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<h1>Source code for MMTK.Subspace</h1><div class="highlight"><pre>
<span class="c"># This module implements subspaces for motion analysis etc.</span>
<span class="c">#</span>
<span class="c"># Written by Konrad Hinsen</span>
<span class="c">#</span>
<span class="sd">"""</span>
<span class="sd">Linear subspaces for infinitesimal motions</span>
<span class="sd">This module implements subspaces for infinitesimal (or finite</span>
<span class="sd">small-amplitude) atomic motions. They can be used in normal mode</span>
<span class="sd">calculations or for analyzing complex motions. For an explanation, see:</span>
<span class="sd"> | K. Hinsen and G.R. Kneller</span>
<span class="sd"> | Projection methods for the analysis of complex motions in macromolecules</span>
<span class="sd"> | Mol. Sim. 23:275-292 (2000)</span>
<span class="sd">"""</span>
<span class="n">__docformat__</span> <span class="o">=</span> <span class="s">'restructuredtext'</span>
<span class="kn">from</span> <span class="nn">MMTK</span> <span class="kn">import</span> <span class="n">Utility</span><span class="p">,</span> <span class="n">ParticleProperties</span>
<span class="kn">from</span> <span class="nn">Scientific.Geometry</span> <span class="kn">import</span> <span class="n">Vector</span><span class="p">,</span> <span class="n">ex</span><span class="p">,</span> <span class="n">ey</span><span class="p">,</span> <span class="n">ez</span>
<span class="kn">from</span> <span class="nn">Scientific</span> <span class="kn">import</span> <span class="n">N</span>
<span class="kn">import</span> <span class="nn">copy</span>
<span class="c">#</span>
<span class="c"># Import LAPACK routines</span>
<span class="c">#</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">array_package</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">package</span>
<span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
<span class="n">array_package</span> <span class="o">=</span> <span class="s">"Numeric"</span>
<span class="n">dgesdd</span> <span class="o">=</span> <span class="bp">None</span>
<span class="k">try</span><span class="p">:</span>
<span class="k">if</span> <span class="n">array_package</span> <span class="o">==</span> <span class="s">"Numeric"</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">lapack_lite</span> <span class="kn">import</span> <span class="n">dgesdd</span><span class="p">,</span> <span class="n">LapackError</span>
<span class="k">else</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">numpy.linalg.lapack_lite</span> <span class="kn">import</span> <span class="n">dgesdd</span><span class="p">,</span> <span class="n">LapackError</span>
<span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span> <span class="k">pass</span>
<span class="k">if</span> <span class="n">dgesdd</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="k">try</span><span class="p">:</span>
<span class="c"># PyLAPACK</span>
<span class="kn">from</span> <span class="nn">lapack_dge</span> <span class="kn">import</span> <span class="n">dgesdd</span>
<span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span> <span class="k">pass</span>
<span class="k">if</span> <span class="n">dgesdd</span><span class="p">:</span>
<span class="n">n</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">array</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="n">n</span><span class="p">),</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">sv</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">n</span><span class="p">,),</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="n">n</span><span class="p">),</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">vt</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="n">n</span><span class="p">),</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">work</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1</span><span class="p">,),</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">int_types</span> <span class="o">=</span> <span class="p">[</span><span class="n">N</span><span class="o">.</span><span class="n">Int</span><span class="p">,</span> <span class="n">N</span><span class="o">.</span><span class="n">Int8</span><span class="p">,</span> <span class="n">N</span><span class="o">.</span><span class="n">Int16</span><span class="p">,</span> <span class="n">N</span><span class="o">.</span><span class="n">Int32</span><span class="p">]</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">int_types</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">N</span><span class="o">.</span><span class="n">Int64</span><span class="p">)</span>
<span class="n">int_types</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">N</span><span class="o">.</span><span class="n">Int128</span><span class="p">)</span>
<span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
<span class="k">pass</span>
<span class="k">for</span> <span class="n">int_type</span> <span class="ow">in</span> <span class="n">int_types</span><span class="p">:</span>
<span class="n">iwork</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1</span><span class="p">,),</span> <span class="n">int_type</span><span class="p">)</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">dgesdd</span><span class="p">(</span><span class="s">'S'</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">array</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">sv</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">vt</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">work</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">iwork</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="k">break</span>
<span class="k">except</span> <span class="n">LapackError</span><span class="p">:</span>
<span class="k">pass</span>
<span class="k">del</span> <span class="n">n</span><span class="p">,</span> <span class="n">array</span><span class="p">,</span> <span class="n">sv</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">vt</span><span class="p">,</span> <span class="n">work</span><span class="p">,</span> <span class="n">iwork</span><span class="p">,</span> <span class="n">int_types</span>
<span class="k">del</span> <span class="n">array_package</span>
<span class="c">#</span>
<span class="c"># A set of particle vectors that define a subspace</span>
<span class="c">#</span>
<span class="k">class</span> <span class="nc">ParticleVectorSet</span><span class="p">(</span><span class="nb">object</span><span class="p">):</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">universe</span><span class="p">,</span> <span class="n">data</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">universe</span> <span class="o">=</span> <span class="n">universe</span>
<span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">data</span><span class="p">)</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">arraytype</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">n</span> <span class="o">=</span> <span class="n">data</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="bp">self</span><span class="o">.</span><span class="n">array</span> <span class="o">=</span> <span class="n">data</span>
<span class="k">else</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">n</span> <span class="o">=</span> <span class="n">data</span>
<span class="bp">self</span><span class="o">.</span><span class="n">array</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">n</span><span class="p">,</span> <span class="n">universe</span><span class="o">.</span><span class="n">numberOfAtoms</span><span class="p">(),</span> <span class="mi">3</span><span class="p">),</span>
<span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">n</span>
<span class="k">def</span> <span class="nf">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
<span class="k">if</span> <span class="n">i</span> <span class="o">>=</span> <span class="bp">self</span><span class="o">.</span><span class="n">n</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">IndexError</span>
<span class="k">return</span> <span class="n">ParticleProperties</span><span class="o">.</span><span class="n">ParticleVector</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">array</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<div class="viewcode-block" id="Subspace"><a class="viewcode-back" href="../../modules.html#MMTK.Subspace.Subspace">[docs]</a><span class="k">class</span> <span class="nc">Subspace</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Subspace of infinitesimal atomic motions</span>
<span class="sd"> """</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">universe</span><span class="p">,</span> <span class="n">vectors</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> :param universe: the universe for which the subspace is created</span>
<span class="sd"> :type universe: :class:`~MMTK.Universe.Universe`</span>
<span class="sd"> :param vectors: a list of :class:`~MMTK.ParticleProperties.ParticleVector`</span>
<span class="sd"> objects that define the subspace. They need not be</span>
<span class="sd"> orthogonal or linearly independent.</span>
<span class="sd"> :type vectors: list</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">universe</span> <span class="o">=</span> <span class="n">universe</span>
<span class="bp">self</span><span class="o">.</span><span class="n">vectors</span> <span class="o">=</span> <span class="n">vectors</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_basis</span> <span class="o">=</span> <span class="bp">None</span>
<span class="k">def</span> <span class="nf">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
<span class="k">return</span> <span class="n">Subspace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">vectors</span><span class="o">+</span><span class="n">other</span><span class="o">.</span><span class="n">vectors</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">vectors</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">vectors</span><span class="p">[</span><span class="n">item</span><span class="p">]</span>
<div class="viewcode-block" id="Subspace.getBasis"><a class="viewcode-back" href="../../modules.html#MMTK.Subspace.Subspace.getBasis">[docs]</a> <span class="k">def</span> <span class="nf">getBasis</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Construct a basis for the subspace by orthonormalization of</span>
<span class="sd"> the input vectors using Singular Value Decomposition. The</span>
<span class="sd"> basis consists of a sequence of</span>
<span class="sd"> :class:`~MMTK.ParticleProperties.ParticleVector`</span>
<span class="sd"> objects that are orthonormal in configuration space.</span>
<span class="sd"> :returns: the basis</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_basis</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">basis</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">v</span><span class="o">.</span><span class="n">array</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">vectors</span><span class="p">],</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">shape</span> <span class="o">=</span> <span class="n">basis</span><span class="o">.</span><span class="n">shape</span>
<span class="n">nvectors</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">natoms</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">basis</span><span class="o">.</span><span class="n">shape</span> <span class="o">=</span> <span class="p">(</span><span class="n">nvectors</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">)</span>
<span class="n">sv</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="nb">min</span><span class="p">(</span><span class="n">nvectors</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">),),</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">min_n_m</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span> <span class="n">nvectors</span><span class="p">)</span>
<span class="n">vt</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">nvectors</span><span class="p">,</span> <span class="n">min_n_m</span><span class="p">),</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">work</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">1</span><span class="p">,),</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">iwork</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">8</span><span class="o">*</span><span class="n">min_n_m</span><span class="p">,),</span> <span class="n">int_type</span><span class="p">)</span>
<span class="k">if</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span> <span class="o">>=</span> <span class="n">nvectors</span><span class="p">:</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">dgesdd</span><span class="p">(</span><span class="s">'O'</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span> <span class="n">nvectors</span><span class="p">,</span> <span class="n">basis</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span>
<span class="n">sv</span><span class="p">,</span> <span class="n">basis</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span> <span class="n">vt</span><span class="p">,</span> <span class="n">min_n_m</span><span class="p">,</span>
<span class="n">work</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">iwork</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">work</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="nb">int</span><span class="p">(</span><span class="n">work</span><span class="p">[</span><span class="mi">0</span><span class="p">]),),</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">dgesdd</span><span class="p">(</span><span class="s">'O'</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span> <span class="n">nvectors</span><span class="p">,</span> <span class="n">basis</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span>
<span class="n">sv</span><span class="p">,</span> <span class="n">basis</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span> <span class="n">vt</span><span class="p">,</span> <span class="n">min_n_m</span><span class="p">,</span>
<span class="n">work</span><span class="p">,</span> <span class="n">work</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">iwork</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">basis</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">min_n_m</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">),</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">dgesdd</span><span class="p">(</span><span class="s">'S'</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span> <span class="n">nvectors</span><span class="p">,</span> <span class="n">basis</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span>
<span class="n">sv</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span> <span class="n">vt</span><span class="p">,</span> <span class="n">min_n_m</span><span class="p">,</span>
<span class="n">work</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">iwork</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">work</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="nb">int</span><span class="p">(</span><span class="n">work</span><span class="p">[</span><span class="mi">0</span><span class="p">]),),</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">dgesdd</span><span class="p">(</span><span class="s">'S'</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span> <span class="n">nvectors</span><span class="p">,</span> <span class="n">basis</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span>
<span class="n">sv</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="n">natoms</span><span class="p">,</span> <span class="n">vt</span><span class="p">,</span> <span class="n">min_n_m</span><span class="p">,</span>
<span class="n">work</span><span class="p">,</span> <span class="n">work</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">iwork</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="k">if</span> <span class="n">result</span><span class="p">[</span><span class="s">'info'</span><span class="p">]</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">'Lapack SVD: '</span> <span class="o">+</span> <span class="sb">`result['info']`</span><span class="p">)</span>
<span class="n">svmax</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">maximum</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">sv</span><span class="p">)</span>
<span class="n">nvectors</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">add</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">N</span><span class="o">.</span><span class="n">greater</span><span class="p">(</span><span class="n">sv</span><span class="p">,</span> <span class="mf">1.e-10</span><span class="o">*</span><span class="n">svmax</span><span class="p">))</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">u</span><span class="p">[:</span><span class="n">nvectors</span><span class="p">]</span>
<span class="n">u</span><span class="o">.</span><span class="n">shape</span> <span class="o">=</span> <span class="p">(</span><span class="n">nvectors</span><span class="p">,</span> <span class="n">natoms</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_basis</span> <span class="o">=</span> <span class="n">ParticleVectorSet</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_basis</span>
</div>
<div class="viewcode-block" id="Subspace.projectionOf"><a class="viewcode-back" href="../../modules.html#MMTK.Subspace.Subspace.projectionOf">[docs]</a> <span class="k">def</span> <span class="nf">projectionOf</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vector</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> :param vector: a particle vector</span>
<span class="sd"> :type vector: :class:`~MMTK.ParticleProperties.ParticleVector`</span>
<span class="sd"> :returns: the projection of the vector onto the subspace.</span>
<span class="sd"> """</span>
<span class="n">vector</span> <span class="o">=</span> <span class="n">vector</span><span class="o">.</span><span class="n">array</span>
<span class="n">basis</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">getBasis</span><span class="p">()</span><span class="o">.</span><span class="n">array</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">vector</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">N</span><span class="o">.</span><span class="n">Float</span><span class="p">)</span>
<span class="k">for</span> <span class="n">bv</span> <span class="ow">in</span> <span class="n">basis</span><span class="p">:</span>
<span class="n">N</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">N</span><span class="o">.</span><span class="n">add</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">N</span><span class="o">.</span><span class="n">ravel</span><span class="p">(</span><span class="n">bv</span><span class="o">*</span><span class="n">vector</span><span class="p">))</span><span class="o">*</span><span class="n">bv</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
<span class="k">return</span> <span class="n">ParticleProperties</span><span class="o">.</span><span class="n">ParticleVector</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
</div>
<div class="viewcode-block" id="Subspace.projectionComplementOf"><a class="viewcode-back" href="../../modules.html#MMTK.Subspace.Subspace.projectionComplementOf">[docs]</a> <span class="k">def</span> <span class="nf">projectionComplementOf</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vector</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> :param vector: a particle vector</span>
<span class="sd"> :type vector: :class:`~MMTK.ParticleProperties.ParticleVector`</span>
<span class="sd"> :returns: the projection of the vector onto the orthogonal complement</span>
<span class="sd"> of the subspace.</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">vector</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">projectionOf</span><span class="p">(</span><span class="n">vector</span><span class="p">)</span>
</div>
<div class="viewcode-block" id="Subspace.complement"><a class="viewcode-back" href="../../modules.html#MMTK.Subspace.Subspace.complement">[docs]</a> <span class="k">def</span> <span class="nf">complement</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> :returns: the orthogonal complement subspace</span>
<span class="sd"> :rtype: :class:`~MMTK.Subspace.Subspace`</span>
<span class="sd"> """</span>
<span class="n">basis</span> <span class="o">=</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="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="o">.</span><span class="n">numberOfAtoms</span><span class="p">()):</span>
<span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="p">[</span><span class="n">ex</span><span class="p">,</span> <span class="n">ey</span><span class="p">,</span> <span class="n">ez</span><span class="p">]:</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">ParticleProperties</span><span class="o">.</span><span class="n">ParticleVector</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="p">)</span>
<span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">e</span>
<span class="n">basis</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">projectionComplementOf</span><span class="p">(</span><span class="n">p</span><span class="p">))</span>
<span class="k">return</span> <span class="n">Subspace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="p">,</span> <span class="n">basis</span><span class="p">)</span>
</div></div>
<div class="viewcode-block" id="LinkedRigidBodyMotionSubspace"><a class="viewcode-back" href="../../modules.html#MMTK.Subspace.LinkedRigidBodyMotionSubspace">[docs]</a><span class="k">class</span> <span class="nc">LinkedRigidBodyMotionSubspace</span><span class="p">(</span><span class="n">Subspace</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Subspace for the motion of linked rigid bodies</span>
<span class="sd"> This class describes the same subspace as RigidBodyMotionSubspace,</span>
<span class="sd"> and is used by the latter. For collections of several chains of</span>
<span class="sd"> linked rigid bodies, RigidBodyMotionSubspace is more efficient.</span>
<span class="sd"> """</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">universe</span><span class="p">,</span> <span class="n">rigid_bodies</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> :param universe: the universe for which the subspace is created</span>
<span class="sd"> :type universe: :class:`~MMTK.Universe.Universe`</span>
<span class="sd"> :param rigid_bodies: a list or set of rigid bodies</span>
<span class="sd"> with some common atoms</span>
<span class="sd"> """</span>
<span class="n">ex_ey_ez</span> <span class="o">=</span> <span class="p">[</span><span class="n">Vector</span><span class="p">(</span><span class="mf">1.</span><span class="p">,</span><span class="mf">0.</span><span class="p">,</span><span class="mf">0.</span><span class="p">),</span> <span class="n">Vector</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span><span class="mf">1.</span><span class="p">,</span><span class="mf">0.</span><span class="p">),</span> <span class="n">Vector</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span><span class="mf">0.</span><span class="p">,</span><span class="mf">1.</span><span class="p">)]</span>
<span class="c"># Constructs</span>
<span class="c"># 1) a list of vectors describing the rigid-body motions of each</span>
<span class="c"># rigid body as if it were independent.</span>
<span class="c"># 2) a list of pair-distance constraint vectors for all pairs of</span>
<span class="c"># atoms inside a rigid body.</span>
<span class="c"># The LRB subspace is constructed from the projections of the</span>
<span class="c"># first set of vectors onto the orthogonal complement of the</span>
<span class="c"># subspace generated by the second set of vectors.</span>
<span class="n">vectors</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">c_vectors</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">rb</span> <span class="ow">in</span> <span class="n">rigid_bodies</span><span class="p">:</span>
<span class="n">atoms</span> <span class="o">=</span> <span class="n">rb</span><span class="o">.</span><span class="n">atomList</span><span class="p">()</span>
<span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">ex_ey_ez</span><span class="p">:</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">ParticleProperties</span><span class="o">.</span><span class="n">ParticleVector</span><span class="p">(</span><span class="n">universe</span><span class="p">)</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">atoms</span><span class="p">:</span>
<span class="n">v</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">d</span>
<span class="n">vectors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">atoms</span><span class="p">)</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span>
<span class="n">center</span> <span class="o">=</span> <span class="n">rb</span><span class="o">.</span><span class="n">centerOfMass</span><span class="p">()</span>
<span class="n">iv</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">vectors</span><span class="p">)</span><span class="o">-</span><span class="mi">3</span>
<span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">ex_ey_ez</span><span class="p">:</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">ParticleProperties</span><span class="o">.</span><span class="n">ParticleVector</span><span class="p">(</span><span class="n">universe</span><span class="p">)</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">atoms</span><span class="p">:</span>
<span class="n">v</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">cross</span><span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">position</span><span class="p">()</span><span class="o">-</span><span class="n">center</span><span class="p">)</span>
<span class="k">for</span> <span class="n">vt</span> <span class="ow">in</span> <span class="n">vectors</span><span class="p">[</span><span class="n">iv</span><span class="p">:]:</span>
<span class="n">v</span> <span class="o">-=</span> <span class="n">v</span><span class="o">.</span><span class="n">dotProduct</span><span class="p">(</span><span class="n">vt</span><span class="p">)</span><span class="o">*</span><span class="n">vt</span>
<span class="k">if</span> <span class="n">v</span><span class="o">.</span><span class="n">dotProduct</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="o">></span> <span class="mf">0.</span><span class="p">:</span>
<span class="n">vectors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="k">for</span> <span class="n">a1</span><span class="p">,</span> <span class="n">a2</span> <span class="ow">in</span> <span class="n">Utility</span><span class="o">.</span><span class="n">pairs</span><span class="p">(</span><span class="n">atoms</span><span class="p">):</span>
<span class="n">distance</span> <span class="o">=</span> <span class="n">universe</span><span class="o">.</span><span class="n">distanceVector</span><span class="p">(</span><span class="n">a1</span><span class="o">.</span><span class="n">position</span><span class="p">(),</span>
<span class="n">a2</span><span class="o">.</span><span class="n">position</span><span class="p">())</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">ParticleProperties</span><span class="o">.</span><span class="n">ParticleVector</span><span class="p">(</span><span class="n">universe</span><span class="p">)</span>
<span class="n">v</span><span class="p">[</span><span class="n">a1</span><span class="p">]</span> <span class="o">=</span> <span class="n">distance</span>
<span class="n">v</span><span class="p">[</span><span class="n">a2</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="n">distance</span>
<span class="n">c_vectors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="k">if</span> <span class="n">c_vectors</span><span class="p">:</span>
<span class="n">constraints</span> <span class="o">=</span> <span class="n">Subspace</span><span class="p">(</span><span class="n">universe</span><span class="p">,</span> <span class="n">c_vectors</span><span class="p">)</span>
<span class="n">vectors</span> <span class="o">=</span> <span class="p">[</span><span class="n">constraints</span><span class="o">.</span><span class="n">projectionComplementOf</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">vectors</span><span class="p">]</span>
<span class="n">Subspace</span><span class="o">.</span><span class="n">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">universe</span><span class="p">,</span> <span class="n">vectors</span><span class="p">)</span>
</div>
<div class="viewcode-block" id="RigidMotionSubspace"><a class="viewcode-back" href="../../modules.html#MMTK.Subspace.RigidMotionSubspace">[docs]</a><span class="k">class</span> <span class="nc">RigidMotionSubspace</span><span class="p">(</span><span class="n">Subspace</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Subspace of rigid-body motions</span>
<span class="sd"> A rigid-body motion subspace is the subspace which contains</span>
<span class="sd"> the rigid-body motions of any number of chemical objects.</span>
<span class="sd"> """</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">universe</span><span class="p">,</span> <span class="n">objects</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> :param universe: the universe for which the subspace is created</span>
<span class="sd"> :type universe: :class:`~MMTK.Universe.Universe`</span>
<span class="sd"> :param objects: a sequence of objects whose rigid-body motion is</span>
<span class="sd"> included in the subspace</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">Utility</span><span class="o">.</span><span class="n">isSequenceObject</span><span class="p">(</span><span class="n">objects</span><span class="p">):</span>
<span class="n">objects</span> <span class="o">=</span> <span class="p">[</span><span class="n">objects</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">objects</span> <span class="o">=</span> <span class="n">copy</span><span class="o">.</span><span class="n">copy</span><span class="p">(</span><span class="n">objects</span><span class="p">)</span>
<span class="c"># Identify connected sets of linked rigid bodies and remove</span>
<span class="c"># them from the plain rigid body list.</span>
<span class="n">atom_map</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">objects</span><span class="p">:</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">o</span><span class="o">.</span><span class="n">atomIterator</span><span class="p">():</span>
<span class="n">am</span> <span class="o">=</span> <span class="n">atom_map</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">[])</span>
<span class="n">am</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">o</span><span class="p">)</span>
<span class="n">atom_map</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">am</span>
<span class="n">rb_map</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">rbs</span> <span class="ow">in</span> <span class="n">atom_map</span><span class="o">.</span><span class="n">values</span><span class="p">():</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">rbs</span><span class="p">)</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span>
<span class="k">for</span> <span class="n">rb</span> <span class="ow">in</span> <span class="n">rbs</span><span class="p">:</span>
<span class="n">rb_map</span><span class="p">[</span><span class="n">rb</span><span class="p">]</span> <span class="o">=</span> <span class="n">rb_map</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">rb</span><span class="p">,</span> <span class="nb">frozenset</span><span class="p">())</span> \
<span class="o">.</span><span class="n">union</span><span class="p">(</span><span class="nb">frozenset</span><span class="p">(</span><span class="n">rbs</span><span class="p">))</span>
<span class="k">for</span> <span class="n">rb</span> <span class="ow">in</span> <span class="n">rb_map</span><span class="o">.</span><span class="n">keys</span><span class="p">():</span>
<span class="n">objects</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">rb</span><span class="p">)</span>
<span class="k">while</span> <span class="bp">True</span><span class="p">:</span>
<span class="n">changed</span> <span class="o">=</span> <span class="bp">False</span>
<span class="k">for</span> <span class="n">rbs</span> <span class="ow">in</span> <span class="n">rb_map</span><span class="o">.</span><span class="n">values</span><span class="p">():</span>
<span class="k">for</span> <span class="n">rb</span> <span class="ow">in</span> <span class="n">rbs</span><span class="p">:</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">rb_map</span><span class="p">[</span><span class="n">rb</span><span class="p">]</span>
<span class="n">rb_map</span><span class="p">[</span><span class="n">rb</span><span class="p">]</span> <span class="o">=</span> <span class="n">s</span><span class="o">.</span><span class="n">union</span><span class="p">(</span><span class="n">rbs</span><span class="p">)</span>
<span class="k">if</span> <span class="n">s</span> <span class="o">!=</span> <span class="n">rb_map</span><span class="p">[</span><span class="n">rb</span><span class="p">]:</span>
<span class="n">changed</span> <span class="o">=</span> <span class="bp">True</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">changed</span><span class="p">:</span>
<span class="k">break</span>
<span class="n">lrbs</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">(</span><span class="n">rb_map</span><span class="o">.</span><span class="n">values</span><span class="p">())</span>
<span class="c"># Generate the subspace vectors for the isolated rigid bodies.</span>
<span class="n">ex_ey_ez</span> <span class="o">=</span> <span class="p">[</span><span class="n">Vector</span><span class="p">(</span><span class="mf">1.</span><span class="p">,</span><span class="mf">0.</span><span class="p">,</span><span class="mf">0.</span><span class="p">),</span> <span class="n">Vector</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span><span class="mf">1.</span><span class="p">,</span><span class="mf">0.</span><span class="p">),</span> <span class="n">Vector</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span><span class="mf">0.</span><span class="p">,</span><span class="mf">1.</span><span class="p">)]</span>
<span class="n">vectors</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">objects</span><span class="p">:</span>
<span class="n">rb_atoms</span> <span class="o">=</span> <span class="n">o</span><span class="o">.</span><span class="n">atomList</span><span class="p">()</span>
<span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">ex_ey_ez</span><span class="p">:</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">ParticleProperties</span><span class="o">.</span><span class="n">ParticleVector</span><span class="p">(</span><span class="n">universe</span><span class="p">)</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">rb_atoms</span><span class="p">:</span>
<span class="n">v</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">d</span>
<span class="n">vectors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="o">/</span><span class="n">N</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">rb_atoms</span><span class="p">)))</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">rb_atoms</span><span class="p">)</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span>
<span class="n">center</span> <span class="o">=</span> <span class="n">o</span><span class="o">.</span><span class="n">centerOfMass</span><span class="p">()</span>
<span class="n">iv</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">vectors</span><span class="p">)</span><span class="o">-</span><span class="mi">3</span>
<span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">ex_ey_ez</span><span class="p">:</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">ParticleProperties</span><span class="o">.</span><span class="n">ParticleVector</span><span class="p">(</span><span class="n">universe</span><span class="p">)</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">rb_atoms</span><span class="p">:</span>
<span class="n">v</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">cross</span><span class="p">(</span><span class="n">a</span><span class="o">.</span><span class="n">position</span><span class="p">()</span><span class="o">-</span><span class="n">center</span><span class="p">)</span>
<span class="k">for</span> <span class="n">vt</span> <span class="ow">in</span> <span class="n">vectors</span><span class="p">[</span><span class="n">iv</span><span class="p">:]:</span>
<span class="n">v</span> <span class="o">-=</span> <span class="n">v</span><span class="o">.</span><span class="n">dotProduct</span><span class="p">(</span><span class="n">vt</span><span class="p">)</span><span class="o">*</span><span class="n">vt</span>
<span class="n">norm_sq</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">v</span><span class="o">.</span><span class="n">dotProduct</span><span class="p">(</span><span class="n">v</span><span class="p">))</span>
<span class="k">if</span> <span class="n">norm_sq</span> <span class="o">></span> <span class="mf">0.</span><span class="p">:</span>
<span class="n">vectors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="o">/</span><span class="n">norm_sq</span><span class="p">)</span>
<span class="c"># Generate the subspace vectors for the linked rigid bodies.</span>
<span class="k">for</span> <span class="n">lrb</span> <span class="ow">in</span> <span class="n">lrbs</span><span class="p">:</span>
<span class="n">lrb_ss</span> <span class="o">=</span> <span class="n">LinkedRigidBodyMotionSubspace</span><span class="p">(</span><span class="n">universe</span><span class="p">,</span> <span class="n">lrb</span><span class="p">)</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">lrb_ss</span><span class="o">.</span><span class="n">getBasis</span><span class="p">():</span>
<span class="n">vectors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">Subspace</span><span class="o">.</span><span class="n">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">universe</span><span class="p">,</span> <span class="n">vectors</span><span class="p">)</span>
<span class="c"># The vector set is already orthonormal by construction,</span>
<span class="c"># so we can skip the lengthy SVD procedure.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_basis</span> <span class="o">=</span> <span class="n">ParticleVectorSet</span><span class="p">(</span><span class="n">universe</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">vectors</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="nb">len</span><span class="p">(</span><span class="n">vectors</span><span class="p">)):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_basis</span><span class="o">.</span><span class="n">array</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">vectors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">array</span>
</div>
<div class="viewcode-block" id="PairDistanceSubspace"><a class="viewcode-back" href="../../modules.html#MMTK.Subspace.PairDistanceSubspace">[docs]</a><span class="k">class</span> <span class="nc">PairDistanceSubspace</span><span class="p">(</span><span class="n">Subspace</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Subspace of pair-distance motions</span>
<span class="sd"> A pair-distance motion subspace is the subspace which contains</span>
<span class="sd"> the relative motions of any number of atom pairs along</span>
<span class="sd"> their distance vector, e.g. bond elongation between two</span>
<span class="sd"> bonded atoms.</span>
<span class="sd"> """</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">universe</span><span class="p">,</span> <span class="n">atom_pairs</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> :param universe: the universe for which the subspace is created</span>
<span class="sd"> :type universe: :class:`~MMTK.Universe.Universe`</span>
<span class="sd"> :param atom_pairs: a sequence of atom pairs whose distance-vector</span>
<span class="sd"> motion is included in the subspace</span>
<span class="sd"> """</span>
<span class="n">vectors</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">atom1</span><span class="p">,</span> <span class="n">atom2</span> <span class="ow">in</span> <span class="n">atom_pairs</span><span class="p">:</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">ParticleProperties</span><span class="o">.</span><span class="n">ParticleVector</span><span class="p">(</span><span class="n">universe</span><span class="p">)</span>
<span class="n">distance</span> <span class="o">=</span> <span class="n">atom1</span><span class="o">.</span><span class="n">position</span><span class="p">()</span><span class="o">-</span><span class="n">atom2</span><span class="o">.</span><span class="n">position</span><span class="p">()</span>
<span class="n">v</span><span class="p">[</span><span class="n">atom1</span><span class="p">]</span> <span class="o">=</span> <span class="n">distance</span>
<span class="n">v</span><span class="p">[</span><span class="n">atom2</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="n">distance</span>
<span class="n">vectors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">Subspace</span><span class="o">.</span><span class="n">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">universe</span><span class="p">,</span> <span class="n">vectors</span><span class="p">)</span></div>
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