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<h1>Source code for MMTK.NormalModes.BrownianModes</h1><div class="highlight"><pre>
<span class="c"># Brownian 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">Brownian 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="p">,</span> <span class="n">Random</span>
<span class="kn">from</span> <span class="nn">Scientific.Functions.Interpolation</span> <span class="kn">import</span> <span class="n">InterpolatingFunction</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">MMTK.NormalModes</span> <span class="kn">import</span> <span class="n">Core</span>
<span class="c">#</span>
<span class="c"># Class for a single mode</span>
<span class="c">#</span>
<div class="viewcode-block" id="BrownianMode"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.BrownianModes.BrownianMode">[docs]</a><span class="k">class</span> <span class="nc">BrownianMode</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 Brownian normal mode</span>
<span class="sd"> Mode objects are created by indexing a :class:`~MMTK.NormalModes.BrownianModes.BrownianModes` object.</span>
<span class="sd"> They contain the atomic displacements corresponding to a single</span>
<span class="sd"> mode. In addition, the inverse of the relaxation time corresponding</span>
<span class="sd"> to the mode is stored in the attribute "inv_relaxation_time".</span>
<span class="sd"> Note: the Brownian mode vectors are not friction weighted and therefore</span>
<span class="sd"> not orthogonal to each other.</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">inv_relaxation_time</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">inv_relaxation_time</span> <span class="o">=</span> <span class="n">inv_relaxation_time</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 inverse relaxation time '</span> \
<span class="o">+</span> <span class="sb">`self.inv_relaxation_time`</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="BrownianModes"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.BrownianModes.BrownianModes">[docs]</a><span class="k">class</span> <span class="nc">BrownianModes</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"> Brownian modes describe the independent relaxation motions of a</span>
<span class="sd"> harmonic system with friction. They are obtained by diagonalizing the</span>
<span class="sd"> friction-weighted force constant matrix.</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:`~MMTK.NormalModes.BrownianModes.BrownianMode`)</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"> Brownian modes describe the independent relaxation motions of a</span>
<span class="sd"> harmonic system with friction. They are obtained by diagonalizing the</span>
<span class="sd"> friction-weighted force constant matrix.</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"> A BrownianModes object behaves like a sequence of modes.</span>
<span class="sd"> Individual modes (see :class:`~MMTK.NormalModes.BrownianMode`)</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">friction</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="mf">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 friction: the friction coefficient for each particle.</span>
<span class="sd"> Note: The friction coefficients are not mass-weighted,</span>
<span class="sd"> i.e. they have the dimension of an inverse time.</span>
<span class="sd"> :type friction: :class:`~MMTK.ParticleProperties.ParticleScalar`</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">'inv_relaxation_times'</span><span class="p">])</span>
<span class="bp">self</span><span class="o">.</span><span class="n">friction</span> <span class="o">=</span> <span class="n">friction</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">sqrt</span><span class="p">(</span><span class="n">friction</span><span class="o">.</span><span class="n">array</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">weights</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">weights</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="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">inv_relaxation_times</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">inv_relaxation_times</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="k">return</span> <span class="n">BrownianMode</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">inv_relaxation_times</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><span class="o">/</span><span class="bp">self</span><span class="o">.</span><span class="n">weights</span><span class="p">)</span>
<div class="viewcode-block" id="BrownianModes.rawMode"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.BrownianModes.BrownianModes.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.BrownianModes.BrownianMode`</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="k">return</span> <span class="n">BrownianMode</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">inv_relaxation_times</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">inv_relaxation_time</span>
<span class="n">f</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="o">*</span><span class="n">f</span><span class="o">/</span><span class="bp">self</span><span class="o">.</span><span class="n">friction</span>
<span class="k">return</span> <span class="n">f</span>
<div class="viewcode-block" id="BrownianModes.meanSquareDisplacement"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.BrownianModes.BrownianModes.meanSquareDisplacement">[docs]</a> <span class="k">def</span> <span class="nf">meanSquareDisplacement</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">subset</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">weights</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span>
<span class="n">time_range</span> <span class="o">=</span> <span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</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="sd">"""</span>
<span class="sd"> :param subset: the subset of the universe used in the calculation</span>
<span class="sd"> (default: the whole universe)</span>
<span class="sd"> :type subset: :class:`~MMTK.Collections.GroupOfAtoms`</span>
<span class="sd"> :param weights: the weight to be given to each atom in the average</span>
<span class="sd"> (default: atomic masses)</span>
<span class="sd"> :type weights: :class:`~MMTK.ParticleProperties.ParticleScalar`</span>
<span class="sd"> :param time_range: the time values at which the mean-square</span>
<span class="sd"> displacement is evaluated, specified as a</span>
<span class="sd"> range tuple (first, last, step).</span>
<span class="sd"> The defaults are first=0, last=</span>
<span class="sd"> 20 times the longest vibration perdiod,</span>
<span class="sd"> and step defined such that 300 points are</span>
<span class="sd"> used in total.</span>
<span class="sd"> :type time_range: tuple</span>
<span class="sd"> :param first_mode: the first mode to be taken into account for</span>
<span class="sd"> the fluctuation calculation. The default value</span>
<span class="sd"> of 6 is right for molecules in vacuum.</span>
<span class="sd"> :type first_mode: int</span>
<span class="sd"> :returns: the averaged mean-square displacement of the</span>
<span class="sd"> atoms in subset as a function of time</span>
<span class="sd"> :rtype: Scientific.Functions.Interpolation.InterpolatingFunction</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">subset</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">subset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">universe</span>
<span class="k">if</span> <span class="n">weights</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">weights</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="o">.</span><span class="n">masses</span><span class="p">()</span>
<span class="n">weights</span> <span class="o">=</span> <span class="n">weights</span><span class="o">*</span><span class="n">subset</span><span class="o">.</span><span class="n">booleanMask</span><span class="p">()</span>
<span class="n">total</span> <span class="o">=</span> <span class="n">weights</span><span class="o">.</span><span class="n">sumOverParticles</span><span class="p">()</span>
<span class="n">weights</span> <span class="o">=</span> <span class="n">weights</span><span class="o">/</span><span class="p">(</span><span class="n">total</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">friction</span><span class="p">)</span>
<span class="n">first</span><span class="p">,</span> <span class="n">last</span><span class="p">,</span> <span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">time_range</span> <span class="o">+</span> <span class="p">(</span><span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">))[:</span><span class="mi">3</span><span class="p">]</span>
<span class="k">if</span> <span class="n">last</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">last</span> <span class="o">=</span> <span class="mf">3.</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">first_mode</span><span class="p">)</span><span class="o">.</span><span class="n">inv_relaxation_time</span>
<span class="k">if</span> <span class="n">step</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">last</span><span class="o">-</span><span class="n">first</span><span class="p">)</span><span class="o">/</span><span class="mf">300.</span>
<span class="n">time</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">first</span><span class="p">,</span> <span class="n">last</span><span class="p">,</span> <span class="n">step</span><span class="p">)</span>
<span class="n">msd</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">time</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">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">rt</span> <span class="o">=</span> <span class="n">mode</span><span class="o">.</span><span class="n">inv_relaxation_time</span>
<span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="n">weights</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">sumOverParticles</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">msd</span><span class="p">,</span> <span class="n">d</span><span class="o">*</span><span class="p">(</span><span class="mf">1.</span><span class="o">-</span><span class="n">N</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">rt</span><span class="o">*</span><span class="n">time</span><span class="p">))</span><span class="o">/</span><span class="n">rt</span><span class="p">,</span> <span class="n">msd</span><span class="p">)</span>
<span class="n">N</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">msd</span><span class="p">,</span> <span class="mf">2.</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="p">,</span> <span class="n">msd</span><span class="p">)</span>
<span class="k">return</span> <span class="n">InterpolatingFunction</span><span class="p">((</span><span class="n">time</span><span class="p">,),</span> <span class="n">msd</span><span class="p">)</span>
</div>
<div class="viewcode-block" id="BrownianModes.staticStructureFactor"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.BrownianModes.BrownianModes.staticStructureFactor">[docs]</a> <span class="k">def</span> <span class="nf">staticStructureFactor</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">q_range</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">15.</span><span class="p">),</span> <span class="n">subset</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span>
<span class="n">weights</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">random_vectors</span><span class="o">=</span><span class="mi">15</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="sd">"""</span>
<span class="sd"> :param q_range: the range of angular wavenumber values</span>
<span class="sd"> :type q_range: tuple</span>
<span class="sd"> :param subset: the subset of the universe used in the calculation</span>
<span class="sd"> (default: the whole universe)</span>
<span class="sd"> :type subset: :class:`~MMTK.Collections.GroupOfAtoms`</span>
<span class="sd"> :param weights: the weight to be given to each atom in the average</span>
<span class="sd"> (default: coherent scattering lengths)</span>
<span class="sd"> :type weights: :class:`~MMTK.ParticleProperties.ParticleScalar`</span>
<span class="sd"> :param random_vectors: the number of random direction vectors</span>
<span class="sd"> used in the orientational average</span>
<span class="sd"> :type random_vectors: int</span>
<span class="sd"> :param first_mode: the first mode to be taken into account for</span>
<span class="sd"> the fluctuation calculation. The default value</span>
<span class="sd"> of 6 is right for molecules in vacuum.</span>
<span class="sd"> :type first_mode: int</span>
<span class="sd"> :returns: the Static Structure Factor as a</span>
<span class="sd"> function of angular wavenumber</span>
<span class="sd"> :rtype: Scientific.Functions.Interpolation.InterpolatingFunction</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">subset</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">subset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">universe</span>
<span class="k">if</span> <span class="n">weights</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">weights</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="o">.</span><span class="n">getParticleScalar</span><span class="p">(</span><span class="s">'b_coherent'</span><span class="p">)</span>
<span class="n">mask</span> <span class="o">=</span> <span class="n">subset</span><span class="o">.</span><span class="n">booleanMask</span><span class="p">()</span>
<span class="n">weights</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">weights</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</span>
<span class="n">weights</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">sqrt</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">weights</span><span class="o">*</span><span class="n">weights</span><span class="p">))</span>
<span class="n">friction</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="bp">self</span><span class="o">.</span><span class="n">friction</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</span>
<span class="n">r</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="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="o">.</span><span class="n">configuration</span><span class="p">()</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</span>
<span class="n">first</span><span class="p">,</span> <span class="n">last</span><span class="p">,</span> <span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">q_range</span><span class="o">+</span><span class="p">(</span><span class="bp">None</span><span class="p">,))[:</span><span class="mi">3</span><span class="p">]</span>
<span class="k">if</span> <span class="n">step</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">last</span><span class="o">-</span><span class="n">first</span><span class="p">)</span><span class="o">/</span><span class="mf">50.</span>
<span class="n">q</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">first</span><span class="p">,</span> <span class="n">last</span><span class="p">,</span> <span class="n">step</span><span class="p">)</span>
<span class="n">kT</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="n">natoms</span> <span class="o">=</span> <span class="n">subset</span><span class="o">.</span><span class="n">numberOfAtoms</span><span class="p">()</span>
<span class="n">sq</span> <span class="o">=</span> <span class="mf">0.</span>
<span class="n">random_vectors</span> <span class="o">=</span> <span class="n">Random</span><span class="o">.</span><span class="n">randomDirections</span><span class="p">(</span><span class="n">random_vectors</span><span class="p">)</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">random_vectors</span><span class="p">:</span>
<span class="n">sab</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">natoms</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="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">irt</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="o">.</span><span class="n">inv_relaxation_time</span>
<span class="n">d</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="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="o">*</span><span class="n">v</span><span class="p">)</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</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">friction</span><span class="p">)</span>
<span class="n">sab</span> <span class="o">=</span> <span class="n">sab</span> <span class="o">+</span> <span class="p">(</span><span class="n">d</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">d</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="mi">2</span><span class="o">/</span><span class="n">irt</span>
<span class="n">sab</span> <span class="o">=</span> <span class="n">sab</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">q</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="n">N</span><span class="o">.</span><span class="n">NewAxis</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span>
<span class="n">phase</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mf">1.j</span><span class="o">*</span><span class="n">q</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">N</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">v</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">weights</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="n">temp</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">phase</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">N</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mf">0.5</span><span class="o">*</span><span class="n">kT</span><span class="o">*</span><span class="n">sab</span><span class="p">),</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">temp</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">N</span><span class="o">.</span><span class="n">conjugate</span><span class="p">(</span><span class="n">phase</span><span class="p">)</span><span class="o">*</span><span class="n">temp</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">sq</span> <span class="o">=</span> <span class="n">sq</span> <span class="o">+</span> <span class="n">temp</span><span class="o">.</span><span class="n">real</span>
<span class="k">return</span> <span class="n">InterpolatingFunction</span><span class="p">((</span><span class="n">q</span><span class="p">,),</span> <span class="n">sq</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">random_vectors</span><span class="p">))</span>
</div>
<div class="viewcode-block" id="BrownianModes.coherentScatteringFunction"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.BrownianModes.BrownianModes.coherentScatteringFunction">[docs]</a> <span class="k">def</span> <span class="nf">coherentScatteringFunction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">time_range</span> <span class="o">=</span> <span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">),</span>
<span class="n">subset</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">weights</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span>
<span class="n">random_vectors</span><span class="o">=</span><span class="mi">15</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="sd">"""</span>
<span class="sd"> :param q: the angular wavenumber</span>
<span class="sd"> :type q: float</span>
<span class="sd"> :param time_range: the time values at which the mean-square</span>
<span class="sd"> displacement is evaluated, specified as a</span>
<span class="sd"> range tuple (first, last, step).</span>
<span class="sd"> The defaults are first=0, last=</span>
<span class="sd"> 20 times the longest vibration perdiod,</span>
<span class="sd"> and step defined such that 300 points are</span>
<span class="sd"> used in total.</span>
<span class="sd"> :type time_range: tuple</span>
<span class="sd"> :param subset: the subset of the universe used in the calculation</span>
<span class="sd"> (default: the whole universe)</span>
<span class="sd"> :type subset: :class:`~MMTK.Collections.GroupOfAtoms`</span>
<span class="sd"> :param weights: the weight to be given to each atom in the average</span>
<span class="sd"> (default: coherent scattering lengths)</span>
<span class="sd"> :type weights: :class:`~MMTK.ParticleProperties.ParticleScalar`</span>
<span class="sd"> :param random_vectors: the number of random direction vectors</span>
<span class="sd"> used in the orientational average</span>
<span class="sd"> :type random_vectors: int</span>
<span class="sd"> :param first_mode: the first mode to be taken into account for</span>
<span class="sd"> the fluctuation calculation. The default value</span>
<span class="sd"> of 6 is right for molecules in vacuum.</span>
<span class="sd"> :type first_mode: int</span>
<span class="sd"> :returns: the Coherent Scattering Function as a function of time</span>
<span class="sd"> :rtype: Scientific.Functions.Interpolation.InterpolatingFunction</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">subset</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">subset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">universe</span>
<span class="k">if</span> <span class="n">weights</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">weights</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="o">.</span><span class="n">getParticleScalar</span><span class="p">(</span><span class="s">'b_coherent'</span><span class="p">)</span>
<span class="n">mask</span> <span class="o">=</span> <span class="n">subset</span><span class="o">.</span><span class="n">booleanMask</span><span class="p">()</span>
<span class="n">weights</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">weights</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</span>
<span class="n">weights</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">sqrt</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">weights</span><span class="o">*</span><span class="n">weights</span><span class="p">))</span>
<span class="n">friction</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="bp">self</span><span class="o">.</span><span class="n">friction</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</span>
<span class="n">r</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="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="o">.</span><span class="n">configuration</span><span class="p">()</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</span>
<span class="n">first</span><span class="p">,</span> <span class="n">last</span><span class="p">,</span> <span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">time_range</span> <span class="o">+</span> <span class="p">(</span><span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">))[:</span><span class="mi">3</span><span class="p">]</span>
<span class="k">if</span> <span class="n">last</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">last</span> <span class="o">=</span> <span class="mf">3.</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">first_mode</span><span class="p">)</span><span class="o">.</span><span class="n">inv_relaxation_time</span>
<span class="k">if</span> <span class="n">step</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">last</span><span class="o">-</span><span class="n">first</span><span class="p">)</span><span class="o">/</span><span class="mf">300.</span>
<span class="n">time</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">first</span><span class="p">,</span> <span class="n">last</span><span class="p">,</span> <span class="n">step</span><span class="p">)</span>
<span class="n">natoms</span> <span class="o">=</span> <span class="n">subset</span><span class="o">.</span><span class="n">numberOfAtoms</span><span class="p">()</span>
<span class="n">kT</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="n">fcoh</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">len</span><span class="p">(</span><span class="n">time</span><span class="p">),),</span> <span class="n">N</span><span class="o">.</span><span class="n">Complex</span><span class="p">)</span>
<span class="n">random_vectors</span> <span class="o">=</span> <span class="n">Random</span><span class="o">.</span><span class="n">randomDirections</span><span class="p">(</span><span class="n">random_vectors</span><span class="p">)</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">random_vectors</span><span class="p">:</span>
<span class="n">phase</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mf">1.j</span><span class="o">*</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">r</span><span class="p">,</span> <span class="n">v</span><span class="o">.</span><span class="n">array</span><span class="p">))</span>
<span class="k">for</span> <span class="n">ai</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">fbt</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">natoms</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">time</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">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">irt</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="o">.</span><span class="n">inv_relaxation_time</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">q</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="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="o">*</span><span class="n">v</span><span class="p">)</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</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">friction</span><span class="p">)</span>
<span class="n">ft</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">irt</span><span class="o">*</span><span class="n">time</span><span class="p">)</span><span class="o">/</span><span class="n">irt</span>
<span class="n">N</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">fbt</span><span class="p">,</span>
<span class="n">d</span><span class="p">[</span><span class="n">ai</span><span class="p">]</span> <span class="o">*</span> <span class="n">d</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">ft</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="n">fbt</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">fbt</span><span class="p">,</span>
<span class="p">(</span><span class="o">-</span><span class="mf">0.5</span><span class="o">/</span><span class="n">irt</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">d</span><span class="p">[</span><span class="n">ai</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">d</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="mi">2</span><span class="p">),</span>
<span class="n">fbt</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">fcoh</span><span class="p">,</span>
<span class="n">weights</span><span class="p">[</span><span class="n">ai</span><span class="p">]</span><span class="o">*</span><span class="n">phase</span><span class="p">[</span><span class="n">ai</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="n">weights</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">conjugate</span><span class="p">(</span><span class="n">phase</span><span class="p">),</span>
<span class="n">N</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">kT</span><span class="o">*</span><span class="n">fbt</span><span class="p">)),</span>
<span class="n">fcoh</span><span class="p">)</span>
<span class="k">return</span> <span class="n">InterpolatingFunction</span><span class="p">((</span><span class="n">time</span><span class="p">,),</span> <span class="n">fcoh</span><span class="o">.</span><span class="n">real</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">random_vectors</span><span class="p">))</span>
</div>
<div class="viewcode-block" id="BrownianModes.incoherentScatteringFunction"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.BrownianModes.BrownianModes.incoherentScatteringFunction">[docs]</a> <span class="k">def</span> <span class="nf">incoherentScatteringFunction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">time_range</span> <span class="o">=</span> <span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">),</span>
<span class="n">subset</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">random_vectors</span><span class="o">=</span><span class="mi">15</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="sd">"""</span>
<span class="sd"> :param q: the angular wavenumber</span>
<span class="sd"> :type q: float</span>
<span class="sd"> :param time_range: the time values at which the mean-square</span>
<span class="sd"> displacement is evaluated, specified as a</span>
<span class="sd"> range tuple (first, last, step).</span>
<span class="sd"> The defaults are first=0, last=</span>
<span class="sd"> 20 times the longest vibration perdiod,</span>
<span class="sd"> and step defined such that 300 points are</span>
<span class="sd"> used in total.</span>
<span class="sd"> :type time_range: tuple</span>
<span class="sd"> :param subset: the subset of the universe used in the calculation</span>
<span class="sd"> (default: the whole universe)</span>
<span class="sd"> :type subset: :class:`~MMTK.Collections.GroupOfAtoms`</span>
<span class="sd"> :param random_vectors: the number of random direction vectors</span>
<span class="sd"> used in the orientational average</span>
<span class="sd"> :type random_vectors: int</span>
<span class="sd"> :param first_mode: the first mode to be taken into account for</span>
<span class="sd"> the fluctuation calculation. The default value</span>
<span class="sd"> of 6 is right for molecules in vacuum.</span>
<span class="sd"> :type first_mode: int</span>
<span class="sd"> :returns: the Incoherent Scattering Function as a function of time</span>
<span class="sd"> :rtype: Scientific.Functions.Interpolation.InterpolatingFunction</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">subset</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">subset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">universe</span>
<span class="n">mask</span> <span class="o">=</span> <span class="n">subset</span><span class="o">.</span><span class="n">booleanMask</span><span class="p">()</span>
<span class="n">weights_inc</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="o">.</span><span class="n">getParticleScalar</span><span class="p">(</span><span class="s">'b_incoherent'</span><span class="p">)</span>
<span class="n">weights_inc</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">weights_inc</span><span class="o">.</span><span class="n">array</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</span>
<span class="n">weights_inc</span> <span class="o">=</span> <span class="n">weights_inc</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">weights_inc</span><span class="p">)</span>
<span class="n">friction</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="bp">self</span><span class="o">.</span><span class="n">friction</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</span>
<span class="n">mass</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="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="o">.</span><span class="n">masses</span><span class="p">()</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</span>
<span class="n">r</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="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="o">.</span><span class="n">configuration</span><span class="p">()</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</span>
<span class="n">first</span><span class="p">,</span> <span class="n">last</span><span class="p">,</span> <span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">time_range</span> <span class="o">+</span> <span class="p">(</span><span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">))[:</span><span class="mi">3</span><span class="p">]</span>
<span class="k">if</span> <span class="n">last</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">last</span> <span class="o">=</span> <span class="mf">3.</span><span class="o">/</span><span class="bp">self</span><span class="o">.</span><span class="n">weighedMode</span><span class="p">(</span><span class="n">first_mode</span><span class="p">)</span><span class="o">.</span><span class="n">inv_relaxation_time</span>
<span class="k">if</span> <span class="n">step</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">last</span><span class="o">-</span><span class="n">first</span><span class="p">)</span><span class="o">/</span><span class="mf">300.</span>
<span class="n">time</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">first</span><span class="p">,</span> <span class="n">last</span><span class="p">,</span> <span class="n">step</span><span class="p">)</span>
<span class="n">natoms</span> <span class="o">=</span> <span class="n">subset</span><span class="o">.</span><span class="n">numberOfAtoms</span><span class="p">()</span>
<span class="n">kT</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="n">finc</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">len</span><span class="p">(</span><span class="n">time</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">eisf</span> <span class="o">=</span> <span class="mf">0.</span>
<span class="n">random_vectors</span> <span class="o">=</span> <span class="n">Random</span><span class="o">.</span><span class="n">randomDirections</span><span class="p">(</span><span class="n">random_vectors</span><span class="p">)</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">random_vectors</span><span class="p">:</span>
<span class="n">phase</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mf">1.j</span><span class="o">*</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">r</span><span class="p">,</span> <span class="n">v</span><span class="o">.</span><span class="n">array</span><span class="p">))</span>
<span class="n">faat</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">natoms</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">time</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">eisf_sum</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">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="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">irt</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="o">.</span><span class="n">inv_relaxation_time</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">q</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="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="o">*</span><span class="n">v</span><span class="p">)</span><span class="o">.</span><span class="n">array</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">array</span><span class="p">)</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">friction</span><span class="p">)</span>
<span class="n">ft</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">irt</span><span class="o">*</span><span class="n">time</span><span class="p">)</span><span class="o">-</span><span class="mf">1.</span><span class="p">)</span><span class="o">/</span><span class="n">irt</span>
<span class="n">N</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">faat</span><span class="p">,</span>
<span class="n">d</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="mi">2</span> <span class="o">*</span> <span class="n">ft</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="n">faat</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">eisf_sum</span><span class="p">,</span> <span class="o">-</span><span class="n">d</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="n">irt</span><span class="p">,</span> <span class="n">eisf_sum</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">finc</span><span class="p">,</span>
<span class="n">N</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">weights_inc</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">N</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">kT</span><span class="o">*</span><span class="n">faat</span><span class="p">),</span> <span class="mi">0</span><span class="p">),</span>
<span class="n">finc</span><span class="p">)</span>
<span class="n">eisf</span> <span class="o">=</span> <span class="n">eisf</span> <span class="o">+</span> <span class="n">N</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">weights_inc</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">kT</span><span class="o">*</span><span class="n">eisf_sum</span><span class="p">))</span>
<span class="k">return</span> <span class="n">InterpolatingFunction</span><span class="p">((</span><span class="n">time</span><span class="p">,),</span> <span class="n">finc</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">random_vectors</span><span class="p">))</span>
</div>
<div class="viewcode-block" id="BrownianModes.EISF"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.BrownianModes.BrownianModes.EISF">[docs]</a> <span class="k">def</span> <span class="nf">EISF</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">q_range</span> <span class="o">=</span> <span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">15.</span><span class="p">),</span> <span class="n">subset</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">weights</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span>
<span class="n">random_vectors</span> <span class="o">=</span> <span class="mi">15</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="sd">"""</span>
<span class="sd"> :param q_range: the range of angular wavenumber values</span>
<span class="sd"> :type q_range: tuple</span>
<span class="sd"> :param subset: the subset of the universe used in the calculation</span>
<span class="sd"> (default: the whole universe)</span>
<span class="sd"> :type subset: :class:`~MMTK.Collections.GroupOfAtoms`</span>
<span class="sd"> :param weights: the weight to be given to each atom in the average</span>
<span class="sd"> (default: incoherent scattering lengths)</span>
<span class="sd"> :type weights: :class:`~MMTK.ParticleProperties.ParticleScalar`</span>
<span class="sd"> :param random_vectors: the number of random direction vectors</span>
<span class="sd"> used in the orientational average</span>
<span class="sd"> :type random_vectors: int</span>
<span class="sd"> :param first_mode: the first mode to be taken into account for</span>
<span class="sd"> the fluctuation calculation. The default value</span>
<span class="sd"> of 6 is right for molecules in vacuum.</span>
<span class="sd"> :type first_mode: int</span>
<span class="sd"> :returns: the Elastic Incoherent Structure Factor (EISF) as a</span>
<span class="sd"> function of angular wavenumber</span>
<span class="sd"> :rtype: Scientific.Functions.Interpolation.InterpolatingFunction</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">subset</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">subset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">universe</span>
<span class="k">if</span> <span class="n">weights</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">weights</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">universe</span><span class="o">.</span><span class="n">getParticleScalar</span><span class="p">(</span><span class="s">'b_incoherent'</span><span class="p">)</span>
<span class="n">weights</span> <span class="o">=</span> <span class="n">weights</span><span class="o">*</span><span class="n">weights</span>
<span class="n">weights</span> <span class="o">=</span> <span class="n">weights</span><span class="o">*</span><span class="n">subset</span><span class="o">.</span><span class="n">booleanMask</span><span class="p">()</span>
<span class="n">total</span> <span class="o">=</span> <span class="n">weights</span><span class="o">.</span><span class="n">sumOverParticles</span><span class="p">()</span>
<span class="n">weights</span> <span class="o">=</span> <span class="n">weights</span><span class="o">/</span><span class="n">total</span>
<span class="n">first</span><span class="p">,</span> <span class="n">last</span><span class="p">,</span> <span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">q_range</span><span class="o">+</span><span class="p">(</span><span class="bp">None</span><span class="p">,))[:</span><span class="mi">3</span><span class="p">]</span>
<span class="k">if</span> <span class="n">step</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">last</span><span class="o">-</span><span class="n">first</span><span class="p">)</span><span class="o">/</span><span class="mf">50.</span>
<span class="n">q</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">first</span><span class="p">,</span> <span class="n">last</span><span class="p">,</span> <span class="n">step</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">f</span> <span class="o">=</span> <span class="n">f</span> <span class="o">+</span> <span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="n">mode</span><span class="o">.</span><span class="n">inv_relaxation_time</span><span class="p">)</span><span class="o">*</span><span class="n">mode</span><span class="o">.</span><span class="n">dyadicProduct</span><span class="p">(</span><span class="n">mode</span><span class="p">)</span>
<span class="n">f</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="o">*</span><span class="n">f</span><span class="o">/</span><span class="bp">self</span><span class="o">.</span><span class="n">friction</span>
<span class="n">eisf</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">q</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="n">random_vectors</span> <span class="o">=</span> <span class="n">Random</span><span class="o">.</span><span class="n">randomDirections</span><span class="p">(</span><span class="n">random_vectors</span><span class="p">)</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">random_vectors</span><span class="p">:</span>
<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">subset</span><span class="o">.</span><span class="n">atomList</span><span class="p">():</span>
<span class="n">exp</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">v</span><span class="o">*</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="o">*</span><span class="n">v</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">eisf</span><span class="p">,</span> <span class="n">weights</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="o">*</span><span class="n">exp</span><span class="o">**</span><span class="p">(</span><span class="n">q</span><span class="o">*</span><span class="n">q</span><span class="p">),</span> <span class="n">eisf</span><span class="p">)</span>
<span class="k">return</span> <span class="n">InterpolatingFunction</span><span class="p">((</span><span class="n">q</span><span class="p">,),</span> <span class="n">eisf</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">random_vectors</span><span class="p">))</span></div></div>
</pre></div>
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