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<h1>Source code for MMTK.NormalModes.EnergeticModes</h1><div class="highlight"><pre>
<span class="c"># Energetic normal mode calculations.</span>
<span class="c">#</span>
<span class="c"># Written by Konrad Hinsen</span>
<span class="c">#</span>
<span class="sd">"""</span>
<span class="sd">Energetic normal modes</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">Features</span><span class="p">,</span> <span class="n">Units</span><span class="p">,</span> <span class="n">ParticleProperties</span>
<span class="kn">from</span> <span class="nn">MMTK.NormalModes</span> <span class="kn">import</span> <span class="n">Core</span>
<span class="kn">from</span> <span class="nn">Scientific</span> <span class="kn">import</span> <span class="n">N</span>
<span class="c">#</span>
<span class="c"># Class for a single mode</span>
<span class="c">#</span>
<div class="viewcode-block" id="EnergeticMode"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.EnergeticModes.EnergeticMode">[docs]</a><span class="k">class</span> <span class="nc">EnergeticMode</span><span class="p">(</span><span class="n">Core</span><span class="o">.</span><span class="n">Mode</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Single energetic normal mode</span>
<span class="sd"> Mode objects are created by indexing a :class:`MMTK.NormalModes.EnergeticModes.EnergeticModes` object.</span>
<span class="sd"> They contain the atomic displacements corresponding to a</span>
<span class="sd"> single mode. In addition, the force constant corresponding to the mode</span>
<span class="sd"> is stored in the attribute "force_constant".</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">n</span><span class="p">,</span> <span class="n">force_constant</span><span class="p">,</span> <span class="n">mode</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">force_constant</span> <span class="o">=</span> <span class="n">force_constant</span>
<span class="n">Core</span><span class="o">.</span><span class="n">Mode</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">n</span><span class="p">,</span> <span class="n">mode</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="s">'Mode '</span> <span class="o">+</span> <span class="sb">`self.number`</span> <span class="o">+</span> <span class="s">' with force constant '</span> <span class="o">+</span> \
<span class="sb">`self.force_constant`</span>
<span class="n">__repr__</span> <span class="o">=</span> <span class="n">__str__</span>
<span class="c">#</span>
<span class="c"># Class for a full set of normal modes</span>
<span class="c">#</span></div>
<div class="viewcode-block" id="EnergeticModes"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.EnergeticModes.EnergeticModes">[docs]</a><span class="k">class</span> <span class="nc">EnergeticModes</span><span class="p">(</span><span class="n">Core</span><span class="o">.</span><span class="n">NormalModes</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Energetic modes describe the principal axes of an harmonic approximation</span>
<span class="sd"> to the potential energy surface of a system. They are obtained by</span>
<span class="sd"> diagonalizing the force constant matrix without prior mass-weighting.</span>
<span class="sd"> In order to obtain physically reasonable normal modes, the configuration</span>
<span class="sd"> of the universe must correspond to a local minimum of the potential</span>
<span class="sd"> energy.</span>
<span class="sd"> Individual modes (see class :class:`~MMTK.NormalModes.EnergeticModes.EnergeticMode`)</span>
<span class="sd"> can be extracted by indexing with an integer. Looping over the modes</span>
<span class="sd"> is possible as well.</span>
<span class="sd"> """</span>
<span class="n">features</span> <span class="o">=</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="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">temperature</span> <span class="o">=</span> <span class="mi">300</span><span class="o">*</span><span class="n">Units</span><span class="o">.</span><span class="n">K</span><span class="p">,</span>
<span class="n">subspace</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span> <span class="n">delta</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span> <span class="n">sparse</span> <span class="o">=</span> <span class="bp">False</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> :param universe: the system for which the normal modes are calculated;</span>
<span class="sd"> it must have a force field which provides the second</span>
<span class="sd"> derivatives of the potential energy</span>
<span class="sd"> :type universe: :class:`~MMTK.Universe.Universe`</span>
<span class="sd"> :param temperature: the temperature for which the amplitudes of the</span>
<span class="sd"> atomic displacement vectors are calculated. A</span>
<span class="sd"> value of None can be specified to have no scaling</span>
<span class="sd"> at all. In that case the mass-weighted norm</span>
<span class="sd"> of each normal mode is one.</span>
<span class="sd"> :type temperature: float</span>
<span class="sd"> :param subspace: the basis for the subspace in which the normal modes</span>
<span class="sd"> are calculated (or, more precisely, a set of vectors</span>
<span class="sd"> spanning the subspace; it does not have to be</span>
<span class="sd"> orthogonal). This can either be a sequence of</span>
<span class="sd"> :class:`~MMTK.ParticleProperties.ParticleVector` objects</span>
<span class="sd"> or a tuple of two such sequences. In the second case,</span>
<span class="sd"> the subspace is defined by the space spanned by the</span>
<span class="sd"> second set of vectors projected on the complement of</span>
<span class="sd"> the space spanned by the first set of vectors.</span>
<span class="sd"> The first set thus defines directions that are</span>
<span class="sd"> excluded from the subspace.</span>
<span class="sd"> The default value of None indicates a standard</span>
<span class="sd"> normal mode calculation in the 3N-dimensional</span>
<span class="sd"> configuration space.</span>
<span class="sd"> :param delta: the rms step length for numerical differentiation.</span>
<span class="sd"> The default value of None indicates analytical</span>
<span class="sd"> differentiation.</span>
<span class="sd"> Numerical differentiation is available only when a</span>
<span class="sd"> subspace basis is used as well. Instead of calculating</span>
<span class="sd"> the full force constant matrix and then multiplying</span>
<span class="sd"> with the subspace basis, the subspace force constant</span>
<span class="sd"> matrix is obtained by numerical differentiation of the</span>
<span class="sd"> energy gradients along the basis vectors of the subspace.</span>
<span class="sd"> If the basis is much smaller than the full configuration</span>
<span class="sd"> space, this approach needs much less memory.</span>
<span class="sd"> :type delta: float</span>
<span class="sd"> :param sparse: a flag that indicates if a sparse representation of</span>
<span class="sd"> the force constant matrix is to be used. This is of</span>
<span class="sd"> interest when there are no long-range interactions and</span>
<span class="sd"> a subspace of smaller size then 3N is specified. In that</span>
<span class="sd"> case, the calculation will use much less memory with a</span>
<span class="sd"> sparse representation.</span>
<span class="sd"> :type sparse: bool</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">universe</span> <span class="o">==</span> <span class="bp">None</span><span class="p">:</span>
<span class="k">return</span>
<span class="n">Features</span><span class="o">.</span><span class="n">checkFeatures</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">Core</span><span class="o">.</span><span class="n">NormalModes</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">subspace</span><span class="p">,</span> <span class="n">delta</span><span class="p">,</span> <span class="n">sparse</span><span class="p">,</span>
<span class="p">[</span><span class="s">'array'</span><span class="p">,</span> <span class="s">'force_constants'</span><span class="p">])</span>
<span class="bp">self</span><span class="o">.</span><span class="n">temperature</span> <span class="o">=</span> <span class="n">temperature</span>
<span class="bp">self</span><span class="o">.</span><span class="n">weights</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">1</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="bp">self</span><span class="o">.</span><span class="n">_forceConstantMatrix</span><span class="p">()</span>
<span class="n">ev</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_diagonalize</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">force_constants</span> <span class="o">=</span> <span class="n">ev</span>
<span class="bp">self</span><span class="o">.</span><span class="n">sort_index</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">force_constants</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">shape</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nmodes</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</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">cleanup</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="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sort_index</span><span class="p">[</span><span class="n">item</span><span class="p">]</span>
<span class="n">f</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">force_constants</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
<span class="c">#!!</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">temperature</span> <span class="ow">is</span> <span class="bp">None</span> <span class="ow">or</span> <span class="n">item</span> <span class="o"><</span> <span class="mi">6</span><span class="p">:</span>
<span class="n">amplitude</span> <span class="o">=</span> <span class="mf">1.</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">amplitude</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="mf">2.</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">temperature</span><span class="o">*</span><span class="n">Units</span><span class="o">.</span><span class="n">k_B</span>
<span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">force_constants</span><span class="p">[</span><span class="n">index</span><span class="p">])</span>
<span class="k">return</span> <span class="n">EnergeticMode</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">item</span><span class="p">,</span>
<span class="bp">self</span><span class="o">.</span><span class="n">force_constants</span><span class="p">[</span><span class="n">index</span><span class="p">],</span>
<span class="n">amplitude</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">array</span><span class="p">[</span><span class="n">index</span><span class="p">])</span>
<div class="viewcode-block" id="EnergeticModes.rawMode"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.EnergeticModes.EnergeticModes.rawMode">[docs]</a> <span class="k">def</span> <span class="nf">rawMode</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="sd">"""</span>
<span class="sd"> :param item: the index of a normal mode</span>
<span class="sd"> :type item: int</span>
<span class="sd"> :returns: the unscaled mode vector</span>
<span class="sd"> :rtype: :class:`~MMTK.NormalModes.EnergeticModes.EnergeticMode`</span>
<span class="sd"> """</span>
<span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sort_index</span><span class="p">[</span><span class="n">item</span><span class="p">]</span>
<span class="n">f</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">force_constants</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
<span class="k">return</span> <span class="n">EnergeticMode</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">item</span><span class="p">,</span>
<span class="bp">self</span><span class="o">.</span><span class="n">force_constants</span><span class="p">[</span><span class="n">index</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">index</span><span class="p">])</span>
</div>
<span class="k">def</span> <span class="nf">fluctuations</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">first_mode</span><span class="o">=</span><span class="mi">6</span><span class="p">):</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">ParticleProperties</span><span class="o">.</span><span class="n">ParticleScalar</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="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">first_mode</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nmodes</span><span class="p">):</span>
<span class="n">mode</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rawMode</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<span class="n">f</span> <span class="o">+=</span> <span class="p">(</span><span class="n">mode</span><span class="o">*</span><span class="n">mode</span><span class="p">)</span><span class="o">/</span><span class="n">mode</span><span class="o">.</span><span class="n">force_constant</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">temperature</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">f</span><span class="o">.</span><span class="n">array</span> <span class="o">*=</span> <span class="n">Units</span><span class="o">.</span><span class="n">k_B</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">temperature</span>
<span class="k">return</span> <span class="n">f</span>
<span class="k">def</span> <span class="nf">anisotropicFluctuations</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">first_mode</span><span class="o">=</span><span class="mi">6</span><span class="p">):</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">ParticleProperties</span><span class="o">.</span><span class="n">ParticleTensor</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="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">first_mode</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nmodes</span><span class="p">):</span>
<span class="n">mode</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rawMode</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<span class="n">array</span> <span class="o">=</span> <span class="n">mode</span><span class="o">.</span><span class="n">array</span>
<span class="n">f</span><span class="o">.</span><span class="n">array</span> <span class="o">+=</span> <span class="p">(</span><span class="n">array</span><span class="p">[:,</span> <span class="p">:,</span> <span class="n">N</span><span class="o">.</span><span class="n">NewAxis</span><span class="p">]</span><span class="o">*</span><span class="n">array</span><span class="p">[:,</span> <span class="n">N</span><span class="o">.</span><span class="n">NewAxis</span><span class="p">,</span> <span class="p">:])</span> \
<span class="o">/</span> <span class="n">mode</span><span class="o">.</span><span class="n">force_constant</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">temperature</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">f</span><span class="o">.</span><span class="n">array</span> <span class="o">*=</span> <span class="n">Units</span><span class="o">.</span><span class="n">k_B</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">temperature</span>
<span class="k">return</span> <span class="n">f</span></div>
</pre></div>
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