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<h1>Source code for grogupy.grogu</h1><div class="highlight"><pre>
<span></span><span class="c1"># Copyright (c) [2024] []</span>
<span class="c1">#</span>
<span class="c1"># Permission is hereby granted, free of charge, to any person obtaining a copy</span>
<span class="c1"># of this software and associated documentation files (the &quot;Software&quot;), to deal</span>
<span class="c1"># in the Software without restriction, including without limitation the rights</span>
<span class="c1"># to use, copy, modify, merge, publish, distribute, sublicense, and/or sell</span>
<span class="c1"># copies of the Software, and to permit persons to whom the Software is</span>
<span class="c1"># furnished to do so, subject to the following conditions:</span>
<span class="c1">#</span>
<span class="c1"># The above copyright notice and this permission notice shall be included in all</span>
<span class="c1"># copies or substantial portions of the Software.</span>
<span class="c1">#</span>
<span class="c1"># THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<span class="c1"># IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<span class="c1"># FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<span class="c1"># AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<span class="c1"># LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<span class="c1"># OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<span class="c1"># SOFTWARE.</span>
<span class="kn">import</span> <span class="nn">warnings</span>
<span class="kn">from</span> <span class="nn">sys</span> <span class="kn">import</span> <span class="n">getsizeof</span>
<span class="kn">from</span> <span class="nn">timeit</span> <span class="kn">import</span> <span class="n">default_timer</span> <span class="k">as</span> <span class="n">timer</span>
<span class="c1"># use numpy number of threads one</span>
<span class="k">try</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">threadpoolctl</span> <span class="kn">import</span> <span class="n">threadpool_info</span><span class="p">,</span> <span class="n">threadpool_limits</span>
<span class="n">user_api</span> <span class="o">=</span> <span class="n">threadpool_info</span><span class="p">()[</span><span class="s2">&quot;user_api&quot;</span><span class="p">]</span>
<span class="n">threadpool_limits</span><span class="p">(</span><span class="n">limits</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">user_api</span><span class="o">=</span><span class="n">user_api</span><span class="p">)</span>
<span class="k">except</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Warning: threadpoolctl could not make numpy use single thread!&quot;</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">sisl</span>
<span class="kn">from</span> <span class="nn">mpi4py</span> <span class="kn">import</span> <span class="n">MPI</span>
<span class="k">try</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">tqdm</span> <span class="kn">import</span> <span class="n">tqdm</span>
<span class="n">tqdm_imported</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">except</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Please install tqdm for nice progress bar.&quot;</span><span class="p">)</span>
<span class="n">tqdm_imported</span> <span class="o">=</span> <span class="kc">False</span>
<span class="kn">from</span> <span class="nn">grogupy</span> <span class="kn">import</span> <span class="o">*</span>
<div class="viewcode-block" id="main">
<a class="viewcode-back" href="../../implementation/grogupy.grogu.html#grogupy.grogu.main">[docs]</a>
<span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
<span class="c1"># runtime information</span>
<span class="n">times</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
<span class="n">times</span><span class="p">[</span><span class="s2">&quot;start_time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">timer</span><span class="p">()</span>
<span class="c1"># input output stuff</span>
<span class="c1">######################################################################</span>
<span class="c1">######################################################################</span>
<span class="c1">######################################################################</span>
<span class="n">infile</span> <span class="o">=</span> <span class="s2">&quot;/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf&quot;</span>
<span class="n">outfile</span> <span class="o">=</span> <span class="s2">&quot;./Fe3GeTe2_notebook&quot;</span>
<span class="n">magnetic_entities</span> <span class="o">=</span> <span class="p">[</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">atom</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">l</span><span class="o">=</span><span class="mi">2</span><span class="p">),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">atom</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">l</span><span class="o">=</span><span class="mi">2</span><span class="p">),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">atom</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">l</span><span class="o">=</span><span class="mi">2</span><span class="p">),</span>
<span class="p">]</span>
<span class="n">pairs</span> <span class="o">=</span> <span class="p">[</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">ai</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">aj</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">Ruc</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">ai</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">aj</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">Ruc</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">ai</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">aj</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">Ruc</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">ai</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">aj</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">Ruc</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">ai</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">aj</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">Ruc</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">ai</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">aj</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">Ruc</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">ai</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">aj</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">Ruc</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">ai</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">aj</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">Ruc</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">ai</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">aj</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">Ruc</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])),</span>
<span class="p">]</span>
<span class="n">simulation_parameters</span> <span class="o">=</span> <span class="n">default_args</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;infile&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">infile</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;outfile&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">outfile</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;kset&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">20</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;kdirs&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;xy&quot;</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;eset&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">600</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;esetp&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">10000</span>
<span class="c1">######################################################################</span>
<span class="c1">######################################################################</span>
<span class="c1">######################################################################</span>
<span class="c1"># MPI parameters</span>
<span class="n">comm</span> <span class="o">=</span> <span class="n">MPI</span><span class="o">.</span><span class="n">COMM_WORLD</span>
<span class="n">size</span> <span class="o">=</span> <span class="n">comm</span><span class="o">.</span><span class="n">Get_size</span><span class="p">()</span>
<span class="n">rank</span> <span class="o">=</span> <span class="n">comm</span><span class="o">.</span><span class="n">Get_rank</span><span class="p">()</span>
<span class="n">root_node</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">if</span> <span class="n">rank</span> <span class="o">==</span> <span class="n">root_node</span><span class="p">:</span>
<span class="c1"># include parallel size in simulation parameters</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;parallel_size&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">size</span>
<span class="c1"># check versions for debugging</span>
<span class="k">try</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;sisl version: &quot;</span><span class="p">,</span> <span class="n">sisl</span><span class="o">.</span><span class="n">__version__</span><span class="p">)</span>
<span class="k">except</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;sisl version unknown.&quot;</span><span class="p">)</span>
<span class="k">try</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;numpy version: &quot;</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">__version__</span><span class="p">)</span>
<span class="k">except</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;numpy version unknown.&quot;</span><span class="p">)</span>
<span class="c1"># rename outfile</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;outfile&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">endswith</span><span class="p">(</span><span class="s2">&quot;.pickle&quot;</span><span class="p">):</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;outfile&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="s2">&quot;.pickle&quot;</span>
<span class="c1"># if ebot is not given put it 0.1 eV under the smallest energy</span>
<span class="k">if</span> <span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;ebot&quot;</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">eigfile</span> <span class="o">=</span> <span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;infile&quot;</span><span class="p">][:</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="o">+</span> <span class="s2">&quot;EIG&quot;</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;ebot&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">read_siesta_emin</span><span class="p">(</span><span class="n">eigfile</span><span class="p">)</span> <span class="o">-</span> <span class="mf">0.1</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;automatic_ebot&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">except</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Could not determine ebot.&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Parameter was not given and .EIG file was not found.&quot;</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;automatic_ebot&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span>
<span class="c1"># read sile</span>
<span class="n">fdf</span> <span class="o">=</span> <span class="n">sisl</span><span class="o">.</span><span class="n">get_sile</span><span class="p">(</span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;infile&quot;</span><span class="p">])</span>
<span class="c1"># read in hamiltonian</span>
<span class="n">dh</span> <span class="o">=</span> <span class="n">fdf</span><span class="o">.</span><span class="n">read_hamiltonian</span><span class="p">()</span>
<span class="c1"># read unit cell vectors</span>
<span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;cell&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">fdf</span><span class="o">.</span><span class="n">read_geometry</span><span class="p">()</span><span class="o">.</span><span class="n">cell</span>
<span class="c1"># unit cell index</span>
<span class="n">uc_in_sc_idx</span> <span class="o">=</span> <span class="n">dh</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">sc_index</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="k">if</span> <span class="n">rank</span> <span class="o">==</span> <span class="n">root_node</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n\n\n\n\n</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">&quot;#################################################################### JOB INFORMATION ###########################################################################&quot;</span>
<span class="p">)</span>
<span class="n">print_job_description</span><span class="p">(</span><span class="n">simulation_parameters</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">&quot;################################################################################################################################################################&quot;</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n\n\n\n\n</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="n">times</span><span class="p">[</span><span class="s2">&quot;setup_time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">timer</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Setup done. Elapsed time: </span><span class="si">{</span><span class="n">times</span><span class="p">[</span><span class="s1">&#39;setup_time&#39;</span><span class="p">]</span><span class="si">}</span><span class="s2"> s&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">&quot;================================================================================================================================================================&quot;</span>
<span class="p">)</span>
<span class="n">NO</span> <span class="o">=</span> <span class="n">dh</span><span class="o">.</span><span class="n">no</span> <span class="c1"># shorthand for number of orbitals in the unit cell</span>
<span class="c1"># reformat Hamltonian and Overlap matrix for manipulations</span>
<span class="n">hh</span><span class="p">,</span> <span class="n">ss</span> <span class="o">=</span> <span class="n">build_hh_ss</span><span class="p">(</span><span class="n">dh</span><span class="p">)</span>
<span class="c1"># symmetrizing Hamiltonian and Overlap matrix to make them hermitian</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dh</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">sc_off</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
<span class="n">j</span> <span class="o">=</span> <span class="n">dh</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">sc_index</span><span class="p">(</span><span class="o">-</span><span class="n">dh</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">sc_off</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="n">h1</span><span class="p">,</span> <span class="n">h1d</span> <span class="o">=</span> <span class="n">hh</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">hh</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
<span class="n">hh</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">hh</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">h1</span> <span class="o">+</span> <span class="n">h1d</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">conj</span><span class="p">())</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="n">h1d</span> <span class="o">+</span> <span class="n">h1</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">conj</span><span class="p">())</span> <span class="o">/</span> <span class="mi">2</span>
<span class="n">s1</span><span class="p">,</span> <span class="n">s1d</span> <span class="o">=</span> <span class="n">ss</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">ss</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
<span class="n">ss</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">ss</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">s1</span> <span class="o">+</span> <span class="n">s1d</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">conj</span><span class="p">())</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="n">s1d</span> <span class="o">+</span> <span class="n">s1</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">conj</span><span class="p">())</span> <span class="o">/</span> <span class="mi">2</span>
<span class="c1"># identifying TRS and TRB parts of the Hamiltonian</span>
<span class="n">TAUY</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">kron</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">NO</span><span class="p">),</span> <span class="n">tau_y</span><span class="p">)</span>
<span class="n">hTR</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">TAUY</span> <span class="o">@</span> <span class="n">hh</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">conj</span><span class="p">()</span> <span class="o">@</span> <span class="n">TAUY</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dh</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">nsc</span><span class="o">.</span><span class="n">prod</span><span class="p">())])</span>
<span class="n">hTRS</span> <span class="o">=</span> <span class="p">(</span><span class="n">hh</span> <span class="o">+</span> <span class="n">hTR</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
<span class="n">hTRB</span> <span class="o">=</span> <span class="p">(</span><span class="n">hh</span> <span class="o">-</span> <span class="n">hTR</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
<span class="c1"># extracting the exchange field</span>
<span class="n">traced</span> <span class="o">=</span> <span class="p">[</span><span class="n">spin_tracer</span><span class="p">(</span><span class="n">hTRB</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dh</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">nsc</span><span class="o">.</span><span class="n">prod</span><span class="p">())]</span> <span class="c1"># equation 77</span>
<span class="n">XCF</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span>
<span class="p">[</span>
<span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">f</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">/</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">traced</span><span class="p">]),</span>
<span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">f</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">/</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">traced</span><span class="p">]),</span>
<span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">f</span><span class="p">[</span><span class="s2">&quot;z&quot;</span><span class="p">]</span> <span class="o">/</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">traced</span><span class="p">]),</span>
<span class="p">]</span>
<span class="p">)</span>
<span class="c1"># check if exchange field has scalar part</span>
<span class="n">max_xcfs</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">f</span><span class="p">[</span><span class="s2">&quot;c&quot;</span><span class="p">]</span> <span class="o">/</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">traced</span><span class="p">])))</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="k">if</span> <span class="n">max_xcfs</span> <span class="o">&gt;</span> <span class="mf">1e-12</span><span class="p">:</span>
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">&quot;Exchange field has non negligible scalar part. Largest value is </span><span class="si">{</span><span class="n">max_xcfs</span><span class="si">}</span><span class="s2">&quot;</span>
<span class="p">)</span>
<span class="k">if</span> <span class="n">rank</span> <span class="o">==</span> <span class="n">root_node</span><span class="p">:</span>
<span class="n">times</span><span class="p">[</span><span class="s2">&quot;H_and_XCF_time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">timer</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">&quot;Hamiltonian and exchange field rotated. Elapsed time: </span><span class="si">{</span><span class="n">times</span><span class="p">[</span><span class="s1">&#39;H_and_XCF_time&#39;</span><span class="p">]</span><span class="si">}</span><span class="s2"> s&quot;</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">&quot;================================================================================================================================================================&quot;</span>
<span class="p">)</span>
<span class="c1"># initialize pairs and magnetic entities based on input information</span>
<span class="n">pairs</span><span class="p">,</span> <span class="n">magnetic_entities</span> <span class="o">=</span> <span class="n">setup_pairs_and_magnetic_entities</span><span class="p">(</span>
<span class="n">magnetic_entities</span><span class="p">,</span> <span class="n">pairs</span><span class="p">,</span> <span class="n">dh</span><span class="p">,</span> <span class="n">simulation_parameters</span>
<span class="p">)</span>
<span class="k">if</span> <span class="n">rank</span> <span class="o">==</span> <span class="n">root_node</span><span class="p">:</span>
<span class="n">times</span><span class="p">[</span><span class="s2">&quot;site_and_pair_dictionaries_time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">timer</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">&quot;Site and pair dictionaries created. Elapsed time: </span><span class="si">{</span><span class="n">times</span><span class="p">[</span><span class="s1">&#39;site_and_pair_dictionaries_time&#39;</span><span class="p">]</span><span class="si">}</span><span class="s2"> s&quot;</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">&quot;================================================================================================================================================================&quot;</span>
<span class="p">)</span>
<span class="c1"># generate k space sampling</span>
<span class="n">kset</span> <span class="o">=</span> <span class="n">make_kset</span><span class="p">(</span>
<span class="n">dirs</span><span class="o">=</span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;kdirs&quot;</span><span class="p">],</span> <span class="n">NUMK</span><span class="o">=</span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;kset&quot;</span><span class="p">]</span>
<span class="p">)</span>
<span class="c1"># generate weights for k points</span>
<span class="n">wkset</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">kset</span><span class="p">))</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">kset</span><span class="p">)</span>
<span class="c1"># split the k points based on MPI size</span>
<span class="n">kpcs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array_split</span><span class="p">(</span><span class="n">kset</span><span class="p">,</span> <span class="n">size</span><span class="p">)</span>
<span class="c1"># use progress bar if available</span>
<span class="k">if</span> <span class="n">rank</span> <span class="o">==</span> <span class="n">root_node</span> <span class="ow">and</span> <span class="n">tqdm_imported</span><span class="p">:</span>
<span class="n">kpcs</span><span class="p">[</span><span class="n">root_node</span><span class="p">]</span> <span class="o">=</span> <span class="n">tqdm</span><span class="p">(</span><span class="n">kpcs</span><span class="p">[</span><span class="n">root_node</span><span class="p">],</span> <span class="n">desc</span><span class="o">=</span><span class="s2">&quot;k loop&quot;</span><span class="p">)</span>
<span class="k">if</span> <span class="n">rank</span> <span class="o">==</span> <span class="n">root_node</span><span class="p">:</span>
<span class="n">times</span><span class="p">[</span><span class="s2">&quot;k_set_time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">timer</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;k set created. Elapsed time: </span><span class="si">{</span><span class="n">times</span><span class="p">[</span><span class="s1">&#39;k_set_time&#39;</span><span class="p">]</span><span class="si">}</span><span class="s2"> s&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">&quot;================================================================================================================================================================&quot;</span>
<span class="p">)</span>
<span class="c1"># this will contain the three Hamiltonian in the</span>
<span class="c1"># reference directions needed to calculate the energy</span>
<span class="c1"># variations upon rotation</span>
<span class="n">hamiltonians</span> <span class="o">=</span> <span class="p">[]</span>
<span class="c1"># iterate over the reference directions (quantization axes)</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">orient</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;ref_xcf_orientations&quot;</span><span class="p">]):</span>
<span class="c1"># obtain rotated exchange field and Hamiltonian</span>
<span class="n">R</span> <span class="o">=</span> <span class="n">RotMa2b</span><span class="p">(</span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;scf_xcf_orientation&quot;</span><span class="p">],</span> <span class="n">orient</span><span class="p">[</span><span class="s2">&quot;o&quot;</span><span class="p">])</span>
<span class="n">rot_XCF</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s2">&quot;ij,jklm-&gt;iklm&quot;</span><span class="p">,</span> <span class="n">R</span><span class="p">,</span> <span class="n">XCF</span><span class="p">)</span>
<span class="n">rot_H_XCF</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span>
<span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">kron</span><span class="p">(</span><span class="n">rot_XCF</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">tau</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">tau</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">([</span><span class="n">tau_x</span><span class="p">,</span> <span class="n">tau_y</span><span class="p">,</span> <span class="n">tau_z</span><span class="p">])]</span>
<span class="p">)</span>
<span class="n">rot_H_XCF_uc</span> <span class="o">=</span> <span class="n">rot_H_XCF</span><span class="p">[</span><span class="n">uc_in_sc_idx</span><span class="p">]</span>
<span class="c1"># obtain total Hamiltonian with the rotated exchange field</span>
<span class="n">rot_H</span> <span class="o">=</span> <span class="n">hTRS</span> <span class="o">+</span> <span class="n">rot_H_XCF</span> <span class="c1"># equation 76</span>
<span class="c1"># store the relevant information of the Hamiltonian</span>
<span class="n">hamiltonians</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">dict</span><span class="p">(</span><span class="n">orient</span><span class="o">=</span><span class="n">orient</span><span class="p">[</span><span class="s2">&quot;o&quot;</span><span class="p">],</span> <span class="n">H</span><span class="o">=</span><span class="n">rot_H</span><span class="p">))</span>
<span class="c1"># these are the rotations (for now) perpendicular to the quantization axis</span>
<span class="k">for</span> <span class="n">u</span> <span class="ow">in</span> <span class="n">orient</span><span class="p">[</span><span class="s2">&quot;vw&quot;</span><span class="p">]:</span>
<span class="c1"># section 2.H</span>
<span class="n">Tu</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">kron</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">NO</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">int</span><span class="p">),</span> <span class="n">tau_u</span><span class="p">(</span><span class="n">u</span><span class="p">))</span>
<span class="n">Vu1</span><span class="p">,</span> <span class="n">Vu2</span> <span class="o">=</span> <span class="n">calc_Vu</span><span class="p">(</span><span class="n">rot_H_XCF_uc</span><span class="p">,</span> <span class="n">Tu</span><span class="p">)</span>
<span class="k">for</span> <span class="n">mag_ent</span> <span class="ow">in</span> <span class="n">magnetic_entities</span><span class="p">:</span>
<span class="n">idx</span> <span class="o">=</span> <span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;spin_box_indices&quot;</span><span class="p">]</span>
<span class="c1"># fill up the perturbed potentials (for now) based on the on-site projections</span>
<span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;Vu1&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">onsite_projection</span><span class="p">(</span><span class="n">Vu1</span><span class="p">,</span> <span class="n">idx</span><span class="p">,</span> <span class="n">idx</span><span class="p">))</span>
<span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;Vu2&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">onsite_projection</span><span class="p">(</span><span class="n">Vu2</span><span class="p">,</span> <span class="n">idx</span><span class="p">,</span> <span class="n">idx</span><span class="p">))</span>
<span class="k">if</span> <span class="n">rank</span> <span class="o">==</span> <span class="n">root_node</span><span class="p">:</span>
<span class="n">times</span><span class="p">[</span><span class="s2">&quot;reference_rotations_time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">timer</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">&quot;Rotations done perpendicular to quantization axis. Elapsed time: </span><span class="si">{</span><span class="n">times</span><span class="p">[</span><span class="s1">&#39;reference_rotations_time&#39;</span><span class="p">]</span><span class="si">}</span><span class="s2"> s&quot;</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">&quot;================================================================================================================================================================&quot;</span>
<span class="p">)</span>
<span class="c1"># provide helpful information to estimate the runtime and memory</span>
<span class="c1"># requirements of the Greens function calculations</span>
<span class="k">if</span> <span class="n">rank</span> <span class="o">==</span> <span class="n">root_node</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Starting matrix inversions.&quot;</span><span class="p">)</span>
<span class="k">if</span> <span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;padawan_mode&quot;</span><span class="p">]:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Padawan mode: &quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Total number of k points: </span><span class="si">{</span><span class="n">kset</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">&quot;Number of energy samples per k point: </span><span class="si">{</span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s1">&#39;eset&#39;</span><span class="p">]</span><span class="si">}</span><span class="s2">&quot;</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Total number of directions: </span><span class="si">{</span><span class="nb">len</span><span class="p">(</span><span class="n">hamiltonians</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">&quot;Total number of matrix inversions: </span><span class="si">{</span><span class="n">kset</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="n">hamiltonians</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s1">&#39;eset&#39;</span><span class="p">]</span><span class="si">}</span><span class="s2">&quot;</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">&quot;The shape of the Hamiltonian and the Greens function is </span><span class="si">{</span><span class="n">NO</span><span class="si">}</span><span class="s2">x</span><span class="si">{</span><span class="n">NO</span><span class="si">}</span><span class="s2">=</span><span class="si">{</span><span class="n">NO</span><span class="o">*</span><span class="n">NO</span><span class="si">}</span><span class="s2">&quot;</span>
<span class="p">)</span>
<span class="c1"># https://stackoverflow.com/questions/70746660/how-to-predict-memory-requirement-for-np-linalg-inv</span>
<span class="c1"># memory is O(64 n**2) for complex matrices</span>
<span class="n">memory_size</span> <span class="o">=</span> <span class="n">getsizeof</span><span class="p">(</span><span class="n">hamiltonians</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="s2">&quot;H&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">base</span><span class="p">)</span> <span class="o">/</span> <span class="mi">1024</span>
<span class="nb">print</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">&quot;Memory taken by a single Hamiltonian is: </span><span class="si">{</span><span class="n">getsizeof</span><span class="p">(</span><span class="n">hamiltonians</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="s1">&#39;H&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">1024</span><span class="si">}</span><span class="s2"> KB&quot;</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Expected memory usage per matrix inversion: </span><span class="si">{</span><span class="n">memory_size</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">32</span><span class="si">}</span><span class="s2"> KB&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">&quot;Expected memory usage per k point for parallel inversion: </span><span class="si">{</span><span class="n">memory_size</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="n">hamiltonians</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s1">&#39;eset&#39;</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">32</span><span class="si">}</span><span class="s2"> KB&quot;</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">&quot;Expected memory usage on root node: </span><span class="si">{</span><span class="nb">len</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array_split</span><span class="p">(</span><span class="n">kset</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">memory_size</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="n">hamiltonians</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s1">&#39;eset&#39;</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">32</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">1024</span><span class="si">}</span><span class="s2"> MB&quot;</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">&quot;================================================================================================================================================================&quot;</span>
<span class="p">)</span>
<span class="c1"># MPI barrier</span>
<span class="n">comm</span><span class="o">.</span><span class="n">Barrier</span><span class="p">()</span>
<span class="c1"># make energy contour</span>
<span class="n">cont</span> <span class="o">=</span> <span class="n">make_contour</span><span class="p">(</span>
<span class="n">emin</span><span class="o">=</span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;ebot&quot;</span><span class="p">],</span>
<span class="n">enum</span><span class="o">=</span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;eset&quot;</span><span class="p">],</span>
<span class="n">p</span><span class="o">=</span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;esetp&quot;</span><span class="p">],</span>
<span class="p">)</span>
<span class="n">eran</span> <span class="o">=</span> <span class="n">cont</span><span class="o">.</span><span class="n">ze</span>
<span class="c1"># sampling the integrand on the contour and the BZ</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">kpcs</span><span class="p">[</span><span class="n">rank</span><span class="p">]:</span>
<span class="c1"># weight of k point in BZ integral</span>
<span class="n">wk</span> <span class="o">=</span> <span class="n">wkset</span><span class="p">[</span><span class="n">rank</span><span class="p">]</span>
<span class="c1"># iterate over reference directions</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">hamiltonian_orientation</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">hamiltonians</span><span class="p">):</span>
<span class="c1"># calculate Hamiltonian and Overlap matrix in a given k point</span>
<span class="n">H</span> <span class="o">=</span> <span class="n">hamiltonian_orientation</span><span class="p">[</span><span class="s2">&quot;H&quot;</span><span class="p">]</span>
<span class="n">HK</span><span class="p">,</span> <span class="n">SK</span> <span class="o">=</span> <span class="n">hsk</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="n">ss</span><span class="p">,</span> <span class="n">dh</span><span class="o">.</span><span class="n">sc_off</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
<span class="k">if</span> <span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;parallel_solver_for_Gk&quot;</span><span class="p">]:</span>
<span class="n">Gk</span> <span class="o">=</span> <span class="n">parallel_Gk</span><span class="p">(</span><span class="n">HK</span><span class="p">,</span> <span class="n">SK</span><span class="p">,</span> <span class="n">eran</span><span class="p">,</span> <span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;eset&quot;</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># solve Greens function sequentially for the energies, because of memory bound</span>
<span class="n">Gk</span> <span class="o">=</span> <span class="n">sequential_GK</span><span class="p">(</span><span class="n">HK</span><span class="p">,</span> <span class="n">SK</span><span class="p">,</span> <span class="n">eran</span><span class="p">,</span> <span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;eset&quot;</span><span class="p">])</span>
<span class="c1"># store the Greens function slice of the magnetic entities</span>
<span class="k">for</span> <span class="n">mag_ent</span> <span class="ow">in</span> <span class="n">magnetic_entities</span><span class="p">:</span>
<span class="n">idx</span> <span class="o">=</span> <span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;spin_box_indices&quot;</span><span class="p">]</span>
<span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;Gii_tmp&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="o">+=</span> <span class="n">onsite_projection</span><span class="p">(</span><span class="n">Gk</span><span class="p">,</span> <span class="n">idx</span><span class="p">,</span> <span class="n">idx</span><span class="p">)</span> <span class="o">*</span> <span class="n">wk</span>
<span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">pairs</span><span class="p">:</span>
<span class="c1"># add phase shift based on the cell difference</span>
<span class="n">phase</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">k</span> <span class="o">@</span> <span class="n">pair</span><span class="p">[</span><span class="s2">&quot;Ruc&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
<span class="c1"># get the pair orbital sizes from the magnetic entities</span>
<span class="n">ai</span> <span class="o">=</span> <span class="n">magnetic_entities</span><span class="p">[</span><span class="n">pair</span><span class="p">[</span><span class="s2">&quot;ai&quot;</span><span class="p">]][</span><span class="s2">&quot;spin_box_indices&quot;</span><span class="p">]</span>
<span class="n">aj</span> <span class="o">=</span> <span class="n">magnetic_entities</span><span class="p">[</span><span class="n">pair</span><span class="p">[</span><span class="s2">&quot;aj&quot;</span><span class="p">]][</span><span class="s2">&quot;spin_box_indices&quot;</span><span class="p">]</span>
<span class="c1"># store the Greens function slice of the magnetic entities</span>
<span class="n">pair</span><span class="p">[</span><span class="s2">&quot;Gij_tmp&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="o">+=</span> <span class="n">onsite_projection</span><span class="p">(</span><span class="n">Gk</span><span class="p">,</span> <span class="n">ai</span><span class="p">,</span> <span class="n">aj</span><span class="p">)</span> <span class="o">*</span> <span class="n">phase</span> <span class="o">*</span> <span class="n">wk</span>
<span class="n">pair</span><span class="p">[</span><span class="s2">&quot;Gji_tmp&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="o">+=</span> <span class="n">onsite_projection</span><span class="p">(</span><span class="n">Gk</span><span class="p">,</span> <span class="n">aj</span><span class="p">,</span> <span class="n">ai</span><span class="p">)</span> <span class="o">/</span> <span class="n">phase</span> <span class="o">*</span> <span class="n">wk</span>
<span class="c1"># summ reduce partial results of mpi nodes</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">hamiltonians</span><span class="p">)):</span>
<span class="k">for</span> <span class="n">mag_ent</span> <span class="ow">in</span> <span class="n">magnetic_entities</span><span class="p">:</span>
<span class="n">comm</span><span class="o">.</span><span class="n">Reduce</span><span class="p">(</span><span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;Gii_tmp&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">],</span> <span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;Gii&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">],</span> <span class="n">root</span><span class="o">=</span><span class="n">root_node</span><span class="p">)</span>
<span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">pairs</span><span class="p">:</span>
<span class="n">comm</span><span class="o">.</span><span class="n">Reduce</span><span class="p">(</span><span class="n">pair</span><span class="p">[</span><span class="s2">&quot;Gij_tmp&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">],</span> <span class="n">pair</span><span class="p">[</span><span class="s2">&quot;Gij&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">],</span> <span class="n">root</span><span class="o">=</span><span class="n">root_node</span><span class="p">)</span>
<span class="n">comm</span><span class="o">.</span><span class="n">Reduce</span><span class="p">(</span><span class="n">pair</span><span class="p">[</span><span class="s2">&quot;Gji_tmp&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">],</span> <span class="n">pair</span><span class="p">[</span><span class="s2">&quot;Gji&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">],</span> <span class="n">root</span><span class="o">=</span><span class="n">root_node</span><span class="p">)</span>
<span class="k">if</span> <span class="n">rank</span> <span class="o">==</span> <span class="n">root_node</span><span class="p">:</span>
<span class="n">times</span><span class="p">[</span><span class="s2">&quot;green_function_inversion_time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">timer</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">&quot;Calculated Greens functions. Elapsed time: </span><span class="si">{</span><span class="n">times</span><span class="p">[</span><span class="s1">&#39;green_function_inversion_time&#39;</span><span class="p">]</span><span class="si">}</span><span class="s2"> s&quot;</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">&quot;================================================================================================================================================================&quot;</span>
<span class="p">)</span>
<span class="k">if</span> <span class="n">rank</span> <span class="o">==</span> <span class="n">root_node</span><span class="p">:</span>
<span class="c1"># iterate over the magnetic entities</span>
<span class="k">for</span> <span class="n">tracker</span><span class="p">,</span> <span class="n">mag_ent</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">magnetic_entities</span><span class="p">):</span>
<span class="c1"># iterate over the quantization axes</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">Gii</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;Gii&quot;</span><span class="p">]):</span>
<span class="n">storage</span> <span class="o">=</span> <span class="p">[]</span>
<span class="c1"># iterate over the first and second order local perturbations</span>
<span class="k">for</span> <span class="n">Vu1</span><span class="p">,</span> <span class="n">Vu2</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;Vu1&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">],</span> <span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;Vu2&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">]):</span>
<span class="c1"># The Szunyogh-Lichtenstein formula</span>
<span class="n">traced</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">trace</span><span class="p">(</span>
<span class="p">(</span><span class="n">Vu2</span> <span class="o">@</span> <span class="n">Gii</span> <span class="o">+</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">Gii</span> <span class="o">@</span> <span class="n">Vu1</span> <span class="o">@</span> <span class="n">Gii</span><span class="p">),</span> <span class="n">axis1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">axis2</span><span class="o">=</span><span class="mi">2</span>
<span class="p">)</span> <span class="c1"># this is the on site projection</span>
<span class="c1"># evaluation of the contour integral</span>
<span class="n">storage</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">int_de_ke</span><span class="p">(</span><span class="n">traced</span><span class="p">,</span> <span class="n">cont</span><span class="o">.</span><span class="n">we</span><span class="p">))</span>
<span class="c1"># fill up the magnetic entities dictionary with the energies</span>
<span class="n">magnetic_entities</span><span class="p">[</span><span class="n">tracker</span><span class="p">][</span><span class="s2">&quot;energies&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">storage</span><span class="p">)</span>
<span class="c1"># convert to np array</span>
<span class="n">magnetic_entities</span><span class="p">[</span><span class="n">tracker</span><span class="p">][</span><span class="s2">&quot;energies&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span>
<span class="n">magnetic_entities</span><span class="p">[</span><span class="n">tracker</span><span class="p">][</span><span class="s2">&quot;energies&quot;</span><span class="p">]</span>
<span class="p">)</span>
<span class="c1"># iterate over the pairs</span>
<span class="k">for</span> <span class="n">tracker</span><span class="p">,</span> <span class="n">pair</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">pairs</span><span class="p">):</span>
<span class="c1"># iterate over the quantization axes</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="p">(</span><span class="n">Gij</span><span class="p">,</span> <span class="n">Gji</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">pair</span><span class="p">[</span><span class="s2">&quot;Gij&quot;</span><span class="p">],</span> <span class="n">pair</span><span class="p">[</span><span class="s2">&quot;Gji&quot;</span><span class="p">])):</span>
<span class="n">site_i</span> <span class="o">=</span> <span class="n">magnetic_entities</span><span class="p">[</span><span class="n">pair</span><span class="p">[</span><span class="s2">&quot;ai&quot;</span><span class="p">]]</span>
<span class="n">site_j</span> <span class="o">=</span> <span class="n">magnetic_entities</span><span class="p">[</span><span class="n">pair</span><span class="p">[</span><span class="s2">&quot;aj&quot;</span><span class="p">]]</span>
<span class="n">storage</span> <span class="o">=</span> <span class="p">[]</span>
<span class="c1"># iterate over the first order local perturbations in all possible orientations for the two sites</span>
<span class="k">for</span> <span class="n">Vui</span> <span class="ow">in</span> <span class="n">site_i</span><span class="p">[</span><span class="s2">&quot;Vu1&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">]:</span>
<span class="k">for</span> <span class="n">Vuj</span> <span class="ow">in</span> <span class="n">site_j</span><span class="p">[</span><span class="s2">&quot;Vu1&quot;</span><span class="p">][</span><span class="n">i</span><span class="p">]:</span>
<span class="c1"># The Szunyogh-Lichtenstein formula</span>
<span class="n">traced</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">trace</span><span class="p">(</span>
<span class="p">(</span><span class="n">Vui</span> <span class="o">@</span> <span class="n">Gij</span> <span class="o">@</span> <span class="n">Vuj</span> <span class="o">@</span> <span class="n">Gji</span><span class="p">),</span> <span class="n">axis1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">axis2</span><span class="o">=</span><span class="mi">2</span>
<span class="p">)</span> <span class="c1"># this is the on site projection</span>
<span class="c1"># evaluation of the contour integral</span>
<span class="n">storage</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">int_de_ke</span><span class="p">(</span><span class="n">traced</span><span class="p">,</span> <span class="n">cont</span><span class="o">.</span><span class="n">we</span><span class="p">))</span>
<span class="c1"># fill up the pairs dictionary with the energies</span>
<span class="n">pairs</span><span class="p">[</span><span class="n">tracker</span><span class="p">][</span><span class="s2">&quot;energies&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">storage</span><span class="p">)</span>
<span class="c1"># convert to np array</span>
<span class="n">pairs</span><span class="p">[</span><span class="n">tracker</span><span class="p">][</span><span class="s2">&quot;energies&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">pairs</span><span class="p">[</span><span class="n">tracker</span><span class="p">][</span><span class="s2">&quot;energies&quot;</span><span class="p">])</span>
<span class="c1"># calculate magnetic parameters</span>
<span class="k">for</span> <span class="n">mag_ent</span> <span class="ow">in</span> <span class="n">magnetic_entities</span><span class="p">:</span>
<span class="n">Kxx</span><span class="p">,</span> <span class="n">Kyy</span><span class="p">,</span> <span class="n">Kzz</span><span class="p">,</span> <span class="n">consistency</span> <span class="o">=</span> <span class="n">calculate_anisotropy_tensor</span><span class="p">(</span><span class="n">mag_ent</span><span class="p">)</span>
<span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;K&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">Kxx</span><span class="p">,</span> <span class="n">Kyy</span><span class="p">,</span> <span class="n">Kzz</span><span class="p">])</span> <span class="o">*</span> <span class="n">sisl</span><span class="o">.</span><span class="n">unit_convert</span><span class="p">(</span><span class="s2">&quot;eV&quot;</span><span class="p">,</span> <span class="s2">&quot;meV&quot;</span><span class="p">)</span>
<span class="n">mag_ent</span><span class="p">[</span><span class="s2">&quot;K_consistency&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">consistency</span>
<span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">pairs</span><span class="p">:</span>
<span class="n">J_iso</span><span class="p">,</span> <span class="n">J_S</span><span class="p">,</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span> <span class="o">=</span> <span class="n">calculate_exchange_tensor</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
<span class="n">pair</span><span class="p">[</span><span class="s2">&quot;J_iso&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">J_iso</span> <span class="o">*</span> <span class="n">sisl</span><span class="o">.</span><span class="n">unit_convert</span><span class="p">(</span><span class="s2">&quot;eV&quot;</span><span class="p">,</span> <span class="s2">&quot;meV&quot;</span><span class="p">)</span>
<span class="n">pair</span><span class="p">[</span><span class="s2">&quot;J_S&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">J_S</span> <span class="o">*</span> <span class="n">sisl</span><span class="o">.</span><span class="n">unit_convert</span><span class="p">(</span><span class="s2">&quot;eV&quot;</span><span class="p">,</span> <span class="s2">&quot;meV&quot;</span><span class="p">)</span>
<span class="n">pair</span><span class="p">[</span><span class="s2">&quot;D&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">D</span> <span class="o">*</span> <span class="n">sisl</span><span class="o">.</span><span class="n">unit_convert</span><span class="p">(</span><span class="s2">&quot;eV&quot;</span><span class="p">,</span> <span class="s2">&quot;meV&quot;</span><span class="p">)</span>
<span class="n">pair</span><span class="p">[</span><span class="s2">&quot;J&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">J</span> <span class="o">*</span> <span class="n">sisl</span><span class="o">.</span><span class="n">unit_convert</span><span class="p">(</span><span class="s2">&quot;eV&quot;</span><span class="p">,</span> <span class="s2">&quot;meV&quot;</span><span class="p">)</span>
<span class="n">times</span><span class="p">[</span><span class="s2">&quot;end_time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">timer</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n\n\n\n\n</span><span class="s2">&quot;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">&quot;##################################################################### GROGU OUTPUT #############################################################################&quot;</span>
<span class="p">)</span>
<span class="n">print_parameters</span><span class="p">(</span><span class="n">simulation_parameters</span><span class="p">)</span>
<span class="n">print_atoms_and_pairs</span><span class="p">(</span><span class="n">magnetic_entities</span><span class="p">,</span> <span class="n">pairs</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">&quot;################################################################################################################################################################&quot;</span>
<span class="p">)</span>
<span class="n">print_runtime_information</span><span class="p">(</span><span class="n">times</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;&quot;</span><span class="p">)</span>
<span class="c1"># remove unwanted stuff before saving</span>
<span class="n">pairs</span><span class="p">,</span> <span class="n">magnetic_entities</span> <span class="o">=</span> <span class="n">remove_clutter_for_save</span><span class="p">(</span><span class="n">pairs</span><span class="p">,</span> <span class="n">magnetic_entities</span><span class="p">)</span>
<span class="c1"># create output dictionary with all the relevant data</span>
<span class="n">results</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span>
<span class="n">parameters</span><span class="o">=</span><span class="n">simulation_parameters</span><span class="p">,</span>
<span class="n">magnetic_entities</span><span class="o">=</span><span class="n">magnetic_entities</span><span class="p">,</span>
<span class="n">pairs</span><span class="o">=</span><span class="n">pairs</span><span class="p">,</span>
<span class="n">runtime</span><span class="o">=</span><span class="n">times</span><span class="p">,</span>
<span class="p">)</span>
<span class="c1"># save results</span>
<span class="n">save_pickle</span><span class="p">(</span><span class="n">simulation_parameters</span><span class="p">[</span><span class="s2">&quot;outfile&quot;</span><span class="p">],</span> <span class="n">results</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n\n\n\n\n</span><span class="s2">&quot;</span><span class="p">)</span></div>
<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s2">&quot;__main__&quot;</span><span class="p">:</span>
<span class="n">main</span><span class="p">()</span>
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