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<li class="toctree-l4"><a class="reference internal" href="#grogupy.utilities.RotM"><code class="docutils literal notranslate"><span class="pre">RotM()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#grogupy.utilities.RotMa2b"><code class="docutils literal notranslate"><span class="pre">RotMa2b()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#grogupy.utilities.commutator"><code class="docutils literal notranslate"><span class="pre">commutator()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#grogupy.utilities.crossM"><code class="docutils literal notranslate"><span class="pre">crossM()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#grogupy.utilities.hsk"><code class="docutils literal notranslate"><span class="pre">hsk()</span></code></a></li>
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<li class="toctree-l4"><a class="reference internal" href="#grogupy.utilities.read_siesta_emin"><code class="docutils literal notranslate"><span class="pre">read_siesta_emin()</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#grogupy.utilities.tau_u"><code class="docutils literal notranslate"><span class="pre">tau_u()</span></code></a></li>
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<section id="module-grogupy.utilities">
<span id="grogupy-utilities-module"></span><h1>grogupy.utilities module<a class="headerlink" href="#module-grogupy.utilities" title="Link to this heading"></a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="grogupy.utilities.RotM">
<span class="sig-prename descclassname"><span class="pre">grogupy.utilities.</span></span><span class="sig-name descname"><span class="pre">RotM</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">theta</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">u</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-10</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/grogupy/utilities.html#RotM"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#grogupy.utilities.RotM" title="Link to this definition"></a></dt>
<dd><p>Definition of rotation matrix with angle theta around direction u.</p>
<dl class="simple">
<dt>Args:</dt><dd><dl class="simple">
<dt>theta<span class="classifier">float</span></dt><dd><p>The angle of rotation</p>
</dd>
<dt>u<span class="classifier">np.array_like</span></dt><dd><p>The rotation axis</p>
</dd>
<dt>eps<span class="classifier">float, optional</span></dt><dd><p>Cutoff for small elements in the resulting matrix. Defaults to 1e-10</p>
</dd>
</dl>
</dd>
<dt>Returns:</dt><dd><dl class="simple">
<dt>np.array_like</dt><dd><p>The rotation matrix</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="grogupy.utilities.RotMa2b">
<span class="sig-prename descclassname"><span class="pre">grogupy.utilities.</span></span><span class="sig-name descname"><span class="pre">RotMa2b</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-10</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/grogupy/utilities.html#RotMa2b"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#grogupy.utilities.RotMa2b" title="Link to this definition"></a></dt>
<dd><p>Definition of rotation matrix rotating unit vector a to unit vector b.</p>
<p>Function returns array R such that R &#64; a = b holds.</p>
<dl class="simple">
<dt>Args:</dt><dd><dl class="simple">
<dt>a<span class="classifier">np.array_like</span></dt><dd><p>First vector</p>
</dd>
<dt>b<span class="classifier">np.array_like</span></dt><dd><p>Second vector</p>
</dd>
<dt>eps<span class="classifier">float, optional</span></dt><dd><p>Cutoff for small elements in the resulting matrix. Defaults to 1e-10</p>
</dd>
</dl>
</dd>
<dt>Returns:</dt><dd><dl class="simple">
<dt>np.array_like</dt><dd><p>The rotation matrix with the above property</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="grogupy.utilities.commutator">
<span class="sig-prename descclassname"><span class="pre">grogupy.utilities.</span></span><span class="sig-name descname"><span class="pre">commutator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/grogupy/utilities.html#commutator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#grogupy.utilities.commutator" title="Link to this definition"></a></dt>
<dd><p>Shorthand for commutator.</p>
<p>Commutator of two matrices in the mathematical sense.</p>
<dl class="simple">
<dt>Args:</dt><dd><dl class="simple">
<dt>a<span class="classifier">np.array_like</span></dt><dd><p>The first matrix</p>
</dd>
<dt>b<span class="classifier">np.array_like</span></dt><dd><p>The second matrix</p>
</dd>
</dl>
</dd>
<dt>Returns:</dt><dd><dl class="simple">
<dt>np.array_like</dt><dd><p>The commutator of a and b</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="grogupy.utilities.crossM">
<span class="sig-prename descclassname"><span class="pre">grogupy.utilities.</span></span><span class="sig-name descname"><span class="pre">crossM</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">u</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/grogupy/utilities.html#crossM"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#grogupy.utilities.crossM" title="Link to this definition"></a></dt>
<dd><p>Definition for the cross-product matrix.</p>
<p>It acts as a cross product with vector u.</p>
<dl class="simple">
<dt>Args:</dt><dd><dl class="simple">
<dt>u<span class="classifier">list or np.array_like</span></dt><dd><p>The second vector in the cross product</p>
</dd>
</dl>
</dd>
<dt>Returns:</dt><dd><dl class="simple">
<dt>np.array_like</dt><dd><p>The matrix that represents teh cross product with a vector</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="grogupy.utilities.hsk">
<span class="sig-prename descclassname"><span class="pre">grogupy.utilities.</span></span><span class="sig-name descname"><span class="pre">hsk</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">H</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ss</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sc_off</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">k</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(0,</span> <span class="pre">0,</span> <span class="pre">0)</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/grogupy/utilities.html#hsk"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#grogupy.utilities.hsk" title="Link to this definition"></a></dt>
<dd><p>Speed up Hk and Sk generation.</p>
<p>Calculates the Hamiltonian and the Overlap matrix at a given k point. It is faster that the sisl version.</p>
<dl class="simple">
<dt>Args:</dt><dd><dl class="simple">
<dt>H<span class="classifier">np.array_like</span></dt><dd><p>Hamiltonian in spin box form</p>
</dd>
<dt>ss<span class="classifier">np.array_like</span></dt><dd><p>Overlap matrix in spin box form</p>
</dd>
<dt>sc_off<span class="classifier">list</span></dt><dd><p>supercell indexes of the Hamiltonian</p>
</dd>
<dt>k<span class="classifier">tuple, optional</span></dt><dd><p>The k point where the matrices are set up. Defaults to (0, 0, 0)</p>
</dd>
</dl>
</dd>
<dt>Returns:</dt><dd><dl class="simple">
<dt>np.array_like</dt><dd><p>Hamiltonian at the given k point</p>
</dd>
<dt>np.array_like</dt><dd><p>Overlap matrix at the given k point</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="grogupy.utilities.int_de_ke">
<span class="sig-prename descclassname"><span class="pre">grogupy.utilities.</span></span><span class="sig-name descname"><span class="pre">int_de_ke</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">traced</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">we</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/grogupy/utilities.html#int_de_ke"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#grogupy.utilities.int_de_ke" title="Link to this definition"></a></dt>
<dd><p>It numerically integrates the traced matrix.</p>
<p>It is a wrapper from numpy.trapz and it contains the
relevant constants to calculate the energy integral from
equation 93 or 96.</p>
<dl class="simple">
<dt>Args:</dt><dd><dl class="simple">
<dt>traced<span class="classifier">np.array_like</span></dt><dd><p>The trace of a matrix or a matrix product</p>
</dd>
<dt>we<span class="classifier">float</span></dt><dd><p>The weight of a point on the contour</p>
</dd>
</dl>
</dd>
<dt>Returns:</dt><dd><dl class="simple">
<dt>float</dt><dd><p>The energy calculated from the integral formula</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="grogupy.utilities.make_contour">
<span class="sig-prename descclassname"><span class="pre">grogupy.utilities.</span></span><span class="sig-name descname"><span class="pre">make_contour</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">emin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">-20</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">emax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enum</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">42</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">150</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/grogupy/utilities.html#make_contour"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#grogupy.utilities.make_contour" title="Link to this definition"></a></dt>
<dd><p>A more sophisticated contour generator.</p>
<p>Calculates the parameters for the complex contour integral. It uses the
Legendre-Gauss quadrature method. It returns a class that contains
the information for the contour integral.</p>
<dl class="simple">
<dt>Args:</dt><dd><dl class="simple">
<dt>emin<span class="classifier">int, optional</span></dt><dd><p>Energy minimum of the contour. Defaults to -20</p>
</dd>
<dt>emax<span class="classifier">float, optional</span></dt><dd><p>Energy maximum of the contour. Defaults to 0.0, so the Fermi level</p>
</dd>
<dt>enum<span class="classifier">int, optional</span></dt><dd><p>Number of sample points along the contour. Defaults to 42</p>
</dd>
<dt>p<span class="classifier">int, optional</span></dt><dd><p>Shape parameter that describes the distribution of the sample points. Defaults to 150</p>
</dd>
</dl>
</dd>
<dt>Returns:</dt><dd><dl class="simple">
<dt>ccont</dt><dd><p>Contains all the information for the contour integral</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="grogupy.utilities.make_kset">
<span class="sig-prename descclassname"><span class="pre">grogupy.utilities.</span></span><span class="sig-name descname"><span class="pre">make_kset</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dirs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'xyz'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">NUMK</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/grogupy/utilities.html#make_kset"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#grogupy.utilities.make_kset" title="Link to this definition"></a></dt>
<dd><p>Simple k-grid generator to sample the Brillouin zone.</p>
<p>Depending on the value of the dirs
argument k sampling in 1,2 or 3 dimensions is generated.
If dirs argument does not contain either of x, y or z
a kset of a single k-pont at the origin is returned. The total number of k points is the NUMK**(dimensions)</p>
<dl class="simple">
<dt>Args:</dt><dd><dl class="simple">
<dt>dirs<span class="classifier">str, optional</span></dt><dd><p>Directions of the k points in the Brillouin zone. They are the three lattice vectors. Defaults to “xyz”</p>
</dd>
<dt>NUMK<span class="classifier">int, optional</span></dt><dd><p>The number of k points in a direction. Defaults to 20</p>
</dd>
</dl>
</dd>
<dt>Returns:</dt><dd><dl class="simple">
<dt>np.array_like</dt><dd><p>An array of k points that uniformly sample the Brillouin zone in the given directions</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="grogupy.utilities.read_siesta_emin">
<span class="sig-prename descclassname"><span class="pre">grogupy.utilities.</span></span><span class="sig-name descname"><span class="pre">read_siesta_emin</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">eigfile</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/grogupy/utilities.html#read_siesta_emin"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#grogupy.utilities.read_siesta_emin" title="Link to this definition"></a></dt>
<dd><p>It reads the lowest energy level from the siesta run.</p>
<p>It uses the .EIG file from siesta that contains the eigenvalues.</p>
<dl class="simple">
<dt>Args:</dt><dd><dl class="simple">
<dt>eigfile<span class="classifier">str</span></dt><dd><p>The path to the .EIG file</p>
</dd>
</dl>
</dd>
<dt>Returns:</dt><dd><dl class="simple">
<dt>float</dt><dd><p>The energy minimum</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="grogupy.utilities.tau_u">
<span class="sig-prename descclassname"><span class="pre">grogupy.utilities.</span></span><span class="sig-name descname"><span class="pre">tau_u</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">u</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/grogupy/utilities.html#tau_u"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#grogupy.utilities.tau_u" title="Link to this definition"></a></dt>
<dd><p>Pauli matrix in direction u.</p>
<p>Returns the vector u in the basis of the Pauli matrices.</p>
<dl class="simple">
<dt>Args:</dt><dd><dl class="simple">
<dt>u<span class="classifier">list or np.array_like</span></dt><dd><p>The direction</p>
</dd>
</dl>
</dd>
<dt>Returns:</dt><dd><dl class="simple">
<dt>np.array_like</dt><dd><p>Arbitrary direction in the base of the Pauli matrices</p>
</dd>
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