Uh oh!
There was an error while loading. Please reload this page.
- Notifications
You must be signed in to change notification settings - Fork 1
Expand file tree
/
Copy pathexamples.html
More file actions
Latest commit
492 lines (339 loc) · 38.8 KB
/
Copy pathexamples.html
File metadata and controls
492 lines (339 loc) · 38.8 KB
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
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--><htmlclass="no-js" lang="en" ><!--<![endif]-->
<head>
<metacharset="utf-8">
<metaname="viewport" content="width=device-width, initial-scale=1.0">
<title>Examples — QML 0.4.0 documentation</title>
<linkrel="stylesheet" href="_static/css/theme.css" type="text/css" />
<linkrel="stylesheet" href="_static/pygments.css" type="text/css" />
<linkrel="index" title="Index" href="genindex.html" />
<linkrel="search" title="Search" href="search.html" />
<linkrel="next" title="Python API documentation" href="qml.html" />
<linkrel="prev" title="QML Tutorial" href="tutorial.html" />
<scriptsrc="_static/js/modernizr.min.js"></script>
</head>
<bodyclass="wy-body-for-nav">
<divclass="wy-grid-for-nav">
<navdata-toggle="wy-nav-shift" class="wy-nav-side">
<divclass="wy-side-scroll">
<divclass="wy-side-nav-search">
<ahref="index.html" class="icon icon-home"> QML
</a>
<divrole="search">
<formid="rtd-search-form" class="wy-form" action="search.html" method="get">
<inputtype="text" name="q" placeholder="Search docs" />
<inputtype="hidden" name="check_keywords" value="yes" />
<inputtype="hidden" name="area" value="default" />
</form>
</div>
</div>
<divclass="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation">
<pclass="caption"><spanclass="caption-text">GETTING STARTED:</span></p>
<ulclass="current">
<liclass="toctree-l1"><aclass="reference internal" href="installation.html">Installing QML</a></li>
<liclass="toctree-l1"><aclass="reference internal" href="citation.html">Citing use of QML</a></li>
<liclass="toctree-l1"><aclass="reference internal" href="tutorial.html">QML Tutorial</a></li>
<liclass="toctree-l1 current"><aclass="current reference internal" href="#">Examples</a><ul>
<liclass="toctree-l2"><aclass="reference internal" href="#generating-representations-using-the-compound-class">Generating representations using the <codeclass="docutils literal notranslate"><spanclass="pre">Compound</span></code> class</a></li>
<liclass="toctree-l2"><aclass="reference internal" href="#generating-representations-via-the-qml-representations-module">Generating representations via the <codeclass="docutils literal notranslate"><spanclass="pre">qml.representations</span></code> module</a></li>
<liclass="toctree-l2"><aclass="reference internal" href="#calculating-a-gaussian-kernel">Calculating a Gaussian kernel</a></li>
<liclass="toctree-l2"><aclass="reference internal" href="#calculating-a-gaussian-kernel-using-a-local-representation">Calculating a Gaussian kernel using a local representation</a></li>
<liclass="toctree-l2"><aclass="reference internal" href="#generating-the-slatm-representation">Generating the SLATM representation</a></li>
<liclass="toctree-l2"><aclass="reference internal" href="#generating-the-fchl-representation">Generating the FCHL representation</a></li>
<liclass="toctree-l2"><aclass="reference internal" href="#generating-the-fchl-kernel">Generating the FCHL kernel</a></li>
</ul>
</li>
</ul>
<pclass="caption"><spanclass="caption-text">SOURCE DOCUMENTATION:</span></p>
<ul>
<liclass="toctree-l1"><aclass="reference internal" href="qml.html">Python API documentation</a></li>
</ul>
</div>
</div>
</nav>
<sectiondata-toggle="wy-nav-shift" class="wy-nav-content-wrap">
<navclass="wy-nav-top" aria-label="top navigation">
<idata-toggle="wy-nav-top" class="fa fa-bars"></i>
<ahref="index.html">QML</a>
</nav>
<divclass="wy-nav-content">
<divclass="rst-content">
<divrole="navigation" aria-label="breadcrumbs navigation">
<ulclass="wy-breadcrumbs">
<li><ahref="index.html">Docs</a> »</li>
<li>Examples</li>
<liclass="wy-breadcrumbs-aside">
<ahref="_sources/examples.rst.txt" rel="nofollow"> View page source</a>
</li>
</ul>
<hr/>
</div>
<divrole="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
<divitemprop="articleBody">
<divclass="section" id="examples">
<h1>Examples<aclass="headerlink" href="#examples" title="Permalink to this headline">¶</a></h1>
<divclass="section" id="generating-representations-using-the-compound-class">
<h2>Generating representations using the <codeclass="docutils literal notranslate"><spanclass="pre">Compound</span></code> class<aclass="headerlink" href="#generating-representations-using-the-compound-class" title="Permalink to this headline">¶</a></h2>
<p>The following example demonstrates how to generate a representation via
the <codeclass="docutils literal notranslate"><spanclass="pre">qml.Compound</span></code> class.</p>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="c1"># Read in an xyz or cif file.</span>
<spanclass="n">water</span><spanclass="o">=</span><spanclass="n">Compound</span><spanclass="p">(</span><spanclass="n">xyz</span><spanclass="o">=</span><spanclass="s2">"water.xyz"</span><spanclass="p">)</span>
<spanclass="c1"># Generate a molecular coulomb matrices sorted by row norm.</span>
<spanclass="n">water</span><spanclass="o">.</span><spanclass="n">generate_coulomb_matrix</span><spanclass="p">(</span><spanclass="n">size</span><spanclass="o">=</span><spanclass="mi">5</span><spanclass="p">,</span><spanclass="n">sorting</span><spanclass="o">=</span><spanclass="s2">"row-norm"</span><spanclass="p">)</span>
<spanclass="nb">print</span><spanclass="p">(</span><spanclass="n">water</span><spanclass="o">.</span><spanclass="n">representation</span><spanclass="p">)</span>
</pre></div>
</div>
<p>Might print the following representation:</p>
<divclass="code highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="p">[</span><spanclass="mf">73.51669472</span><spanclass="mf">8.3593106</span><spanclass="mf">0.5</span><spanclass="mf">8.35237809</span><spanclass="mf">0.66066557</span><spanclass="mf">0.5</span>
<spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span>
<spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="p">]</span>
</pre></div>
</div>
</div>
<divclass="section" id="generating-representations-via-the-qml-representations-module">
<h2>Generating representations via the <codeclass="docutils literal notranslate"><spanclass="pre">qml.representations</span></code> module<aclass="headerlink" href="#generating-representations-via-the-qml-representations-module" title="Permalink to this headline">¶</a></h2>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="kn">import</span><spanclass="nn">numpy</span><spanclass="k">as</span><spanclass="nn">np</span>
<spanclass="kn">from</span><spanclass="nn">qml.representations</span><spanclass="k">import</span><spanclass="o">*</span>
<spanclass="c1"># Dummy coordinates for a water molecule</span>
<spanclass="n">coordinates</span><spanclass="o">=</span><spanclass="n">np</span><spanclass="o">.</span><spanclass="n">array</span><spanclass="p">([[</span><spanclass="mf">1.464</span><spanclass="p">,</span><spanclass="mf">0.707</span><spanclass="p">,</span><spanclass="mf">1.056</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.878</span><spanclass="p">,</span><spanclass="mf">1.218</span><spanclass="p">,</span><spanclass="mf">0.498</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">2.319</span><spanclass="p">,</span><spanclass="mf">1.126</span><spanclass="p">,</span><spanclass="mf">0.952</span><spanclass="p">]])</span>
<spanclass="c1"># Oxygen, Hydrogen, Hydrogen</span>
<spanclass="n">nuclear_charges</span><spanclass="o">=</span><spanclass="n">np</span><spanclass="o">.</span><spanclass="n">array</span><spanclass="p">([</span><spanclass="mi">8</span><spanclass="p">,</span><spanclass="mi">1</span><spanclass="p">,</span><spanclass="mi">1</span><spanclass="p">])</span>
<spanclass="c1"># Generate a molecular coulomb matrices sorted by row norm.</span>
<spanclass="n">cm1</span><spanclass="o">=</span><spanclass="n">generate_coulomb_matrix</span><spanclass="p">(</span><spanclass="n">nuclear_charges</span><spanclass="p">,</span><spanclass="n">coordinates</span><spanclass="p">,</span>
<spanclass="n">size</span><spanclass="o">=</span><spanclass="mi">5</span><spanclass="p">,</span><spanclass="n">sorting</span><spanclass="o">=</span><spanclass="s2">"row-norm"</span><spanclass="p">)</span>
<spanclass="nb">print</span><spanclass="p">(</span><spanclass="n">cm1</span><spanclass="p">)</span>
</pre></div>
</div>
<p>The resulting Coulomb-matrix for water:</p>
<divclass="code highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="p">[</span><spanclass="mf">73.51669472</span><spanclass="mf">8.3593106</span><spanclass="mf">0.5</span><spanclass="mf">8.35237809</span><spanclass="mf">0.66066557</span><spanclass="mf">0.5</span>
<spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span>
<spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="p">]</span>
</pre></div>
</div>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="c1"># Generate all atomic coulomb matrices sorted by distance to</span>
<spanclass="c1"># query atom.</span>
<spanclass="n">cm2</span><spanclass="o">=</span><spanclass="n">generate_atomic_coulomb_matrix</span><spanclass="p">(</span><spanclass="n">atomtypes</span><spanclass="p">,</span><spanclass="n">coordinates</span><spanclass="p">,</span>
<spanclass="n">size</span><spanclass="o">=</span><spanclass="mi">5</span><spanclass="p">,</span><spanclass="n">sort</span><spanclass="o">=</span><spanclass="s2">"distance"</span><spanclass="p">)</span>
<spanclass="nb">print</span><spanclass="n">cm2</span>
</pre></div>
</div>
<divclass="code highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="p">[[</span><spanclass="mf">73.51669472</span><spanclass="mf">8.3593106</span><spanclass="mf">0.5</span><spanclass="mf">8.35237809</span><spanclass="mf">0.66066557</span><spanclass="mf">0.5</span>
<spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span>
<spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="p">]</span>
<spanclass="p">[</span><spanclass="mf">0.5</span><spanclass="mf">8.3593106</span><spanclass="mf">73.51669472</span><spanclass="mf">0.66066557</span><spanclass="mf">8.35237809</span><spanclass="mf">0.5</span>
<spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span>
<spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="p">]</span>
<spanclass="p">[</span><spanclass="mf">0.5</span><spanclass="mf">8.35237809</span><spanclass="mf">73.51669472</span><spanclass="mf">0.66066557</span><spanclass="mf">8.3593106</span><spanclass="mf">0.5</span>
<spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span>
<spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="mf">0.</span><spanclass="p">]]</span>
</pre></div>
</div>
</div>
<divclass="section" id="calculating-a-gaussian-kernel">
<h2>Calculating a Gaussian kernel<aclass="headerlink" href="#calculating-a-gaussian-kernel" title="Permalink to this headline">¶</a></h2>
<p>The input for most of the kernels in QML is a numpy array, where the first dimension is the number of representations, and the second dimension is the size of each representation. An brief example is presented here, where <codeclass="docutils literal notranslate"><spanclass="pre">compounds</span></code> is a list of <codeclass="docutils literal notranslate"><spanclass="pre">Compound()</span></code> objects:</p>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="kn">import</span><spanclass="nn">numpy</span><spanclass="k">as</span><spanclass="nn">np</span>
<spanclass="kn">from</span><spanclass="nn">qml.kernels</span><spanclass="k">import</span><spanclass="n">gaussian_kernel</span>
<spanclass="c1"># Generate a numpy-array of the representation</span>
<spanclass="n">X</span><spanclass="o">=</span><spanclass="n">np</span><spanclass="o">.</span><spanclass="n">array</span><spanclass="p">([</span><spanclass="n">c</span><spanclass="o">.</span><spanclass="n">representation</span><spanclass="k">for</span><spanclass="n">c</span><spanclass="ow">in</span><spanclass="n">compounds</span><spanclass="p">])</span>
<spanclass="c1"># Kernel-width</span>
<spanclass="n">sigma</span><spanclass="o">=</span><spanclass="mf">100.0</span>
<spanclass="c1"># Calculate the kernel-matrix</span>
<spanclass="n">K</span><spanclass="o">=</span><spanclass="n">gaussian_kernel</span><spanclass="p">(</span><spanclass="n">X</span><spanclass="p">,</span><spanclass="n">X</span><spanclass="p">,</span><spanclass="n">sigma</span><spanclass="p">)</span>
</pre></div>
</div>
</div>
<divclass="section" id="calculating-a-gaussian-kernel-using-a-local-representation">
<h2>Calculating a Gaussian kernel using a local representation<aclass="headerlink" href="#calculating-a-gaussian-kernel-using-a-local-representation" title="Permalink to this headline">¶</a></h2>
<p>The easiest way to calculate the kernel matrix using an explicit, local representation is via the wrappers module. Note that here the sigmas is a list of sigmas, and the result is a kernel for each sigma. The following examples currently work with the atomic coulomb matrix representation and the local SLATM representation:</p>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="kn">import</span><spanclass="nn">numpy</span><spanclass="k">as</span><spanclass="nn">np</span>
<spanclass="kn">from</span><spanclass="nn">qml.kernels</span><spanclass="k">import</span><spanclass="n">get_local_kernels_gaussian</span>
<spanclass="c1"># Assume the QM7 dataset is loaded into a list of Compound()</span>
<spanclass="k">for</span><spanclass="n">compound</span><spanclass="ow">in</span><spanclass="n">qm7</span><spanclass="p">:</span>
<spanclass="c1"># Generate the desired representation for each compound</span>
<spanclass="n">compound</span><spanclass="o">.</span><spanclass="n">generate_atomic_coulomb_matrix</span><spanclass="p">(</span><spanclass="n">size</span><spanclass="o">=</span><spanclass="mi">23</span><spanclass="p">,</span><spanclass="n">sort</span><spanclass="o">=</span><spanclass="s2">"row-norm"</span><spanclass="p">)</span>
<spanclass="c1"># Make a big array with all the atomic representations</span>
<spanclass="n">X</span><spanclass="o">=</span><spanclass="n">np</span><spanclass="o">.</span><spanclass="n">concatenate</span><spanclass="p">([</span><spanclass="n">mol</span><spanclass="o">.</span><spanclass="n">representation</span><spanclass="k">for</span><spanclass="n">mol</span><spanclass="ow">in</span><spanclass="n">qm7</span><spanclass="p">])</span>
<spanclass="c1"># Make an array with the number of atoms in each compound</span>
<spanclass="n">N</span><spanclass="o">=</span><spanclass="n">np</span><spanclass="o">.</span><spanclass="n">array</span><spanclass="p">([</span><spanclass="n">mol</span><spanclass="o">.</span><spanclass="n">natoms</span><spanclass="k">for</span><spanclass="n">mol</span><spanclass="ow">in</span><spanclass="n">qm7</span><spanclass="p">])</span>
<spanclass="c1"># List of kernel-widths</span>
<spanclass="n">sigmas</span><spanclass="o">=</span><spanclass="p">[</span><spanclass="mf">50.0</span><spanclass="p">,</span><spanclass="mf">100.0</span><spanclass="p">,</span><spanclass="mf">200.0</span><spanclass="p">]</span>
<spanclass="c1"># Calculate the kernel-matrix</span>
<spanclass="n">K</span><spanclass="o">=</span><spanclass="n">get_local_kernels_gaussian</span><spanclass="p">(</span><spanclass="n">X</span><spanclass="p">,</span><spanclass="n">X</span><spanclass="p">,</span><spanclass="n">N</span><spanclass="p">,</span><spanclass="n">N</span><spanclass="p">,</span><spanclass="n">sigmas</span><spanclass="p">)</span>
<spanclass="nb">print</span><spanclass="p">(</span><spanclass="n">K</span><spanclass="o">.</span><spanclass="n">shape</span><spanclass="p">)</span>
</pre></div>
</div>
<divclass="code highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="p">(</span><spanclass="mi">3</span><spanclass="p">,</span><spanclass="mi">7101</span><spanclass="p">,</span><spanclass="mi">7101</span><spanclass="p">)</span>
</pre></div>
</div>
<p>Note that <codeclass="docutils literal notranslate"><spanclass="pre">mol.representation</span></code> is just a 1D numpy array.</p>
</div>
<divclass="section" id="generating-the-slatm-representation">
<h2>Generating the SLATM representation<aclass="headerlink" href="#generating-the-slatm-representation" title="Permalink to this headline">¶</a></h2>
<p>The Spectrum of London and Axillrod-Teller-Muto potential (SLATM) representation requires additional input to reduce the size of the representation.
This input (the types of many-body terms) is generate via the <codeclass="docutils literal notranslate"><spanclass="pre">get_slatm_mbtypes()</span></code> function. The function takes a list of the nuclear charges for each molecule in the dataset as input. E.g.:</p>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="kn">from</span><spanclass="nn">qml.representations</span><spanclass="k">import</span><spanclass="n">get_slatm_mbtypes</span>
<spanclass="c1"># Assume 'qm7' is a list of Compound() objects.</span>
<spanclass="n">mbtypes</span><spanclass="o">=</span><spanclass="n">get_slatm_mbtypes</span><spanclass="p">([</span><spanclass="n">mol</span><spanclass="o">.</span><spanclass="n">nuclear_charges</span><spanclass="k">for</span><spanclass="n">compound</span><spanclass="ow">in</span><spanclass="n">qm7</span><spanclass="p">])</span>
<spanclass="c1"># Assume the QM7 dataset is loaded into a list of Compound()</span>
<spanclass="k">for</span><spanclass="n">compound</span><spanclass="ow">in</span><spanclass="n">qm7</span><spanclass="p">:</span>
<spanclass="c1"># Generate the desired representation for each compound</span>
<spanclass="n">compound</span><spanclass="o">.</span><spanclass="n">generate_slatm</span><spanclass="p">(</span><spanclass="n">mbtypes</span><spanclass="p">,</span><spanclass="n">local</span><spanclass="o">=</span><spanclass="kc">True</span><spanclass="p">)</span>
</pre></div>
</div>
<p>The <codeclass="docutils literal notranslate"><spanclass="pre">local</span></code> keyword in this example specifies that a local representation is produced. Alternatively the SLATM representation can be generate via the <codeclass="docutils literal notranslate"><spanclass="pre">qml.representations</span></code> module:</p>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="kn">from</span><spanclass="nn">qml.representations</span><spanclass="k">import</span><spanclass="n">generate_slatm</span>
<spanclass="c1"># Dummy coordinates</span>
<spanclass="n">coordinates</span><spanclass="o">=</span><spanclass="o">...</span>
<spanclass="c1"># Dummy nuclear charges</span>
<spanclass="n">nuclear_charges</span><spanclass="o">=</span><spanclass="o">...</span>
<spanclass="c1"># Dummy mbtypes</span>
<spanclass="n">mbtypes</span><spanclass="o">=</span><spanclass="n">get_slatm_mbtypes</span><spanclass="p">(</span><spanclass="o">...</span><spanclass="p">)</span>
<spanclass="c1"># Generate one representation</span>
<spanclass="n">rep</span><spanclass="o">=</span><spanclass="n">generate_slatm</span><spanclass="p">(</span><spanclass="n">coordinates</span><spanclass="p">,</span><spanclass="n">nuclear_charges</span><spanclass="p">,</span><spanclass="n">mbtypes</span><spanclass="p">)</span>
</pre></div>
</div>
<p>Here <codeclass="docutils literal notranslate"><spanclass="pre">coordinates</span></code> is an Nx3 numpy array, and <codeclass="docutils literal notranslate"><spanclass="pre">nuclear_charges</span></code> is simply a list of charges.</p>
</div>
<divclass="section" id="generating-the-fchl-representation">
<h2>Generating the FCHL representation<aclass="headerlink" href="#generating-the-fchl-representation" title="Permalink to this headline">¶</a></h2>
<p>The FCHL representation does not have an explicit representation in the form of a vector, and the kernel elements must be calculated analytically in a separate kernel function.
The syntax is analogous to the explicit representations (e.g. Coulomb matrix, BoB, SLATM, etc), but is handled by kernels from the separate <codeclass="docutils literal notranslate"><spanclass="pre">qml.fchl</span></code> module.</p>
<p>The code below show three ways to create the input representations for the FHCL kernel functions.</p>
<p>First using the <codeclass="docutils literal notranslate"><spanclass="pre">Compound</span></code> class:</p>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="c1"># Assume the dataset is loaded into a list of Compound()</span>
<spanclass="k">for</span><spanclass="n">compound</span><spanclass="ow">in</span><spanclass="n">mols</span><spanclass="p">:</span>
<spanclass="c1"># Generate the desired representation for each compound, cut off in angstrom</span>
<spanclass="n">compound</span><spanclass="o">.</span><spanclass="n">generate_fchl_representation</span><spanclass="p">(</span><spanclass="n">size</span><spanclass="o">=</span><spanclass="mi">23</span><spanclass="p">,</span><spanclass="n">cut_off</span><spanclass="o">=</span><spanclass="mf">10.0</span><spanclass="p">)</span>
<spanclass="c1"># Make Numpy array of the representation, which can be parsed to the kernel</span>
<spanclass="n">X</span><spanclass="o">=</span><spanclass="n">np</span><spanclass="o">.</span><spanclass="n">array</span><spanclass="p">([</span><spanclass="n">c</span><spanclass="o">.</span><spanclass="n">representation</span><spanclass="k">for</span><spanclass="n">c</span><spanclass="ow">in</span><spanclass="n">mols</span><spanclass="p">])</span>
</pre></div>
</div>
<p>The dimensions of the array should be <codeclass="docutils literal notranslate"><spanclass="pre">(number_molecules,</span><spanclass="pre">size,</span><spanclass="pre">5,</span><spanclass="pre">size)</span></code>, where <codeclass="docutils literal notranslate"><spanclass="pre">size</span></code> is the
size keyword used when generating the representations.</p>
<p>In addition to using the <codeclass="docutils literal notranslate"><spanclass="pre">Compound</span></code> class to generate the representations, FCHL representations can also be generated via the <codeclass="docutils literal notranslate"><spanclass="pre">qml.fchl.generate_fchl_representation()</span></code> function, using similar notation to the functions in the <codeclass="docutils literal notranslate"><spanclass="pre">qml.representations.*</span></code> functions.</p>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="kn">from</span><spanclass="nn">qml.fchl</span><spanclass="k">import</span><spanclass="n">generate_representation</span>
<spanclass="c1"># Dummy coordinates for a water molecule</span>
<spanclass="n">coordinates</span><spanclass="o">=</span><spanclass="n">np</span><spanclass="o">.</span><spanclass="n">array</span><spanclass="p">([[</span><spanclass="mf">1.464</span><spanclass="p">,</span><spanclass="mf">0.707</span><spanclass="p">,</span><spanclass="mf">1.056</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.878</span><spanclass="p">,</span><spanclass="mf">1.218</span><spanclass="p">,</span><spanclass="mf">0.498</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">2.319</span><spanclass="p">,</span><spanclass="mf">1.126</span><spanclass="p">,</span><spanclass="mf">0.952</span><spanclass="p">]])</span>
<spanclass="c1"># Oxygen, Hydrogen, Hydrogen</span>
<spanclass="n">nuclear_charges</span><spanclass="o">=</span><spanclass="n">np</span><spanclass="o">.</span><spanclass="n">array</span><spanclass="p">([</span><spanclass="mi">8</span><spanclass="p">,</span><spanclass="mi">1</span><spanclass="p">,</span><spanclass="mi">1</span><spanclass="p">])</span>
<spanclass="n">rep</span><spanclass="o">=</span><spanclass="n">generate_representation</span><spanclass="p">(</span><spanclass="n">coordinates</span><spanclass="p">,</span><spanclass="n">nuclear_charges</span><spanclass="p">)</span>
</pre></div>
</div>
<p>To create the representation for a crystal, the notation is as follows:</p>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="kn">from</span><spanclass="nn">qml.fchl</span><spanclass="k">import</span><spanclass="n">generate_representation</span>
<spanclass="c1"># Dummy fractional coordinates</span>
<spanclass="n">fractional_coordinates</span><spanclass="o">=</span><spanclass="n">np</span><spanclass="o">.</span><spanclass="n">array</span><spanclass="p">(</span>
<spanclass="p">[[</span><spanclass="mf">0.</span><spanclass="p">,</span><spanclass="mf">0.</span><spanclass="p">,</span><spanclass="mf">0.</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.75000042</span><spanclass="p">,</span><spanclass="mf">0.50000027</span><spanclass="p">,</span><spanclass="mf">0.25000015</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.15115386</span><spanclass="p">,</span><spanclass="mf">0.81961403</span><spanclass="p">,</span><spanclass="mf">0.33154037</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.51192691</span><spanclass="p">,</span><spanclass="mf">0.18038651</span><spanclass="p">,</span><spanclass="mf">0.3315404</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.08154025</span><spanclass="p">,</span><spanclass="mf">0.31961376</span><spanclass="p">,</span><spanclass="mf">0.40115401</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.66846017</span><spanclass="p">,</span><spanclass="mf">0.81961403</span><spanclass="p">,</span><spanclass="mf">0.48807366</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.08154025</span><spanclass="p">,</span><spanclass="mf">0.68038678</span><spanclass="p">,</span><spanclass="mf">0.76192703</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.66846021</span><spanclass="p">,</span><spanclass="mf">0.18038651</span><spanclass="p">,</span><spanclass="mf">0.84884672</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.23807355</span><spanclass="p">,</span><spanclass="mf">0.31961376</span><spanclass="p">,</span><spanclass="mf">0.91846033</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.59884657</span><spanclass="p">,</span><spanclass="mf">0.68038678</span><spanclass="p">,</span><spanclass="mf">0.91846033</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.50000031</span><spanclass="p">,</span><spanclass="mf">0.</span><spanclass="p">,</span><spanclass="mf">0.50000031</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">0.25000015</span><spanclass="p">,</span><spanclass="mf">0.50000027</span><spanclass="p">,</span><spanclass="mf">0.75000042</span><spanclass="p">]]</span>
<spanclass="p">)</span>
<spanclass="c1"># Dummy nuclear charges</span>
<spanclass="n">nuclear_charges</span><spanclass="o">=</span><spanclass="n">np</span><spanclass="o">.</span><spanclass="n">array</span><spanclass="p">(</span>
<spanclass="p">[</span><spanclass="mi">58</span><spanclass="p">,</span><spanclass="mi">58</span><spanclass="p">,</span><spanclass="mi">8</span><spanclass="p">,</span><spanclass="mi">8</span><spanclass="p">,</span><spanclass="mi">8</span><spanclass="p">,</span><spanclass="mi">8</span><spanclass="p">,</span><spanclass="mi">8</span><spanclass="p">,</span><spanclass="mi">8</span><spanclass="p">,</span><spanclass="mi">8</span><spanclass="p">,</span><spanclass="mi">8</span><spanclass="p">,</span><spanclass="mi">23</span><spanclass="p">,</span><spanclass="mi">23</span><spanclass="p">]</span>
<spanclass="p">)</span>
<spanclass="c1"># Dummy unit cell</span>
<spanclass="n">unit_cell</span><spanclass="o">=</span><spanclass="n">np</span><spanclass="o">.</span><spanclass="n">array</span><spanclass="p">(</span>
<spanclass="p">[[</span><spanclass="mf">3.699168</span><spanclass="p">,</span><spanclass="mf">3.699168</span><spanclass="p">,</span><spanclass="o">-</span><spanclass="mf">3.255938</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="mf">3.699168</span><spanclass="p">,</span><spanclass="o">-</span><spanclass="mf">3.699168</span><spanclass="p">,</span><spanclass="mf">3.255938</span><spanclass="p">],</span>
<spanclass="p">[</span><spanclass="o">-</span><spanclass="mf">3.699168</span><spanclass="p">,</span><spanclass="o">-</span><spanclass="mf">3.699168</span><spanclass="p">,</span><spanclass="o">-</span><spanclass="mf">3.255938</span><spanclass="p">]]</span>
<spanclass="p">)</span>
<spanclass="c1"># Generate the representation</span>
<spanclass="n">rep</span><spanclass="o">=</span><spanclass="n">generate_representation</span><spanclass="p">(</span><spanclass="n">fractional_coordinates</span><spanclass="p">,</span><spanclass="n">nuclear_charges</span><spanclass="p">,</span>
<spanclass="n">cell</span><spanclass="o">=</span><spanclass="n">unit_cell</span><spanclass="p">,</span><spanclass="n">neighbors</span><spanclass="o">=</span><spanclass="mi">100</span><spanclass="p">,</span><spanclass="n">cut_distance</span><spanclass="o">=</span><spanclass="mf">7.0</span><spanclass="p">)</span>
</pre></div>
</div>
<p>The neighbors keyword is the max number of atoms with the cutoff-distance</p>
</div>
<divclass="section" id="generating-the-fchl-kernel">
<h2>Generating the FCHL kernel<aclass="headerlink" href="#generating-the-fchl-kernel" title="Permalink to this headline">¶</a></h2>
<p>The following example demonstrates how to calculate the local FCHL kernel elements between FCHL representations. <codeclass="docutils literal notranslate"><spanclass="pre">X1</span></code> and <codeclass="docutils literal notranslate"><spanclass="pre">X2</span></code> are numpy arrays with the shape <codeclass="docutils literal notranslate"><spanclass="pre">(number_compounds,max_size,</span><spanclass="pre">5,neighbors)</span></code>, as generated in one of the previous examples. You MUST use the same, or larger, cut-off distance to generate the representation, as to calculate the kernel.</p>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="kn">from</span><spanclass="nn">qml.fchl</span><spanclass="k">import</span><spanclass="n">get_local_kernels</span>
<spanclass="c1"># You can get kernels for multiple kernel-widths</span>
<spanclass="n">sigmas</span><spanclass="o">=</span><spanclass="p">[</span><spanclass="mf">2.5</span><spanclass="p">,</span><spanclass="mf">5.0</span><spanclass="p">,</span><spanclass="mf">10.0</span><spanclass="p">]</span>
<spanclass="c1"># Calculate the kernel-matrices for each sigma</span>
<spanclass="n">K</span><spanclass="o">=</span><spanclass="n">get_local_kernels</span><spanclass="p">(</span><spanclass="n">X1</span><spanclass="p">,</span><spanclass="n">X2</span><spanclass="p">,</span><spanclass="n">sigmas</span><spanclass="p">,</span><spanclass="n">cut_distance</span><spanclass="o">=</span><spanclass="mf">10.0</span><spanclass="p">)</span>
<spanclass="nb">print</span><spanclass="p">(</span><spanclass="n">K</span><spanclass="o">.</span><spanclass="n">shape</span><spanclass="p">)</span>
</pre></div>
</div>
<p>As output you will get a kernel for each kernel-width.</p>
<divclass="code highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="p">(</span><spanclass="mi">3</span><spanclass="p">,</span><spanclass="mi">100</span><spanclass="p">,</span><spanclass="mi">200</span><spanclass="p">)</span>
</pre></div>
</div>
<p>In case <codeclass="docutils literal notranslate"><spanclass="pre">X1</span></code> and <codeclass="docutils literal notranslate"><spanclass="pre">X2</span></code> are identical, K will be symmetrical. This is handled by a separate function with exploits this symmetry (thus being twice as fast).</p>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="kn">from</span><spanclass="nn">qml.fchl</span><spanclass="k">import</span><spanclass="n">get_local_symmetric_kernels</span>
<spanclass="c1"># You can get kernels for multiple kernel-widths</span>
<spanclass="n">sigmas</span><spanclass="o">=</span><spanclass="p">[</span><spanclass="mf">2.5</span><spanclass="p">,</span><spanclass="mf">5.0</span><spanclass="p">,</span><spanclass="mf">10.0</span><spanclass="p">]</span>
<spanclass="c1"># Calculate the kernel-matrices for each sigma</span>
<spanclass="n">K</span><spanclass="o">=</span><spanclass="n">get_local_kernels</span><spanclass="p">(</span><spanclass="n">X1</span><spanclass="p">,</span><spanclass="n">sigmas</span><spanclass="p">,</span><spanclass="n">cut_distance</span><spanclass="o">=</span><spanclass="mf">10.0</span><spanclass="p">)</span>
<spanclass="nb">print</span><spanclass="p">(</span><spanclass="n">K</span><spanclass="o">.</span><spanclass="n">shape</span><spanclass="p">)</span>
</pre></div>
</div>
<divclass="code highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="p">(</span><spanclass="mi">3</span><spanclass="p">,</span><spanclass="mi">100</span><spanclass="p">,</span><spanclass="mi">100</span><spanclass="p">)</span>
</pre></div>
</div>
<p>In addition to the local kernel, the FCHL module also provides kernels for atomic properties (e.g. chemical shifts, partial charges, etc). These have the name “atomic”, rather than “local”.</p>
<divclass="code python highlight-default notranslate"><divclass="highlight"><pre><span></span><spanclass="kn">from</span><spanclass="nn">qml.fchl</span><spanclass="k">import</span><spanclass="n">get_atomic_kernels</span>
<spanclass="kn">from</span><spanclass="nn">qml.fchl</span><spanclass="k">import</span><spanclass="n">get_atomic_symmetric_kernels</span>
</pre></div>
</div>
<p>The only difference between the local and atomic kernels is the shape of the input.
Since the atomic kernel outputs kernels with atomic resolution, the atomic input has the shape <codeclass="docutils literal notranslate"><spanclass="pre">(number_atoms,</span><spanclass="pre">5,</span><spanclass="pre">size)</span></code>.</p>
</div>
</div>
</div>
</div>
<footer>
<divclass="rst-footer-buttons" role="navigation" aria-label="footer navigation">
<ahref="qml.html" class="btn btn-neutral float-right" title="Python API documentation" accesskey="n" rel="next">Next <spanclass="fa fa-arrow-circle-right"></span></a>
<ahref="tutorial.html" class="btn btn-neutral" title="QML Tutorial" accesskey="p" rel="prev"><spanclass="fa fa-arrow-circle-left"></span> Previous</a>
</div>
<hr/>
<divrole="contentinfo">
<p>
© Copyright 2017, Anders S. Christensen.
</p>
</div>
Built with <ahref="http://sphinx-doc.org/">Sphinx</a> using a <ahref="https://github.com/rtfd/sphinx_rtd_theme">theme</a> provided by <ahref="https://readthedocs.org">Read the Docs</a>.
</footer>
</div>
</div>
</section>
</div>
<scripttype="text/javascript">
varDOCUMENTATION_OPTIONS={
URL_ROOT:'./',
VERSION:'0.4.0',
LANGUAGE:'None',
COLLAPSE_INDEX:false,
FILE_SUFFIX:'.html',
HAS_SOURCE: true,
SOURCELINK_SUFFIX: '.txt'
};
</script>
<scripttype="text/javascript" src="_static/jquery.js"></script>
<scripttype="text/javascript" src="_static/underscore.js"></script>
<scripttype="text/javascript" src="_static/doctools.js"></script>
<scripttype="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<scripttype="text/javascript" src="_static/js/theme.js"></script>
<scripttype="text/javascript">
jQuery(function(){
SphinxRtdTheme.Navigation.enable(true);
});
</script>
</body>
</html>