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<!DOCTYPE html>
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<div class="section" id="python-api-documentation">
<h1>Python API documentation<a class="headerlink" href="#python-api-documentation" title="Permalink to this headline">¶</a></h1>
<div class="section" id="module-qml.representations">
<span id="qml-representations-module"></span><h2>qml.representations module<a class="headerlink" href="#module-qml.representations" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="qml.representations.generate_atomic_coulomb_matrix">
<code class="descclassname">qml.representations.</code><code class="descname">generate_atomic_coulomb_matrix</code><span class="sig-paren">(</span><em>nuclear_charges</em>, <em>coordinates</em>, <em>size=23</em>, <em>sorting='distance'</em>, <em>central_cutoff=1000000.0</em>, <em>central_decay=-1</em>, <em>interaction_cutoff=1000000.0</em>, <em>interaction_decay=-1</em>, <em>indices=None</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.representations.generate_atomic_coulomb_matrix" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates a Coulomb Matrix representation of the local environment of a central atom.
For each central atom <span class="math notranslate nohighlight">\(k\)</span>, a matrix <span class="math notranslate nohighlight">\(M\)</span> is constructed with elements</p>
<div class="math notranslate nohighlight">
\[\begin{split}M_{ij}(k) =
\begin{cases}
\tfrac{1}{2} Z_{i}^{2.4} \cdot f_{ik}^2 & \text{if } i = j \\
\frac{Z_{i}Z_{j}}{\| {\bf R}_{i} - {\bf R}_{j}\|} \cdot f_{ik}f_{jk}f_{ij} & \text{if } i \neq j
\end{cases},\end{split}\]</div>
<p>where <span class="math notranslate nohighlight">\(i\)</span>, <span class="math notranslate nohighlight">\(j\)</span> and <span class="math notranslate nohighlight">\(k\)</span> are atom indices, <span class="math notranslate nohighlight">\(Z\)</span> is nuclear charge and
<span class="math notranslate nohighlight">\(\bf R\)</span> is the coordinate in euclidean space.</p>
<p><span class="math notranslate nohighlight">\(f_{ij}\)</span> is a function that masks long range effects:</p>
<div class="math notranslate nohighlight">
\[\begin{split}f_{ij} =
\begin{cases}
1 & \text{if } \|{\bf R}_{i} - {\bf R}_{j} \| \leq r - \Delta r \\
\tfrac{1}{2} \big(1 + \cos\big(\pi \tfrac{\|{\bf R}_{i} - {\bf R}_{j} \|
- r + \Delta r}{\Delta r} \big)\big)
& \text{if } r - \Delta r < \|{\bf R}_{i} - {\bf R}_{j} \| \leq r - \Delta r \\
0 & \text{if } \|{\bf R}_{i} - {\bf R}_{j} \| > r
\end{cases},\end{split}\]</div>
<p>where the parameters <code class="docutils literal notranslate"><span class="pre">central_cutoff</span></code> and <code class="docutils literal notranslate"><span class="pre">central_decay</span></code> corresponds to the variables
<span class="math notranslate nohighlight">\(r\)</span> and <span class="math notranslate nohighlight">\(\Delta r\)</span> respectively for interactions involving the central atom,
and <code class="docutils literal notranslate"><span class="pre">interaction_cutoff</span></code> and <code class="docutils literal notranslate"><span class="pre">interaction_decay</span></code> corresponds to the variables
<span class="math notranslate nohighlight">\(r\)</span> and <span class="math notranslate nohighlight">\(\Delta r\)</span> respectively for interactions not involving the central atom.</p>
<p>if <code class="docutils literal notranslate"><span class="pre">sorting</span> <span class="pre">=</span> <span class="pre">'row-norm'</span></code>, the atom indices are ordered such that</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(\sum_j M_{1j}(k)^2 \geq \sum_j M_{2j}(k)^2 \geq ... \geq \sum_j M_{nj}(k)^2\)</span></div></blockquote>
<p>if <code class="docutils literal notranslate"><span class="pre">sorting</span> <span class="pre">=</span> <span class="pre">'distance'</span></code>, the atom indices are ordered such that</p>
<div class="math notranslate nohighlight">
\[\|{\bf R}_{1} - {\bf R}_{k}\| \leq \|{\bf R}_{2} - {\bf R}_{k}\|
\leq ... \leq \|{\bf R}_{n} - {\bf R}_{k}\|\]</div>
<p>The upper triangular of M, including the diagonal, is concatenated to a 1D
vector representation.</p>
<p>The representation can be calculated for a subset by either specifying
<code class="docutils literal notranslate"><span class="pre">indices</span> <span class="pre">=</span> <span class="pre">[0,1,...]</span></code>, where <span class="math notranslate nohighlight">\([0,1,...]\)</span> are the requested atom indices,
or by specifying <code class="docutils literal notranslate"><span class="pre">indices</span> <span class="pre">=</span> <span class="pre">'C'</span></code> to only calculate central carbon atoms.</p>
<p>The representation is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>nuclear_charges</strong> (<em>numpy array</em>) – Nuclear charges of the atoms in the molecule</li>
<li><strong>coordinates</strong> (<em>numpy array</em>) – 3D Coordinates of the atoms in the molecule</li>
<li><strong>size</strong> (<em>integer</em>) – The size of the largest molecule supported by the representation</li>
<li><strong>sorting</strong> (<em>string</em>) – How the atom indices are sorted (‘row-norm’, ‘distance’)</li>
<li><strong>central_cutoff</strong> (<em>float</em>) – The distance from the central atom, where the coulomb interaction
element will be zero</li>
<li><strong>central_decay</strong> (<em>float</em>) – The distance over which the the coulomb interaction decays from full to none</li>
<li><strong>interaction_cutoff</strong> (<em>float</em>) – The distance between two non-central atom, where the coulomb interaction
element will be zero</li>
<li><strong>interaction_decay</strong> (<em>float</em>) – The distance over which the the coulomb interaction decays from full to none</li>
<li><strong>indices</strong> (<em>Nonetype/array/string</em>) – Subset indices or atomtype</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">nD representation - shape (<span class="math notranslate nohighlight">\(N_{atoms}\)</span>, size(size+1)/2)</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.representations.generate_bob">
<code class="descclassname">qml.representations.</code><code class="descname">generate_bob</code><span class="sig-paren">(</span><em>nuclear_charges</em>, <em>coordinates</em>, <em>atomtypes</em>, <em>size=23</em>, <em>asize={'C': 7</em>, <em>'H': 16</em>, <em>'N': 3</em>, <em>'O': 3</em>, <em>'S': 1}</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.representations.generate_bob" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates a Bag of Bonds (BOB) representation of a molecule.
The representation expands on the coulomb matrix representation.
For each element a bag (vector) is constructed for self interactions
(e.g. (‘C’, ‘H’, ‘O’)).
For each element pair a bag is constructed for interatomic interactions
(e.g. (‘CC’, ‘CH’, ‘CO’, ‘HH’, ‘HO’, ‘OO’)), sorted by value.
The self interaction of element <span class="math notranslate nohighlight">\(I\)</span> is given by</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(\tfrac{1}{2} Z_{I}^{2.4}\)</span>,</div></blockquote>
<p>with <span class="math notranslate nohighlight">\(Z_{i}\)</span> being the nuclear charge of element <span class="math notranslate nohighlight">\(i\)</span>
The interaction between atom <span class="math notranslate nohighlight">\(i\)</span> of element <span class="math notranslate nohighlight">\(I\)</span> and
atom <span class="math notranslate nohighlight">\(j\)</span> of element <span class="math notranslate nohighlight">\(J\)</span> is given by</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(\frac{Z_{I}Z_{J}}{\| {\bf R}_{i} - {\bf R}_{j}\|}\)</span></div></blockquote>
<p>with <span class="math notranslate nohighlight">\(R_{i}\)</span> being the euclidean coordinate of atom <span class="math notranslate nohighlight">\(i\)</span>.
The sorted bags are concatenated to an 1D vector representation.
The representation is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>nuclear_charges</strong> (<em>numpy array</em>) – Nuclear charges of the atoms in the molecule</li>
<li><strong>coordinates</strong> (<em>numpy array</em>) – 3D Coordinates of the atoms in the molecule</li>
<li><strong>size</strong> (<em>integer</em>) – The maximum number of atoms in the representation</li>
<li><strong>asize</strong> (<em>dictionary</em>) – The maximum number of atoms of each element type supported by the representation</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">1D representation</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.representations.generate_coulomb_matrix">
<code class="descclassname">qml.representations.</code><code class="descname">generate_coulomb_matrix</code><span class="sig-paren">(</span><em>nuclear_charges</em>, <em>coordinates</em>, <em>size=23</em>, <em>sorting='row-norm'</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.representations.generate_coulomb_matrix" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates a Coulomb Matrix representation of a molecule.
Sorting of the elements can either be done by <code class="docutils literal notranslate"><span class="pre">sorting="row-norm"</span></code> or <code class="docutils literal notranslate"><span class="pre">sorting="unsorted"</span></code>.
A matrix <span class="math notranslate nohighlight">\(M\)</span> is constructed with elements</p>
<div class="math notranslate nohighlight">
\[\begin{split}M_{ij} =
\begin{cases}
\tfrac{1}{2} Z_{i}^{2.4} & \text{if } i = j \\
\frac{Z_{i}Z_{j}}{\| {\bf R}_{i} - {\bf R}_{j}\|} & \text{if } i \neq j
\end{cases},\end{split}\]</div>
<p>where <span class="math notranslate nohighlight">\(i\)</span> and <span class="math notranslate nohighlight">\(j\)</span> are atom indices, <span class="math notranslate nohighlight">\(Z\)</span> is nuclear charge and
<span class="math notranslate nohighlight">\(\bf R\)</span> is the coordinate in euclidean space.
If <code class="docutils literal notranslate"><span class="pre">sorting</span> <span class="pre">=</span> <span class="pre">'row-norm'</span></code>, the atom indices are reordered such that</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(\sum_j M_{1j}^2 \geq \sum_j M_{2j}^2 \geq ... \geq \sum_j M_{nj}^2\)</span></div></blockquote>
<p>The upper triangular of M, including the diagonal, is concatenated to a 1D
vector representation.</p>
<p>If <code class="docutils literal notranslate"><span class="pre">sorting</span> <span class="pre">=</span> <span class="pre">'unsorted</span></code>, the elements are sorted in the same order as the input coordinates
and nuclear charges.</p>
<p>The representation is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>nuclear_charges</strong> (<em>numpy array</em>) – Nuclear charges of the atoms in the molecule</li>
<li><strong>coordinates</strong> (<em>numpy array</em>) – 3D Coordinates of the atoms in the molecule</li>
<li><strong>size</strong> (<em>integer</em>) – The size of the largest molecule supported by the representation</li>
<li><strong>sorting</strong> (<em>string</em>) – How the atom indices are sorted (‘row-norm’, ‘unsorted’)</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">1D representation - shape (size(size+1)/2,)</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.representations.generate_eigenvalue_coulomb_matrix">
<code class="descclassname">qml.representations.</code><code class="descname">generate_eigenvalue_coulomb_matrix</code><span class="sig-paren">(</span><em>nuclear_charges</em>, <em>coordinates</em>, <em>size=23</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.representations.generate_eigenvalue_coulomb_matrix" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates an eigenvalue Coulomb Matrix representation of a molecule.
A matrix <span class="math notranslate nohighlight">\(M\)</span> is constructed with elements</p>
<div class="math notranslate nohighlight">
\[\begin{split}M_{ij} =
\begin{cases}
\tfrac{1}{2} Z_{i}^{2.4} & \text{if } i = j \\
\frac{Z_{i}Z_{j}}{\| {\bf R}_{i} - {\bf R}_{j}\|} & \text{if } i \neq j
\end{cases},\end{split}\]</div>
<p>where <span class="math notranslate nohighlight">\(i\)</span> and <span class="math notranslate nohighlight">\(j\)</span> are atom indices, <span class="math notranslate nohighlight">\(Z\)</span> is nuclear charge and
<span class="math notranslate nohighlight">\(\bf R\)</span> is the coordinate in euclidean space.
The molecular representation of the molecule is then the sorted eigenvalues of M.
The representation is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>nuclear_charges</strong> (<em>numpy array</em>) – Nuclear charges of the atoms in the molecule</li>
<li><strong>coordinates</strong> (<em>numpy array</em>) – 3D Coordinates of the atoms in the molecule</li>
<li><strong>size</strong> (<em>integer</em>) – The size of the largest molecule supported by the representation</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">1D representation - shape (size, )</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.representations.generate_slatm">
<code class="descclassname">qml.representations.</code><code class="descname">generate_slatm</code><span class="sig-paren">(</span><em>coordinates, nuclear_charges, mbtypes, unit_cell=None, local=False, sigmas=[0.05, 0.05], dgrids=[0.03, 0.03], rcut=4.8, alchemy=False, pbc='000', rpower=6</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.representations.generate_slatm" title="Permalink to this definition">¶</a></dt>
<dd><p>Generate Spectrum of London and Axillrod-Teller-Muto potential (SLATM) representation.
Both global (<code class="docutils literal notranslate"><span class="pre">local=False</span></code>) and local (<code class="docutils literal notranslate"><span class="pre">local=True</span></code>) SLATM are available.</p>
<p>A version that works for periodic boundary conditions will be released soon.</p>
<p>NOTE: You will need to run the <code class="docutils literal notranslate"><span class="pre">get_slatm_mbtypes()</span></code> function to get the <code class="docutils literal notranslate"><span class="pre">mbtypes</span></code> input (or generate it manually).</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>coordinates</strong> (<em>numpy array</em>) – Input coordinates</li>
<li><strong>nuclear_charges</strong> (<em>numpy array</em>) – List of nuclear charges.</li>
<li><strong>mbtypes</strong> (<em>list</em>) – Many-body types for the whole dataset, including 1-, 2- and 3-body types. Could be obtained by calling <code class="docutils literal notranslate"><span class="pre">get_slatm_mbtypes()</span></code>.</li>
<li><strong>local</strong> (<em>bool</em>) – Generate a local representation. Defaulted to False (i.e., global representation); otherwise, atomic version.</li>
<li><strong>sigmas</strong> (<em>list</em>) – Controlling the width of Gaussian smearing function for 2- and 3-body parts, defaulted to [0.05,0.05], usually these do not need to be adjusted.</li>
<li><strong>dgrids</strong> (<em>list</em>) – The interval between two sampled internuclear distances and angles, defaulted to [0.03,0.03], no need for change, compromised for speed and accuracy.</li>
<li><strong>rcut</strong> (<em>float</em>) – Cut-off radius, defaulted to 4.8 Angstrom.</li>
<li><strong>alchemy</strong> (<em>bool</em>) – Swith to use the alchemy version of SLATM. (default=False)</li>
<li><strong>pbc</strong> (<em>string</em>) – defaulted to ‘000’, meaning it’s a molecule; the three digits in the string corresponds to x,y,z direction</li>
<li><strong>rpower</strong> (<em>float</em>) – The power of R in 2-body potential, defaulted to London potential (=6).</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">1D SLATM representation</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.representations.get_slatm_mbtypes">
<code class="descclassname">qml.representations.</code><code class="descname">get_slatm_mbtypes</code><span class="sig-paren">(</span><em>nuclear_charges</em>, <em>pbc='000'</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.representations.get_slatm_mbtypes" title="Permalink to this definition">¶</a></dt>
<dd><p>Get the list of minimal types of many-body terms in a dataset. This resulting list
is necessary as input in the <code class="docutils literal notranslate"><span class="pre">generate_slatm_representation()</span></code> function.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>nuclear_charges</strong> (<em>list of numpy arrays</em>) – A list of the nuclear charges for each compound in the dataset.</li>
<li><strong>pbc</strong> (<em>string</em>) – periodic boundary condition along x,y,z direction, defaulted to ‘000’, i.e., molecule</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">A list containing the types of many-body terms.</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">list</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.representations.vector_to_matrix">
<code class="descclassname">qml.representations.</code><code class="descname">vector_to_matrix</code><span class="sig-paren">(</span><em>v</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.representations.vector_to_matrix" title="Permalink to this definition">¶</a></dt>
<dd><p>Converts a representation from 1D vector to 2D square matrix.
:param v: 1D input representation.
:type v: numpy array
:return: Square matrix representation.
:rtype: numpy array</p>
</dd></dl>
</div>
<div class="section" id="module-qml.kernels">
<span id="qml-kernels-module"></span><h2>qml.kernels module<a class="headerlink" href="#module-qml.kernels" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="qml.kernels.gaussian_kernel">
<code class="descclassname">qml.kernels.</code><code class="descname">gaussian_kernel</code><span class="sig-paren">(</span><em>A</em>, <em>B</em>, <em>sigma</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.kernels.gaussian_kernel" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the Gaussian kernel matrix K, where <span class="math notranslate nohighlight">\(K_{ij}\)</span>:</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(K_{ij} = \exp \big( -\frac{\|A_i - B_j\|_2^2}{2\sigma^2} \big)\)</span></div></blockquote>
<p>Where <span class="math notranslate nohighlight">\(A_{i}\)</span> and <span class="math notranslate nohighlight">\(B_{j}\)</span> are representation vectors.
K is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – 2D array of representations - shape (N, representation size).</li>
<li><strong>B</strong> (<em>numpy array</em>) – 2D array of representations - shape (M, representation size).</li>
<li><strong>sigma</strong> (<em>float</em>) – The value of sigma in the kernel matrix.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The Gaussian kernel matrix - shape (N, M)</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.kernels.get_local_kernels_gaussian">
<code class="descclassname">qml.kernels.</code><code class="descname">get_local_kernels_gaussian</code><span class="sig-paren">(</span><em>A</em>, <em>B</em>, <em>na</em>, <em>nb</em>, <em>sigmas</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.kernels.get_local_kernels_gaussian" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the Gaussian kernel matrix K, for a local representation where <span class="math notranslate nohighlight">\(K_{ij}\)</span>:</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(K_{ij} = \sum_{a \in i} \sum_{b \in j} \exp \big( -\frac{\|A_a - B_b\|_2^2}{2\sigma^2} \big)\)</span></div></blockquote>
<p>Where <span class="math notranslate nohighlight">\(A_{a}\)</span> and <span class="math notranslate nohighlight">\(B_{b}\)</span> are representation vectors.</p>
<p>Note that the input array is one big 2D array with all atoms concatenated along the same axis.
Further more a series of kernels is produced (since calculating the distance matrix is expensive
but getting the resulting kernels elements for several sigmas is not.)</p>
<p>K is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – 2D array of descriptors - shape (total atoms A, representation size).</li>
<li><strong>B</strong> (<em>numpy array</em>) – 2D array of descriptors - shape (total atoms B, representation size).</li>
<li><strong>na</strong> (<em>numpy array</em>) – 1D array containing numbers of atoms in each compound.</li>
<li><strong>nb</strong> (<em>numpy array</em>) – 1D array containing numbers of atoms in each compound.</li>
<li><strong>sigma</strong> (<em>float</em>) – The value of sigma in the kernel matrix.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The Gaussian kernel matrix - shape (nsigmas, N, M)</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.kernels.get_local_kernels_laplacian">
<code class="descclassname">qml.kernels.</code><code class="descname">get_local_kernels_laplacian</code><span class="sig-paren">(</span><em>A</em>, <em>B</em>, <em>na</em>, <em>nb</em>, <em>sigmas</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.kernels.get_local_kernels_laplacian" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the Local Laplacian kernel matrix K, for a local representation where <span class="math notranslate nohighlight">\(K_{ij}\)</span>:</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(K_{ij} = \sum_{a \in i} \sum_{b \in j} \exp \big( -\frac{\|A_a - B_b\|_1}{\sigma} \big)\)</span></div></blockquote>
<p>Where <span class="math notranslate nohighlight">\(A_{a}\)</span> and <span class="math notranslate nohighlight">\(B_{b}\)</span> are representation vectors.</p>
<p>Note that the input array is one big 2D array with all atoms concatenated along the same axis.
Further more a series of kernels is produced (since calculating the distance matrix is expensive
but getting the resulting kernels elements for several sigmas is not.)</p>
<p>K is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – 2D array of descriptors - shape (N, representation size).</li>
<li><strong>B</strong> (<em>numpy array</em>) – 2D array of descriptors - shape (M, representation size).</li>
<li><strong>na</strong> (<em>numpy array</em>) – 1D array containing numbers of atoms in each compound.</li>
<li><strong>nb</strong> (<em>numpy array</em>) – 1D array containing numbers of atoms in each compound.</li>
<li><strong>sigmas</strong> (<em>list</em>) – List of the sigmas.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The Laplacian kernel matrix - shape (nsigmas, N, M)</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.kernels.laplacian_kernel">
<code class="descclassname">qml.kernels.</code><code class="descname">laplacian_kernel</code><span class="sig-paren">(</span><em>A</em>, <em>B</em>, <em>sigma</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.kernels.laplacian_kernel" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the Laplacian kernel matrix K, where <span class="math notranslate nohighlight">\(K_{ij}\)</span>:</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(K_{ij} = \exp \big( -\frac{\|A_i - B_j\|_1}{\sigma} \big)\)</span></div></blockquote>
<p>Where <span class="math notranslate nohighlight">\(A_{i}\)</span> and <span class="math notranslate nohighlight">\(B_{j}\)</span> are representation vectors.
K is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – 2D array of representations - shape (N, representation size).</li>
<li><strong>B</strong> (<em>numpy array</em>) – 2D array of representations - shape (M, representation size).</li>
<li><strong>sigma</strong> (<em>float</em>) – The value of sigma in the kernel matrix.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The Laplacian kernel matrix - shape (N, M)</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.kernels.linear_kernel">
<code class="descclassname">qml.kernels.</code><code class="descname">linear_kernel</code><span class="sig-paren">(</span><em>A</em>, <em>B</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.kernels.linear_kernel" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the linear kernel matrix K, where <span class="math notranslate nohighlight">\(K_{ij}\)</span>:</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(K_{ij} = A_i \cdot B_j\)</span></div></blockquote>
<p>VWhere <span class="math notranslate nohighlight">\(A_{i}\)</span> and <span class="math notranslate nohighlight">\(B_{j}\)</span> are representation vectors.</p>
<p>K is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – 2D array of representations - shape (N, representation size).</li>
<li><strong>B</strong> (<em>numpy array</em>) – 2D array of representations - shape (M, representation size).</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The Gaussian kernel matrix - shape (N, M)</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.kernels.matern_kernel">
<code class="descclassname">qml.kernels.</code><code class="descname">matern_kernel</code><span class="sig-paren">(</span><em>A</em>, <em>B</em>, <em>sigma</em>, <em>order=0</em>, <em>metric='l1'</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.kernels.matern_kernel" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the Matern kernel matrix K, where <span class="math notranslate nohighlight">\(K_{ij}\)</span>:</p>
<blockquote>
<div><dl class="docutils">
<dt>for order = 0:</dt>
<dd><span class="math notranslate nohighlight">\(K_{ij} = \exp\big( -\frac{d}{\sigma} \big)\)</span></dd>
<dt>for order = 1:</dt>
<dd><span class="math notranslate nohighlight">\(K_{ij} = \exp\big( -\frac{\sqrt{3} d}{\sigma} \big) \big(1 + \frac{\sqrt{3} d}{\sigma} \big)\)</span></dd>
<dt>for order = 2:</dt>
<dd><span class="math notranslate nohighlight">\(K_{ij} = \exp\big( -\frac{\sqrt{5} d}{d} \big) \big( 1 + \frac{\sqrt{5} d}{\sigma} + \frac{5 d^2}{3\sigma^2} \big)\)</span></dd>
</dl>
</div></blockquote>
<p>Where <span class="math notranslate nohighlight">\(A_i\)</span> and <span class="math notranslate nohighlight">\(B_j\)</span> are representation vectors, and d is a distance measure.</p>
<p>K is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – 2D array of representations - shape (N, representation size).</li>
<li><strong>B</strong> (<em>numpy array</em>) – 2D array of representations - shape (M, representation size).</li>
<li><strong>sigma</strong> (<em>float</em>) – The value of sigma in the kernel matrix.</li>
<li><strong>order</strong> (<em>integer</em>) – The order of the polynomial (0, 1, 2)</li>
<li><strong>metric</strong> (<em>string</em>) – The distance metric (‘l1’, ‘l2’)</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The Matern kernel matrix - shape (N, M)</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.kernels.sargan_kernel">
<code class="descclassname">qml.kernels.</code><code class="descname">sargan_kernel</code><span class="sig-paren">(</span><em>A</em>, <em>B</em>, <em>sigma</em>, <em>gammas</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.kernels.sargan_kernel" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the Sargan kernel matrix K, where <span class="math notranslate nohighlight">\(K_{ij}\)</span>:</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(K_{ij} = \exp \big( -\frac{\| A_i - B_j \|_1)}{\sigma} \big) \big(1 + \sum_{k} \frac{\gamma_{k} \| A_i - B_j \|_1^k}{\sigma^k} \big)\)</span></div></blockquote>
<p>Where <span class="math notranslate nohighlight">\(A_{i}\)</span> and <span class="math notranslate nohighlight">\(B_{j}\)</span> are representation vectors.
K is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – 2D array of representations - shape (N, representation size).</li>
<li><strong>B</strong> (<em>numpy array</em>) – 2D array of representations - shape (M, representation size).</li>
<li><strong>sigma</strong> (<em>float</em>) – The value of sigma in the kernel matrix.</li>
<li><strong>gammas</strong> (<em>numpy array</em>) – 1D array of parameters in the kernel matrix.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The Sargan kernel matrix - shape (N, M).</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</div>
<div class="section" id="module-qml.distance">
<span id="qml-distance-module"></span><h2>qml.distance module<a class="headerlink" href="#module-qml.distance" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="qml.distance.l2_distance">
<code class="descclassname">qml.distance.</code><code class="descname">l2_distance</code><span class="sig-paren">(</span><em>A</em>, <em>B</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.distance.l2_distance" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the L2 distances, D, between two
Numpy arrays of representations.</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(D_{ij} = \|A_i - B_j\|_2\)</span></div></blockquote>
<p>Where <span class="math notranslate nohighlight">\(A_{i}\)</span> and <span class="math notranslate nohighlight">\(B_{j}\)</span> are representation vectors.
D is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – 2D array of descriptors - shape (N, representation size).</li>
<li><strong>B</strong> (<em>numpy array</em>) – 2D array of descriptors - shape (M, representation size).</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The L2-distance matrix.</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.distance.manhattan_distance">
<code class="descclassname">qml.distance.</code><code class="descname">manhattan_distance</code><span class="sig-paren">(</span><em>A</em>, <em>B</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.distance.manhattan_distance" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the Manhattan distances, D, between two
Numpy arrays of representations.</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(D_{ij} = \|A_i - B_j\|_1\)</span></div></blockquote>
<p>Where <span class="math notranslate nohighlight">\(A_{i}\)</span> and <span class="math notranslate nohighlight">\(B_{j}\)</span> are representation vectors.
D is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – 2D array of descriptors - shape (N, representation size).</li>
<li><strong>B</strong> (<em>numpy array</em>) – 2D array of descriptors - shape (M, representation size).</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The Manhattan-distance matrix.</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.distance.p_distance">
<code class="descclassname">qml.distance.</code><code class="descname">p_distance</code><span class="sig-paren">(</span><em>A</em>, <em>B</em>, <em>p=2</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.distance.p_distance" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the p-norm distances between two
Numpy arrays of representations.
The value of the keyword argument <code class="docutils literal notranslate"><span class="pre">p</span> <span class="pre">=</span></code> sets the norm order.
E.g. <code class="docutils literal notranslate"><span class="pre">p</span> <span class="pre">=</span> <span class="pre">1.0</span></code> and <code class="docutils literal notranslate"><span class="pre">p</span> <span class="pre">=</span> <span class="pre">2.0</span></code> with yield the Manhattan and L2 distances, respectively.</p>
<blockquote>
<div><div class="math notranslate nohighlight">
\[D_{ij} = \|A_i - B_j\|_p\]</div>
</div></blockquote>
<p>Where <span class="math notranslate nohighlight">\(A_{i}\)</span> and <span class="math notranslate nohighlight">\(B_{j}\)</span> are representation vectors.
D is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – 2D array of descriptors - shape (N, representation size).</li>
<li><strong>B</strong> (<em>numpy array</em>) – 2D array of descriptors - shape (M, representation size).</li>
<li><strong>p</strong> (<em>float</em>) – The norm order</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The distance matrix.</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</div>
<div class="section" id="module-qml.math">
<span id="qml-math-module"></span><h2>qml.math module<a class="headerlink" href="#module-qml.math" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="qml.math.bkf_invert">
<code class="descclassname">qml.math.</code><code class="descname">bkf_invert</code><span class="sig-paren">(</span><em>A</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.math.bkf_invert" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the inverse of a positive definite matrix, using a Cholesky decomposition
via calls to LAPACK dpotrf and dpotri in the F2PY module.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>A</strong> (<em>numpy array</em>) – Matrix (symmetric and positive definite, left-hand side).</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">The inverse matrix</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body">numpy array</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.math.bkf_solve">
<code class="descclassname">qml.math.</code><code class="descname">bkf_solve</code><span class="sig-paren">(</span><em>A</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.math.bkf_solve" title="Permalink to this definition">¶</a></dt>
<dd><p>Solves the equation</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(A x = y\)</span></div></blockquote>
<p>for x using a Cholesky decomposition via calls to LAPACK dpotrf and dpotrs in the F2PY module. Preserves the input matrix A.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – Matrix (symmetric and positive definite, left-hand side).</li>
<li><strong>y</strong> (<em>numpy array</em>) – Vector (right-hand side of the equation).</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The solution vector.</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.math.cho_invert">
<code class="descclassname">qml.math.</code><code class="descname">cho_invert</code><span class="sig-paren">(</span><em>A</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.math.cho_invert" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the inverse of a positive definite matrix, using a Cholesky decomposition
via calls to LAPACK dpotrf and dpotri in the F2PY module.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>A</strong> (<em>numpy array</em>) – Matrix (symmetric and positive definite, left-hand side).</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">The inverse matrix</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body">numpy array</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="qml.math.cho_solve">
<code class="descclassname">qml.math.</code><code class="descname">cho_solve</code><span class="sig-paren">(</span><em>A</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.math.cho_solve" title="Permalink to this definition">¶</a></dt>
<dd><p>Solves the equation</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(A x = y\)</span></div></blockquote>
<p>for x using a Cholesky decomposition via calls to LAPACK dpotrf and dpotrs in the F2PY module. Preserves the input matrix A.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>A</strong> (<em>numpy array</em>) – Matrix (symmetric and positive definite, left-hand side).</li>
<li><strong>y</strong> (<em>numpy array</em>) – Vector (right-hand side of the equation).</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The solution vector.</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</div>
<div class="section" id="qml-compound-class">
<h2>qml.Compound class<a class="headerlink" href="#qml-compound-class" title="Permalink to this headline">¶</a></h2>
<dl class="class">
<dt id="qml.Compound">
<em class="property">class </em><code class="descclassname">qml.</code><code class="descname">Compound</code><span class="sig-paren">(</span><em>xyz=None</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.Compound" title="Permalink 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>The <code class="docutils literal notranslate"><span class="pre">Compound</span></code> class is used to store data from</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>xyz</strong> (<em>string</em>) – Option to initialize the <code class="docutils literal notranslate"><span class="pre">Compound</span></code> with data from an XYZ file.</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="qml.Compound.generate_atomic_coulomb_matrix">
<code class="descname">generate_atomic_coulomb_matrix</code><span class="sig-paren">(</span><em>size=23</em>, <em>sorting='row-norm'</em>, <em>central_cutoff=1000000.0</em>, <em>central_decay=-1</em>, <em>interaction_cutoff=1000000.0</em>, <em>interaction_decay=-1</em>, <em>indices=None</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.Compound.generate_atomic_coulomb_matrix" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates a Coulomb Matrix representation of the local environment of a central atom.
For each central atom <span class="math notranslate nohighlight">\(k\)</span>, a matrix <span class="math notranslate nohighlight">\(M\)</span> is constructed with elements</p>
<div class="math notranslate nohighlight">
\[\begin{split}M_{ij}(k) =
\begin{cases}
\tfrac{1}{2} Z_{i}^{2.4} \cdot f_{ik}^2 & \text{if } i = j \\
\frac{Z_{i}Z_{j}}{\| {\bf R}_{i} - {\bf R}_{j}\|} \cdot f_{ik}f_{jk}f_{ij} & \text{if } i \neq j
\end{cases},\end{split}\]</div>
<p>where <span class="math notranslate nohighlight">\(i\)</span>, <span class="math notranslate nohighlight">\(j\)</span> and <span class="math notranslate nohighlight">\(k\)</span> are atom indices, <span class="math notranslate nohighlight">\(Z\)</span> is nuclear charge and
<span class="math notranslate nohighlight">\(\bf R\)</span> is the coordinate in euclidean space.</p>
<p><span class="math notranslate nohighlight">\(f_{ij}\)</span> is a function that masks long range effects:</p>
<div class="math notranslate nohighlight">
\[\begin{split}f_{ij} =
\begin{cases}
1 & \text{if } \|{\bf R}_{i} - {\bf R}_{j} \| \leq r - \Delta r \\
\tfrac{1}{2} \big(1 + \cos\big(\pi \tfrac{\|{\bf R}_{i} - {\bf R}_{j} \|
- r + \Delta r}{\Delta r} \big)\big)
& \text{if } r - \Delta r < \|{\bf R}_{i} - {\bf R}_{j} \| \leq r - \Delta r \\
0 & \text{if } \|{\bf R}_{i} - {\bf R}_{j} \| > r
\end{cases},\end{split}\]</div>
<p>where the parameters <code class="docutils literal notranslate"><span class="pre">central_cutoff</span></code> and <code class="docutils literal notranslate"><span class="pre">central_decay</span></code> corresponds to the variables
<span class="math notranslate nohighlight">\(r\)</span> and <span class="math notranslate nohighlight">\(\Delta r\)</span> respectively for interactions involving the central atom,
and <code class="docutils literal notranslate"><span class="pre">interaction_cutoff</span></code> and <code class="docutils literal notranslate"><span class="pre">interaction_decay</span></code> corresponds to the variables
<span class="math notranslate nohighlight">\(r\)</span> and <span class="math notranslate nohighlight">\(\Delta r\)</span> respectively for interactions not involving the central atom.</p>
<p>if <code class="docutils literal notranslate"><span class="pre">sorting</span> <span class="pre">=</span> <span class="pre">'row-norm'</span></code>, the atom indices are ordered such that</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(\sum_j M_{1j}(k)^2 \geq \sum_j M_{2j}(k)^2 \geq ... \geq \sum_j M_{nj}(k)^2\)</span></div></blockquote>
<p>if <code class="docutils literal notranslate"><span class="pre">sorting</span> <span class="pre">=</span> <span class="pre">'distance'</span></code>, the atom indices are ordered such that</p>
<div class="math notranslate nohighlight">
\[\|{\bf R}_{1} - {\bf R}_{k}\| \leq \|{\bf R}_{2} - {\bf R}_{k}\|
\leq ... \leq \|{\bf R}_{n} - {\bf R}_{k}\|\]</div>
<p>The upper triangular of M, including the diagonal, is concatenated to a 1D
vector representation.</p>
<p>The representation can be calculated for a subset by either specifying
<code class="docutils literal notranslate"><span class="pre">indices</span> <span class="pre">=</span> <span class="pre">[0,1,...]</span></code>, where <span class="math notranslate nohighlight">\([0,1,...]\)</span> are the requested atom indices,
or by specifying <code class="docutils literal notranslate"><span class="pre">indices</span> <span class="pre">=</span> <span class="pre">'C'</span></code> to only calculate central carbon atoms.</p>
<p>The representation is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>size</strong> (<em>integer</em>) – The size of the largest molecule supported by the representation</li>
<li><strong>sorting</strong> (<em>string</em>) – How the atom indices are sorted (‘row-norm’, ‘distance’)</li>
<li><strong>central_cutoff</strong> (<em>float</em>) – The distance from the central atom, where the coulomb interaction
element will be zero</li>
<li><strong>central_decay</strong> (<em>float</em>) – The distance over which the the coulomb interaction decays from full to none</li>
<li><strong>interaction_cutoff</strong> (<em>float</em>) – The distance between two non-central atom, where the coulomb interaction
element will be zero</li>
<li><strong>interaction_decay</strong> (<em>float</em>) – The distance over which the the coulomb interaction decays from full to none</li>
<li><strong>indices</strong> (<em>Nonetype/array/string</em>) – Subset indices or atomtype</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">nD representation - shape (<span class="math notranslate nohighlight">\(N_{atoms}\)</span>, size(size+1)/2)</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="qml.Compound.generate_bob">
<code class="descname">generate_bob</code><span class="sig-paren">(</span><em>size=23</em>, <em>asize={'C': 7</em>, <em>'H': 16</em>, <em>'N': 3</em>, <em>'O': 3</em>, <em>'S': 1}</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.Compound.generate_bob" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates a Bag of Bonds (BOB) representation of a molecule.
The representation expands on the coulomb matrix representation.
For each element a bag (vector) is constructed for self interactions
(e.g. (‘C’, ‘H’, ‘O’)).
For each element pair a bag is constructed for interatomic interactions
(e.g. (‘CC’, ‘CH’, ‘CO’, ‘HH’, ‘HO’, ‘OO’)), sorted by value.
The self interaction of element <span class="math notranslate nohighlight">\(I\)</span> is given by</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(\tfrac{1}{2} Z_{I}^{2.4}\)</span>,</div></blockquote>
<p>with <span class="math notranslate nohighlight">\(Z_{i}\)</span> being the nuclear charge of element <span class="math notranslate nohighlight">\(i\)</span>
The interaction between atom <span class="math notranslate nohighlight">\(i\)</span> of element <span class="math notranslate nohighlight">\(I\)</span> and
atom <span class="math notranslate nohighlight">\(j\)</span> of element <span class="math notranslate nohighlight">\(J\)</span> is given by</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(\frac{Z_{I}Z_{J}}{\| {\bf R}_{i} - {\bf R}_{j}\|}\)</span></div></blockquote>
<p>with <span class="math notranslate nohighlight">\(R_{i}\)</span> being the euclidean coordinate of atom <span class="math notranslate nohighlight">\(i\)</span>.
The sorted bags are concatenated to an 1D vector representation.
The representation is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>asize</strong> – The maximum number of atoms of each element type supported by the representation</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">1D representation</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body">numpy array</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="qml.Compound.generate_coulomb_matrix">
<code class="descname">generate_coulomb_matrix</code><span class="sig-paren">(</span><em>size=23</em>, <em>sorting='row-norm'</em>, <em>indices=None</em><span class="sig-paren">)</span><a class="headerlink" href="#qml.Compound.generate_coulomb_matrix" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates a Coulomb Matrix representation of a molecule.
A matrix <span class="math notranslate nohighlight">\(M\)</span> is constructed with elements</p>
<div class="math notranslate nohighlight">
\[\begin{split}M_{ij} =
\begin{cases}
\tfrac{1}{2} Z_{i}^{2.4} & \text{if } i = j \\
\frac{Z_{i}Z_{j}}{\| {\bf R}_{i} - {\bf R}_{j}\|} & \text{if } i \neq j
\end{cases},\end{split}\]</div>
<p>where <span class="math notranslate nohighlight">\(i\)</span> and <span class="math notranslate nohighlight">\(j\)</span> are atom indices, <span class="math notranslate nohighlight">\(Z\)</span> is nuclear charge and
<span class="math notranslate nohighlight">\(\bf R\)</span> is the coordinate in euclidean space.
if <code class="docutils literal notranslate"><span class="pre">sorting</span> <span class="pre">=</span> <span class="pre">'row-norm'</span></code>, the atom indices are reordered such that</p>
<blockquote>
<div><span class="math notranslate nohighlight">\(\sum_j M_{1j}^2 \geq \sum_j M_{2j}^2 \geq ... \geq \sum_j M_{nj}^2\)</span></div></blockquote>
<p>The upper triangular of M, including the diagonal, is concatenated to a 1D
vector representation.
The representation is calculated using an OpenMP parallel Fortran routine.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>size</strong> (<em>integer</em>) – The size of the largest molecule supported by the representation</li>
<li><strong>sorting</strong> (<em>string</em>) – How the atom indices are sorted (‘row-norm’, ‘unsorted’)</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">1D representation - shape (size(size+1)/2,)</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">numpy array</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">