-10.4,1.1-13-3.5s-1.1-10.4,3.5-13l0,0
			
 
				+		C26.6,21.2,32.4,22.7,35.1,27.3z"/>
			
 
				+	<path class="st2" d="M25.9,17.8c2.6,4.6,1.1,10.4-3.5,13s-10.4,1.1-13-3.5s-1.1-10.4,3.5-13l0,0C17.5,11.7,23.3,13.2,25.9,17.8z"/>
			
 
				+	<path class="st1" d="M19.2,26.4c3.1-4.3,9.1-5.2,13.3-2.1c1.1,0.8,2,1.8,2.7,3"/>
			
 
				+	<path class="st0" d="M19.9,19.4c-3.6-3.9-3.4-9.9,0.5-13.5s9.9-3.4,13.5,0.5"/>
			
 
				+</g>
			
 
				+</svg>
			
--- a/_static/images/logo_colab.png
+++ b/_static/images/logo_colab.png
--- a/_static/images/logo_jupyterhub.svg
+++ b/_static/images/logo_jupyterhub.svg
--- a/_static/jquery-3.5.1.js
+++ b/_static/jquery-3.5.1.js
--- a/_static/jquery.js
+++ b/_static/jquery.js
--- a/_static/js/index.be7d3bbb2ef33a8344ce.js
+++ b/_static/js/index.be7d3bbb2ef33a8344ce.js
--- a/_static/language_data.js
+++ b/_static/language_data.js
@@ -0,0 +1,297 @@
 
				+/*
			
 
				+ * language_data.js
			
 
				+ * ~~~~~~~~~~~~~~~~
			
 
				+ *
			
 
				+ * This script contains the language-specific data used by searchtools.js,
			
 
				+ * namely the list of stopwords, stemmer, scorer and splitter.
			
 
				+ *
			
 
				+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
			
 
				+ * :license: BSD, see LICENSE for details.
			
 
				+ *
			
 
				+ */
			
 
				+
			
 
				+var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"];
			
 
				+
			
 
				+
			
 
				+/* Non-minified version is copied as a separate JS file, is available */
			
 
				+
			
 
				+/**
			
 
				+ * Porter Stemmer
			
 
				+ */
			
 
				+var Stemmer = function() {
			
 
				+
			
 
				+  var step2list = {
			
 
				+    ational: 'ate',
			
 
				+    tional: 'tion',
			
 
				+    enci: 'ence',
			
 
				+    anci: 'ance',
			
 
				+    izer: 'ize',
			
 
				+    bli: 'ble',
			
 
				+    alli: 'al',
			
 
				+    entli: 'ent',
			
 
				+    eli: 'e',
			
 
				+    ousli: 'ous',
			
 
				+    ization: 'ize',
			
 
				+    ation: 'ate',
			
 
				+    ator: 'ate',
			
 
				+    alism: 'al',
			
 
				+    iveness: 'ive',
			
 
				+    fulness: 'ful',
			
 
				+    ousness: 'ous',
			
 
				+    aliti: 'al',
			
 
				+    iviti: 'ive',
			
 
				+    biliti: 'ble',
			
 
				+    logi: 'log'
			
 
				+  };
			
 
				+
			
 
				+  var step3list = {
			
 
				+    icate: 'ic',
			
 
				+    ative: '',
			
 
				+    alize: 'al',
			
 
				+    iciti: 'ic',
			
 
				+    ical: 'ic',
			
 
				+    ful: '',
			
 
				+    ness: ''
			
 
				+  };
			
 
				+
			
 
				+  var c = "[^aeiou]";          // consonant
			
 
				+  var v = "[aeiouy]";          // vowel
			
 
				+  var C = c + "[^aeiouy]*";    // consonant sequence
			
 
				+  var V = v + "[aeiou]*";      // vowel sequence
			
 
				+
			
 
				+  var mgr0 = "^(" + C + ")?" + V + C;                      // [C]VC... is m>0
			
 
				+  var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$";    // [C]VC[V] is m=1
			
 
				+  var mgr1 = "^(" + C + ")?" + V + C + V + C;              // [C]VCVC... is m>1
			
 
				+  var s_v   = "^(" + C + ")?" + v;                         // vowel in stem
			
 
				+
			
 
				+  this.stemWord = function (w) {
			
 
				+    var stem;
			
 
				+    var suffix;
			
 
				+    var firstch;
			
 
				+    var origword = w;
			
 
				+
			
 
				+    if (w.length < 3)
			
 
				+      return w;
			
 
				+
			
 
				+    var re;
			
 
				+    var re2;
			
 
				+    var re3;
			
 
				+    var re4;
			
 
				+
			
 
				+    firstch = w.substr(0,1);
			
 
				+    if (firstch == "y")
			
 
				+      w = firstch.toUpperCase() + w.substr(1);
			
 
				+
			
 
				+    // Step 1a
			
 
				+    re = /^(.+?)(ss|i)es$/;
			
 
				+    re2 = /^(.+?)([^s])s$/;
			
 
				+
			
 
				+    if (re.test(w))
			
 
				+      w = w.replace(re,"$1$2");
			
 
				+    else if (re2.test(w))
			
 
				+      w = w.replace(re2,"$1$2");
			
 
				+
			
 
				+    // Step 1b
			
 
				+    re = /^(.+?)eed$/;
			
 
				+    re2 = /^(.+?)(ed|ing)$/;
			
 
				+    if (re.test(w)) {
			
 
				+      var fp = re.exec(w);
			
 
				+      re = new RegExp(mgr0);
			
 
				+      if (re.test(fp[1])) {
			
 
				+        re = /.$/;
			
 
				+        w = w.replace(re,"");
			
 
				+      }
			
 
				+    }
			
 
				+    else if (re2.test(w)) {
			
 
				+      var fp = re2.exec(w);
			
 
				+      stem = fp[1];
			
 
				+      re2 = new RegExp(s_v);
			
 
				+      if (re2.test(stem)) {
			
 
				+        w = stem;
			
 
				+        re2 = /(at|bl|iz)$/;
			
 
				+        re3 = new RegExp("([^aeiouylsz])\\1$");
			
 
				+        re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
			
 
				+        if (re2.test(w))
			
 
				+          w = w + "e";
			
 
				+        else if (re3.test(w)) {
			
 
				+          re = /.$/;
			
 
				+          w = w.replace(re,"");
			
 
				+        }
			
 
				+        else if (re4.test(w))
			
 
				+          w = w + "e";
			
 
				+      }
			
 
				+    }
			
 
				+
			
 
				+    // Step 1c
			
 
				+    re = /^(.+?)y$/;
			
 
				+    if (re.test(w)) {
			
 
				+      var fp = re.exec(w);
			
 
				+      stem = fp[1];
			
 
				+      re = new RegExp(s_v);
			
 
				+      if (re.test(stem))
			
 
				+        w = stem + "i";
			
 
				+    }
			
 
				+
			
 
				+    // Step 2
			
 
				+    re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
			
 
				+    if (re.test(w)) {
			
 
				+      var fp = re.exec(w);
			
 
				+      stem = fp[1];
			
 
				+      suffix = fp[2];
			
 
				+      re = new RegExp(mgr0);
			
 
				+      if (re.test(stem))
			
 
				+        w = stem + step2list[suffix];
			
 
				+    }
			
 
				+
			
 
				+    // Step 3
			
 
				+    re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
			
 
				+    if (re.test(w)) {
			
 
				+      var fp = re.exec(w);
			
 
				+      stem = fp[1];
			
 
				+      suffix = fp[2];
			
 
				+      re = new RegExp(mgr0);
			
 
				+      if (re.test(stem))
			
 
				+        w = stem + step3list[suffix];
			
 
				+    }
			
 
				+
			
 
				+    // Step 4
			
 
				+    re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
			
 
				+    re2 = /^(.+?)(s|t)(ion)$/;
			
 
				+    if (re.test(w)) {
			
 
				+      var fp = re.exec(w);
			
 
				+      stem = fp[1];
			
 
				+      re = new RegExp(mgr1);
			
 
				+      if (re.test(stem))
			
 
				+        w = stem;
			
 
				+    }
			
 
				+    else if (re2.test(w)) {
			
 
				+      var fp = re2.exec(w);
			
 
				+      stem = fp[1] + fp[2];
			
 
				+      re2 = new RegExp(mgr1);
			
 
				+      if (re2.test(stem))
			
 
				+        w = stem;
			
 
				+    }
			
 
				+
			
 
				+    // Step 5
			
 
				+    re = /^(.+?)e$/;
			
 
				+    if (re.test(w)) {
			
 
				+      var fp = re.exec(w);
			
 
				+      stem = fp[1];
			
 
				+      re = new RegExp(mgr1);
			
 
				+      re2 = new RegExp(meq1);
			
 
				+      re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
			
 
				+      if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
			
 
				+        w = stem;
			
 
				+    }
			
 
				+    re = /ll$/;
			
 
				+    re2 = new RegExp(mgr1);
			
 
				+    if (re.test(w) && re2.test(w)) {
			
 
				+      re = /.$/;
			
 
				+      w = w.replace(re,"");
			
 
				+    }
			
 
				+
			
 
				+    // and turn initial Y back to y
			
 
				+    if (firstch == "y")
			
 
				+      w = firstch.toLowerCase() + w.substr(1);
			
 
				+    return w;
			
 
				+  }
			
 
				+}
			
 
				+
			
 
				+
			
 
				+
			
 
				+
			
 
				+var splitChars = (function() {
			
 
				+    var result = {};
			
 
				+    var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648,
			
 
				+         1748, 1809, 2416, 2473, 2481, 2526, 2601, 2609, 2612, 2615, 2653, 2702,
			
 
				+         2706, 2729, 2737, 2740, 2857, 2865, 2868, 2910, 2928, 2948, 2961, 2971,
			
 
				+         2973, 3085, 3089, 3113, 3124, 3213, 3217, 3241, 3252, 3295, 3341, 3345,
			
 
				+         3369, 3506, 3516, 3633, 3715, 3721, 3736, 3744, 3748, 3750, 3756, 3761,
			
 
				+         3781, 3912, 4239, 4347, 4681, 4695, 4697, 4745, 4785, 4799, 4801, 4823,
			
 
				+         4881, 5760, 5901, 5997, 6313, 7405, 8024, 8026, 8028, 8030, 8117, 8125,
			
 
				+         8133, 8181, 8468, 8485, 8487, 8489, 8494, 8527, 11311, 11359, 11687, 11695,
			
 
				+         11703, 11711, 11719, 11727, 11735, 12448, 12539, 43010, 43014, 43019, 43587,
			
 
				+         43696, 43713, 64286, 64297, 64311, 64317, 64319, 64322, 64325, 65141];
			
 
				+    var i, j, start, end;
			
 
				+    for (i = 0; i < singles.length; i++) {
			
 
				+        result[singles[i]] = true;
			
 
				+    }
			
 
				+    var ranges = [[0, 47], [58, 64], [91, 94], [123, 169], [171, 177], [182, 184], [706, 709],
			
 
				+         [722, 735], [741, 747], [751, 879], [888, 889], [894, 901], [1154, 1161],
			
 
				+         [1318, 1328], [1367, 1368], [1370, 1376], [1416, 1487], [1515, 1519], [1523, 1568],
			
 
				+         [1611, 1631], [1642, 1645], [1750, 1764], [1767, 1773], [1789, 1790], [1792, 1807],
			
 
				+         [1840, 1868], [1958, 1968], [1970, 1983], [2027, 2035], [2038, 2041], [2043, 2047],
			
 
				+         [2070, 2073], [2075, 2083], [2085, 2087], [2089, 2307], [2362, 2364], [2366, 2383],
			
 
				+         [2385, 2391], [2402, 2405], [2419, 2424], [2432, 2436], [2445, 2446], [2449, 2450],
			
 
				+         [2483, 2485], [2490, 2492], [2494, 2509], [2511, 2523], [2530, 2533], [2546, 2547],
			
 
				+         [2554, 2564], [2571, 2574], [2577, 2578], [2618, 2648], [2655, 2661], [2672, 2673],
			
 
				+         [2677, 2692], [2746, 2748], [2750, 2767], [2769, 2783], [2786, 2789], [2800, 2820],
			
 
				+         [2829, 2830], [2833, 2834], [2874, 2876], [2878, 2907], [2914, 2917], [2930, 2946],
			
 
				+         [2955, 2957], [2966, 2968], [2976, 2978], [2981, 2983], [2987, 2989], [3002, 3023],
			
 
				+         [3025, 3045], [3059, 3076], [3130, 3132], [3134, 3159], [3162, 3167], [3170, 3173],
			
 
				+         [3184, 3191], [3199, 3204], [3258, 3260], [3262, 3293], [3298, 3301], [3312, 3332],
			
 
				+         [3386, 3388], [3390, 3423], [3426, 3429], [3446, 3449], [3456, 3460], [3479, 3481],
			
 
				+         [3518, 3519], [3527, 3584], [3636, 3647], [3655, 3663], [3674, 3712], [3717, 3718],
			
 
				+         [3723, 3724], [3726, 3731], [3752, 3753], [3764, 3772], [3774, 3775], [3783, 3791],
			
 
				+         [3802, 3803], [3806, 3839], [3841, 3871], [3892, 3903], [3949, 3975], [3980, 4095],
			
 
				+         [4139, 4158], [4170, 4175], [4182, 4185], [4190, 4192], [4194, 4196], [4199, 4205],
			
 
				+         [4209, 4212], [4226, 4237], [4250, 4255], [4294, 4303], [4349, 4351], [4686, 4687],
			
 
				+         [4702, 4703], [4750, 4751], [4790, 4791], [4806, 4807], [4886, 4887], [4955, 4968],
			
 
				+         [4989, 4991], [5008, 5023], [5109, 5120], [5741, 5742], [5787, 5791], [5867, 5869],
			
 
				+         [5873, 5887], [5906, 5919], [5938, 5951], [5970, 5983], [6001, 6015], [6068, 6102],
			
 
				+         [6104, 6107], [6109, 6111], [6122, 6127], [6138, 6159], [6170, 6175], [6264, 6271],
			
 
				+         [6315, 6319], [6390, 6399], [6429, 6469], [6510, 6511], [6517, 6527], [6572, 6592],
			
 
				+         [6600, 6607], [6619, 6655], [6679, 6687], [6741, 6783], [6794, 6799], [6810, 6822],
			
 
				+         [6824, 6916], [6964, 6980], [6988, 6991], [7002, 7042], [7073, 7085], [7098, 7167],
			
 
				+         [7204, 7231], [7242, 7244], [7294, 7400], [7410, 7423], [7616, 7679], [7958, 7959],
			
 
				+         [7966, 7967], [8006, 8007], [8014, 8015], [8062, 8063], [8127, 8129], [8141, 8143],
			
 
				+         [8148, 8149], [8156, 8159], [8173, 8177], [8189, 8303], [8306, 8307], [8314, 8318],
			
 
				+         [8330, 8335], [8341, 8449], [8451, 8454], [8456, 8457], [8470, 8472], [8478, 8483],
			
 
				+         [8506, 8507], [8512, 8516], [8522, 8525], [8586, 9311], [9372, 9449], [9472, 10101],
			
 
				+         [10132, 11263], [11493, 11498], [11503, 11516], [11518, 11519], [11558, 11567],
			
 
				+         [11622, 11630], [11632, 11647], [11671, 11679], [11743, 11822], [11824, 12292],
			
 
				+         [12296, 12320], [12330, 12336], [12342, 12343], [12349, 12352], [12439, 12444],
			
 
				+         [12544, 12548], [12590, 12592], [12687, 12689], [12694, 12703], [12728, 12783],
			
 
				+         [12800, 12831], [12842, 12880], [12896, 12927], [12938, 12976], [12992, 13311],
			
 
				+         [19894, 19967], [40908, 40959], [42125, 42191], [42238, 42239], [42509, 42511],
			
 
				+         [42540, 42559], [42592, 42593], [42607, 42622], [42648, 42655], [42736, 42774],
			
 
				+         [42784, 42785], [42889, 42890], [42893, 43002], [43043, 43055], [43062, 43071],
			
 
				+         [43124, 43137], [43188, 43215], [43226, 43249], [43256, 43258], [43260, 43263],
			
 
				+         [43302, 43311], [43335, 43359], [43389, 43395], [43443, 43470], [43482, 43519],
			
 
				+         [43561, 43583], [43596, 43599], [43610, 43615], [43639, 43641], [43643, 43647],
			
 
				+         [43698, 43700], [43703, 43704], [43710, 43711], [43715, 43738], [43742, 43967],
			
 
				+         [44003, 44015], [44026, 44031], [55204, 55215], [55239, 55242], [55292, 55295],
			
 
				+         [57344, 63743], [64046, 64047], [64110, 64111], [64218, 64255], [64263, 64274],
			
 
				+         [64280, 64284], [64434, 64466], [64830, 64847], [64912, 64913], [64968, 65007],
			
 
				+         [65020, 65135], [65277, 65295], [65306, 65312], [65339, 65344], [65371, 65381],
			
 
				+         [65471, 65473], [65480, 65481], [65488, 65489], [65496, 65497]];
			
 
				+    for (i = 0; i < ranges.length; i++) {
			
 
				+        start = ranges[i][0];
			
 
				+        end = ranges[i][1];
			
 
				+        for (j = start; j <= end; j++) {
			
 
				+            result[j] = true;
			
 
				+        }
			
 
				+    }
			
 
				+    return result;
			
 
				+})();
			
 
				+
			
 
				+function splitQuery(query) {
			
 
				+    var result = [];
			
 
				+    var start = -1;
			
 
				+    for (var i = 0; i < query.length; i++) {
			
 
				+        if (splitChars[query.charCodeAt(i)]) {
			
 
				+            if (start !== -1) {
			
 
				+                result.push(query.slice(start, i));
			
 
				+                start = -1;
			
 
				+            }
			
 
				+        } else if (start === -1) {
			
 
				+            start = i;
			
 
				+        }
			
 
				+    }
			
 
				+    if (start !== -1) {
			
 
				+        result.push(query.slice(start));
			
 
				+    }
			
 
				+    return result;
			
 
				+}
			
 
				+
			
 
				+
			
--- a/_static/minus.png
+++ b/_static/minus.png
--- a/_static/mystnb.css
+++ b/_static/mystnb.css
--- a/_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css
+++ b/_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css
--- a/_static/panels-variables.06eb56fa6e07937060861dad626602ad.css
+++ b/_static/panels-variables.06eb56fa6e07937060861dad626602ad.css
@@ -0,0 +1,7 @@
 
				+:root {
			
 
				+--tabs-color-label-active: hsla(231, 99%, 66%, 1);
			
 
				+--tabs-color-label-inactive: rgba(178, 206, 245, 0.62);
			
 
				+--tabs-color-overline: rgb(207, 236, 238);
			
 
				+--tabs-color-underline: rgb(207, 236, 238);
			
 
				+--tabs-size-label: 1rem;
			
 
				+}
			
--- a/_static/plus.png
+++ b/_static/plus.png
--- a/_static/pygments.css
+++ b/_static/pygments.css
@@ -0,0 +1,74 @@
 
				+pre { line-height: 125%; }
			
 
				+td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
			
 
				+span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
			
 
				+td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
			
 
				+span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
			
 
				+.highlight .hll { background-color: #ffffcc }
			
 
				+.highlight { background: #eeffcc; }
			
 
				+.highlight .c { color: #408090; font-style: italic } /* Comment */
			
 
				+.highlight .err { border: 1px solid #FF0000 } /* Error */
			
 
				+.highlight .k { color: #007020; font-weight: bold } /* Keyword */
			
 
				+.highlight .o { color: #666666 } /* Operator */
			
 
				+.highlight .ch { color: #408090; font-style: italic } /* Comment.Hashbang */
			
 
				+.highlight .cm { color: #408090; font-style: italic } /* Comment.Multiline */
			
 
				+.highlight .cp { color: #007020 } /* Comment.Preproc */
			
 
				+.highlight .cpf { color: #408090; font-style: italic } /* Comment.PreprocFile */
			
 
				+.highlight .c1 { color: #408090; font-style: italic } /* Comment.Single */
			
 
				+.highlight .cs { color: #408090; background-color: #fff0f0 } /* Comment.Special */
			
 
				+.highlight .gd { color: #A00000 } /* Generic.Deleted */
			
 
				+.highlight .ge { font-style: italic } /* Generic.Emph */
			
 
				+.highlight .gr { color: #FF0000 } /* Generic.Error */
			
 
				+.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
			
 
				+.highlight .gi { color: #00A000 } /* Generic.Inserted */
			
 
				+.highlight .go { color: #333333 } /* Generic.Output */
			
 
				+.highlight .gp { color: #c65d09; font-weight: bold } /* Generic.Prompt */
			
 
				+.highlight .gs { font-weight: bold } /* Generic.Strong */
			
 
				+.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
			
 
				+.highlight .gt { color: #0044DD } /* Generic.Traceback */
			
 
				+.highlight .kc { color: #007020; font-weight: bold } /* Keyword.Constant */
			
 
				+.highlight .kd { color: #007020; font-weight: bold } /* Keyword.Declaration */
			
 
				+.highlight .kn { color: #007020; font-weight: bold } /* Keyword.Namespace */
			
 
				+.highlight .kp { color: #007020 } /* Keyword.Pseudo */
			
 
				+.highlight .kr { color: #007020; font-weight: bold } /* Keyword.Reserved */
			
 
				+.highlight .kt { color: #902000 } /* Keyword.Type */
			
 
				+.highlight .m { color: #208050 } /* Literal.Number */
			
 
				+.highlight .s { color: #4070a0 } /* Literal.String */
			
 
				+.highlight .na { color: #4070a0 } /* Name.Attribute */
			
 
				+.highlight .nb { color: #007020 } /* Name.Builtin */
			
 
				+.highlight .nc { color: #0e84b5; font-weight: bold } /* Name.Class */
			
 
				+.highlight .no { color: #60add5 } /* Name.Constant */
			
 
				+.highlight .nd { color: #555555; font-weight: bold } /* Name.Decorator */
			
 
				+.highlight .ni { color: #d55537; font-weight: bold } /* Name.Entity */
			
 
				+.highlight .ne { color: #007020 } /* Name.Exception */
			
 
				+.highlight .nf { color: #06287e } /* Name.Function */
			
 
				+.highlight .nl { color: #002070; font-weight: bold } /* Name.Label */
			
 
				+.highlight .nn { color: #0e84b5; font-weight: bold } /* Name.Namespace */
			
 
				+.highlight .nt { color: #062873; font-weight: bold } /* Name.Tag */
			
 
				+.highlight .nv { color: #bb60d5 } /* Name.Variable */
			
 
				+.highlight .ow { color: #007020; font-weight: bold } /* Operator.Word */
			
 
				+.highlight .w { color: #bbbbbb } /* Text.Whitespace */
			
 
				+.highlight .mb { color: #208050 } /* Literal.Number.Bin */
			
 
				+.highlight .mf { color: #208050 } /* Literal.Number.Float */
			
 
				+.highlight .mh { color: #208050 } /* Literal.Number.Hex */
			
 
				+.highlight .mi { color: #208050 } /* Literal.Number.Integer */
			
 
				+.highlight .mo { color: #208050 } /* Literal.Number.Oct */
			
 
				+.highlight .sa { color: #4070a0 } /* Literal.String.Affix */
			
 
				+.highlight .sb { color: #4070a0 } /* Literal.String.Backtick */
			
 
				+.highlight .sc { color: #4070a0 } /* Literal.String.Char */
			
 
				+.highlight .dl { color: #4070a0 } /* Literal.String.Delimiter */
			
 
				+.highlight .sd { color: #4070a0; font-style: italic } /* Literal.String.Doc */
			
 
				+.highlight .s2 { color: #4070a0 } /* Literal.String.Double */
			
 
				+.highlight .se { color: #4070a0; font-weight: bold } /* Literal.String.Escape */
			
 
				+.highlight .sh { color: #4070a0 } /* Literal.String.Heredoc */
			
 
				+.highlight .si { color: #70a0d0; font-style: italic } /* Literal.String.Interpol */
			
 
				+.highlight .sx { color: #c65d09 } /* Literal.String.Other */
			
 
				+.highlight .sr { color: #235388 } /* Literal.String.Regex */
			
 
				+.highlight .s1 { color: #4070a0 } /* Literal.String.Single */
			
 
				+.highlight .ss { color: #517918 } /* Literal.String.Symbol */
			
 
				+.highlight .bp { color: #007020 } /* Name.Builtin.Pseudo */
			
 
				+.highlight .fm { color: #06287e } /* Name.Function.Magic */
			
 
				+.highlight .vc { color: #bb60d5 } /* Name.Variable.Class */
			
 
				+.highlight .vg { color: #bb60d5 } /* Name.Variable.Global */
			
 
				+.highlight .vi { color: #bb60d5 } /* Name.Variable.Instance */
			
 
				+.highlight .vm { color: #bb60d5 } /* Name.Variable.Magic */
			
 
				+.highlight .il { color: #208050 } /* Literal.Number.Integer.Long */
			
--- a/_static/searchtools.js
+++ b/_static/searchtools.js
@@ -0,0 +1,525 @@
 
				+/*
			
 
				+ * searchtools.js
			
 
				+ * ~~~~~~~~~~~~~~~~
			
 
				+ *
			
 
				+ * Sphinx JavaScript utilities for the full-text search.
			
 
				+ *
			
 
				+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
			
 
				+ * :license: BSD, see LICENSE for details.
			
 
				+ *
			
 
				+ */
			
 
				+
			
 
				+if (!Scorer) {
			
 
				+  /**
			
 
				+   * Simple result scoring code.
			
 
				+   */
			
 
				+  var Scorer = {
			
 
				+    // Implement the following function to further tweak the score for each result
			
 
				+    // The function takes a result array [filename, title, anchor, descr, score]
			
 
				+    // and returns the new score.
			
 
				+    /*
			
 
				+    score: function(result) {
			
 
				+      return result[4];
			
 
				+    },
			
 
				+    */
			
 
				+
			
 
				+    // query matches the full name of an object
			
 
				+    objNameMatch: 11,
			
 
				+    // or matches in the last dotted part of the object name
			
 
				+    objPartialMatch: 6,
			
 
				+    // Additive scores depending on the priority of the object
			
 
				+    objPrio: {0:  15,   // used to be importantResults
			
 
				+              1:  5,   // used to be objectResults
			
 
				+              2: -5},  // used to be unimportantResults
			
 
				+    //  Used when the priority is not in the mapping.
			
 
				+    objPrioDefault: 0,
			
 
				+
			
 
				+    // query found in title
			
 
				+    title: 15,
			
 
				+    partialTitle: 7,
			
 
				+    // query found in terms
			
 
				+    term: 5,
			
 
				+    partialTerm: 2
			
 
				+  };
			
 
				+}
			
 
				+
			
 
				+if (!splitQuery) {
			
 
				+  function splitQuery(query) {
			
 
				+    return query.split(/\s+/);
			
 
				+  }
			
 
				+}
			
 
				+
			
 
				+/**
			
 
				+ * Search Module
			
 
				+ */
			
 
				+var Search = {
			
 
				+
			
 
				+  _index : null,
			
 
				+  _queued_query : null,
			
 
				+  _pulse_status : -1,
			
 
				+
			
 
				+  htmlToText : function(htmlString) {
			
 
				+      var virtualDocument = document.implementation.createHTMLDocument('virtual');
			
 
				+      var htmlElement = $(htmlString, virtualDocument);
			
 
				+      htmlElement.find('.headerlink').remove();
			
 
				+      docContent = htmlElement.find('[role=main]')[0];
			
 
				+      if(docContent === undefined) {
			
 
				+          console.warn("Content block not found. Sphinx search tries to obtain it " +
			
 
				+                       "via '[role=main]'. Could you check your theme or template.");
			
 
				+          return "";
			
 
				+      }
			
 
				+      return docContent.textContent || docContent.innerText;
			
 
				+  },
			
 
				+
			
 
				+  init : function() {
			
 
				+      var params = $.getQueryParameters();
			
 
				+      if (params.q) {
			
 
				+          var query = params.q[0];
			
 
				+          $('input[name="q"]')[0].value = query;
			
 
				+          this.performSearch(query);
			
 
				+      }
			
 
				+  },
			
 
				+
			
 
				+  loadIndex : function(url) {
			
 
				+    $.ajax({type: "GET", url: url, data: null,
			
 
				+            dataType: "script", cache: true,
			
 
				+            complete: function(jqxhr, textstatus) {
			
 
				+              if (textstatus != "success") {
			
 
				+                document.getElementById("searchindexloader").src = url;
			
 
				+              }
			
 
				+            }});
			
 
				+  },
			
 
				+
			
 
				+  setIndex : function(index) {
			
 
				+    var q;
			
 
				+    this._index = index;
			
 
				+    if ((q = this._queued_query) !== null) {
			
 
				+      this._queued_query = null;
			
 
				+      Search.query(q);
			
 
				+    }
			
 
				+  },
			
 
				+
			
 
				+  hasIndex : function() {
			
 
				+      return this._index !== null;
			
 
				+  },
			
 
				+
			
 
				+  deferQuery : function(query) {
			
 
				+      this._queued_query = query;
			
 
				+  },
			
 
				+
			
 
				+  stopPulse : function() {
			
 
				+      this._pulse_status = 0;
			
 
				+  },
			
 
				+
			
 
				+  startPulse : function() {
			
 
				+    if (this._pulse_status >= 0)
			
 
				+        return;
			
 
				+    function pulse() {
			
 
				+      var i;
			
 
				+      Search._pulse_status = (Search._pulse_status + 1) % 4;
			
 
				+      var dotString = '';
			
 
				+      for (i = 0; i < Search._pulse_status; i++)
			
 
				+        dotString += '.';
			
 
				+      Search.dots.text(dotString);
			
 
				+      if (Search._pulse_status > -1)
			
 
				+        window.setTimeout(pulse, 500);
			
 
				+    }
			
 
				+    pulse();
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * perform a search for something (or wait until index is loaded)
			
 
				+   */
			
 
				+  performSearch : function(query) {
			
 
				+    // create the required interface elements
			
 
				+    this.out = $('#search-results');
			
 
				+    this.title = $('<h2>' + _('Searching') + '</h2>').appendTo(this.out);
			
 
				+    this.dots = $('<span></span>').appendTo(this.title);
			
 
				+    this.status = $('<p class="search-summary">&nbsp;</p>').appendTo(this.out);
			
 
				+    this.output = $('<ul class="search"/>').appendTo(this.out);
			
 
				+
			
 
				+    $('#search-progress').text(_('Preparing search...'));
			
 
				+    this.startPulse();
			
 
				+
			
 
				+    // index already loaded, the browser was quick!
			
 
				+    if (this.hasIndex())
			
 
				+      this.query(query);
			
 
				+    else
			
 
				+      this.deferQuery(query);
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * execute search (requires search index to be loaded)
			
 
				+   */
			
 
				+  query : function(query) {
			
 
				+    var i;
			
 
				+
			
 
				+    // stem the searchterms and add them to the correct list
			
 
				+    var stemmer = new Stemmer();
			
 
				+    var searchterms = [];
			
 
				+    var excluded = [];
			
 
				+    var hlterms = [];
			
 
				+    var tmp = splitQuery(query);
			
 
				+    var objectterms = [];
			
 
				+    for (i = 0; i < tmp.length; i++) {
			
 
				+      if (tmp[i] !== "") {
			
 
				+          objectterms.push(tmp[i].toLowerCase());
			
 
				+      }
			
 
				+
			
 
				+      if ($u.indexOf(stopwords, tmp[i].toLowerCase()) != -1 || tmp[i] === "") {
			
 
				+        // skip this "word"
			
 
				+        continue;
			
 
				+      }
			
 
				+      // stem the word
			
 
				+      var word = stemmer.stemWord(tmp[i].toLowerCase());
			
 
				+      var toAppend;
			
 
				+      // select the correct list
			
 
				+      if (word[0] == '-') {
			
 
				+        toAppend = excluded;
			
 
				+        word = word.substr(1);
			
 
				+      }
			
 
				+      else {
			
 
				+        toAppend = searchterms;
			
 
				+        hlterms.push(tmp[i].toLowerCase());
			
 
				+      }
			
 
				+      // only add if not already in the list
			
 
				+      if (!$u.contains(toAppend, word))
			
 
				+        toAppend.push(word);
			
 
				+    }
			
 
				+    var highlightstring = '?highlight=' + $.urlencode(hlterms.join(" "));
			
 
				+
			
 
				+    // console.debug('SEARCH: searching for:');
			
 
				+    // console.info('required: ', searchterms);
			
 
				+    // console.info('excluded: ', excluded);
			
 
				+
			
 
				+    // prepare search
			
 
				+    var terms = this._index.terms;
			
 
				+    var titleterms = this._index.titleterms;
			
 
				+
			
 
				+    // array of [filename, title, anchor, descr, score]
			
 
				+    var results = [];
			
 
				+    $('#search-progress').empty();
			
 
				+
			
 
				+    // lookup as object
			
 
				+    for (i = 0; i < objectterms.length; i++) {
			
 
				+      var others = [].concat(objectterms.slice(0, i),
			
 
				+                             objectterms.slice(i+1, objectterms.length));
			
 
				+      results = results.concat(this.performObjectSearch(objectterms[i], others));
			
 
				+    }
			
 
				+
			
 
				+    // lookup as search terms in fulltext
			
 
				+    results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms));
			
 
				+
			
 
				+    // let the scorer override scores with a custom scoring function
			
 
				+    if (Scorer.score) {
			
 
				+      for (i = 0; i < results.length; i++)
			
 
				+        results[i][4] = Scorer.score(results[i]);
			
 
				+    }
			
 
				+
			
 
				+    // now sort the results by score (in opposite order of appearance, since the
			
 
				+    // display function below uses pop() to retrieve items) and then
			
 
				+    // alphabetically
			
 
				+    results.sort(function(a, b) {
			
 
				+      var left = a[4];
			
 
				+      var right = b[4];
			
 
				+      if (left > right) {
			
 
				+        return 1;
			
 
				+      } else if (left < right) {
			
 
				+        return -1;
			
 
				+      } else {
			
 
				+        // same score: sort alphabetically
			
 
				+        left = a[1].toLowerCase();
			
 
				+        right = b[1].toLowerCase();
			
 
				+        return (left > right) ? -1 : ((left < right) ? 1 : 0);
			
 
				+      }
			
 
				+    });
			
 
				+
			
 
				+    // for debugging
			
 
				+    //Search.lastresults = results.slice();  // a copy
			
 
				+    //console.info('search results:', Search.lastresults);
			
 
				+
			
 
				+    // print the results
			
 
				+    var resultCount = results.length;
			
 
				+    function displayNextItem() {
			
 
				+      // results left, load the summary and display it
			
 
				+      if (results.length) {
			
 
				+        var item = results.pop();
			
 
				+        var listItem = $('<li></li>');
			
 
				+        var requestUrl = "";
			
 
				+        var linkUrl = "";
			
 
				+        if (DOCUMENTATION_OPTIONS.BUILDER === 'dirhtml') {
			
 
				+          // dirhtml builder
			
 
				+          var dirname = item[0] + '/';
			
 
				+          if (dirname.match(/\/index\/$/)) {
			
 
				+            dirname = dirname.substring(0, dirname.length-6);
			
 
				+          } else if (dirname == 'index/') {
			
 
				+            dirname = '';
			
 
				+          }
			
 
				+          requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + dirname;
			
 
				+          linkUrl = requestUrl;
			
 
				+
			
 
				+        } else {
			
 
				+          // normal html builders
			
 
				+          requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX;
			
 
				+          linkUrl = item[0] + DOCUMENTATION_OPTIONS.LINK_SUFFIX;
			
 
				+        }
			
 
				+        listItem.append($('<a/>').attr('href',
			
 
				+            linkUrl +
			
 
				+            highlightstring + item[2]).html(item[1]));
			
 
				+        if (item[3]) {
			
 
				+          listItem.append($('<span> (' + item[3] + ')</span>'));
			
 
				+          Search.output.append(listItem);
			
 
				+          setTimeout(function() {
			
 
				+            displayNextItem();
			
 
				+          }, 5);
			
 
				+        } else if (DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY) {
			
 
				+          $.ajax({url: requestUrl,
			
 
				+                  dataType: "text",
			
 
				+                  complete: function(jqxhr, textstatus) {
			
 
				+                    var data = jqxhr.responseText;
			
 
				+                    if (data !== '' && data !== undefined) {
			
 
				+                      var summary = Search.makeSearchSummary(data, searchterms, hlterms);
			
 
				+                      if (summary) {
			
 
				+                        listItem.append(summary);
			
 
				+                      }
			
 
				+                    }
			
 
				+                    Search.output.append(listItem);
			
 
				+                    setTimeout(function() {
			
 
				+                      displayNextItem();
			
 
				+                    }, 5);
			
 
				+                  }});
			
 
				+        } else {
			
 
				+          // just display title
			
 
				+          Search.output.append(listItem);
			
 
				+          setTimeout(function() {
			
 
				+            displayNextItem();
			
 
				+          }, 5);
			
 
				+        }
			
 
				+      }
			
 
				+      // search finished, update title and status message
			
 
				+      else {
			
 
				+        Search.stopPulse();
			
 
				+        Search.title.text(_('Search Results'));
			
 
				+        if (!resultCount)
			
 
				+          Search.status.text(_('Your search did not match any documents. Please make sure that all words are spelled correctly and that you\'ve selected enough categories.'));
			
 
				+        else
			
 
				+            Search.status.text(_('Search finished, found %s page(s) matching the search query.').replace('%s', resultCount));
			
 
				+        Search.status.fadeIn(500);
			
 
				+      }
			
 
				+    }
			
 
				+    displayNextItem();
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * search for object names
			
 
				+   */
			
 
				+  performObjectSearch : function(object, otherterms) {
			
 
				+    var filenames = this._index.filenames;
			
 
				+    var docnames = this._index.docnames;
			
 
				+    var objects = this._index.objects;
			
 
				+    var objnames = this._index.objnames;
			
 
				+    var titles = this._index.titles;
			
 
				+
			
 
				+    var i;
			
 
				+    var results = [];
			
 
				+
			
 
				+    for (var prefix in objects) {
			
 
				+      for (var iMatch = 0; iMatch != objects[prefix].length; ++iMatch) {
			
 
				+        var match = objects[prefix][iMatch];
			
 
				+        var name = match[4];
			
 
				+        var fullname = (prefix ? prefix + '.' : '') + name;
			
 
				+        var fullnameLower = fullname.toLowerCase()
			
 
				+        if (fullnameLower.indexOf(object) > -1) {
			
 
				+          var score = 0;
			
 
				+          var parts = fullnameLower.split('.');
			
 
				+          // check for different match types: exact matches of full name or
			
 
				+          // "last name" (i.e. last dotted part)
			
 
				+          if (fullnameLower == object || parts[parts.length - 1] == object) {
			
 
				+            score += Scorer.objNameMatch;
			
 
				+          // matches in last name
			
 
				+          } else if (parts[parts.length - 1].indexOf(object) > -1) {
			
 
				+            score += Scorer.objPartialMatch;
			
 
				+          }
			
 
				+          var objname = objnames[match[1]][2];
			
 
				+          var title = titles[match[0]];
			
 
				+          // If more than one term searched for, we require other words to be
			
 
				+          // found in the name/title/description
			
 
				+          if (otherterms.length > 0) {
			
 
				+            var haystack = (prefix + ' ' + name + ' ' +
			
 
				+                            objname + ' ' + title).toLowerCase();
			
 
				+            var allfound = true;
			
 
				+            for (i = 0; i < otherterms.length; i++) {
			
 
				+              if (haystack.indexOf(otherterms[i]) == -1) {
			
 
				+                allfound = false;
			
 
				+                break;
			
 
				+              }
			
 
				+            }
			
 
				+            if (!allfound) {
			
 
				+              continue;
			
 
				+            }
			
 
				+          }
			
 
				+          var descr = objname + _(', in ') + title;
			
 
				+
			
 
				+          var anchor = match[3];
			
 
				+          if (anchor === '')
			
 
				+            anchor = fullname;
			
 
				+          else if (anchor == '-')
			
 
				+            anchor = objnames[match[1]][1] + '-' + fullname;
			
 
				+          // add custom score for some objects according to scorer
			
 
				+          if (Scorer.objPrio.hasOwnProperty(match[2])) {
			
 
				+            score += Scorer.objPrio[match[2]];
			
 
				+          } else {
			
 
				+            score += Scorer.objPrioDefault;
			
 
				+          }
			
 
				+          results.push([docnames[match[0]], fullname, '#'+anchor, descr, score, filenames[match[0]]]);
			
 
				+        }
			
 
				+      }
			
 
				+    }
			
 
				+
			
 
				+    return results;
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions
			
 
				+   */
			
 
				+  escapeRegExp : function(string) {
			
 
				+    return string.replace(/[.*+\-?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * search for full-text terms in the index
			
 
				+   */
			
 
				+  performTermsSearch : function(searchterms, excluded, terms, titleterms) {
			
 
				+    var docnames = this._index.docnames;
			
 
				+    var filenames = this._index.filenames;
			
 
				+    var titles = this._index.titles;
			
 
				+
			
 
				+    var i, j, file;
			
 
				+    var fileMap = {};
			
 
				+    var scoreMap = {};
			
 
				+    var results = [];
			
 
				+
			
 
				+    // perform the search on the required terms
			
 
				+    for (i = 0; i < searchterms.length; i++) {
			
 
				+      var word = searchterms[i];
			
 
				+      var files = [];
			
 
				+      var _o = [
			
 
				+        {files: terms[word], score: Scorer.term},
			
 
				+        {files: titleterms[word], score: Scorer.title}
			
 
				+      ];
			
 
				+      // add support for partial matches
			
 
				+      if (word.length > 2) {
			
 
				+        var word_regex = this.escapeRegExp(word);
			
 
				+        for (var w in terms) {
			
 
				+          if (w.match(word_regex) && !terms[word]) {
			
 
				+            _o.push({files: terms[w], score: Scorer.partialTerm})
			
 
				+          }
			
 
				+        }
			
 
				+        for (var w in titleterms) {
			
 
				+          if (w.match(word_regex) && !titleterms[word]) {
			
 
				+              _o.push({files: titleterms[w], score: Scorer.partialTitle})
			
 
				+          }
			
 
				+        }
			
 
				+      }
			
 
				+
			
 
				+      // no match but word was a required one
			
 
				+      if ($u.every(_o, function(o){return o.files === undefined;})) {
			
 
				+        break;
			
 
				+      }
			
 
				+      // found search word in contents
			
 
				+      $u.each(_o, function(o) {
			
 
				+        var _files = o.files;
			
 
				+        if (_files === undefined)
			
 
				+          return
			
 
				+
			
 
				+        if (_files.length === undefined)
			
 
				+          _files = [_files];
			
 
				+        files = files.concat(_files);
			
 
				+
			
 
				+        // set score for the word in each file to Scorer.term
			
 
				+        for (j = 0; j < _files.length; j++) {
			
 
				+          file = _files[j];
			
 
				+          if (!(file in scoreMap))
			
 
				+            scoreMap[file] = {};
			
 
				+          scoreMap[file][word] = o.score;
			
 
				+        }
			
 
				+      });
			
 
				+
			
 
				+      // create the mapping
			
 
				+      for (j = 0; j < files.length; j++) {
			
 
				+        file = files[j];
			
 
				+        if (file in fileMap && fileMap[file].indexOf(word) === -1)
			
 
				+          fileMap[file].push(word);
			
 
				+        else
			
 
				+          fileMap[file] = [word];
			
 
				+      }
			
 
				+    }
			
 
				+
			
 
				+    // now check if the files don't contain excluded terms
			
 
				+    for (file in fileMap) {
			
 
				+      var valid = true;
			
 
				+
			
 
				+      // check if all requirements are matched
			
 
				+      var filteredTermCount = // as search terms with length < 3 are discarded: ignore
			
 
				+        searchterms.filter(function(term){return term.length > 2}).length
			
 
				+      if (
			
 
				+        fileMap[file].length != searchterms.length &&
			
 
				+        fileMap[file].length != filteredTermCount
			
 
				+      ) continue;
			
 
				+
			
 
				+      // ensure that none of the excluded terms is in the search result
			
 
				+      for (i = 0; i < excluded.length; i++) {
			
 
				+        if (terms[excluded[i]] == file ||
			
 
				+            titleterms[excluded[i]] == file ||
			
 
				+            $u.contains(terms[excluded[i]] || [], file) ||
			
 
				+            $u.contains(titleterms[excluded[i]] || [], file)) {
			
 
				+          valid = false;
			
 
				+          break;
			
 
				+        }
			
 
				+      }
			
 
				+
			
 
				+      // if we have still a valid result we can add it to the result list
			
 
				+      if (valid) {
			
 
				+        // select one (max) score for the file.
			
 
				+        // for better ranking, we should calculate ranking by using words statistics like basic tf-idf...
			
 
				+        var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]}));
			
 
				+        results.push([docnames[file], titles[file], '', null, score, filenames[file]]);
			
 
				+      }
			
 
				+    }
			
 
				+    return results;
			
 
				+  },
			
 
				+
			
 
				+  /**
			
 
				+   * helper function to return a node containing the
			
 
				+   * search summary for a given text. keywords is a list
			
 
				+   * of stemmed words, hlwords is the list of normal, unstemmed
			
 
				+   * words. the first one is used to find the occurrence, the
			
 
				+   * latter for highlighting it.
			
 
				+   */
			
 
				+  makeSearchSummary : function(htmlText, keywords, hlwords) {
			
 
				+    var text = Search.htmlToText(htmlText);
			
 
				+    if (text == "") {
			
 
				+      return null;
			
 
				+    }
			
 
				+    var textLower = text.toLowerCase();
			
 
				+    var start = 0;
			
 
				+    $.each(keywords, function() {
			
 
				+      var i = textLower.indexOf(this.toLowerCase());
			
 
				+      if (i > -1)
			
 
				+        start = i;
			
 
				+    });
			
 
				+    start = Math.max(start - 120, 0);
			
 
				+    var excerpt = ((start > 0) ? '...' : '') +
			
 
				+      $.trim(text.substr(start, 240)) +
			
 
				+      ((start + 240 - text.length) ? '...' : '');
			
 
				+    var rv = $('<p class="context"></p>').text(excerpt);
			
 
				+    $.each(hlwords, function() {
			
 
				+      rv = rv.highlightText(this, 'highlighted');
			
 
				+    });
			
 
				+    return rv;
			
 
				+  }
			
 
				+};
			
 
				+
			
 
				+$(document).ready(function() {
			
 
				+  Search.init();
			
 
				+});
			
--- a/_static/sphinx-book-theme.css
+++ b/_static/sphinx-book-theme.css
--- a/_static/sphinx-book-theme.d59cb220de22ca1c485ebbdc042f0030.js
+++ b/_static/sphinx-book-theme.d59cb220de22ca1c485ebbdc042f0030.js
--- a/_static/sphinx-book-theme.e2363ea40746bee74734a24ffefccd78.css
+++ b/_static/sphinx-book-theme.e2363ea40746bee74734a24ffefccd78.css
--- a/_static/sphinx-thebe.css
+++ b/_static/sphinx-thebe.css
@@ -0,0 +1,129 @@
 
				+/* Thebelab Buttons */
			
 
				+.thebelab-button {
			
 
				+  z-index: 999;
			
 
				+  display: inline-block;
			
 
				+  padding: 0.35em 1.2em;
			
 
				+  margin: 0px 1px;
			
 
				+  border-radius: 0.12em;
			
 
				+  box-sizing: border-box;
			
 
				+  text-decoration: none;
			
 
				+  font-family: "Roboto", sans-serif;
			
 
				+  font-weight: 300;
			
 
				+  text-align: center;
			
 
				+  transition: all 0.2s;
			
 
				+  background-color: #dddddd;
			
 
				+  border: 0.05em solid white;
			
 
				+  color: #000000;
			
 
				+}
			
 
				+
			
 
				+.thebelab-button:hover {
			
 
				+  border: 0.05em solid black;
			
 
				+  background-color: #fcfcfc;
			
 
				+}
			
 
				+
			
 
				+.thebe-launch-button {
			
 
				+  height: 2.2em;
			
 
				+  font-size: 0.8em;
			
 
				+  border: 1px black solid;
			
 
				+}
			
 
				+
			
 
				+/* Thebelab Cell */
			
 
				+.thebelab-cell pre {
			
 
				+  background: none;
			
 
				+}
			
 
				+
			
 
				+.thebelab-cell .thebelab-input {
			
 
				+  padding-left: 1em;
			
 
				+  margin-bottom: 0.5em;
			
 
				+  margin-top: 0.5em;
			
 
				+}
			
 
				+
			
 
				+.thebelab-cell .jp-OutputArea {
			
 
				+  margin-top: 0.5em;
			
 
				+  margin-left: 1em;
			
 
				+}
			
 
				+
			
 
				+button.thebelab-button.thebelab-run-button {
			
 
				+  margin-left: 1.5em;
			
 
				+  margin-bottom: 0.5em;
			
 
				+}
			
 
				+
			
 
				+/* Loading button */
			
 
				+button.thebe-launch-button div.spinner {
			
 
				+  float: left;
			
 
				+  margin-right: 1em;
			
 
				+}
			
 
				+
			
 
				+/* Remove the spinner when thebelab is ready */
			
 
				+.thebe-launch-button.thebe-status-ready .spinner {
			
 
				+  display: none;
			
 
				+}
			
 
				+
			
 
				+.thebe-launch-button span.status {
			
 
				+  font-family: monospace;
			
 
				+  font-weight: bold;
			
 
				+}
			
 
				+
			
 
				+.thebe-launch-button.thebe-status-ready span.status {
			
 
				+  color: green;
			
 
				+}
			
 
				+
			
 
				+.spinner {
			
 
				+  height: 2em;
			
 
				+  text-align: center;
			
 
				+  font-size: 0.7em;
			
 
				+}
			
 
				+
			
 
				+.spinner > div {
			
 
				+  background-color: #f37726;
			
 
				+  height: 100%;
			
 
				+  width: 6px;
			
 
				+  display: inline-block;
			
 
				+
			
 
				+  -webkit-animation: sk-stretchdelay 1.2s infinite ease-in-out;
			
 
				+  animation: sk-stretchdelay 1.2s infinite ease-in-out;
			
 
				+}
			
 
				+
			
 
				+.spinner .rect2 {
			
 
				+  -webkit-animation-delay: -1.1s;
			
 
				+  animation-delay: -1.1s;
			
 
				+}
			
 
				+
			
 
				+.spinner .rect3 {
			
 
				+  -webkit-animation-delay: -1s;
			
 
				+  animation-delay: -1s;
			
 
				+}
			
 
				+
			
 
				+.spinner .rect4 {
			
 
				+  -webkit-animation-delay: -0.9s;
			
 
				+  animation-delay: -0.9s;
			
 
				+}
			
 
				+
			
 
				+.spinner .rect5 {
			
 
				+  -webkit-animation-delay: -0.8s;
			
 
				+  animation-delay: -0.8s;
			
 
				+}
			
 
				+
			
 
				+@-webkit-keyframes sk-stretchdelay {
			
 
				+  0%,
			
 
				+  40%,
			
 
				+  100% {
			
 
				+    -webkit-transform: scaleY(0.4);
			
 
				+  }
			
 
				+  20% {
			
 
				+    -webkit-transform: scaleY(1);
			
 
				+  }
			
 
				+}
			
 
				+
			
 
				+@keyframes sk-stretchdelay {
			
 
				+  0%,
			
 
				+  40%,
			
 
				+  100% {
			
 
				+    transform: scaleY(0.4);
			
 
				+    -webkit-transform: scaleY(0.4);
			
 
				+  }
			
 
				+  20% {
			
 
				+    transform: scaleY(1);
			
 
				+    -webkit-transform: scaleY(1);
			
 
				+  }
			
 
				+}
			
--- a/_static/sphinx-thebe.js
+++ b/_static/sphinx-thebe.js
@@ -0,0 +1,126 @@
 
				+/**
			
 
				+ * Add attributes to Thebe blocks to initialize thebe properly
			
 
				+ */
			
 
				+var configureThebe = () => {
			
 
				+  // Load thebe config in case we want to update it as some point
			
 
				+  console.log("[sphinx-thebe]: Loading thebe config...");
			
 
				+  thebe_config = $('script[type="text/x-thebe-config"]')[0];
			
 
				+
			
 
				+  // If we already detect a Thebe cell, don't re-run
			
 
				+  if (document.querySelectorAll("div.thebe-cell").length > 0) {
			
 
				+    return;
			
 
				+  }
			
 
				+
			
 
				+  // Update thebe buttons with loading message
			
 
				+  $(".thebe-launch-button").each((ii, button) => {
			
 
				+    button.innerHTML = `
			
 
				+        <div class="spinner">
			
 
				+            <div class="rect1"></div>
			
 
				+            <div class="rect2"></div>
			
 
				+            <div class="rect3"></div>
			
 
				+            <div class="rect4"></div>
			
 
				+        </div>
			
 
				+        <span class="loading-text"></span>`;
			
 
				+  });
			
 
				+
			
 
				+  // Set thebe event hooks
			
 
				+  var thebeStatus;
			
 
				+  thebelab.on("status", function (evt, data) {
			
 
				+    console.log("Status changed:", data.status, data.message);
			
 
				+
			
 
				+    $(".thebe-launch-button ")
			
 
				+      .removeClass("thebe-status-" + thebeStatus)
			
 
				+      .addClass("thebe-status-" + data.status)
			
 
				+      .find(".loading-text")
			
 
				+      .html(
			
 
				+        "<span class='launch_msg'>Launching from mybinder.org: </span><span class='status'>" +
			
 
				+          data.status +
			
 
				+          "</span>"
			
 
				+      );
			
 
				+
			
 
				+    // Now update our thebe status
			
 
				+    thebeStatus = data.status;
			
 
				+
			
 
				+    // Find any cells with an initialization tag and ask thebe to run them when ready
			
 
				+    if (data.status === "ready") {
			
 
				+      var thebeInitCells = document.querySelectorAll(
			
 
				+        ".thebe-init, .tag_thebe-init"
			
 
				+      );
			
 
				+      thebeInitCells.forEach((cell) => {
			
 
				+        console.log("Initializing Thebe with cell: " + cell.id);
			
 
				+        cell.querySelector(".thebelab-run-button").click();
			
 
				+      });
			
 
				+    }
			
 
				+  });
			
 
				+};
			
 
				+
			
 
				+/**
			
 
				+ * Update the page DOM to use Thebe elements
			
 
				+ */
			
 
				+var modifyDOMForThebe = () => {
			
 
				+  // Find all code cells, replace with Thebe interactive code cells
			
 
				+  const codeCells = document.querySelectorAll(thebe_selector);
			
 
				+  codeCells.forEach((codeCell, index) => {
			
 
				+    const codeCellId = (index) => `codecell${index}`;
			
 
				+    codeCell.id = codeCellId(index);
			
 
				+    codeCellText = codeCell.querySelector(thebe_selector_input);
			
 
				+    codeCellOutput = codeCell.querySelector(thebe_selector_output);
			
 
				+
			
 
				+    // Clean up the language to make it work w/ CodeMirror and add it to the cell
			
 
				+    dataLanguage = detectLanguage(kernelName);
			
 
				+
			
 
				+    // Re-arrange the cell and add metadata
			
 
				+    if (codeCellText) {
			
 
				+      codeCellText.setAttribute("data-language", dataLanguage);
			
 
				+      codeCellText.setAttribute("data-executable", "true");
			
 
				+
			
 
				+      // If we had an output, insert it just after the `pre` cell
			
 
				+      if (codeCellOutput) {
			
 
				+        $(codeCellOutput).attr("data-output", "");
			
 
				+        $(codeCellOutput).insertAfter(codeCellText);
			
 
				+      }
			
 
				+    }
			
 
				+
			
 
				+    // Remove sphinx-copybutton blocks, which are common in Sphinx
			
 
				+    codeCell.querySelectorAll("button.copybtn").forEach((el) => {
			
 
				+      el.remove();
			
 
				+    });
			
 
				+  });
			
 
				+};
			
 
				+
			
 
				+var initThebe = () => {
			
 
				+  // Load thebe dynamically if it's not already loaded
			
 
				+  if (typeof thebelab === "undefined") {
			
 
				+    console.log("[sphinx-thebe]: Loading thebe from CDN...");
			
 
				+    $(".thebe-launch-button ").text("Loading thebe from CDN...");
			
 
				+
			
 
				+    const script = document.createElement("script");
			
 
				+    script.src = `${THEBE_JS_URL}`;
			
 
				+    document.head.appendChild(script);
			
 
				+
			
 
				+    // Runs once the script has finished loading
			
 
				+    script.addEventListener("load", () => {
			
 
				+      console.log("[sphinx-thebe]: Finished loading thebe from CDN...");
			
 
				+      configureThebe();
			
 
				+      modifyDOMForThebe();
			
 
				+      thebelab.bootstrap();
			
 
				+    });
			
 
				+  } else {
			
 
				+    console.log(
			
 
				+      "[sphinx-thebe]: thebe already loaded, not loading from CDN..."
			
 
				+    );
			
 
				+    configureThebe();
			
 
				+    modifyDOMForThebe();
			
 
				+    thebelab.bootstrap();
			
 
				+  }
			
 
				+};
			
 
				+
			
 
				+// Helper function to munge the language name
			
 
				+var detectLanguage = (language) => {
			
 
				+  if (language.indexOf("python") > -1) {
			
 
				+    language = "python";
			
 
				+  } else if (language === "ir") {
			
 
				+    language = "r";
			
 
				+  }
			
 
				+  return language;
			
 
				+};
			
--- a/_static/togglebutton.css
+++ b/_static/togglebutton.css
@@ -0,0 +1,130 @@
 
				+/**
			
 
				+ * Admonition-based toggles
			
 
				+ */
			
 
				+
			
 
				+/* Visibility of the target */
			
 
				+.admonition.toggle .admonition-title ~ * {
			
 
				+    transition: opacity .3s, height .3s;
			
 
				+}
			
 
				+
			
 
				+/* Toggle buttons inside admonitions so we see the title */
			
 
				+.toggle.admonition {
			
 
				+    position: relative;
			
 
				+}
			
 
				+
			
 
				+/* Titles should cut off earlier to avoid overlapping w/ button */
			
 
				+.toggle.admonition .admonition-title {
			
 
				+    padding-right: 25%;
			
 
				+    cursor: pointer;
			
 
				+}
			
 
				+
			
 
				+/* hides all the content of a page until de-toggled */
			
 
				+.toggle-hidden.admonition .admonition-title ~ * {
			
 
				+    height: 0;
			
 
				+    margin: 0;
			
 
				+    float: left; /* so they overlap when hidden */
			
 
				+    opacity: 0;
			
 
				+    visibility: hidden;
			
 
				+}
			
 
				+
			
 
				+/* General button style and position*/
			
 
				+button.toggle-button {
			
 
				+    /**
			
 
				+     * Background and shape. By default there's no background
			
 
				+     * but users can style as they wish
			
 
				+     */  
			
 
				+    background: none;
			
 
				+    border: none;
			
 
				+    outline: none;
			
 
				+
			
 
				+    /* Positioning just inside the amonition title */
			
 
				+    margin-right: 0.5em;
			
 
				+    position: absolute;
			
 
				+    right: 0em;
			
 
				+    top: .5em;
			
 
				+    float: right;
			
 
				+    padding: 0px;
			
 
				+    display: flex;
			
 
				+}
			
 
				+
			
 
				+/* Display the toggle hint on wide screens */
			
 
				+@media (min-width: 768px) {
			
 
				+    button.toggle-button.toggle-button-hidden:before {
			
 
				+        content: attr(data-toggle-hint);  /* This will be filled in by JS */
			
 
				+        font-size: .8em;
			
 
				+        align-self: center;
			
 
				+    }
			
 
				+}
			
 
				+
			
 
				+/* Icon behavior */
			
 
				+.tb-icon {
			
 
				+    transition: transform .2s ease-out;
			
 
				+    height: 1.5em;
			
 
				+    width: 1.5em;
			
 
				+    stroke: currentColor;  /* So that we inherit the color of other text */
			
 
				+}
			
 
				+
			
 
				+details.toggle-details .tb-icon {
			
 
				+    height: 1.3em;
			
 
				+    width: 1.3em;
			
 
				+}
			
 
				+
			
 
				+.toggle-button-hidden .tb-icon {
			
 
				+    transform: rotate(90deg);
			
 
				+}
			
 
				+
			
 
				+/**
			
 
				+ * Details-based toggles.
			
 
				+ * In this case, we wrap elements with `.toggle` in a details block.
			
 
				+ */
			
 
				+
			
 
				+/* Details blocks */
			
 
				+details.toggle-details {
			
 
				+    margin: 1em 0;
			
 
				+}
			
 
				+
			
 
				+details.toggle-details summary {
			
 
				+    display: flex;
			
 
				+    align-items: center;
			
 
				+    width: fit-content;
			
 
				+    cursor: pointer;
			
 
				+    list-style: none;
			
 
				+    border-radius: .4em;
			
 
				+    border: 1px solid #ccc;
			
 
				+    background: #f8f8f8;
			
 
				+    padding: 0.4em 1em 0.4em 0.5em; /* Less padding on left because the SVG has left margin */
			
 
				+    font-size: .9em;
			
 
				+}
			
 
				+
			
 
				+details.toggle-details summary:hover {
			
 
				+    background: #f6f6f6;
			
 
				+}
			
 
				+
			
 
				+details.toggle-details summary:active {
			
 
				+    background: #eee;
			
 
				+}
			
 
				+
			
 
				+details.toggle-details[open] summary {
			
 
				+    margin-bottom: .5em;
			
 
				+}
			
 
				+
			
 
				+details.toggle-details[open] summary .tb-icon {
			
 
				+    transform: rotate(90deg);
			
 
				+}
			
 
				+
			
 
				+details.toggle-details[open] summary ~ * {
			
 
				+    animation: toggle-fade-in .3s ease-out;
			
 
				+}
			
 
				+
			
 
				+@keyframes toggle-fade-in {
			
 
				+  from {opacity: 0%;}
			
 
				+  to {opacity: 100%;}
			
 
				+}
			
 
				+
			
 
				+/* Print rules - we hide all toggle button elements at print */
			
 
				+@media print {
			
 
				+    /* Always hide the summary so the button doesn't show up */
			
 
				+    details.toggle-details summary {
			
 
				+        display: none;
			
 
				+    }
			
 
				+}
			
--- a/_static/togglebutton.js
+++ b/_static/togglebutton.js
@@ -0,0 +1,172 @@
 
				+/**
			
 
				+ * Add Toggle Buttons to elements
			
 
				+ */
			
 
				+
			
 
				+let toggleChevron = `
			
 
				+<svg xmlns="http://www.w3.org/2000/svg" class="tb-icon toggle-chevron-right" width="44" height="44" viewBox="0 0 24 24" stroke-width="1.5" stroke="#000000" fill="none" stroke-linecap="round" stroke-linejoin="round">
			
 
				+<path stroke="none" d="M0 0h24v24H0z" fill="none"/>
			
 
				+<polyline points="9 6 15 12 9 18" />
			
 
				+</svg>`;
			
 
				+
			
 
				+var initToggleItems = () => {
			
 
				+  var itemsToToggle = document.querySelectorAll(togglebuttonSelector);
			
 
				+  console.log(`[togglebutton]: Adding toggle buttons to ${itemsToToggle.length} items`)
			
 
				+  // Add the button to each admonition and hook up a callback to toggle visibility
			
 
				+  itemsToToggle.forEach((item, index) => {
			
 
				+    if (item.classList.contains("admonition")) {
			
 
				+      // If it's an admonition block, then we'll add a button inside
			
 
				+      // Generate unique IDs for this item
			
 
				+      var toggleID = `toggle-${index}`;
			
 
				+      var buttonID = `button-${toggleID}`;
			
 
				+
			
 
				+      item.setAttribute('id', toggleID);
			
 
				+      if (!item.classList.contains("toggle")){
			
 
				+        item.classList.add("toggle");
			
 
				+      }
			
 
				+      // This is the button that will be added to each item to trigger the toggle
			
 
				+      var collapseButton = `
			
 
				+        <button type="button" id="${buttonID}" class="toggle-button" data-target="${toggleID}" data-button="${buttonID}", data-toggle-hint="${toggleHintShow}">
			
 
				+            ${toggleChevron}
			
 
				+        </button>`;
			
 
				+
			
 
				+      item.insertAdjacentHTML("afterbegin", collapseButton);
			
 
				+      thisButton = document.getElementById(buttonID);
			
 
				+
			
 
				+      // Add click handlers for the button + admonition title (if admonition)
			
 
				+      thisButton.addEventListener('click', toggleClickHandler);
			
 
				+      admonitionTitle = document.querySelector(`#${toggleID} > .admonition-title`)
			
 
				+      if (admonitionTitle) {
			
 
				+        admonitionTitle.addEventListener('click', toggleClickHandler);
			
 
				+        admonitionTitle.dataset.target = toggleID
			
 
				+        admonitionTitle.dataset.button = buttonID
			
 
				+      }
			
 
				+
			
 
				+      // Now hide the item for this toggle button unless explicitly noted to show
			
 
				+      if (!item.classList.contains("toggle-shown")) {
			
 
				+        toggleHidden(thisButton);
			
 
				+      }
			
 
				+    } else {
			
 
				+      // If not an admonition, wrap the block in a <details> block
			
 
				+      // Define the structure of the details block and insert it as a sibling
			
 
				+      var detailsBlock = `
			
 
				+        <details class="toggle-details">
			
 
				+            <summary>
			
 
				+              ${toggleChevron}
			
 
				+              <span>${toggleHintShow}</span>
			
 
				+            </summary>
			
 
				+        </details>`;
			
 
				+      item.insertAdjacentHTML("beforebegin", detailsBlock);
			
 
				+
			
 
				+      // Now move the toggle-able content inside of the details block
			
 
				+      details = item.previousElementSibling
			
 
				+      details.appendChild(item)
			
 
				+
			
 
				+      // Set up a click trigger to change the text as needed
			
 
				+      details.addEventListener('click', (click) => {
			
 
				+        let parent = click.target.parentElement;
			
 
				+        if (parent.tagName.toLowerCase() == "details") {
			
 
				+          summary = parent.querySelector("summary");
			
 
				+          details = parent;
			
 
				+        } else {
			
 
				+          summary = parent;
			
 
				+          details = parent.parentElement;
			
 
				+        }
			
 
				+        // Update the inner text for the proper hint
			
 
				+        if (details.open) {
			
 
				+          summary.querySelector("span").innerText = toggleHintShow;
			
 
				+        } else {
			
 
				+          summary.querySelector("span").innerText = toggleHintHide;
			
 
				+        }
			
 
				+        
			
 
				+      });
			
 
				+
			
 
				+      // If we have a toggle-shown class, open details block should be open
			
 
				+      if (item.classList.contains("toggle-shown")) {
			
 
				+        details.click();
			
 
				+      }
			
 
				+    }
			
 
				+  })
			
 
				+};
			
 
				+
			
 
				+// This should simply add / remove the collapsed class and change the button text
			
 
				+var toggleHidden = (button) => {
			
 
				+  target = button.dataset['target']
			
 
				+  var itemToToggle = document.getElementById(target);
			
 
				+  if (itemToToggle.classList.contains("toggle-hidden")) {
			
 
				+    itemToToggle.classList.remove("toggle-hidden");
			
 
				+    button.classList.remove("toggle-button-hidden");
			
 
				+  } else {
			
 
				+    itemToToggle.classList.add("toggle-hidden");
			
 
				+    button.classList.add("toggle-button-hidden");
			
 
				+  }
			
 
				+}
			
 
				+
			
 
				+var toggleClickHandler = (click) => {
			
 
				+  if (click.target.classList.contains("admonition-title")) {
			
 
				+    // If it's an admonition title, the button will be just before
			
 
				+    button = click.target.previousElementSibling;
			
 
				+  } else {
			
 
				+    // If not, we've clicked the button itself or its content, so search upwards
			
 
				+    button = click.currentTarget;
			
 
				+  }
			
 
				+  target = document.getElementById(button.dataset['button']);
			
 
				+  toggleHidden(target);
			
 
				+}
			
 
				+
			
 
				+// If we want to blanket-add toggle classes to certain cells
			
 
				+var addToggleToSelector = () => {
			
 
				+  const selector = "";
			
 
				+  if (selector.length > 0) {
			
 
				+    document.querySelectorAll(selector).forEach((item) => {
			
 
				+      item.classList.add("toggle");
			
 
				+    })
			
 
				+  }
			
 
				+}
			
 
				+
			
 
				+// Helper function to run when the DOM is finished
			
 
				+const sphinxToggleRunWhenDOMLoaded = cb => {
			
 
				+  if (document.readyState != 'loading') {
			
 
				+    cb()
			
 
				+  } else if (document.addEventListener) {
			
 
				+    document.addEventListener('DOMContentLoaded', cb)
			
 
				+  } else {
			
 
				+    document.attachEvent('onreadystatechange', function() {
			
 
				+      if (document.readyState == 'complete') cb()
			
 
				+    })
			
 
				+  }
			
 
				+}
			
 
				+sphinxToggleRunWhenDOMLoaded(addToggleToSelector)
			
 
				+sphinxToggleRunWhenDOMLoaded(initToggleItems)
			
 
				+
			
 
				+/** Toggle details blocks to be open when printing */
			
 
				+if (toggleOpenOnPrint == "true") {
			
 
				+  window.addEventListener("beforeprint", () => {
			
 
				+    // Open the details
			
 
				+    document.querySelectorAll("details.toggle-details").forEach((el) => {
			
 
				+      el.dataset["togglestatus"] = el.open;
			
 
				+      el.open = true;
			
 
				+    });
			
 
				+  
			
 
				+    // Open the admonitions
			
 
				+    document.querySelectorAll(".admonition.toggle.toggle-hidden").forEach((el) => {
			
 
				+      console.log(el);
			
 
				+      el.querySelector("button.toggle-button").click();
			
 
				+      el.dataset["toggle_after_print"] = "true";
			
 
				+    });
			
 
				+  });
			
 
				+  window.addEventListener("afterprint", () => {
			
 
				+    // Re-close the details that were closed
			
 
				+    document.querySelectorAll("details.toggle-details").forEach((el) => {
			
 
				+      el.open = el.dataset["togglestatus"] == "true";
			
 
				+      delete el.dataset["togglestatus"];
			
 
				+    });
			
 
				+  
			
 
				+    // Re-close the admonition toggle buttons
			
 
				+    document.querySelectorAll(".admonition.toggle").forEach((el) => {
			
 
				+      if (el.dataset["toggle_after_print"] == "true") {
			
 
				+        el.querySelector("button.toggle-button").click();
			
 
				+        delete el.dataset["toggle_after_print"];
			
 
				+      }
			
 
				+    });
			
 
				+  });
			
 
				+}
			
--- a/_static/underscore-1.13.1.js
+++ b/_static/underscore-1.13.1.js
--- a/_static/underscore.js
+++ b/_static/underscore.js
--- a/_static/vendor/fontawesome/5.13.0/LICENSE.txt
+++ b/_static/vendor/fontawesome/5.13.0/LICENSE.txt
@@ -0,0 +1,34 @@
 
				+Font Awesome Free License
			
 
				+-------------------------
			
 
				+
			
 
				+Font Awesome Free is free, open source, and GPL friendly. You can use it for
			
 
				+commercial projects, open source projects, or really almost whatever you want.
			
 
				+Full Font Awesome Free license: https://fontawesome.com/license/free.
			
 
				+
			
 
				+# Icons: CC BY 4.0 License (https://creativecommons.org/licenses/by/4.0/)
			
 
				+In the Font Awesome Free download, the CC BY 4.0 license applies to all icons
			
 
				+packaged as SVG and JS file types.
			
 
				+
			
 
				+# Fonts: SIL OFL 1.1 License (https://scripts.sil.org/OFL)
			
 
				+In the Font Awesome Free download, the SIL OFL license applies to all icons
			
 
				+packaged as web and desktop font files.
			
 
				+
			
 
				+# Code: MIT License (https://opensource.org/licenses/MIT)
			
 
				+In the Font Awesome Free download, the MIT license applies to all non-font and
			
 
				+non-icon files.
			
 
				+
			
 
				+# Attribution
			
 
				+Attribution is required by MIT, SIL OFL, and CC BY licenses. Downloaded Font
			
 
				+Awesome Free files already contain embedded comments with sufficient
			
 
				+attribution, so you shouldn't need to do anything additional when using these
			
 
				+files normally.
			
 
				+
			
 
				+We've kept attribution comments terse, so we ask that you do not actively work
			
 
				+to remove them from files, especially code. They're a great way for folks to
			
 
				+learn about Font Awesome.
			
 
				+
			
 
				+# Brand Icons
			
 
				+All brand icons are trademarks of their respective owners. The use of these
			
 
				+trademarks does not indicate endorsement of the trademark holder by Font
			
 
				+Awesome, nor vice versa. **Please do not use brand logos for any purpose except
			
 
				+to represent the company, product, or service to which they refer.**
			
--- a/_static/vendor/fontawesome/5.13.0/css/all.min.css
+++ b/_static/vendor/fontawesome/5.13.0/css/all.min.css