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_modules/blackjax/mcmc/integrators.html

@@ -667,9 +667,11 @@ <h1>Source code for blackjax.mcmc.integrators</h1><div class="highlight"><pre>
 <span class="n">yoshida</span> <span class="o">=</span> <span class="n">generate_euclidean_integrator</span><span class="p">(</span><span class="n">yoshida_coefficients</span><span class="p">)</span></div>
 
 
-<span class="sd">&quot;&quot;&quot;11 stage Omelyan integrator [I.P. Omelyan, I.M. Mryglod and R. Folk, Comput. Phys. Commun. 151 (2003) 272.],</span>
-<span class="sd">4MN5FV in [Takaishi, Tetsuya, and Philippe De Forcrand. &quot;Testing and tuning symplectic integrators for the hybrid Monte Carlo algorithm in lattice QCD.&quot; Physical Review E 73.3 (2006): 036706.]</span>
-<span class="sd">popular in LQCD&quot;&quot;&quot;</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Eleven-stage palindromic symplectic integrator derived in :cite:p:`omelyan2003symplectic`.</span>
+
+<span class="sd">Popular in LQCD, see also :cite:p:`takaishi2006testing`.</span>
+<span class="sd">&quot;&quot;&quot;</span>
 <span class="n">b1</span> <span class="o">=</span> <span class="mf">0.08398315262876693</span>
 <span class="n">a1</span> <span class="o">=</span> <span class="mf">0.2539785108410595</span>
 <span class="n">b2</span> <span class="o">=</span> <span class="mf">0.6822365335719091</span>

_sources/autoapi/blackjax/mcmc/integrators/index.rst

@@ -60,9 +60,9 @@ Module Contents
 
 .. py:data:: yoshida
 
-   11 stage Omelyan integrator [I.P. Omelyan, I.M. Mryglod and R. Folk, Comput. Phys. Commun. 151 (2003) 272.],
-   4MN5FV in [Takaishi, Tetsuya, and Philippe De Forcrand. "Testing and tuning symplectic integrators for the hybrid Monte Carlo algorithm in lattice QCD." Physical Review E 73.3 (2006): 036706.]
-   popular in LQCD
+   Eleven-stage palindromic symplectic integrator derived in :cite:p:`omelyan2003symplectic`.
+
+   Popular in LQCD, see also :cite:p:`takaishi2006testing`.
 
 .. py:data:: omelyan
 

autoapi/blackjax/mcmc/integrators/index.html

@@ -404,7 +404,7 @@ <h2>Attributes<a class="headerlink" href="#attributes" title="Link to this headi
 <td><p>Three stages palindromic symplectic integrator derived in <span id="id2">[<a class="reference internal" href="../../../../bib.html#id19" title="Robert I McLachlan. On the numerical integration of ordinary differential equations by symmetric composition methods. SIAM Journal on Scientific Computing, 16(1):151–168, 1995.">McL95</a>]</span></p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="#blackjax.mcmc.integrators.yoshida" title="blackjax.mcmc.integrators.yoshida"><code class="xref py py-obj docutils literal notranslate"><span class="pre">yoshida</span></code></a></p></td>
-<td><p>11 stage Omelyan integrator [I.P. Omelyan, I.M. Mryglod and R. Folk, Comput. Phys. Commun. 151 (2003) 272.],</p></td>
+<td><p>Eleven-stage palindromic symplectic integrator derived in <span id="id3">[<a class="reference internal" href="../../../../bib.html#id52" title="IP Omelyan, IM Mryglod, and R Folk. Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations. Computer Physics Communications, 151(3):272–314, 2003.">OMF03</a>]</span>.</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="#blackjax.mcmc.integrators.omelyan" title="blackjax.mcmc.integrators.omelyan"><code class="xref py py-obj docutils literal notranslate"><span class="pre">omelyan</span></code></a></p></td>
 <td><p></p></td>
@@ -442,32 +442,31 @@ <h2>Module Contents<a class="headerlink" href="#module-contents" title="Link to
 <dl class="py data">
 <dt class="sig sig-object py" id="blackjax.mcmc.integrators.velocity_verlet">
 <span class="sig-name descname"><span class="pre">velocity_verlet</span></span><a class="reference internal" href="../../../../_modules/blackjax/mcmc/integrators.html#velocity_verlet"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#blackjax.mcmc.integrators.velocity_verlet" title="Link to this definition">#</a></dt>
-<dd><p>Two-stage palindromic symplectic integrator derived in <span id="id3">[<a class="reference internal" href="../../../../bib.html#id22" title="Sergio Blanes, Fernando Casas, and Jesús Marıa Sanz-Serna. Numerical integrators for the hybrid monte carlo method. SIAM Journal on Scientific Computing, 36(4):A1556–A1580, 2014.">BCSS14</a>]</span>.</p>
+<dd><p>Two-stage palindromic symplectic integrator derived in <span id="id4">[<a class="reference internal" href="../../../../bib.html#id22" title="Sergio Blanes, Fernando Casas, and Jesús Marıa Sanz-Serna. Numerical integrators for the hybrid monte carlo method. SIAM Journal on Scientific Computing, 36(4):A1556–A1580, 2014.">BCSS14</a>]</span>.</p>
 <p>The integrator is of the form (b1, a1, b2, a1, b1). The choice of the parameters
 determine both the bound on the integration error and the stability of the
 method with respect to the value of <cite>step_size</cite>. The values used here are
-the ones derived in <span id="id4">[<a class="reference internal" href="../../../../bib.html#id19" title="Robert I McLachlan. On the numerical integration of ordinary differential equations by symmetric composition methods. SIAM Journal on Scientific Computing, 16(1):151–168, 1995.">McL95</a>]</span>; note that <span id="id5">[<a class="reference internal" href="../../../../bib.html#id22" title="Sergio Blanes, Fernando Casas, and Jesús Marıa Sanz-Serna. Numerical integrators for the hybrid monte carlo method. SIAM Journal on Scientific Computing, 36(4):A1556–A1580, 2014.">BCSS14</a>]</span>
+the ones derived in <span id="id5">[<a class="reference internal" href="../../../../bib.html#id19" title="Robert I McLachlan. On the numerical integration of ordinary differential equations by symmetric composition methods. SIAM Journal on Scientific Computing, 16(1):151–168, 1995.">McL95</a>]</span>; note that <span id="id6">[<a class="reference internal" href="../../../../bib.html#id22" title="Sergio Blanes, Fernando Casas, and Jesús Marıa Sanz-Serna. Numerical integrators for the hybrid monte carlo method. SIAM Journal on Scientific Computing, 36(4):A1556–A1580, 2014.">BCSS14</a>]</span>
 is more focused on stability and derives different values.</p>
 <p>Also known as the minimal norm integrator.</p>
 </dd></dl>
 
 <dl class="py data">
 <dt class="sig sig-object py" id="blackjax.mcmc.integrators.mclachlan">
 <span class="sig-name descname"><span class="pre">mclachlan</span></span><a class="reference internal" href="../../../../_modules/blackjax/mcmc/integrators.html#mclachlan"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#blackjax.mcmc.integrators.mclachlan" title="Link to this definition">#</a></dt>
-<dd><p>Three stages palindromic symplectic integrator derived in <span id="id6">[<a class="reference internal" href="../../../../bib.html#id19" title="Robert I McLachlan. On the numerical integration of ordinary differential equations by symmetric composition methods. SIAM Journal on Scientific Computing, 16(1):151–168, 1995.">McL95</a>]</span></p>
+<dd><p>Three stages palindromic symplectic integrator derived in <span id="id7">[<a class="reference internal" href="../../../../bib.html#id19" title="Robert I McLachlan. On the numerical integration of ordinary differential equations by symmetric composition methods. SIAM Journal on Scientific Computing, 16(1):151–168, 1995.">McL95</a>]</span></p>
 <p>The integrator is of the form (b1, a1, b2, a2, b2, a1, b1). The choice of
 the parameters determine both the bound on the integration error and the
 stability of the method with respect to the value of <cite>step_size</cite>. The
-values used here are the ones derived in <span id="id7">[<a class="reference internal" href="../../../../bib.html#id19" title="Robert I McLachlan. On the numerical integration of ordinary differential equations by symmetric composition methods. SIAM Journal on Scientific Computing, 16(1):151–168, 1995.">McL95</a>]</span> which
+values used here are the ones derived in <span id="id8">[<a class="reference internal" href="../../../../bib.html#id19" title="Robert I McLachlan. On the numerical integration of ordinary differential equations by symmetric composition methods. SIAM Journal on Scientific Computing, 16(1):151–168, 1995.">McL95</a>]</span> which
 guarantees a stability interval length approximately equal to 4.67.</p>
 </dd></dl>
 
 <dl class="py data">
 <dt class="sig sig-object py" id="blackjax.mcmc.integrators.yoshida">
 <span class="sig-name descname"><span class="pre">yoshida</span></span><a class="reference internal" href="../../../../_modules/blackjax/mcmc/integrators.html#yoshida"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#blackjax.mcmc.integrators.yoshida" title="Link to this definition">#</a></dt>
-<dd><p>11 stage Omelyan integrator [I.P. Omelyan, I.M. Mryglod and R. Folk, Comput. Phys. Commun. 151 (2003) 272.],
-4MN5FV in [Takaishi, Tetsuya, and Philippe De Forcrand. “Testing and tuning symplectic integrators for the hybrid Monte Carlo algorithm in lattice QCD.” Physical Review E 73.3 (2006): 036706.]
-popular in LQCD</p>
+<dd><p>Eleven-stage palindromic symplectic integrator derived in <span id="id9">[<a class="reference internal" href="../../../../bib.html#id52" title="IP Omelyan, IM Mryglod, and R Folk. Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations. Computer Physics Communications, 151(3):272–314, 2003.">OMF03</a>]</span>.</p>
+<p>Popular in LQCD, see also <span id="id10">[<a class="reference internal" href="../../../../bib.html#id53" title="Tetsuya Takaishi and Philippe De Forcrand. Testing and tuning symplectic integrators for the hybrid monte carlo algorithm in lattice qcd. Physical Review E, 73(3):036706, 2006.">TDF06</a>]</span>.</p>
 </dd></dl>
 
 <dl class="py data">
@@ -504,7 +503,7 @@ <h2>Module Contents<a class="headerlink" href="#module-contents" title="Link to
 <dt class="sig sig-object py" id="blackjax.mcmc.integrators.implicit_midpoint">
 <span class="sig-name descname"><span class="pre">implicit_midpoint</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">logdensity_fn</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Callable</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kinetic_energy_fn</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">blackjax.mcmc.metrics.KineticEnergy</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">solver</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">FixedPointSolver</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">solve_fixed_point_iteration</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">solver_kwargs</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Any</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Integrator</span></span></span><a class="reference internal" href="../../../../_modules/blackjax/mcmc/integrators.html#implicit_midpoint"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#blackjax.mcmc.integrators.implicit_midpoint" title="Link to this definition">#</a></dt>
 <dd><p>The implicit midpoint integrator with support for non-stationary kinetic energy</p>
-<p>This is an integrator based on <span id="id8">Brofos and Lederman [<a class="reference internal" href="../../../../bib.html#id20" title="James Brofos and Roy R Lederman. Evaluating the implicit midpoint integrator for riemannian hamiltonian monte carlo. In Marina Meila and Tong Zhang, editors, Proceedings of the 38th International Conference on Machine Learning, volume 139 of Proceedings of Machine Learning Research, 1072–1081. PMLR, 18–24 Jul 2021.">BL21</a>]</span>, which provides
+<p>This is an integrator based on <span id="id11">Brofos and Lederman [<a class="reference internal" href="../../../../bib.html#id20" title="James Brofos and Roy R Lederman. Evaluating the implicit midpoint integrator for riemannian hamiltonian monte carlo. In Marina Meila and Tong Zhang, editors, Proceedings of the 38th International Conference on Machine Learning, volume 139 of Proceedings of Machine Learning Research, 1072–1081. PMLR, 18–24 Jul 2021.">BL21</a>]</span>, which provides
 support for kinetic energies that depend on position. This integrator requires that
 the kinetic energy function takes two arguments: position and momentum.</p>
 <p>The <code class="docutils literal notranslate"><span class="pre">solver</span></code> parameter allows overloading of the fixed point solver. By default, a

bib.html

@@ -501,6 +501,10 @@ <h1>Bibliography<a class="headerlink" href="#bibliography" title="Link to this h
 <span class="label"><span class="fn-bracket">[</span>Nes09<span class="fn-bracket">]</span></span>
 <p>Yurii Nesterov. Primal-dual subgradient methods for convex problems. <em>Mathematical programming</em>, 120(1):221–259, 2009.</p>
 </div>
+<div class="citation" id="id52" role="doc-biblioentry">
+<span class="label"><span class="fn-bracket">[</span>OMF03<span class="fn-bracket">]</span></span>
+<p>IP Omelyan, IM Mryglod, and R Folk. Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations. <em>Computer Physics Communications</em>, 151(3):272–314, 2003.</p>
+</div>
 <div class="citation" id="id26" role="doc-biblioentry">
 <span class="label"><span class="fn-bracket">[</span>PPJ19<span class="fn-bracket">]</span></span>
 <p>Du Phan, Neeraj Pradhan, and Martin Jankowiak. Composable effects for flexible and accelerated probabilistic programming in numpyro. <em>arXiv preprint arXiv:1912.11554</em>, 2019.</p>
@@ -513,6 +517,10 @@ <h1>Bibliography<a class="headerlink" href="#bibliography" title="Link to this h
 <span class="label"><span class="fn-bracket">[</span>RWD17<span class="fn-bracket">]</span></span>
 <p>Geoffrey Roeder, Yuhuai Wu, and David K Duvenaud. Sticking the landing: simple, lower-variance gradient estimators for variational inference. <em>Advances in Neural Information Processing Systems</em>, 2017.</p>
 </div>
+<div class="citation" id="id53" role="doc-biblioentry">
+<span class="label"><span class="fn-bracket">[</span>TDF06<span class="fn-bracket">]</span></span>
+<p>Tetsuya Takaishi and Philippe De Forcrand. Testing and tuning symplectic integrators for the hybrid monte carlo algorithm in lattice qcd. <em>Physical Review E</em>, 73(3):036706, 2006.</p>
+</div>
 <div class="citation" id="id12" role="doc-biblioentry">
 <span class="label"><span class="fn-bracket">[</span>TP18<span class="fn-bracket">]</span></span>
 <p>Michalis K Titsias and Omiros Papaspiliopoulos. Auxiliary gradient-based sampling algorithms. <em>Journal of the Royal Statistical Society. Series B (Statistical Methodology)</em>, 80(4):749–767, 2018.</p>

examples/howto_metropolis_within_gibbs.html

@@ -604,8 +604,8 @@ <h3>Sampling<a class="headerlink" href="#sampling" title="Link to this heading">
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 932 ms, sys: 77 ms, total: 1.01 s
-Wall time: 1 s
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 961 ms, sys: 51.8 ms, total: 1.01 s
+Wall time: 1.01 s
 </pre></div>
 </div>
 </div>
@@ -743,8 +743,8 @@ <h3>Sampling<a class="headerlink" href="#id2" title="Link to this heading">#</a>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 740 ms, sys: 6.29 ms, total: 746 ms
-Wall time: 737 ms
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 715 ms, sys: 6.94 ms, total: 722 ms
+Wall time: 712 ms
 </pre></div>
 </div>
 </div>

examples/howto_sample_multiple_chains.html

@@ -524,8 +524,8 @@ <h3>Using <code class="docutils literal notranslate"><span class="pre">jax.vmap<
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 15 s, sys: 235 ms, total: 15.2 s
-Wall time: 15.2 s
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 14.8 s, sys: 227 ms, total: 15 s
+Wall time: 15 s
 </pre></div>
 </div>
 </div>
@@ -629,8 +629,8 @@ <h3>Back to our example<a class="headerlink" href="#back-to-our-example" title="
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 16.5 s, sys: 47.7 ms, total: 16.5 s
-Wall time: 5.42 s
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 16.3 s, sys: 66.8 ms, total: 16.4 s
+Wall time: 5.35 s
 </pre></div>
 </div>
 </div>

examples/howto_use_aesara.html

@@ -655,7 +655,7 @@ <h1>Use with Aesara models<a class="headerlink" href="#use-with-aesara-models" t
                |Elemwise{sigmoid,no_inplace} [id FD]
 </pre></div>
 </div>
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;ipykernel.iostream.OutStream at 0x7f3cb4d8ddb0&gt;
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;ipykernel.iostream.OutStream at 0x7f5c723d9db0&gt;
 </pre></div>
 </div>
 </div>

examples/howto_use_oryx.html

@@ -546,8 +546,8 @@ <h1>Use with Oryx models<a class="headerlink" href="#use-with-oryx-models" title
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 18.7 s, sys: 477 ms, total: 19.2 s
-Wall time: 19.1 s
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 17.9 s, sys: 482 ms, total: 18.3 s
+Wall time: 18.3 s
 </pre></div>
 </div>
 </div>
@@ -584,8 +584,8 @@ <h1>Use with Oryx models<a class="headerlink" href="#use-with-oryx-models" title
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 17 s, sys: 193 ms, total: 17.2 s
-Wall time: 17.1 s
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CPU times: user 16.7 s, sys: 153 ms, total: 16.9 s
+Wall time: 16.8 s
 </pre></div>
 </div>
 </div>