1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>MMTK.NormalModes.VibrationalModes — MMTK User Guide 2.7.7 documentation</title>
<link rel="stylesheet" href="../../../_static/default.css" type="text/css" />
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT: '../../../',
VERSION: '2.7.7',
COLLAPSE_INDEX: false,
FILE_SUFFIX: '.html',
HAS_SOURCE: true
};
</script>
<script type="text/javascript" src="../../../_static/jquery.js"></script>
<script type="text/javascript" src="../../../_static/underscore.js"></script>
<script type="text/javascript" src="../../../_static/doctools.js"></script>
<link rel="top" title="MMTK User Guide 2.7.7 documentation" href="../../../index.html" />
<link rel="up" title="Module code" href="../../index.html" />
</head>
<body>
<div class="related">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../../../genindex.html" title="General Index"
accesskey="I">index</a></li>
<li class="right" >
<a href="../../../py-modindex.html" title="Python Module Index"
>modules</a> |</li>
<li><a href="../../../index.html">MMTK User Guide 2.7.7 documentation</a> »</li>
<li><a href="../../index.html" accesskey="U">Module code</a> »</li>
</ul>
</div>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body">
<h1>Source code for MMTK.NormalModes.VibrationalModes</h1><div class="highlight"><pre>
<span class="c"># Vibrational 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">Vibrational 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">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="VibrationalMode"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.VibrationalModes.VibrationalMode">[docs]</a><span class="k">class</span> <span class="nc">VibrationalMode</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 vibrational normal mode</span>
<span class="sd"> Mode objects are created by indexing a </span>
<span class="sd"> :class:`~MMTK.NormalModes.VibrationalModes.VibrationalModes` object.</span>
<span class="sd"> They contain the atomic displacements corresponding to a</span>
<span class="sd"> single mode. In addition, the frequency corresponding to the mode</span>
<span class="sd"> is stored in the attribute "frequency".</span>
<span class="sd"> Note: the normal mode vectors are *not* mass 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">frequency</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">frequency</span> <span class="o">=</span> <span class="n">frequency</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 frequency '</span> <span class="o">+</span> <span class="sb">`self.frequency`</span>
<span class="n">__repr__</span> <span class="o">=</span> <span class="n">__str__</span>
<span class="k">def</span> <span class="nf">effectiveMassAndForceConstant</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="n">m</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">massWeightedDotProduct</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span><span class="o">/</span><span class="bp">self</span><span class="o">.</span><span class="n">dotProduct</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">m</span><span class="o">*</span><span class="p">(</span><span class="mf">2.</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">frequency</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
<span class="k">return</span> <span class="n">m</span><span class="p">,</span> <span class="n">k</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="VibrationalModes"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.VibrationalModes.VibrationalModes">[docs]</a><span class="k">class</span> <span class="nc">VibrationalModes</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"> Vibrational modes describe the independent vibrational motions</span>
<span class="sd"> of a harmonic system. They are obtained by diagonalizing the mass-weighted</span>
<span class="sd"> 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.VibrationalModes.VibrationalMode`)</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="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 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">'imaginary'</span><span class="p">,</span>
<span class="s">'frequencies'</span><span class="p">,</span> <span class="s">'omega_sq'</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">sqrt</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="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">imaginary</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">less</span><span class="p">(</span><span class="n">ev</span><span class="p">,</span> <span class="mf">0.</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">omega_sq</span> <span class="o">=</span> <span class="n">ev</span>
<span class="bp">self</span><span class="o">.</span><span class="n">frequencies</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">fabs</span><span class="p">(</span><span class="n">ev</span><span class="p">))</span> <span class="o">/</span> <span class="p">(</span><span class="mf">2.</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">pi</span><span class="p">)</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">frequencies</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">__setstate__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">state</span><span class="p">):</span>
<span class="c"># This fixes unpickled objects from pre-2.5 versions.</span>
<span class="c"># Their modes were stored in un-weighted coordinates.</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">state</span><span class="o">.</span><span class="n">has_key</span><span class="p">(</span><span class="s">'weights'</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">sqrt</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="s">'universe'</span><span class="p">]</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">N</span><span class="o">.</span><span class="n">NewAxis</span><span class="p">]</span>
<span class="n">state</span><span class="p">[</span><span class="s">'weights'</span><span class="p">]</span> <span class="o">=</span> <span class="n">weights</span>
<span class="n">state</span><span class="p">[</span><span class="s">'array'</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="p">:]</span>
<span class="k">if</span> <span class="n">state</span><span class="p">[</span><span class="s">'temperature'</span><span class="p">]</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">factor</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="n">state</span><span class="p">[</span><span class="s">'temperature'</span><span class="p">]</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="n">Units</span><span class="o">.</span><span class="n">amu</span><span class="p">)</span> <span class="o">/</span> \
<span class="p">(</span><span class="mf">2.</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
<span class="n">freq</span> <span class="o">=</span> <span class="n">state</span><span class="p">[</span><span class="s">'frequencies'</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">state</span><span class="p">[</span><span class="s">'nmodes'</span><span class="p">]):</span>
<span class="n">index</span> <span class="o">=</span> <span class="n">state</span><span class="p">[</span><span class="s">'sort_index'</span><span class="p">][</span><span class="n">i</span><span class="p">]</span>
<span class="k">if</span> <span class="n">index</span> <span class="o">>=</span> <span class="mi">6</span><span class="p">:</span>
<span class="n">state</span><span class="p">[</span><span class="s">'array'</span><span class="p">][</span><span class="n">index</span><span class="p">]</span> <span class="o">*=</span> <span class="n">freq</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">/</span><span class="n">factor</span>
<span class="bp">self</span><span class="o">.</span><span class="n">__dict__</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">state</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">frequencies</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">imaginary</span><span class="p">[</span><span class="n">index</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="mf">1.j</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="n">Units</span><span class="o">.</span><span class="n">amu</span><span class="p">)</span> <span class="o">/</span> \
<span class="p">(</span><span class="mf">2.</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
<span class="k">return</span> <span class="n">VibrationalMode</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="n">f</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><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="VibrationalModes.rawMode"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.VibrationalModes.VibrationalModes.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.VibrationalModes.VibrationalMode`</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">frequencies</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">imaginary</span><span class="p">[</span><span class="n">index</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="mf">1.j</span>
<span class="k">return</span> <span class="n">VibrationalMode</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="n">f</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">frequency</span><span class="o">**</span><span class="mi">2</span>
<span class="n">f</span><span class="o">.</span><span class="n">array</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="mi">0</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span>
<span class="n">s</span> <span class="o">=</span> <span class="mf">1.</span><span class="o">/</span><span class="p">(</span><span class="mf">2.</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span><span class="o">**</span><span class="mi">2</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">s</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">f</span><span class="o">.</span><span class="n">array</span> <span class="o">*=</span> <span class="n">s</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">frequency</span><span class="o">**</span><span class="mi">2</span>
<span class="n">s</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span><span class="o">**</span><span class="mi">2</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">s</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">f</span><span class="o">.</span><span class="n">array</span> <span class="o">/=</span> <span class="n">s</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="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="n">N</span><span class="o">.</span><span class="n">NewAxis</span><span class="p">]</span>
<span class="k">return</span> <span class="n">f</span>
<div class="viewcode-block" id="VibrationalModes.meanSquareDisplacement"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.VibrationalModes.VibrationalModes.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">tau</span><span class="o">=</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 tau: the relaxation time of an exponential damping factor</span>
<span class="sd"> (default: no damping)</span>
<span class="sd"> :type tau: float</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="bp">self</span><span class="o">.</span><span class="n">temperature</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">"no temperature available"</span><span class="p">)</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="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">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">20.</span><span class="o">/</span><span class="bp">self</span><span class="p">[</span><span class="n">first_mode</span><span class="p">]</span><span class="o">.</span><span class="n">frequency</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="k">if</span> <span class="n">tau</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span> <span class="n">damping</span> <span class="o">=</span> <span class="mf">1.</span>
<span class="k">else</span><span class="p">:</span> <span class="n">damping</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="p">(</span><span class="n">time</span><span class="o">/</span><span class="n">tau</span><span class="p">)</span><span class="o">**</span><span class="mi">2</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="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">omega</span> <span class="o">=</span> <span class="mf">2.</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">mode</span><span class="o">.</span><span class="n">frequency</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">damping</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">omega</span><span class="o">*</span><span class="n">time</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="VibrationalModes.EISF"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.VibrationalModes.VibrationalModes.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="bp">self</span><span class="o">.</span><span class="n">temperature</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">"no temperature available"</span><span class="p">)</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">MMTK</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="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="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">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="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">random_vectors</span><span class="p">):</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">MMTK</span><span class="o">.</span><span class="n">Random</span><span class="o">.</span><span class="n">randomDirection</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="n">random_vectors</span><span class="p">)</span>
</div>
<div class="viewcode-block" id="VibrationalModes.incoherentScatteringFunction"><a class="viewcode-back" href="../../../modules.html#MMTK.NormalModes.VibrationalModes.VibrationalModes.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">weights</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">tau</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: incoherent scattering lengths)</span>
<span class="sd"> :type weights: :class:`~MMTK.ParticleProperties.ParticleScalar`</span>
<span class="sd"> :param tau: the relaxation time of an exponential damping factor</span>
<span class="sd"> (default: no damping)</span>
<span class="sd"> :type tau: float</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="bp">self</span><span class="o">.</span><span class="n">temperature</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">"no temperature available"</span><span class="p">)</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">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">20.</span><span class="o">/</span><span class="bp">self</span><span class="p">[</span><span class="n">first_mode</span><span class="p">]</span><span class="o">.</span><span class="n">frequency</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">400.</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="k">if</span> <span class="n">tau</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
<span class="n">damping</span> <span class="o">=</span> <span class="mf">1.</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">damping</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="p">(</span><span class="n">time</span><span class="o">/</span><span class="n">tau</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</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="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="n">random_vectors</span> <span class="o">=</span> <span class="n">MMTK</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">msd</span> <span class="o">=</span> <span class="mf">0.</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="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="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="n">v</span><span class="o">*</span><span class="n">mode</span><span class="p">[</span><span class="n">a</span><span class="p">])</span><span class="o">**</span><span class="mi">2</span>
<span class="n">omega</span> <span class="o">=</span> <span class="mf">2.</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">mode</span><span class="o">.</span><span class="n">frequency</span>
<span class="n">msd</span> <span class="o">=</span> <span class="n">msd</span><span class="o">+</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">damping</span><span class="o">*</span><span class="n">N</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">omega</span><span class="o">*</span><span class="n">time</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">weights</span><span class="p">[</span><span class="n">a</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="n">q</span><span class="o">*</span><span class="n">q</span><span class="o">*</span><span class="n">msd</span><span class="p">),</span> <span class="n">finc</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>
</pre></div>
</div>
</div>
</div>
<div class="sphinxsidebar">
<div class="sphinxsidebarwrapper">
<div id="searchbox" style="display: none">
<h3>Quick search</h3>
<form class="search" action="../../../search.html" method="get">
<input type="text" name="q" />
<input type="submit" value="Go" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
<p class="searchtip" style="font-size: 90%">
Enter search terms or a module, class or function name.
</p>
</div>
<script type="text/javascript">$('#searchbox').show(0);</script>
</div>
</div>
<div class="clearer"></div>
</div>
<div class="related">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../../../genindex.html" title="General Index"
>index</a></li>
<li class="right" >
<a href="../../../py-modindex.html" title="Python Module Index"
>modules</a> |</li>
<li><a href="../../../index.html">MMTK User Guide 2.7.7 documentation</a> »</li>
<li><a href="../../index.html" >Module code</a> »</li>
</ul>
</div>
<div class="footer">
© Copyright 2010, Konrad Hinsen.
Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.1.3.
</div>
</body>
</html>
|
