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<li><a class="reference internal" href="#">pymatgen.optimization package</a><ul>
<li><a class="reference internal" href="#submodules">Submodules</a></li>
<li><a class="reference internal" href="#module-pymatgen.optimization.linear_assignment">pymatgen.optimization.linear_assignment module</a><ul>
<li><a class="reference internal" href="#pymatgen.optimization.linear_assignment.LinearAssignment"><code class="docutils literal notranslate"><span class="pre">LinearAssignment</span></code></a><ul>
<li><a class="reference internal" href="#pymatgen.optimization.linear_assignment.LinearAssignment.min_cost"><code class="docutils literal notranslate"><span class="pre">LinearAssignment.min_cost</span></code></a></li>
<li><a class="reference internal" href="#pymatgen.optimization.linear_assignment.LinearAssignment.solution"><code class="docutils literal notranslate"><span class="pre">LinearAssignment.solution</span></code></a></li>
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<li><a class="reference internal" href="#module-pymatgen.optimization.neighbors">pymatgen.optimization.neighbors module</a><ul>
<li><a class="reference internal" href="#pymatgen.optimization.neighbors.find_points_in_spheres"><code class="docutils literal notranslate"><span class="pre">find_points_in_spheres()</span></code></a></li>
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<section id="module-pymatgen.optimization">
<span id="pymatgen-optimization-package"></span><h1>pymatgen.optimization package<a class="headerlink" href="#module-pymatgen.optimization" title="Link to this heading"></a></h1>
<p>Optimization utilities.</p>
<section id="submodules">
<h2>Submodules<a class="headerlink" href="#submodules" title="Link to this heading"></a></h2>
</section>
<section id="module-pymatgen.optimization.linear_assignment">
<span id="pymatgen-optimization-linear-assignment-module"></span><h2>pymatgen.optimization.linear_assignment module<a class="headerlink" href="#module-pymatgen.optimization.linear_assignment" title="Link to this heading"></a></h2>
<p>This module contains the LAPJV algorithm to solve the Linear Assignment Problem.</p>
<dl class="py class">
<dt class="sig sig-object py" id="pymatgen.optimization.linear_assignment.LinearAssignment">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">LinearAssignment</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">costs</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">np.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">epsilon</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</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">1e-13</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/optimization/linear_assignment.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.optimization.linear_assignment.LinearAssignment" title="Link to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
<p>This class finds the solution to the Linear Assignment Problem.
It finds a minimum cost matching between two sets, given a cost
matrix.</p>
<p>This class is an implementation of the LAPJV algorithm described in:
R. Jonker, A. Volgenant. A Shortest Augmenting Path Algorithm for
Dense and Sparse Linear Assignment Problems. Computing 38, 325-340
(1987)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>costs</strong> – The cost matrix of the problem. cost[i,j] should be the
cost of matching x[i] to y[j]. The cost matrix may be
rectangular</p></li>
<li><p><strong>epsilon</strong> – Tolerance for determining if solution vector is < 0</p></li>
</ul>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.optimization.linear_assignment.LinearAssignment.min_cost">
<span class="sig-name descname"><span class="pre">min_cost</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/optimization/linear_assignment.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.optimization.linear_assignment.LinearAssignment.min_cost" title="Link to this definition"></a></dt>
<dd><p>The minimum cost of the matching.</p>
</dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="pymatgen.optimization.linear_assignment.LinearAssignment.solution">
<span class="sig-name descname"><span class="pre">solution</span></span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/optimization/linear_assignment.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.optimization.linear_assignment.LinearAssignment.solution" title="Link to this definition"></a></dt>
<dd><p>The matching of the rows to columns. i.e solution = [1, 2, 0]
would match row 0 to column 1, row 1 to column 2 and row 2
to column 0. Total cost would be c[0, 1] + c[1, 2] + c[2, 0].</p>
</dd></dl>
</dd></dl>
</section>
<section id="module-pymatgen.optimization.neighbors">
<span id="pymatgen-optimization-neighbors-module"></span><h2>pymatgen.optimization.neighbors module<a class="headerlink" href="#module-pymatgen.optimization.neighbors" title="Link to this heading"></a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="pymatgen.optimization.neighbors.find_points_in_spheres">
<span class="sig-name descname"><span class="pre">find_points_in_spheres</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">all_coords</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">center_coords</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">r</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pbc</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lattice</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_r</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/materialsproject/pymatgen/blob/v2025.1.24/src/pymatgen/optimization/neighbors.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pymatgen.optimization.neighbors.find_points_in_spheres" title="Link to this definition"></a></dt>
<dd><p>For each point in <cite>center_coords</cite>, get all the neighboring points in <cite>all_coords</cite>
that are within the cutoff radius <cite>r</cite>. All the coordinates should be Cartesian.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>all_coords</strong> – (np.ndarray[double, dim=2]) all available points.
When periodic boundary is considered, this is all the points in the lattice.</p></li>
<li><p><strong>center_coords</strong> – (np.ndarray[double, dim=2]) all centering points</p></li>
<li><p><strong>r</strong> – (float) cutoff radius</p></li>
<li><p><strong>pbc</strong> – (np.ndarray[np.int64_t, dim=1]) whether to set periodic boundaries</p></li>
<li><p><strong>lattice</strong> – (np.ndarray[double, dim=2]) 3x3 lattice matrix</p></li>
<li><p><strong>tol</strong> – (float) numerical tolerance</p></li>
<li><p><strong>min_r</strong> – (float) minimal cutoff to calculate the neighbor list
directly. If the cutoff is less than this value, the algorithm
will calculate neighbor list using min_r as cutoff and discard
those that have larger distances.</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>Indexes of center_coords.
index2 (n, ): Indexes of all_coords that form the neighbor pair.
offset_vectors (n, 3): The periodic image offsets for all_coords.
distances (n, ).</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>index1 (n, )</p>
</dd>
</dl>
</dd></dl>
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