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    <h1>Source code for nifty.operators.fft_operator.transformations.gllmtransformation</h1><div class="highlight"><pre>
    <span></span><span class="c1"># NIFTy</span>
    <span class="c1"># Copyright (C) 2017 Theo Steininger</span>
    <span class="c1">#</span>
    <span class="c1"># Author: Theo Steininger</span>
    <span class="c1">#</span>
    <span class="c1"># This program is free software: you can redistribute it and/or modify</span>
    <span class="c1"># it under the terms of the GNU General Public License as published by</span>
    <span class="c1"># the Free Software Foundation, either version 3 of the License, or</span>
    <span class="c1"># (at your option) any later version.</span>
    <span class="c1">#</span>
    <span class="c1"># This program is distributed in the hope that it will be useful,</span>
    <span class="c1"># but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
    <span class="c1"># MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span>
    <span class="c1"># GNU General Public License for more details.</span>
    <span class="c1">#</span>
    <span class="c1"># You should have received a copy of the GNU General Public License</span>
    <span class="c1"># along with this program. If not, see &lt;http://www.gnu.org/licenses/&gt;.</span>
    <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
    <span class="kn">from</span> <span class="nn">nifty.config</span> <span class="k">import</span> <span class="n">dependency_injector</span> <span class="k">as</span> <span class="n">gdi</span>
    <span class="kn">from</span> <span class="nn">nifty</span> <span class="k">import</span> <span class="n">GLSpace</span><span class="p">,</span> <span class="n">LMSpace</span>
    <span class="kn">from</span> <span class="nn">slicing_transformation</span> <span class="k">import</span> <span class="n">SlicingTransformation</span>
    <span class="kn">import</span> <span class="nn">lm_transformation_helper</span>
    <span class="n">pyHealpix</span> <span class="o">=</span> <span class="n">gdi</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;pyHealpix&#39;</span><span class="p">)</span>
    <div class="viewcode-block" id="GLLMTransformation"><a class="viewcode-back" href="../../../../../gllm_transformation.html#nifty.GLLMTransformation">[docs]</a><span class="k">class</span> <span class="nc">GLLMTransformation</span><span class="p">(</span><span class="n">SlicingTransformation</span><span class="p">):</span>
    <span class="c1"># ---Overwritten properties and methods---</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">domain</span><span class="p">,</span> <span class="n">codomain</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">module</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
    <span class="n">module</span> <span class="o">=</span> <span class="s1">&#39;pyHealpix&#39;</span>
    <span class="k">if</span> <span class="n">module</span> <span class="o">!=</span> <span class="s1">&#39;pyHealpix&#39;</span><span class="p">:</span>
    <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Unsupported SHT module.&quot;</span><span class="p">)</span>
    <span class="k">if</span> <span class="s1">&#39;pyHealpix&#39;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">gdi</span><span class="p">:</span>
    <span class="k">raise</span> <span class="ne">ImportError</span><span class="p">(</span>
    <span class="s2">&quot;The module pyHealpix is needed but not available.&quot;</span><span class="p">)</span>
    <span class="nb">super</span><span class="p">(</span><span class="n">GLLMTransformation</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">domain</span><span class="p">,</span> <span class="n">codomain</span><span class="p">,</span> <span class="n">module</span><span class="p">)</span>
    <span class="c1"># ---Mandatory properties and methods---</span>
    <span class="nd">@property</span>
    <span class="k">def</span> <span class="nf">unitary</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
    <span class="k">return</span> <span class="kc">False</span>
    <div class="viewcode-block" id="GLLMTransformation.get_codomain"><a class="viewcode-back" href="../../../../../gllm_transformation.html#nifty.GLLMTransformation.get_codomain">[docs]</a> <span class="nd">@classmethod</span>
    <span class="k">def</span> <span class="nf">get_codomain</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">domain</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
    <span class="sd"> Generates a compatible codomain to which transformations are</span>
    <span class="sd"> reasonable, i.e.\ an instance of the :py:class:`lm_space` class.</span>
    <span class="sd"> Parameters</span>
    <span class="sd"> ----------</span>
    <span class="sd"> domain: GLSpace</span>
    <span class="sd"> Space for which a codomain is to be generated</span>
    <span class="sd"> Returns</span>
    <span class="sd"> -------</span>
    <span class="sd"> codomain : LMSpace</span>
    <span class="sd"> A compatible codomain.</span>
    <span class="sd"> &quot;&quot;&quot;</span>
    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">domain</span><span class="p">,</span> <span class="n">GLSpace</span><span class="p">):</span>
    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;domain needs to be a GLSpace&quot;</span><span class="p">)</span>
    <span class="n">nlat</span> <span class="o">=</span> <span class="n">domain</span><span class="o">.</span><span class="n">nlat</span>
    <span class="n">lmax</span> <span class="o">=</span> <span class="n">nlat</span> <span class="o">-</span> <span class="mi">1</span>
    <span class="n">result</span> <span class="o">=</span> <span class="n">LMSpace</span><span class="p">(</span><span class="n">lmax</span><span class="o">=</span><span class="n">lmax</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">result</span></div>
    <span class="nd">@classmethod</span>
    <span class="k">def</span> <span class="nf">check_codomain</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">domain</span><span class="p">,</span> <span class="n">codomain</span><span class="p">):</span>
    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">domain</span><span class="p">,</span> <span class="n">GLSpace</span><span class="p">):</span>
    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;domain is not a GLSpace&quot;</span><span class="p">)</span>
    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">codomain</span><span class="p">,</span> <span class="n">LMSpace</span><span class="p">):</span>
    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;codomain must be a LMSpace.&quot;</span><span class="p">)</span>
    <span class="n">nlat</span> <span class="o">=</span> <span class="n">domain</span><span class="o">.</span><span class="n">nlat</span>
    <span class="n">nlon</span> <span class="o">=</span> <span class="n">domain</span><span class="o">.</span><span class="n">nlon</span>
    <span class="n">lmax</span> <span class="o">=</span> <span class="n">codomain</span><span class="o">.</span><span class="n">lmax</span>
    <span class="n">mmax</span> <span class="o">=</span> <span class="n">codomain</span><span class="o">.</span><span class="n">mmax</span>
    <span class="k">if</span> <span class="n">lmax</span> <span class="o">!=</span> <span class="n">mmax</span><span class="p">:</span>
    <span class="bp">cls</span><span class="o">.</span><span class="n">logger</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">&quot;Unrecommended: codomain has lmax != mmax.&quot;</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">lmax</span> <span class="o">!=</span> <span class="n">nlat</span> <span class="o">-</span> <span class="mi">1</span><span class="p">:</span>
    <span class="bp">cls</span><span class="o">.</span><span class="n">logger</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">&quot;Unrecommended: codomain has lmax != nlat - 1.&quot;</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">nlon</span> <span class="o">!=</span> <span class="mi">2</span><span class="o">*</span><span class="n">nlat</span> <span class="o">-</span> <span class="mi">1</span><span class="p">:</span>
    <span class="bp">cls</span><span class="o">.</span><span class="n">logger</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">&quot;Unrecommended: domain has nlon != 2*nlat - 1.&quot;</span><span class="p">)</span>
    <span class="nb">super</span><span class="p">(</span><span class="n">GLLMTransformation</span><span class="p">,</span> <span class="bp">cls</span><span class="p">)</span><span class="o">.</span><span class="n">check_codomain</span><span class="p">(</span><span class="n">domain</span><span class="p">,</span> <span class="n">codomain</span><span class="p">)</span>
    <span class="k">def</span> <span class="nf">_transformation_of_slice</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">inp</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">inp</span><span class="o">.</span><span class="n">dtype</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">complex</span><span class="p">):</span>
    <span class="bp">self</span><span class="o">.</span><span class="n">logger</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">&quot;The input array has dtype: </span><span class="si">%s</span><span class="s2">. The FFT will &quot;</span>
    <span class="s2">&quot;be performed at double precision.&quot;</span> <span class="o">%</span>
    <span class="nb">str</span><span class="p">(</span><span class="n">inp</span><span class="o">.</span><span class="n">dtype</span><span class="p">))</span>
    <span class="n">nlat</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">domain</span><span class="o">.</span><span class="n">nlat</span>
    <span class="n">nlon</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">domain</span><span class="o">.</span><span class="n">nlon</span>
    <span class="n">lmax</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">codomain</span><span class="o">.</span><span class="n">lmax</span>
    <span class="n">mmax</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">codomain</span><span class="o">.</span><span class="n">mmax</span>
    <span class="n">sjob</span> <span class="o">=</span> <span class="n">pyHealpix</span><span class="o">.</span><span class="n">sharpjob_d</span><span class="p">()</span>
    <span class="n">sjob</span><span class="o">.</span><span class="n">set_Gauss_geometry</span><span class="p">(</span><span class="n">nlat</span><span class="p">,</span> <span class="n">nlon</span><span class="p">)</span>
    <span class="n">sjob</span><span class="o">.</span><span class="n">set_triangular_alm_info</span><span class="p">(</span><span class="n">lmax</span><span class="p">,</span> <span class="n">mmax</span><span class="p">)</span>
    <span class="k">if</span> <span class="nb">issubclass</span><span class="p">(</span><span class="n">inp</span><span class="o">.</span><span class="n">dtype</span><span class="o">.</span><span class="n">type</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">complexfloating</span><span class="p">):</span>
    <span class="p">[</span><span class="n">resultReal</span><span class="p">,</span> <span class="n">resultImag</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="n">sjob</span><span class="o">.</span><span class="n">map2alm</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">(</span><span class="n">inp</span><span class="o">.</span><span class="n">real</span><span class="p">,</span> <span class="n">inp</span><span class="o">.</span><span class="n">imag</span><span class="p">)]</span>
    <span class="p">[</span><span class="n">resultReal</span><span class="p">,</span>
    <span class="n">resultImag</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="n">lm_transformation_helper</span><span class="o">.</span><span class="n">buildIdx</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">lmax</span><span class="o">=</span><span class="n">lmax</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="n">resultReal</span><span class="p">,</span> <span class="n">resultImag</span><span class="p">]]</span>
    <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_combine_complex_result</span><span class="p">(</span><span class="n">resultReal</span><span class="p">,</span> <span class="n">resultImag</span><span class="p">)</span>
    <span class="k">else</span><span class="p">:</span>
    <span class="n">result</span> <span class="o">=</span> <span class="n">sjob</span><span class="o">.</span><span class="n">map2alm</span><span class="p">(</span><span class="n">inp</span><span class="p">)</span>
    <span class="n">result</span> <span class="o">=</span> <span class="n">lm_transformation_helper</span><span class="o">.</span><span class="n">buildIdx</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">lmax</span><span class="o">=</span><span class="n">lmax</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">result</span></div>
    </pre></div>
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    <h1>Source code for nifty.operators.fft_operator.transformations.hplmtransformation</h1><div class="highlight"><pre>
    <span></span><span class="c1"># NIFTy</span>
    <span class="c1"># Copyright (C) 2017 Theo Steininger</span>
    <span class="c1">#</span>
    <span class="c1"># Author: Theo Steininger</span>
    <span class="c1">#</span>
    <span class="c1"># This program is free software: you can redistribute it and/or modify</span>
    <span class="c1"># it under the terms of the GNU General Public License as published by</span>
    <span class="c1"># the Free Software Foundation, either version 3 of the License, or</span>
    <span class="c1"># (at your option) any later version.</span>
    <span class="c1">#</span>
    <span class="c1"># This program is distributed in the hope that it will be useful,</span>
    <span class="c1"># but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
    <span class="c1"># MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span>
    <span class="c1"># GNU General Public License for more details.</span>
    <span class="c1">#</span>
    <span class="c1"># You should have received a copy of the GNU General Public License</span>
    <span class="c1"># along with this program. If not, see &lt;http://www.gnu.org/licenses/&gt;.</span>
    <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
    <span class="kn">from</span> <span class="nn">nifty.config</span> <span class="k">import</span> <span class="n">dependency_injector</span> <span class="k">as</span> <span class="n">gdi</span>
    <span class="kn">from</span> <span class="nn">nifty</span> <span class="k">import</span> <span class="n">HPSpace</span><span class="p">,</span> <span class="n">LMSpace</span>
    <span class="kn">from</span> <span class="nn">slicing_transformation</span> <span class="k">import</span> <span class="n">SlicingTransformation</span>
    <span class="kn">import</span> <span class="nn">lm_transformation_helper</span>
    <span class="n">pyHealpix</span> <span class="o">=</span> <span class="n">gdi</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;pyHealpix&#39;</span><span class="p">)</span>
    <div class="viewcode-block" id="HPLMTransformation"><a class="viewcode-back" href="../../../../../hplm_transformation.html#nifty.HPLMTransformation">[docs]</a><span class="k">class</span> <span class="nc">HPLMTransformation</span><span class="p">(</span><span class="n">SlicingTransformation</span><span class="p">):</span>
    <span class="c1"># ---Overwritten properties and methods---</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">domain</span><span class="p">,</span> <span class="n">codomain</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">module</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
    <span class="n">module</span> <span class="o">=</span> <span class="s1">&#39;pyHealpix&#39;</span>
    <span class="k">if</span> <span class="n">module</span> <span class="o">!=</span> <span class="s1">&#39;pyHealpix&#39;</span><span class="p">:</span>
    <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Unsupported SHT module.&quot;</span><span class="p">)</span>
    <span class="k">if</span> <span class="s1">&#39;pyHealpix&#39;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">gdi</span><span class="p">:</span>
    <span class="k">raise</span> <span class="ne">ImportError</span><span class="p">(</span>
    <span class="s2">&quot;The module pyHealpix is needed but not available&quot;</span><span class="p">)</span>
    <span class="nb">super</span><span class="p">(</span><span class="n">HPLMTransformation</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">domain</span><span class="p">,</span> <span class="n">codomain</span><span class="p">,</span> <span class="n">module</span><span class="p">)</span>
    <span class="c1"># ---Mandatory properties and methods---</span>
    <span class="nd">@property</span>
    <span class="k">def</span> <span class="nf">unitary</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
    <span class="k">return</span> <span class="kc">False</span>
    <div class="viewcode-block" id="HPLMTransformation.get_codomain"><a class="viewcode-back" href="../../../../../hplm_transformation.html#nifty.HPLMTransformation.get_codomain">[docs]</a> <span class="nd">@classmethod</span>
    <span class="k">def</span> <span class="nf">get_codomain</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">domain</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
    <span class="sd"> Generates a compatible codomain to which transformations are</span>
    <span class="sd"> reasonable, i.e.\ an instance of the :py:class:`lm_space` class.</span>
    <span class="sd"> Parameters</span>
    <span class="sd"> ----------</span>
    <span class="sd"> domain: HPSpace</span>
    <span class="sd"> Space for which a codomain is to be generated</span>
    <span class="sd"> Returns</span>
    <span class="sd"> -------</span>
    <span class="sd"> codomain : LMSpace</span>
    <span class="sd"> A compatible codomain.</span>
    <span class="sd"> &quot;&quot;&quot;</span>
    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">domain</span><span class="p">,</span> <span class="n">HPSpace</span><span class="p">):</span>