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<h1>Source code for effmass.extrema</h1><div class="highlight"><pre>
<span></span><span class="ch">#! /usr/bin/env python3</span>
<span class="sd">"""</span>
<span class="sd">A module for finding the band structure extrema and instantiating </span>
<span class="sd">a :class:`Segment` object for each extrema point.</span>
<span class="sd">The extrema are found within an energy range given by the :class:`Settings` class.</span>
<span class="sd">Each `Segment` object contains data for kpoints within an energy range given by the :class:`Settings` class. </span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">warnings</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">numpy.ma</span> <span class="k">as</span> <span class="nn">ma</span>
<span class="kn">from</span> <span class="nn">effmass</span> <span class="kn">import</span> <span class="n">analysis</span>
<span class="kn">from</span> <span class="nn">effmass</span> <span class="kn">import</span> <span class="n">inputs</span>
<span class="k">def</span> <span class="nf">_check_partial_occupancy</span><span class="p">(</span><span class="n">occupancy</span><span class="p">):</span>
<span class="sd">"""Raises warning if there is partial occupancy of bands.</span>
<span class="sd"> Args:</span>
<span class="sd"> occupancy (array): Array with shape (number_of_bands,number_of_kpoints). Each row contains occupation number of the eigenstates for a particular band. Values range from 0-1 (spin-polarised) or 0-2 (non-spin-polarised). See :attr:`effmass.inputs.Data.occupancy`.</span>
<span class="sd"> Returns:</span>
<span class="sd"> None.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">in1d</span><span class="p">(</span><span class="n">occupancy</span><span class="p">,([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</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="s2">"You have partial occupation numbers in Data.occupancy. You should check that the attributes Data.VBM, Data.CBM and Data.fermi_energy are correct, and if not, set them manually."</span>
<span class="p">)</span>
<span class="k">def</span> <span class="nf">_calc_CBM</span><span class="p">(</span><span class="n">occupancy</span><span class="p">,</span> <span class="n">energy</span><span class="p">):</span>
<span class="sd">"""Finds the minimum unoccupied energy eigenstate (conduction band minimum)</span>
<span class="sd"> .</span>
<span class="sd"> Args:</span>
<span class="sd"> occupancy (array): occupancy of eigenstates with shape (number_of_kpoints, number_of_bands)</span>
<span class="sd"> energy (array): energy (eV) of eigenstates with shape (number_of_kpoints, number_of_bands)</span>
<span class="sd"> Returns:</span>
<span class="sd"> float: the minimum unoccupied energy (eV)</span>
<span class="sd"> """</span>
<span class="n">_check_partial_occupancy</span><span class="p">(</span><span class="n">occupancy</span><span class="p">)</span>
<span class="n">energy_unoccupied</span> <span class="o">=</span> <span class="n">ma</span><span class="o">.</span><span class="n">masked_where</span><span class="p">(</span><span class="n">occupancy</span> <span class="o">></span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">energy</span><span class="p">)</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">amin</span><span class="p">(</span><span class="n">energy_unoccupied</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_calc_VBM</span><span class="p">(</span><span class="n">occupancy</span><span class="p">,</span> <span class="n">energy</span><span class="p">):</span>
<span class="sd">"""Finds the minimum unoccupied energy eigenstate (valence band maximum).</span>
<span class="sd"> Args:</span>
<span class="sd"> occupancy (array): occupancy of eigenstates with shape (number_of_kpoints, number_of_bands)</span>
<span class="sd"> energy (array): energy (eV) of eigenstates with shape (number_of_kpoints, number_of_bands)</span>
<span class="sd"> Returns:</span>
<span class="sd"> float: the minimum unoccupied energy (eV)</span>
<span class="sd"> """</span>
<span class="n">_check_partial_occupancy</span><span class="p">(</span><span class="n">occupancy</span><span class="p">)</span>
<span class="n">energy_occupied</span> <span class="o">=</span> <span class="n">ma</span><span class="o">.</span><span class="n">masked_where</span><span class="p">(</span><span class="n">occupancy</span> <span class="o"><</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">energy</span><span class="p">)</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">amax</span><span class="p">(</span><span class="n">energy_occupied</span><span class="p">)</span>
<div class="viewcode-block" id="calculate_direction"><a class="viewcode-back" href="../../extrema.html#effmass.extrema.calculate_direction">[docs]</a><span class="k">def</span> <span class="nf">calculate_direction</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
<span class="sd">"""Calculates the direction vector between two points.</span>
<span class="sd"> Args:</span>
<span class="sd"> a (list): the position vector of point a.</span>
<span class="sd"> b (list): the position vector of point b.</span>
<span class="sd"> Returns:</span>
<span class="sd"> array: The (unnormalised) direction vector between points a and b. The smallest magnitude of an element is 1 (eg: [1,1,2]).</span>
<span class="sd"> """</span>
<span class="n">difference</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">subtract</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">count_nonzero</span><span class="p">(</span><span class="n">difference</span><span class="p">)</span> <span class="o"><</span> <span class="mi">1</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"The two k-points are equal"</span><span class="p">)</span>
<span class="k">return</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="c1"># we need to find the smallest non-zero value within a-b</span>
<span class="n">a</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">a</span><span class="p">)</span>
<span class="n">b</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">b</span><span class="p">)</span>
<span class="n">direction_masked</span> <span class="o">=</span> <span class="n">ma</span><span class="o">.</span><span class="n">masked_equal</span><span class="p">(</span>
<span class="n">a</span> <span class="o">-</span> <span class="n">b</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="c1"># return array with invalid entries where values are equal</span>
<span class="n">direction_filled</span> <span class="o">=</span> <span class="n">ma</span><span class="o">.</span><span class="n">filled</span><span class="p">(</span>
<span class="n">direction_masked</span><span class="p">,</span> <span class="mi">10</span>
<span class="o">**</span><span class="mi">6</span><span class="p">)</span> <span class="c1"># fill invalid elements of array with a large number s</span>
<span class="n">direction_absolute</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">absolute</span><span class="p">(</span>
<span class="n">direction_filled</span><span class="p">)</span> <span class="c1"># return absolute values of each element</span>
<span class="n">smallest</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">amin</span><span class="p">(</span><span class="n">direction_absolute</span><span class="p">)</span>
<span class="n">direction</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">b</span> <span class="o">-</span> <span class="n">a</span><span class="p">)</span> <span class="o">/</span> <span class="n">smallest</span> <span class="c1"># use the minimum absolute value as a divisor a-b</span>
<span class="k">if</span> <span class="o">-</span><span class="mi">1</span> <span class="ow">in</span> <span class="n">direction</span><span class="p">:</span>
<span class="n">direction</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">direction</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">return</span> <span class="n">direction</span></div>
<div class="viewcode-block" id="change_direction"><a class="viewcode-back" href="../../extrema.html#effmass.extrema.change_direction">[docs]</a><span class="k">def</span> <span class="nf">change_direction</span><span class="p">(</span><span class="n">kpoints</span><span class="p">,</span> <span class="n">kpoint_indices</span><span class="p">):</span>
<span class="sd">"""Finds the index of the kpoint (if any) where there is a change of</span>
<span class="sd"> direction in reciprocal space.</span>
<span class="sd"> Args:</span>
<span class="sd"> kpoints (array): array of kpoints with shape (number_of_kpoints, 3). Each row contains the fractional coordinates of a kpoint [kx,ky,kz]. See :attr:`effmass.inputs.Data.kpoints`.</span>
<span class="sd"> kpoint_indices (list (int)): the kpoint indices over which to check for change in direction</span>
<span class="sd"> Returns:</span>
<span class="sd"> int: the index of the kpoint where there is a change of direction. If there is no change of direction, returns None.</span>
<span class="sd"> """</span>
<span class="n">new_direction</span> <span class="o">=</span> <span class="n">calculate_direction</span><span class="p">(</span><span class="n">kpoints</span><span class="p">[</span><span class="n">kpoint_indices</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
<span class="n">kpoints</span><span class="p">[</span><span class="n">kpoint_indices</span><span class="p">[</span><span class="mi">1</span><span class="p">]])</span>
<span class="n">change_index</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">kpoint_indices</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]):</span>
<span class="n">old_direction</span> <span class="o">=</span> <span class="n">new_direction</span>
<span class="n">new_direction</span> <span class="o">=</span> <span class="n">calculate_direction</span><span class="p">(</span><span class="n">kpoints</span><span class="p">[</span><span class="n">kpoint_indices</span><span class="p">[</span><span class="n">i</span><span class="p">]],</span>
<span class="n">kpoints</span><span class="p">[</span><span class="n">kpoint_indices</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]])</span>
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">new_direction</span> <span class="o">-</span> <span class="n">old_direction</span><span class="p">)</span> <span class="o">></span> <span class="mf">0.005</span><span class="p">:</span>
<span class="n">change_index</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">break</span>
<span class="k">return</span> <span class="n">change_index</span></div>
<div class="viewcode-block" id="calc_CBM_VBM_from_Fermi"><a class="viewcode-back" href="../../extrema.html#effmass.extrema.calc_CBM_VBM_from_Fermi">[docs]</a><span class="k">def</span> <span class="nf">calc_CBM_VBM_from_Fermi</span><span class="p">(</span><span class="n">Data</span><span class="p">,</span> <span class="n">CBMVBM_search_depth</span><span class="o">=</span><span class="mf">4.0</span><span class="p">):</span>
<span class="sd">""" This function is used to find the CBM and VBM when there is no occupancy data. It relies upon the Fermi level being in the middle of the band gap.</span>
<span class="sd"> The CBMVBM_search_depth is refereced from the fermi energy.</span>
<span class="sd"> </span>
<span class="sd"> Args:</span>
<span class="sd"> DataASE (DataASE): instance of the :class:`DataASE` class.</span>
<span class="sd"> Returns:</span>
<span class="sd"> (float, float): A tuple containing the conduction band minimum and valence band maximum in eV.</span>
<span class="sd">"""</span>
<span class="n">Data</span><span class="o">.</span><span class="n">CBM</span> <span class="o">=</span> <span class="n">Data</span><span class="o">.</span><span class="n">fermi_energy</span>
<span class="n">Data</span><span class="o">.</span><span class="n">VBM</span> <span class="o">=</span> <span class="n">Data</span><span class="o">.</span><span class="n">fermi_energy</span>
<span class="n">Settings</span> <span class="o">=</span> <span class="n">inputs</span><span class="o">.</span><span class="n">Settings</span><span class="p">(</span><span class="n">extrema_search_depth</span><span class="o">=</span><span class="n">CBMVBM_search_depth</span><span class="p">)</span>
<span class="n">extrema_indices</span><span class="o">=</span><span class="n">find_extrema_indices</span><span class="p">(</span><span class="n">Data</span><span class="p">,</span> <span class="n">Settings</span><span class="p">)</span>
<span class="n">CBM</span> <span class="o">=</span> <span class="nb">min</span><span class="p">([</span><span class="n">Data</span><span class="o">.</span><span class="n">energies</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">j</span> <span class="ow">in</span> <span class="n">extrema_indices</span><span class="p">[</span><span class="mi">1</span><span class="p">]])</span>
<span class="n">VBM</span> <span class="o">=</span> <span class="nb">max</span><span class="p">([</span><span class="n">Data</span><span class="o">.</span><span class="n">energies</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">j</span> <span class="ow">in</span> <span class="n">extrema_indices</span><span class="p">[</span><span class="mi">0</span><span class="p">]])</span>
<span class="k">return</span> <span class="n">CBM</span><span class="p">,</span> <span class="n">VBM</span></div>
<div class="viewcode-block" id="find_extrema_indices"><a class="viewcode-back" href="../../extrema.html#effmass.extrema.find_extrema_indices">[docs]</a><span class="k">def</span> <span class="nf">find_extrema_indices</span><span class="p">(</span><span class="n">Data</span><span class="p">,</span> <span class="n">Settings</span><span class="p">):</span>
<span class="sd">"""Finds the kpoint index and band index of the minimum/maximum energy</span>
<span class="sd"> turning points within :attr:`effmass.inputs.Settings.energy_range` of the</span>
<span class="sd"> conduction band minimum (:attr:`effmass.inputs.Data.CBM`) / valence band</span>
<span class="sd"> maximum (:attr:`effmass.inputs.Data.VBM`).</span>
<span class="sd"> Args:</span>
<span class="sd"> Data (Data): instance of the :class:`Data` class.</span>
<span class="sd"> Settings (Settings): instance of the :class:`Settings` class.</span>
<span class="sd"> Returns:</span>
<span class="sd"> array: A 3-dimensional array of shape (2, ). The first index differentiates between the valence band and conduction band. The second contains [:attr:`efmmas.inputs.Data.bands` index, :attr:`effmass.inputs.Data.kpoints` index] for each extrema.</span>
<span class="sd"> """</span>
<span class="n">energy_CB</span> <span class="o">=</span> <span class="n">ma</span><span class="o">.</span><span class="n">masked_where</span><span class="p">(</span><span class="n">Data</span><span class="o">.</span><span class="n">energies</span> <span class="o"><</span> <span class="n">Data</span><span class="o">.</span><span class="n">CBM</span><span class="p">,</span> <span class="n">Data</span><span class="o">.</span><span class="n">energies</span><span class="p">)</span>
<span class="n">energy_VB</span> <span class="o">=</span> <span class="n">ma</span><span class="o">.</span><span class="n">masked_where</span><span class="p">(</span><span class="n">Data</span><span class="o">.</span><span class="n">energies</span> <span class="o">></span> <span class="n">Data</span><span class="o">.</span><span class="n">VBM</span><span class="p">,</span> <span class="n">Data</span><span class="o">.</span><span class="n">energies</span><span class="p">)</span>
<span class="c1"># returns array of energies within energy_range</span>
<span class="n">holes_in_range</span> <span class="o">=</span> <span class="n">ma</span><span class="o">.</span><span class="n">masked_where</span><span class="p">(</span>
<span class="n">np</span><span class="o">.</span><span class="n">absolute</span><span class="p">(</span><span class="n">energy_VB</span> <span class="o">-</span> <span class="n">Data</span><span class="o">.</span><span class="n">VBM</span><span class="p">)</span> <span class="o">></span>
<span class="n">Settings</span><span class="o">.</span><span class="n">extrema_search_depth</span><span class="p">,</span> <span class="n">energy_VB</span><span class="p">)</span>
<span class="n">VB_maxima</span> <span class="o">=</span> <span class="n">ma</span><span class="o">.</span><span class="n">masked_where</span><span class="p">(</span>
<span class="n">_mark_maxima</span><span class="p">(</span><span class="n">holes_in_range</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">,</span> <span class="n">holes_in_range</span><span class="p">)</span>
<span class="c1"># returns array of energies within energy_range</span>
<span class="n">electrons_in_range</span> <span class="o">=</span> <span class="n">ma</span><span class="o">.</span><span class="n">masked_where</span><span class="p">(</span>
<span class="n">np</span><span class="o">.</span><span class="n">absolute</span><span class="p">(</span><span class="n">energy_CB</span> <span class="o">-</span> <span class="n">Data</span><span class="o">.</span><span class="n">CBM</span><span class="p">)</span> <span class="o">></span>
<span class="n">Settings</span><span class="o">.</span><span class="n">extrema_search_depth</span><span class="p">,</span> <span class="n">energy_CB</span><span class="p">)</span>
<span class="n">CB_minima</span> <span class="o">=</span> <span class="n">ma</span><span class="o">.</span><span class="n">masked_where</span><span class="p">(</span>
<span class="n">_mark_minima</span><span class="p">(</span><span class="n">electrons_in_range</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">,</span> <span class="n">electrons_in_range</span><span class="p">)</span>
<span class="c1"># Returns an array of band numbers and k-points for extrema in the correct energy range.</span>
<span class="c1"># The first index differentiates between the valence band and conduction band.</span>
<span class="c1"># At a given k-point there may be multiple bands with highest energy</span>
<span class="n">extrema_position</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">np</span><span class="o">.</span><span class="n">argwhere</span><span class="p">(</span><span class="n">VB_maxima</span><span class="o">.</span><span class="n">mask</span> <span class="o">==</span> <span class="mi">0</span><span class="p">),</span>
<span class="n">np</span><span class="o">.</span><span class="n">argwhere</span><span class="p">(</span><span class="n">CB_minima</span><span class="o">.</span><span class="n">mask</span> <span class="o">==</span> <span class="mi">0</span><span class="p">)],</span><span class="n">dtype</span><span class="o">=</span><span class="nb">object</span><span class="p">)</span>
<span class="k">return</span> <span class="n">extrema_position</span></div>
<span class="k">def</span> <span class="nf">_mark_maxima</span><span class="p">(</span><span class="n">holes_array</span><span class="p">):</span>
<span class="sd">"""Helper function which takes an array of hole energies and returns an</span>
<span class="sd"> array for masking those which are not maxima."""</span>
<span class="c1"># create array to append to</span>
<span class="n">not_maxima</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">width</span> <span class="o">=</span> <span class="n">holes_array</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">height</span> <span class="o">=</span> <span class="n">holes_array</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="c1"># handle edge cases</span>
<span class="k">for</span> <span class="n">band</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">height</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="n">holes_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">>=</span> <span class="n">holes_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="mi">0</span><span class="p">]):</span>
<span class="n">not_maxima</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">band</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="k">for</span> <span class="n">band</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">height</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="n">holes_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">>=</span> <span class="n">holes_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]):</span>
<span class="n">not_maxima</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">band</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="c1"># find the bands where numbers either side aren't bigger (the maxima)</span>
<span class="c1"># will also include inflexion but needed to get HSP's</span>
<span class="k">for</span> <span class="n">band</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">height</span><span class="p">):</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">width</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="n">holes_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">>=</span> <span class="n">holes_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="n">k</span><span class="p">]</span>
<span class="ow">or</span> <span class="n">holes_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">>=</span> <span class="n">holes_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="n">k</span><span class="p">]):</span>
<span class="n">not_maxima</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">band</span><span class="p">,</span> <span class="n">k</span><span class="p">])</span>
<span class="c1"># Need to assign false after inspection</span>
<span class="c1"># or it screws with the algorithm</span>
<span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">not_maxima</span><span class="p">:</span>
<span class="n">holes_array</span><span class="p">[</span><span class="n">row</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">row</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="o">=</span> <span class="kc">False</span>
<span class="c1"># returns matrix with all non-maxima marked false</span>
<span class="k">return</span> <span class="n">holes_array</span>
<span class="k">def</span> <span class="nf">_mark_minima</span><span class="p">(</span><span class="n">electrons_array</span><span class="p">):</span>
<span class="sd">"""Helper function which takes an array of electron energies and returns an</span>
<span class="sd"> array for masking those which are not minima."""</span>
<span class="c1"># create array to append to</span>
<span class="n">not_minima</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">width</span> <span class="o">=</span> <span class="n">electrons_array</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">height</span> <span class="o">=</span> <span class="n">electrons_array</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="c1"># handle edge cases</span>
<span class="k">for</span> <span class="n">band</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">height</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="n">electrons_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o"><=</span> <span class="n">electrons_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="mi">0</span><span class="p">]):</span>
<span class="n">not_minima</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">band</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="k">for</span> <span class="n">band</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">height</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="n">electrons_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o"><=</span> <span class="n">electrons_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]):</span>
<span class="n">not_minima</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">band</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="c1"># find the bands where numbers either side aren't bigger (the maxima)</span>
<span class="k">for</span> <span class="n">band</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">height</span><span class="p">):</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">width</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="n">electrons_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o"><=</span> <span class="n">electrons_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="n">k</span><span class="p">]</span> <span class="ow">or</span>
<span class="n">electrons_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o"><=</span> <span class="n">electrons_array</span><span class="p">[</span><span class="n">band</span><span class="p">,</span> <span class="n">k</span><span class="p">]):</span>
<span class="n">not_minima</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">band</span><span class="p">,</span> <span class="n">k</span><span class="p">])</span>
<span class="c1"># Need to assign false after inspection</span>
<span class="c1"># or it screws with the algorithm</span>
<span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">not_minima</span><span class="p">:</span>
<span class="n">electrons_array</span><span class="p">[</span><span class="n">row</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">row</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="o">=</span> <span class="kc">False</span>
<span class="c1"># returns matrix with all non-maxima marked false</span>
<span class="k">return</span> <span class="n">electrons_array</span>
<span class="k">def</span> <span class="nf">_within</span><span class="p">(</span><span class="n">band_index</span><span class="p">,</span> <span class="n">kpoint_index</span><span class="p">,</span> <span class="n">trial_kpoint_index</span><span class="p">,</span> <span class="n">Settings</span><span class="p">,</span> <span class="n">Data</span><span class="p">):</span>
<span class="sd">"""Helper function which checks whether trial_kpoint_index is less than</span>
<span class="sd"> :attr:`effmass.inputs.Settings.energy_range`.</span>
<span class="sd"> away from kpoint_index for a given band</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">absolute</span><span class="p">(</span><span class="n">Data</span><span class="o">.</span><span class="n">energies</span><span class="p">[</span><span class="n">band_index</span><span class="p">,</span> <span class="n">trial_kpoint_index</span><span class="p">]</span> <span class="o">-</span>
<span class="n">Data</span><span class="o">.</span><span class="n">energies</span><span class="p">[</span><span class="n">band_index</span><span class="p">,</span> <span class="n">kpoint_index</span><span class="p">])</span>
<span class="p">)</span> <span class="o"><</span> <span class="n">Settings</span><span class="o">.</span><span class="n">energy_range</span><span class="p">:</span>
<span class="k">return</span> <span class="kc">True</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">def</span> <span class="nf">_kpoints_after</span><span class="p">(</span><span class="n">band_index</span><span class="p">,</span> <span class="n">kpoint_index</span><span class="p">,</span> <span class="n">Settings</span><span class="p">,</span> <span class="n">Data</span><span class="p">):</span>
<span class="sd">"""Helper function that returns eigenstates which are 1) on the same band</span>
<span class="sd"> 2) before the given kpoint in the bandstructure route and 3) within</span>
<span class="sd"> :attr:`effmass.inputs.Settings.energy_range`."""</span>
<span class="n">trial_kpoint_index</span> <span class="o">=</span> <span class="n">kpoint_index</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">kpoint_after</span> <span class="o">=</span> <span class="p">[</span><span class="n">kpoint_index</span><span class="p">]</span>
<span class="k">while</span> <span class="p">(</span><span class="n">trial_kpoint_index</span> <span class="o"><</span> <span class="n">Data</span><span class="o">.</span><span class="n">number_of_kpoints</span>
<span class="ow">and</span> <span class="n">_within</span><span class="p">(</span><span class="n">band_index</span><span class="p">,</span> <span class="n">kpoint_index</span><span class="p">,</span> <span class="n">trial_kpoint_index</span><span class="p">,</span> <span class="n">Settings</span><span class="p">,</span>
<span class="n">Data</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">):</span>
<span class="n">kpoint_after</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">trial_kpoint_index</span><span class="p">)</span>
<span class="n">trial_kpoint_index</span> <span class="o">=</span> <span class="n">trial_kpoint_index</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">kpoint_after</span>
<span class="k">def</span> <span class="nf">_kpoints_before</span><span class="p">(</span><span class="n">band_index</span><span class="p">,</span> <span class="n">kpoint_index</span><span class="p">,</span> <span class="n">Settings</span><span class="p">,</span> <span class="n">Data</span><span class="p">):</span>
<span class="sd">"""Helper function that returns eigenstates which are 1) on the same band</span>
<span class="sd"> 2) before the given eigenstate in the route through reciprocal space 3)</span>
<span class="sd"> within :attr:`effmass.inputs.Settings.energy_range`."""</span>
<span class="n">trial_kpoint_index</span> <span class="o">=</span> <span class="n">kpoint_index</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">kpoint_before</span> <span class="o">=</span> <span class="p">[</span><span class="n">kpoint_index</span><span class="p">]</span>
<span class="k">while</span> <span class="n">trial_kpoint_index</span> <span class="o">>=</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">_within</span><span class="p">(</span><span class="n">band_index</span><span class="p">,</span> <span class="n">kpoint_index</span><span class="p">,</span>
<span class="n">trial_kpoint_index</span><span class="p">,</span> <span class="n">Settings</span><span class="p">,</span>
<span class="n">Data</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
<span class="n">kpoint_before</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">trial_kpoint_index</span><span class="p">)</span>
<span class="n">trial_kpoint_index</span> <span class="o">=</span> <span class="n">trial_kpoint_index</span> <span class="o">-</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">kpoint_before</span>
<div class="viewcode-block" id="get_kpoints_before"><a class="viewcode-back" href="../../extrema.html#effmass.extrema.get_kpoints_before">[docs]</a><span class="k">def</span> <span class="nf">get_kpoints_before</span><span class="p">(</span><span class="n">band_index</span><span class="p">,</span>
<span class="n">kpoint_index</span><span class="p">,</span>
<span class="n">Settings</span><span class="p">,</span>
<span class="n">Data</span><span class="p">,</span>
<span class="n">truncate_dir_change</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="sd">"""For a given eigenstate, finds eigenstates which 1) belong to the same</span>
<span class="sd"> band 2) come before the given eigenstate in the route through reciprocal</span>
<span class="sd"> space 3) are within :attr:`effmass.inputs.Settings.energy_range`.</span>
<span class="sd"> Args:</span>
<span class="sd"> band_index (int): index of :attr:`effmass.inputs.Data.bands`.</span>
<span class="sd"> kpoint_index (int): index of :attr:`effmass.inputs.Data.kpoints`.</span>
<span class="sd"> Settings (Settings): instance of the :class:`Settings` class.</span>
<span class="sd"> Data (Data): instance of the :class:`Data` class.</span>
<span class="sd"> truncate_dir_change (bool): If True, truncates eigenstates when there is a change in direction. If False, there is no truncation. Defaults to True.</span>
<span class="sd"> Returns:</span>
<span class="sd"> list(int): indices of :attr:`effmass.inputs.Data.kpoints`.</span>
<span class="sd"> """</span>
<span class="n">kpoints_before</span> <span class="o">=</span> <span class="n">_kpoints_before</span><span class="p">(</span><span class="n">band_index</span><span class="p">,</span> <span class="n">kpoint_index</span><span class="p">,</span> <span class="n">Settings</span><span class="p">,</span> <span class="n">Data</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">kpoints_before</span><span class="p">)</span> <span class="o">></span> <span class="mi">2</span><span class="p">:</span>
<span class="n">change_index</span> <span class="o">=</span> <span class="n">change_direction</span><span class="p">(</span><span class="n">Data</span><span class="o">.</span><span class="n">kpoints</span><span class="p">,</span> <span class="n">kpoints_before</span><span class="p">)</span>
<span class="k">if</span> <span class="n">change_index</span><span class="p">:</span>
<span class="k">if</span> <span class="n">truncate_dir_change</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
<span class="n">kpoints_before</span> <span class="o">=</span> <span class="n">kpoints_before</span><span class="p">[:</span><span class="n">change_index</span><span class="p">]</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">kpoints_before</span><span class="p">)</span> <span class="o"><</span> <span class="mi">3</span><span class="p">:</span>
<span class="n">kpoints_before</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">kpoints_before</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">return</span> <span class="n">kpoints_before</span></div>
<div class="viewcode-block" id="get_kpoints_after"><a class="viewcode-back" href="../../extrema.html#effmass.extrema.get_kpoints_after">[docs]</a><span class="k">def</span> <span class="nf">get_kpoints_after</span><span class="p">(</span><span class="n">band_index</span><span class="p">,</span>
<span class="n">kpoint_index</span><span class="p">,</span>
<span class="n">Settings</span><span class="p">,</span>
<span class="n">Data</span><span class="p">,</span>
<span class="n">truncate_dir_change</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="sd">"""For a given eigenstate, finds eigenstates which 1) belong to the same</span>
<span class="sd"> band 2) come after the given eigenstate in the route through reciprocal</span>
<span class="sd"> space 3) are within :attr:`effmass.inputs.Settings.energy_range`.</span>
<span class="sd"> Args:</span>
<span class="sd"> band_index (int): index of :attr:`effmass.inputs.Data.bands`.</span>
<span class="sd"> kpoint_index (int): index of :attr:`effmass.inputs.Data.kpoints`.</span>
<span class="sd"> Settings (Settings): instance of the :class:`Settings` class.</span>
<span class="sd"> Data (Data): instance of the :class:`Data` class.</span>
<span class="sd"> truncate_dir_change (bool): If True, truncates eigenstates when there is a change in direction. If False, there is no truncation. Defaults to True.</span>
<span class="sd"> Returns:</span>
<span class="sd"> list(int): indices of :attr:`effmass.inputs.Data.kpoints`.</span>
<span class="sd"> """</span>
<span class="n">kpoints_after</span> <span class="o">=</span> <span class="n">_kpoints_after</span><span class="p">(</span><span class="n">band_index</span><span class="p">,</span> <span class="n">kpoint_index</span><span class="p">,</span> <span class="n">Settings</span><span class="p">,</span> <span class="n">Data</span><span class="p">)</span>
<span class="c1"># now make sure that there is not a change in direction for this set of kpoints and that long enough</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">kpoints_after</span><span class="p">)</span> <span class="o">></span> <span class="mi">2</span><span class="p">:</span>
<span class="n">change_index</span> <span class="o">=</span> <span class="n">change_direction</span><span class="p">(</span><span class="n">Data</span><span class="o">.</span><span class="n">kpoints</span><span class="p">,</span> <span class="n">kpoints_after</span><span class="p">)</span>
<span class="k">if</span> <span class="n">change_index</span><span class="p">:</span>
<span class="k">if</span> <span class="n">truncate_dir_change</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
<span class="n">kpoints_after</span> <span class="o">=</span> <span class="n">kpoints_after</span><span class="p">[:</span><span class="n">change_index</span><span class="p">]</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">kpoints_after</span><span class="p">)</span> <span class="o"><</span> <span class="mi">3</span><span class="p">:</span>
<span class="n">kpoints_after</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">kpoints_after</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">return</span> <span class="n">kpoints_after</span></div>
<div class="viewcode-block" id="generate_segments"><a class="viewcode-back" href="../../extrema.html#effmass.extrema.generate_segments">[docs]</a><span class="k">def</span> <span class="nf">generate_segments</span><span class="p">(</span><span class="n">Settings</span><span class="p">,</span> <span class="n">Data</span><span class="p">,</span> <span class="n">bk</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">truncate_dir_change</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="sd">"""Generates a list of Segment objects.</span>
<span class="sd"> Args:</span>
<span class="sd"> Settings (Settings): instance of the :class:`Settings` class.</span>
<span class="sd"> Data (Data): instance of the :class:`Data` class.</span>
<span class="sd"> truncate_dir_change (bool): If True, truncates eigenstates when there is a change in direction. If False, there is no truncation. Defaults to True.</span>
<span class="sd"> bk (list(int)): To manually set an extrema point, in format [:attr:`efmmas.inputs.Data.bands` index, :attr:`effmass.inputs.Data.kpoints` index]. Defaults to None.</span>
<span class="sd"> </span>
<span class="sd"> Returns:</span>
<span class="sd"> list(Segments): A list of :class:`Segment` objects.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">bk</span><span class="p">:</span>
<span class="n">extrema_array</span> <span class="o">=</span> <span class="n">bk</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">extrema_array_3d</span> <span class="o">=</span> <span class="n">find_extrema_indices</span><span class="p">(</span><span class="n">Data</span><span class="p">,</span> <span class="n">Settings</span><span class="p">)</span>
<span class="n">extrema_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">extrema_array_3d</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">extrema_array_3d</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
<span class="n">kpoints_list</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">band_list</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">band</span><span class="p">,</span> <span class="n">kpoint</span> <span class="ow">in</span> <span class="n">extrema_array</span><span class="p">:</span> <span class="c1"># flatten CB and VB arrays to a single array</span>
<span class="n">kpoints_before</span> <span class="o">=</span> <span class="n">get_kpoints_before</span><span class="p">(</span>
<span class="n">band</span><span class="p">,</span>
<span class="n">kpoint</span><span class="p">,</span>
<span class="n">Settings</span><span class="p">,</span>
<span class="n">Data</span><span class="p">,</span>
<span class="n">truncate_dir_change</span><span class="o">=</span><span class="n">truncate_dir_change</span><span class="p">)</span>
<span class="n">kpoints_after</span> <span class="o">=</span> <span class="n">get_kpoints_after</span><span class="p">(</span>
<span class="n">band</span><span class="p">,</span>
<span class="n">kpoint</span><span class="p">,</span>
<span class="n">Settings</span><span class="p">,</span>
<span class="n">Data</span><span class="p">,</span>
<span class="n">truncate_dir_change</span><span class="o">=</span><span class="n">truncate_dir_change</span><span class="p">)</span>
<span class="k">if</span> <span class="n">kpoints_before</span><span class="p">:</span>
<span class="n">kpoints_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">kpoints_before</span><span class="p">)</span>
<span class="n">band_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">band</span><span class="p">)</span>
<span class="k">if</span> <span class="n">kpoints_after</span><span class="p">:</span>
<span class="n">kpoints_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">kpoints_after</span><span class="p">)</span>
<span class="n">band_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">band</span><span class="p">)</span>
<span class="n">segments</span> <span class="o">=</span> <span class="p">[</span>
<span class="n">analysis</span><span class="o">.</span><span class="n">Segment</span><span class="p">(</span><span class="n">Data</span><span class="p">,</span> <span class="n">band</span><span class="p">,</span> <span class="n">kpoints</span><span class="p">)</span>
<span class="k">for</span> <span class="n">band</span><span class="p">,</span> <span class="n">kpoints</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">band_list</span><span class="p">,</span> <span class="n">kpoints_list</span><span class="p">)</span>
<span class="p">]</span>
<span class="k">return</span> <span class="n">segments</span></div>
</pre></div>
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