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<h1>Source code for MMTK.ChargeFit</h1><div class="highlight"><pre>
<span class="c"># This module contains code for charge fitting.</span>
<span class="c">#</span>
<span class="c"># Written by Konrad Hinsen</span>
<span class="c">#</span>
<span class="sd">"""</span>
<span class="sd">Fit of point chages to an electrostatic potential surface</span>
<span class="sd">This module implements a numerically stable method (based on</span>
<span class="sd">Singular Value Decomposition) to fit point charges to values of an</span>
<span class="sd">electrostatic potential surface. Two types of constraints are</span>
<span class="sd">avaiable: a constraint on the total charge of the system or a subset</span>
<span class="sd">of the system, and constraints that force the charges of several atoms</span>
<span class="sd">to be equal. There is also a utility function that selects suitable</span>
<span class="sd">evaluation points for the electrostatic potential surface. For the</span>
<span class="sd">potential evaluation itself, some quantum chemistry program is needed.</span>
<span class="sd">The charge fitting method is described in:</span>
<span class="sd"> | K. Hinsen and B. Roux,</span>
<span class="sd"> | An accurate potential for simulating proton transfer in acetylacetone,</span>
<span class="sd"> | J. Comp. Chem. 18, 1997: 368</span>
<span class="sd">See also Examples/Miscellaneous/charge_fit.py.</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">Random</span><span class="p">,</span> <span class="n">Units</span><span class="p">,</span> <span class="n">Utility</span>
<span class="kn">from</span> <span class="nn">Scientific.Geometry</span> <span class="kn">import</span> <span class="n">Vector</span>
<span class="kn">from</span> <span class="nn">Scientific</span> <span class="kn">import</span> <span class="n">N</span>
<span class="kn">from</span> <span class="nn">Scientific</span> <span class="kn">import</span> <span class="n">LA</span>
<div class="viewcode-block" id="ChargeFit"><a class="viewcode-back" href="../../modules.html#MMTK.ChargeFit.ChargeFit">[docs]</a><span class="k">class</span> <span class="nc">ChargeFit</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Fit of point charges to an electrostatic potential surface</span>
<span class="sd"> A ChargeFit object acts like a dictionary that stores the fitted charge</span>
<span class="sd"> value for each atom in the system.</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">system</span><span class="p">,</span> <span class="n">points</span><span class="p">,</span> <span class="n">constraints</span> <span class="o">=</span> <span class="bp">None</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> :param system: any chemical object (usually a molecule)</span>
<span class="sd"> :param points: a list of point/potential pairs (a vector for the</span>
<span class="sd"> evaluation point, a number for the potential),</span>
<span class="sd"> or a dictionary whose keys are Configuration objects</span>
<span class="sd"> and whose values are lists of point/potential pairs.</span>
<span class="sd"> The latter case permits combined fits for several</span>
<span class="sd"> conformations of the system.</span>
<span class="sd"> :param constraints: an optional list of constraint objects</span>
<span class="sd"> (:class:`~MMTK.ChargeFit.TotalChargeConstraint`</span>
<span class="sd"> and/or</span>
<span class="sd"> :class:`~MMTK.ChargeFit.EqualityConstraint` objects). </span>
<span class="sd"> If the constraints are inconsistent, a warning is</span>
<span class="sd"> printed and the result will satisfy the</span>
<span class="sd"> constraints only in a least-squares sense.</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">atoms</span> <span class="o">=</span> <span class="n">system</span><span class="o">.</span><span class="n">atomList</span><span class="p">()</span>
<span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">points</span><span class="p">)</span> <span class="o">!=</span> <span class="nb">type</span><span class="p">({}):</span>
<span class="n">points</span> <span class="o">=</span> <span class="p">{</span><span class="bp">None</span><span class="p">:</span> <span class="n">points</span><span class="p">}</span>
<span class="k">if</span> <span class="n">constraints</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">constraints</span> <span class="o">=</span> <span class="n">ChargeConstraintSet</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">atoms</span><span class="p">,</span> <span class="n">constraints</span><span class="p">)</span>
<span class="n">npoints</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="nb">len</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">points</span><span class="o">.</span><span class="n">values</span><span class="p">()])</span>
<span class="n">natoms</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">atoms</span><span class="p">)</span>
<span class="k">if</span> <span class="n">npoints</span> <span class="o"><</span> <span class="n">natoms</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">"Not enough data points for fit"</span><span class="p">)</span>
<span class="n">m</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">npoints</span><span class="p">,</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">phi</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">npoints</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">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">conf</span><span class="p">,</span> <span class="n">pointlist</span> <span class="ow">in</span> <span class="n">points</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="k">for</span> <span class="n">r</span><span class="p">,</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">pointlist</span><span class="p">:</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">natoms</span><span class="p">):</span>
<span class="n">m</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="o">=</span> <span class="mf">1.</span><span class="o">/</span><span class="p">(</span><span class="n">r</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">atoms</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">position</span><span class="p">(</span><span class="n">conf</span><span class="p">))</span><span class="o">.</span><span class="n">length</span><span class="p">()</span>
<span class="n">phi</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
<span class="n">i</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">m</span><span class="o">*</span><span class="n">Units</span><span class="o">.</span><span class="n">electrostatic_energy</span>
<span class="n">m_test</span> <span class="o">=</span> <span class="n">m</span>
<span class="n">phi_test</span> <span class="o">=</span> <span class="n">phi</span>
<span class="k">if</span> <span class="n">constraints</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">phi</span> <span class="o">-=</span> <span class="n">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">constraints</span><span class="o">.</span><span class="n">bi_c</span><span class="p">)</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">constraints</span><span class="o">.</span><span class="n">p</span><span class="p">)</span>
<span class="n">c_rank</span> <span class="o">=</span> <span class="n">constraints</span><span class="o">.</span><span class="n">rank</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">c_rank</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">u</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">vt</span> <span class="o">=</span> <span class="n">LA</span><span class="o">.</span><span class="n">singular_value_decomposition</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
<span class="n">s_test</span> <span class="o">=</span> <span class="n">s</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">)</span><span class="o">-</span><span class="n">c_rank</span><span class="p">]</span>
<span class="n">cutoff</span> <span class="o">=</span> <span class="mf">1.e-10</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">s_test</span><span class="p">)</span>
<span class="n">nonzero</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">s_test</span><span class="p">,</span> <span class="n">N</span><span class="o">.</span><span class="n">not_equal</span><span class="p">(</span><span class="n">s_test</span><span class="p">,</span> <span class="mf">0.</span><span class="p">))</span>
<span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nonzero</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">condition</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">nonzero</span><span class="p">)</span> <span class="o">/</span> \
<span class="n">N</span><span class="o">.</span><span class="n">minimum</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">nonzero</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">effective_rank</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">s</span><span class="p">,</span> <span class="n">cutoff</span><span class="p">))</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">effective_rank</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">effective_condition</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">nonzero</span><span class="p">)</span> <span class="o">/</span> <span class="n">cutoff</span>
<span class="k">else</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">effective_condition</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">condition</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">effective_rank</span> <span class="o"><</span> <span class="n">natoms</span><span class="o">-</span><span class="n">c_rank</span><span class="p">:</span>
<span class="n">Utility</span><span class="o">.</span><span class="n">warning</span><span class="p">(</span><span class="s">'Not all charges are uniquely determined'</span> <span class="o">+</span>
<span class="s">' by the available data'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">natoms</span><span class="p">):</span>
<span class="k">if</span> <span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">></span> <span class="n">cutoff</span><span class="p">:</span>
<span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.</span><span class="o">/</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.</span>
<span class="n">q</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">N</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">vt</span><span class="p">),</span>
<span class="n">s</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">N</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">u</span><span class="p">)[:</span><span class="n">natoms</span><span class="p">,</span> <span class="p">:],</span> <span class="n">phi</span><span class="p">))</span>
<span class="k">if</span> <span class="n">constraints</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">q</span> <span class="o">=</span> <span class="n">constraints</span><span class="o">.</span><span class="n">bi_c</span> <span class="o">+</span> <span class="n">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">constraints</span><span class="o">.</span><span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">)</span>
<span class="n">deviation</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">m_test</span><span class="p">,</span> <span class="n">q</span><span class="p">)</span><span class="o">-</span><span class="n">phi_test</span>
<span class="bp">self</span><span class="o">.</span><span class="n">rms_error</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">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">deviation</span><span class="p">,</span> <span class="n">deviation</span><span class="p">))</span>
<span class="n">deviation</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">fabs</span><span class="p">(</span><span class="n">deviation</span><span class="o">/</span><span class="n">phi_test</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">relative_rms_error</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">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">deviation</span><span class="p">,</span> <span class="n">deviation</span><span class="p">))</span>
<span class="bp">self</span><span class="o">.</span><span class="n">charges</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="n">natoms</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">charges</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">atoms</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span> <span class="o">=</span> <span class="n">q</span><span class="p">[</span><span class="n">i</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">charges</span><span class="p">[</span><span class="n">item</span><span class="p">]</span>
</div>
<div class="viewcode-block" id="TotalChargeConstraint"><a class="viewcode-back" href="../../modules.html#MMTK.ChargeFit.TotalChargeConstraint">[docs]</a><span class="k">class</span> <span class="nc">TotalChargeConstraint</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Constraint on the total system charge</span>
<span class="sd"> To be used with :class:`~MMTK.ChargeFit.ChargeFit`</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">system</span><span class="p">,</span> <span class="n">charge</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> :param system: any chamical object whose total charge</span>
<span class="sd"> is to be constrained</span>
<span class="sd"> :param charge: the total charge value</span>
<span class="sd"> :type charge: number</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">atoms</span> <span class="o">=</span> <span class="n">system</span><span class="o">.</span><span class="n">atomList</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">charge</span> <span class="o">=</span> <span class="n">charge</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="mi">1</span>
<span class="k">def</span> <span class="nf">setCoefficients</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">atoms</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">atoms</span><span class="p">:</span>
<span class="n">j</span> <span class="o">=</span> <span class="n">atoms</span><span class="o">.</span><span class="n">index</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="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.</span>
<span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">charge</span>
</div>
<div class="viewcode-block" id="EqualityConstraint"><a class="viewcode-back" href="../../modules.html#MMTK.ChargeFit.EqualityConstraint">[docs]</a><span class="k">class</span> <span class="nc">EqualityConstraint</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Constraint forcing two charges to be equal</span>
<span class="sd"> To be used with :class:`~MMTK.ChargeFit.ChargeFit`</span>
<span class="sd"> Any atom may occur in more than one EqualityConstraint object,</span>
<span class="sd"> in order to keep the charges of more than two atoms equal.</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">atom1</span><span class="p">,</span> <span class="n">atom2</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> :param atom1: the first atom in the equality relation</span>
<span class="sd"> :type atom1: :class:`~MMTK.ChemicalObjects.Atom`</span>
<span class="sd"> :param atom2: the second atom in the equality relation</span>
<span class="sd"> :type atom2: :class:`~MMTK.ChemicalObjects.Atom`</span>
<span class="sd"> """</span>
<span class="bp">self</span><span class="o">.</span><span class="n">a1</span> <span class="o">=</span> <span class="n">atom1</span>
<span class="bp">self</span><span class="o">.</span><span class="n">a2</span> <span class="o">=</span> <span class="n">atom2</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="mi">1</span>
<span class="k">def</span> <span class="nf">setCoefficients</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">atoms</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
<span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">atoms</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">a1</span><span class="p">)]</span> <span class="o">=</span> <span class="mf">1.</span>
<span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">atoms</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">a2</span><span class="p">)]</span> <span class="o">=</span> <span class="o">-</span><span class="mf">1.</span>
<span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.</span>
</div>
<span class="k">class</span> <span class="nc">ChargeConstraintSet</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">atoms</span><span class="p">,</span> <span class="n">constraints</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">atoms</span> <span class="o">=</span> <span class="n">atoms</span>
<span class="n">natoms</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">atoms</span><span class="p">)</span>
<span class="n">nconst</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="nb">len</span><span class="p">(</span><span class="n">c</span><span class="p">)</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">constraints</span><span class="p">])</span>
<span class="n">b</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">nconst</span><span class="p">,</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">c</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">nconst</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">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">cons</span> <span class="ow">in</span> <span class="n">constraints</span><span class="p">:</span>
<span class="n">cons</span><span class="o">.</span><span class="n">setCoefficients</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">atoms</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
<span class="n">i</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">cons</span><span class="p">)</span>
<span class="n">u</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">vt</span> <span class="o">=</span> <span class="n">LA</span><span class="o">.</span><span class="n">singular_value_decomposition</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">=</span> <span class="mi">0</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">min</span><span class="p">(</span><span class="n">natoms</span><span class="p">,</span> <span class="n">nconst</span><span class="p">)):</span>
<span class="k">if</span> <span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">></span> <span class="mf">0.</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">+</span> <span class="mi">1</span>
<span class="bp">self</span><span class="o">.</span><span class="n">b</span> <span class="o">=</span> <span class="n">b</span>
<span class="bp">self</span><span class="o">.</span><span class="n">bi</span> <span class="o">=</span> <span class="n">LA</span><span class="o">.</span><span class="n">generalized_inverse</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">p</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">natoms</span><span class="p">)</span><span class="o">-</span><span class="n">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bi</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">c</span> <span class="o">=</span> <span class="n">c</span>
<span class="bp">self</span><span class="o">.</span><span class="n">bi_c</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bi</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span>
<span class="n">c_test</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">bi_c</span><span class="p">)</span>
<span class="k">if</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">c_test</span><span class="o">-</span><span class="n">c</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">nconst</span> <span class="o">></span> <span class="mf">1.e-12</span><span class="p">:</span>
<span class="n">Utility</span><span class="o">.</span><span class="n">warning</span><span class="p">(</span><span class="s">"The charge constraints are inconsistent."</span>
<span class="s">" They will be applied as a least-squares"</span>
<span class="s">" condition."</span><span class="p">)</span>
<div class="viewcode-block" id="evaluationPoints"><a class="viewcode-back" href="../../modules.html#MMTK.ChargeFit.evaluationPoints">[docs]</a><span class="k">def</span> <span class="nf">evaluationPoints</span><span class="p">(</span><span class="n">system</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">smallest</span> <span class="o">=</span> <span class="mf">0.3</span><span class="p">,</span> <span class="n">largest</span> <span class="o">=</span> <span class="mf">0.5</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Generate points in space around a molecule that are suitable</span>
<span class="sd"> for potential evaluation in view of a subsequent charge fit.</span>
<span class="sd"> The points are chosen at random and uniformly in a shell around the system.</span>
<span class="sd"> :param system: the chemical object for which the charges</span>
<span class="sd"> will be fitted</span>
<span class="sd"> :param n: the number of evaluation points to be generated</span>
<span class="sd"> :param smallest: the smallest allowed distance of any evaluation</span>
<span class="sd"> point from any non-hydrogen atom</span>
<span class="sd"> :param largest: the largest allowed value for the distance</span>
<span class="sd"> from an evaluation point to the nearest atom</span>
<span class="sd"> :returns: a list of evaluation points</span>
<span class="sd"> :rtype: list of Scientific.Geometry.Vector</span>
<span class="sd"> """</span>
<span class="n">atoms</span> <span class="o">=</span> <span class="n">system</span><span class="o">.</span><span class="n">atomList</span><span class="p">()</span>
<span class="n">p1</span><span class="p">,</span> <span class="n">p2</span> <span class="o">=</span> <span class="n">system</span><span class="o">.</span><span class="n">boundingBox</span><span class="p">()</span>
<span class="n">margin</span> <span class="o">=</span> <span class="n">Vector</span><span class="p">(</span><span class="n">largest</span><span class="p">,</span> <span class="n">largest</span><span class="p">,</span> <span class="n">largest</span><span class="p">)</span>
<span class="n">p1</span> <span class="o">-=</span> <span class="n">margin</span>
<span class="n">p2</span> <span class="o">+=</span> <span class="n">margin</span>
<span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">p2</span><span class="o">-</span><span class="n">p1</span><span class="p">)</span>
<span class="n">offset</span> <span class="o">=</span> <span class="mf">0.5</span><span class="o">*</span><span class="n">Vector</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="n">c</span><span class="p">)</span>
<span class="n">points</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">points</span><span class="p">)</span> <span class="o"><</span> <span class="n">n</span><span class="p">:</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">p1</span> <span class="o">+</span> <span class="n">Random</span><span class="o">.</span><span class="n">randomPointInBox</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="n">c</span><span class="p">)</span> <span class="o">+</span> <span class="n">offset</span>
<span class="n">m</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">largest</span>
<span class="n">ok</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">atom</span> <span class="ow">in</span> <span class="n">atoms</span><span class="p">:</span>
<span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="n">p</span><span class="o">-</span><span class="n">atom</span><span class="o">.</span><span class="n">position</span><span class="p">())</span><span class="o">.</span><span class="n">length</span><span class="p">()</span>
<span class="n">m</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span>
<span class="k">if</span> <span class="n">d</span> <span class="o"><</span> <span class="n">smallest</span> <span class="ow">and</span> <span class="n">atom</span><span class="o">.</span><span class="n">symbol</span> <span class="o">!=</span> <span class="s">'H'</span><span class="p">:</span>
<span class="n">ok</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">ok</span><span class="p">:</span> <span class="k">break</span>
<span class="k">if</span> <span class="n">ok</span> <span class="ow">and</span> <span class="n">m</span> <span class="o"><=</span> <span class="n">largest</span><span class="p">:</span>
<span class="n">points</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
<span class="k">return</span> <span class="n">points</span>
</div>
<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">'__main__'</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">MMTK</span> <span class="kn">import</span> <span class="o">*</span>
<span class="n">a1</span> <span class="o">=</span> <span class="n">Atom</span><span class="p">(</span><span class="s">'C'</span><span class="p">,</span> <span class="n">position</span><span class="o">=</span><span class="n">Vector</span><span class="p">(</span><span class="o">-</span><span class="mf">0.05</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">a2</span> <span class="o">=</span> <span class="n">Atom</span><span class="p">(</span><span class="s">'C'</span><span class="p">,</span> <span class="n">position</span><span class="o">=</span><span class="n">Vector</span><span class="p">(</span> <span class="mf">0.05</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">system</span> <span class="o">=</span> <span class="n">Collection</span><span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">a2</span><span class="p">)</span>
<span class="n">a1</span><span class="o">.</span><span class="n">charge</span> <span class="o">=</span> <span class="o">-</span><span class="mf">0.75</span>
<span class="n">a2</span><span class="o">.</span><span class="n">charge</span> <span class="o">=</span> <span class="mf">0.15</span>
<span class="n">points</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">evaluationPoints</span><span class="p">(</span><span class="n">system</span><span class="p">,</span> <span class="mi">50</span><span class="p">):</span>
<span class="n">p</span> <span class="o">=</span> <span class="mf">0.</span>
<span class="k">for</span> <span class="n">atom</span> <span class="ow">in</span> <span class="n">system</span><span class="o">.</span><span class="n">atomList</span><span class="p">():</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">p</span> <span class="o">+</span> <span class="n">atom</span><span class="o">.</span><span class="n">charge</span><span class="o">/</span><span class="p">(</span><span class="n">r</span><span class="o">-</span><span class="n">atom</span><span class="o">.</span><span class="n">position</span><span class="p">())</span><span class="o">.</span><span class="n">length</span><span class="p">()</span>
<span class="n">points</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">r</span><span class="p">,</span> <span class="n">p</span><span class="o">*</span><span class="n">Units</span><span class="o">.</span><span class="n">electrostatic_energy</span><span class="p">))</span>
<span class="n">constraints</span> <span class="o">=</span> <span class="p">[</span><span class="n">TotalChargeConstraint</span><span class="p">(</span><span class="n">system</span><span class="p">,</span> <span class="mf">0.</span><span class="p">)]</span>
<span class="n">constraints</span> <span class="o">=</span> <span class="p">[</span><span class="n">EqualityConstraint</span><span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">a2</span><span class="p">)]</span>
<span class="n">constraints</span> <span class="o">=</span> <span class="bp">None</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">ChargeFit</span><span class="p">(</span><span class="n">system</span><span class="p">,</span> <span class="n">points</span><span class="p">,</span> <span class="n">constraints</span><span class="p">)</span>
<span class="k">print</span> <span class="n">f</span><span class="p">[</span><span class="n">a1</span><span class="p">],</span> <span class="n">a1</span><span class="o">.</span><span class="n">charge</span>
<span class="k">print</span> <span class="n">f</span><span class="p">[</span><span class="n">a2</span><span class="p">],</span> <span class="n">a2</span><span class="o">.</span><span class="n">charge</span>
</pre></div>
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