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56  <span class="target" id="module-GSASIImath"></span><div class="section" id="gsasiimath-computation-module">
57<h1><em>GSASIImath: computation module</em><a class="headerlink" href="#gsasiimath-computation-module" title="Permalink to this headline">¶</a></h1>
58<p>Routines for least-squares minimization and other stuff</p>
59<dl class="function">
60<dt id="GSASIImath.AV2Q">
61<tt class="descclassname">GSASIImath.</tt><tt class="descname">AV2Q</tt><big>(</big><em>A</em>, <em>V</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#AV2Q"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.AV2Q" title="Permalink to this definition">¶</a></dt>
62<dd><p>convert angle (radians) &amp; vector to quaternion
63q=r+ai+bj+ck</p>
64</dd></dl>
65
66<dl class="function">
67<dt id="GSASIImath.AVdeg2Q">
68<tt class="descclassname">GSASIImath.</tt><tt class="descname">AVdeg2Q</tt><big>(</big><em>A</em>, <em>V</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#AVdeg2Q"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.AVdeg2Q" title="Permalink to this definition">¶</a></dt>
69<dd><p>convert angle (degrees) &amp; vector to quaternion
70q=r+ai+bj+ck</p>
71</dd></dl>
72
73<dl class="function">
74<dt id="GSASIImath.AtomTLS2UIJ">
75<tt class="descclassname">GSASIImath.</tt><tt class="descname">AtomTLS2UIJ</tt><big>(</big><em>atomData</em>, <em>atPtrs</em>, <em>Amat</em>, <em>rbObj</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#AtomTLS2UIJ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.AtomTLS2UIJ" title="Permalink to this definition">¶</a></dt>
76<dd><p>default doc string</p>
77<table class="docutils field-list" frame="void" rules="none">
78<col class="field-name" />
79<col class="field-body" />
80<tbody valign="top">
81<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
82</tr>
83<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
84</tr>
85</tbody>
86</table>
87</dd></dl>
88
89<dl class="function">
90<dt id="GSASIImath.AtomUij2TLS">
91<tt class="descclassname">GSASIImath.</tt><tt class="descname">AtomUij2TLS</tt><big>(</big><em>atomData</em>, <em>atPtrs</em>, <em>Amat</em>, <em>Bmat</em>, <em>rbObj</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#AtomUij2TLS"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.AtomUij2TLS" title="Permalink to this definition">¶</a></dt>
92<dd><p>default doc string</p>
93<table class="docutils field-list" frame="void" rules="none">
94<col class="field-name" />
95<col class="field-body" />
96<tbody valign="top">
97<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
98</tr>
99<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
100</tr>
101</tbody>
102</table>
103</dd></dl>
104
105<dl class="function">
106<dt id="GSASIImath.ChargeFlip">
107<tt class="descclassname">GSASIImath.</tt><tt class="descname">ChargeFlip</tt><big>(</big><em>data</em>, <em>reflDict</em>, <em>pgbar</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#ChargeFlip"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.ChargeFlip" title="Permalink to this definition">¶</a></dt>
108<dd><p>default doc string</p>
109<table class="docutils field-list" frame="void" rules="none">
110<col class="field-name" />
111<col class="field-body" />
112<tbody valign="top">
113<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
114</tr>
115<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
116</tr>
117</tbody>
118</table>
119</dd></dl>
120
121<dl class="function">
122<dt id="GSASIImath.Den2Vol">
123<tt class="descclassname">GSASIImath.</tt><tt class="descname">Den2Vol</tt><big>(</big><em>Elements</em>, <em>density</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#Den2Vol"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.Den2Vol" title="Permalink to this definition">¶</a></dt>
124<dd><p>converts density to molecular volume</p>
125<table class="docutils field-list" frame="void" rules="none">
126<col class="field-name" />
127<col class="field-body" />
128<tbody valign="top">
129<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
130<li><strong>Elements</strong> (<em>dict</em>) &#8211; elements in molecular formula;
131each must contain
132Num: number of atoms in formula
133Mass: at. wt.</li>
134<li><strong>density</strong> (<em>float</em>) &#8211; material density in gm/cm^3</li>
135</ul>
136</td>
137</tr>
138<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">float volume: molecular volume in A^3</p>
139</td>
140</tr>
141</tbody>
142</table>
143</dd></dl>
144
145<dl class="function">
146<dt id="GSASIImath.El2EstVol">
147<tt class="descclassname">GSASIImath.</tt><tt class="descname">El2EstVol</tt><big>(</big><em>Elements</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#El2EstVol"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.El2EstVol" title="Permalink to this definition">¶</a></dt>
148<dd><p>Estimate volume from molecular formula; assumes atom volume = 10A^3</p>
149<table class="docutils field-list" frame="void" rules="none">
150<col class="field-name" />
151<col class="field-body" />
152<tbody valign="top">
153<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>Elements</strong> (<em>dict</em>) &#8211; elements in molecular formula;
154each must contain
155Num: number of atoms in formula</td>
156</tr>
157<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">float volume: estimate of molecular volume in A^3</td>
158</tr>
159</tbody>
160</table>
161</dd></dl>
162
163<dl class="function">
164<dt id="GSASIImath.El2Mass">
165<tt class="descclassname">GSASIImath.</tt><tt class="descname">El2Mass</tt><big>(</big><em>Elements</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#El2Mass"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.El2Mass" title="Permalink to this definition">¶</a></dt>
166<dd><p>compute molecular weight from Elements</p>
167<table class="docutils field-list" frame="void" rules="none">
168<col class="field-name" />
169<col class="field-body" />
170<tbody valign="top">
171<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>Elements</strong> (<em>dict</em>) &#8211; elements in molecular formula;
172each must contain
173Num: number of atoms in formula
174Mass: at. wt.</td>
175</tr>
176<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">float mass: molecular weight.</td>
177</tr>
178</tbody>
179</table>
180</dd></dl>
181
182<dl class="function">
183<dt id="GSASIImath.FillAtomLookUp">
184<tt class="descclassname">GSASIImath.</tt><tt class="descname">FillAtomLookUp</tt><big>(</big><em>atomData</em>, <em>indx</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#FillAtomLookUp"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.FillAtomLookUp" title="Permalink to this definition">¶</a></dt>
185<dd><p>create a dictionary of atom indexes with atom IDs as keys</p>
186<table class="docutils field-list" frame="void" rules="none">
187<col class="field-name" />
188<col class="field-body" />
189<tbody valign="top">
190<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>atomData</strong> (<em>list</em>) &#8211; Atom table to be used</td>
191</tr>
192<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">dict atomLookUp: dictionary of atom indexes with atom IDs as keys</td>
193</tr>
194</tbody>
195</table>
196</dd></dl>
197
198<dl class="function">
199<dt id="GSASIImath.FindAtomIndexByIDs">
200<tt class="descclassname">GSASIImath.</tt><tt class="descname">FindAtomIndexByIDs</tt><big>(</big><em>atomData</em>, <em>IDs</em>, <em>Draw=True</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#FindAtomIndexByIDs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.FindAtomIndexByIDs" title="Permalink to this definition">¶</a></dt>
201<dd><p>finds the set of atom array indices for a list of atom IDs. Will search
202either the Atom table or the drawAtom table.</p>
203<table class="docutils field-list" frame="void" rules="none">
204<col class="field-name" />
205<col class="field-body" />
206<tbody valign="top">
207<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
208<li><strong>atomData</strong> (<em>list</em>) &#8211; Atom or drawAtom table containting coordinates, etc.</li>
209<li><strong>IDs</strong> (<em>list</em>) &#8211; atom IDs to be found</li>
210<li><strong>Draw</strong> (<em>bool</em>) &#8211; True if drawAtom table to be searched; False if Atom table
211is searched</li>
212</ul>
213</td>
214</tr>
215<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">list indx: atom (or drawAtom) indices</p>
216</td>
217</tr>
218</tbody>
219</table>
220</dd></dl>
221
222<dl class="function">
223<dt id="GSASIImath.Fourier4DMap">
224<tt class="descclassname">GSASIImath.</tt><tt class="descname">Fourier4DMap</tt><big>(</big><em>data</em>, <em>reflDict</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#Fourier4DMap"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.Fourier4DMap" title="Permalink to this definition">¶</a></dt>
225<dd><p>default doc string</p>
226<table class="docutils field-list" frame="void" rules="none">
227<col class="field-name" />
228<col class="field-body" />
229<tbody valign="top">
230<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
231</tr>
232<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
233</tr>
234</tbody>
235</table>
236</dd></dl>
237
238<dl class="function">
239<dt id="GSASIImath.FourierMap">
240<tt class="descclassname">GSASIImath.</tt><tt class="descname">FourierMap</tt><big>(</big><em>data</em>, <em>reflDict</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#FourierMap"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.FourierMap" title="Permalink to this definition">¶</a></dt>
241<dd><p>default doc string</p>
242<table class="docutils field-list" frame="void" rules="none">
243<col class="field-name" />
244<col class="field-body" />
245<tbody valign="top">
246<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
247</tr>
248<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
249</tr>
250</tbody>
251</table>
252</dd></dl>
253
254<dl class="function">
255<dt id="GSASIImath.GetAngleSig">
256<tt class="descclassname">GSASIImath.</tt><tt class="descname">GetAngleSig</tt><big>(</big><em>Oatoms</em>, <em>Atoms</em>, <em>Amat</em>, <em>SGData</em>, <em>covData={}</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#GetAngleSig"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.GetAngleSig" title="Permalink to this definition">¶</a></dt>
257<dd><p>default doc string</p>
258<table class="docutils field-list" frame="void" rules="none">
259<col class="field-name" />
260<col class="field-body" />
261<tbody valign="top">
262<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
263</tr>
264<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
265</tr>
266</tbody>
267</table>
268</dd></dl>
269
270<dl class="function">
271<dt id="GSASIImath.GetAtomCoordsByID">
272<tt class="descclassname">GSASIImath.</tt><tt class="descname">GetAtomCoordsByID</tt><big>(</big><em>pId</em>, <em>parmDict</em>, <em>AtLookup</em>, <em>indx</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#GetAtomCoordsByID"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.GetAtomCoordsByID" title="Permalink to this definition">¶</a></dt>
273<dd><p>default doc string</p>
274<table class="docutils field-list" frame="void" rules="none">
275<col class="field-name" />
276<col class="field-body" />
277<tbody valign="top">
278<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
279</tr>
280<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
281</tr>
282</tbody>
283</table>
284</dd></dl>
285
286<dl class="function">
287<dt id="GSASIImath.GetAtomItemsById">
288<tt class="descclassname">GSASIImath.</tt><tt class="descname">GetAtomItemsById</tt><big>(</big><em>atomData</em>, <em>atomLookUp</em>, <em>IdList</em>, <em>itemLoc</em>, <em>numItems=1</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#GetAtomItemsById"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.GetAtomItemsById" title="Permalink to this definition">¶</a></dt>
289<dd><p>gets atom parameters for atoms using atom IDs</p>
290<table class="docutils field-list" frame="void" rules="none">
291<col class="field-name" />
292<col class="field-body" />
293<tbody valign="top">
294<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
295<li><strong>atomData</strong> (<em>list</em>) &#8211; Atom table to be used</li>
296<li><strong>atomLookUp</strong> (<em>dict</em>) &#8211; dictionary of atom indexes with atom IDs as keys</li>
297<li><strong>IdList</strong> (<em>list</em>) &#8211; atom IDs to be found</li>
298<li><strong>itemLoc</strong> (<em>int</em>) &#8211; pointer to desired 1st item in an atom table entry</li>
299<li><strong>numItems</strong> (<em>int</em>) &#8211; number of items to be retrieved</li>
300</ul>
301</td>
302</tr>
303<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">type name: description</p>
304</td>
305</tr>
306</tbody>
307</table>
308</dd></dl>
309
310<dl class="function">
311<dt id="GSASIImath.GetAtomsById">
312<tt class="descclassname">GSASIImath.</tt><tt class="descname">GetAtomsById</tt><big>(</big><em>atomData</em>, <em>atomLookUp</em>, <em>IdList</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#GetAtomsById"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.GetAtomsById" title="Permalink to this definition">¶</a></dt>
313<dd><p>gets a list of atoms from Atom table that match a set of atom IDs</p>
314<table class="docutils field-list" frame="void" rules="none">
315<col class="field-name" />
316<col class="field-body" />
317<tbody valign="top">
318<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
319<li><strong>atomData</strong> (<em>list</em>) &#8211; Atom table to be used</li>
320<li><strong>atomLookUp</strong> (<em>dict</em>) &#8211; dictionary of atom indexes with atom IDs as keys</li>
321<li><strong>IdList</strong> (<em>list</em>) &#8211; atom IDs to be found</li>
322</ul>
323</td>
324</tr>
325<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">list atoms: list of atoms found</p>
326</td>
327</tr>
328</tbody>
329</table>
330</dd></dl>
331
332<dl class="function">
333<dt id="GSASIImath.GetDATSig">
334<tt class="descclassname">GSASIImath.</tt><tt class="descname">GetDATSig</tt><big>(</big><em>Oatoms</em>, <em>Atoms</em>, <em>Amat</em>, <em>SGData</em>, <em>covData={}</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#GetDATSig"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.GetDATSig" title="Permalink to this definition">¶</a></dt>
335<dd><p>default doc string</p>
336<table class="docutils field-list" frame="void" rules="none">
337<col class="field-name" />
338<col class="field-body" />
339<tbody valign="top">
340<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
341</tr>
342<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
343</tr>
344</tbody>
345</table>
346</dd></dl>
347
348<dl class="function">
349<dt id="GSASIImath.GetDistSig">
350<tt class="descclassname">GSASIImath.</tt><tt class="descname">GetDistSig</tt><big>(</big><em>Oatoms</em>, <em>Atoms</em>, <em>Amat</em>, <em>SGData</em>, <em>covData={}</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#GetDistSig"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.GetDistSig" title="Permalink to this definition">¶</a></dt>
351<dd><p>default doc string</p>
352<table class="docutils field-list" frame="void" rules="none">
353<col class="field-name" />
354<col class="field-body" />
355<tbody valign="top">
356<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
357</tr>
358<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
359</tr>
360</tbody>
361</table>
362</dd></dl>
363
364<dl class="function">
365<dt id="GSASIImath.GetSHCoeff">
366<tt class="descclassname">GSASIImath.</tt><tt class="descname">GetSHCoeff</tt><big>(</big><em>pId</em>, <em>parmDict</em>, <em>SHkeys</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#GetSHCoeff"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.GetSHCoeff" title="Permalink to this definition">¶</a></dt>
367<dd><p>default doc string</p>
368<table class="docutils field-list" frame="void" rules="none">
369<col class="field-name" />
370<col class="field-body" />
371<tbody valign="top">
372<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
373</tr>
374<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
375</tr>
376</tbody>
377</table>
378</dd></dl>
379
380<dl class="function">
381<dt id="GSASIImath.GetTorsionSig">
382<tt class="descclassname">GSASIImath.</tt><tt class="descname">GetTorsionSig</tt><big>(</big><em>Oatoms</em>, <em>Atoms</em>, <em>Amat</em>, <em>SGData</em>, <em>covData={}</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#GetTorsionSig"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.GetTorsionSig" title="Permalink to this definition">¶</a></dt>
383<dd><p>default doc string</p>
384<table class="docutils field-list" frame="void" rules="none">
385<col class="field-name" />
386<col class="field-body" />
387<tbody valign="top">
388<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
389</tr>
390<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
391</tr>
392</tbody>
393</table>
394</dd></dl>
395
396<dl class="function">
397<dt id="GSASIImath.GetXYZDist">
398<tt class="descclassname">GSASIImath.</tt><tt class="descname">GetXYZDist</tt><big>(</big><em>xyz</em>, <em>XYZ</em>, <em>Amat</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#GetXYZDist"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.GetXYZDist" title="Permalink to this definition">¶</a></dt>
399<dd><dl class="docutils">
400<dt>gets distance from position xyz to all XYZ, xyz &amp; XYZ are np.array </dt>
401<dd>and are in crystal coordinates; Amat is crystal to Cart matrix</dd>
402</dl>
403<table class="docutils field-list" frame="void" rules="none">
404<col class="field-name" />
405<col class="field-body" />
406<tbody valign="top">
407<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
408</tr>
409<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
410</tr>
411</tbody>
412</table>
413</dd></dl>
414
415<dl class="function">
416<dt id="GSASIImath.HessianLSQ">
417<tt class="descclassname">GSASIImath.</tt><tt class="descname">HessianLSQ</tt><big>(</big><em>func</em>, <em>x0</em>, <em>Hess</em>, <em>args=()</em>, <em>ftol=1.49012e-08</em>, <em>xtol=1.49012e-08</em>, <em>maxcyc=0</em>, <em>Print=False</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#HessianLSQ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.HessianLSQ" title="Permalink to this definition">¶</a></dt>
418<dd><p>Minimize the sum of squares of a function (<span class="math">\(f\)</span>) evaluated on a series of
419values (y): <span class="math">\(\sum_{y=0}^{N_{obs}} f(y,{args})\)</span></p>
420<div class="highlight-python"><div class="highlight"><pre>            Nobs
421x = arg min(sum(func(y)**2,axis=0))
422            y=0
423</pre></div>
424</div>
425<table class="docutils field-list" frame="void" rules="none">
426<col class="field-name" />
427<col class="field-body" />
428<tbody valign="top">
429<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
430<li><strong>func</strong> (<em>function</em>) &#8211; callable method or function
431should take at least one (possibly length N vector) argument and
432returns M floating point numbers.</li>
433<li><strong>x0</strong> (<em>np.ndarray</em>) &#8211; The starting estimate for the minimization of length N</li>
434<li><strong>Hess</strong> (<em>function</em>) &#8211; callable method or function
435A required function or method to compute the weighted vector and Hessian for func.
436It must be a symmetric NxN array</li>
437<li><strong>args</strong> (<em>tuple</em>) &#8211; Any extra arguments to func are placed in this tuple.</li>
438<li><strong>ftol</strong> (<em>float</em>) &#8211; Relative error desired in the sum of squares.</li>
439<li><strong>xtol</strong> (<em>float</em>) &#8211; Relative error desired in the approximate solution.</li>
440<li><strong>maxcyc</strong> (<em>int</em>) &#8211; The maximum number of cycles of refinement to execute, if -1 refine
441until other limits are met (ftol, xtol)</li>
442<li><strong>Print</strong> (<em>bool</em>) &#8211; True for printing results (residuals &amp; times) by cycle</li>
443</ul>
444</td>
445</tr>
446<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last"><p>(x,cov_x,infodict) where</p>
447<ul>
448<li><p class="first">x : ndarray
449The solution (or the result of the last iteration for an unsuccessful
450call).</p>
451</li>
452<li><p class="first">cov_x : ndarray
453Uses the fjac and ipvt optional outputs to construct an
454estimate of the jacobian around the solution.  <tt class="docutils literal"><span class="pre">None</span></tt> if a
455singular matrix encountered (indicates very flat curvature in
456some direction).  This matrix must be multiplied by the
457residual standard deviation to get the covariance of the
458parameter estimates &#8211; see curve_fit.</p>
459</li>
460<li><p class="first">infodict : dict
461a dictionary of optional outputs with the keys:</p>
462<blockquote>
463<div><ul class="simple">
464<li>&#8216;fvec&#8217; : the function evaluated at the output</li>
465<li>&#8216;num cyc&#8217;:</li>
466<li>&#8216;nfev&#8217;:</li>
467<li>&#8216;lamMax&#8217;:</li>
468<li>&#8216;psing&#8217;:</li>
469</ul>
470</div></blockquote>
471</li>
472</ul>
473</p>
474</td>
475</tr>
476</tbody>
477</table>
478</dd></dl>
479
480<dl class="function">
481<dt id="GSASIImath.OmitMap">
482<tt class="descclassname">GSASIImath.</tt><tt class="descname">OmitMap</tt><big>(</big><em>data</em>, <em>reflDict</em>, <em>pgbar=None</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#OmitMap"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.OmitMap" title="Permalink to this definition">¶</a></dt>
483<dd><p>default doc string</p>
484<table class="docutils field-list" frame="void" rules="none">
485<col class="field-name" />
486<col class="field-body" />
487<tbody valign="top">
488<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
489</tr>
490<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
491</tr>
492</tbody>
493</table>
494</dd></dl>
495
496<dl class="function">
497<dt id="GSASIImath.PeaksEquiv">
498<tt class="descclassname">GSASIImath.</tt><tt class="descname">PeaksEquiv</tt><big>(</big><em>data</em>, <em>Ind</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#PeaksEquiv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.PeaksEquiv" title="Permalink to this definition">¶</a></dt>
499<dd><p>Find the equivalent map peaks for those selected. Works on the
500contents of data[&#8216;Map Peaks&#8217;].</p>
501<table class="docutils field-list" frame="void" rules="none">
502<col class="field-name" />
503<col class="field-body" />
504<tbody valign="top">
505<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
506<li><strong>data</strong> &#8211; the phase data structure</li>
507<li><strong>Ind</strong> (<em>list</em>) &#8211; list of selected peak indices</li>
508</ul>
509</td>
510</tr>
511<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">augmented list of peaks including those related by symmetry to the
512ones in Ind</p>
513</td>
514</tr>
515</tbody>
516</table>
517</dd></dl>
518
519<dl class="function">
520<dt id="GSASIImath.PeaksUnique">
521<tt class="descclassname">GSASIImath.</tt><tt class="descname">PeaksUnique</tt><big>(</big><em>data</em>, <em>Ind</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#PeaksUnique"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.PeaksUnique" title="Permalink to this definition">¶</a></dt>
522<dd><p>Finds the symmetry unique set of peaks from those selected. Works on the
523contents of data[&#8216;Map Peaks&#8217;].</p>
524<table class="docutils field-list" frame="void" rules="none">
525<col class="field-name" />
526<col class="field-body" />
527<tbody valign="top">
528<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
529<li><strong>data</strong> &#8211; the phase data structure</li>
530<li><strong>Ind</strong> (<em>list</em>) &#8211; list of selected peak indices</li>
531</ul>
532</td>
533</tr>
534<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">the list of symmetry unique peaks from among those given in Ind</p>
535</td>
536</tr>
537</tbody>
538</table>
539</dd></dl>
540
541<dl class="function">
542<dt id="GSASIImath.Q2AV">
543<tt class="descclassname">GSASIImath.</tt><tt class="descname">Q2AV</tt><big>(</big><em>Q</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#Q2AV"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.Q2AV" title="Permalink to this definition">¶</a></dt>
544<dd><p>convert quaternion to angle (radians 0-2pi) &amp; normalized vector
545q=r+ai+bj+ck</p>
546</dd></dl>
547
548<dl class="function">
549<dt id="GSASIImath.Q2AVdeg">
550<tt class="descclassname">GSASIImath.</tt><tt class="descname">Q2AVdeg</tt><big>(</big><em>Q</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#Q2AVdeg"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.Q2AVdeg" title="Permalink to this definition">¶</a></dt>
551<dd><p>convert quaternion to angle (degrees 0-360) &amp; normalized vector
552q=r+ai+bj+ck</p>
553</dd></dl>
554
555<dl class="function">
556<dt id="GSASIImath.Q2Mat">
557<tt class="descclassname">GSASIImath.</tt><tt class="descname">Q2Mat</tt><big>(</big><em>Q</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#Q2Mat"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.Q2Mat" title="Permalink to this definition">¶</a></dt>
558<dd><p>make rotation matrix from quaternion
559q=r+ai+bj+ck</p>
560</dd></dl>
561
562<dl class="function">
563<dt id="GSASIImath.RotateRBXYZ">
564<tt class="descclassname">GSASIImath.</tt><tt class="descname">RotateRBXYZ</tt><big>(</big><em>Bmat</em>, <em>Cart</em>, <em>oriQ</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#RotateRBXYZ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.RotateRBXYZ" title="Permalink to this definition">¶</a></dt>
565<dd><p>rotate &amp; transform cartesian coordinates to crystallographic ones
566no translation applied. To be used for numerical derivatives</p>
567<table class="docutils field-list" frame="void" rules="none">
568<col class="field-name" />
569<col class="field-body" />
570<tbody valign="top">
571<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
572</tr>
573<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
574</tr>
575</tbody>
576</table>
577</dd></dl>
578
579<dl class="function">
580<dt id="GSASIImath.SSChargeFlip">
581<tt class="descclassname">GSASIImath.</tt><tt class="descname">SSChargeFlip</tt><big>(</big><em>data</em>, <em>reflDict</em>, <em>pgbar</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#SSChargeFlip"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.SSChargeFlip" title="Permalink to this definition">¶</a></dt>
582<dd><p>default doc string</p>
583<table class="docutils field-list" frame="void" rules="none">
584<col class="field-name" />
585<col class="field-body" />
586<tbody valign="top">
587<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
588</tr>
589<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
590</tr>
591</tbody>
592</table>
593</dd></dl>
594
595<dl class="function">
596<dt id="GSASIImath.SearchMap">
597<tt class="descclassname">GSASIImath.</tt><tt class="descname">SearchMap</tt><big>(</big><em>generalData</em>, <em>drawingData</em>, <em>Neg=False</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#SearchMap"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.SearchMap" title="Permalink to this definition">¶</a></dt>
598<dd><p>Does a search of a density map for peaks meeting the criterion of peak
599height is greater than mapData[&#8216;cutOff&#8217;]/100 of mapData[&#8216;rhoMax&#8217;] where
600mapData is data[&#8216;General&#8217;][&#8216;mapData&#8217;]; the map is also in mapData.</p>
601<table class="docutils field-list" frame="void" rules="none">
602<col class="field-name" />
603<col class="field-body" />
604<tbody valign="top">
605<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
606<li><strong>generalData</strong> &#8211; the phase data structure; includes the map</li>
607<li><strong>drawingData</strong> &#8211; the drawing data structure</li>
608<li><strong>Neg</strong> &#8211; if True then search for negative peaks (i.e. H-atoms &amp; neutron data)</li>
609</ul>
610</td>
611</tr>
612<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last"><p>(peaks,mags,dzeros) where</p>
613<ul class="simple">
614<li>peaks : ndarray
615x,y,z positions of the peaks found in the map</li>
616<li>mags : ndarray
617the magnitudes of the peaks</li>
618<li>dzeros : ndarray
619the distance of the peaks from  the unit cell origin</li>
620<li>dcent : ndarray
621the distance of the peaks from  the unit cell center</li>
622</ul>
623</p>
624</td>
625</tr>
626</tbody>
627</table>
628</dd></dl>
629
630<dl class="function">
631<dt id="GSASIImath.SetMolCent">
632<tt class="descclassname">GSASIImath.</tt><tt class="descname">SetMolCent</tt><big>(</big><em>model</em>, <em>RBData</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#SetMolCent"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.SetMolCent" title="Permalink to this definition">¶</a></dt>
633<dd><p>default doc string</p>
634<table class="docutils field-list" frame="void" rules="none">
635<col class="field-name" />
636<col class="field-body" />
637<tbody valign="top">
638<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
639</tr>
640<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
641</tr>
642</tbody>
643</table>
644</dd></dl>
645
646<dl class="function">
647<dt id="GSASIImath.TLS2Uij">
648<tt class="descclassname">GSASIImath.</tt><tt class="descname">TLS2Uij</tt><big>(</big><em>xyz</em>, <em>g</em>, <em>Amat</em>, <em>rbObj</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#TLS2Uij"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.TLS2Uij" title="Permalink to this definition">¶</a></dt>
649<dd><p>default doc string</p>
650<table class="docutils field-list" frame="void" rules="none">
651<col class="field-name" />
652<col class="field-body" />
653<tbody valign="top">
654<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
655</tr>
656<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
657</tr>
658</tbody>
659</table>
660</dd></dl>
661
662<dl class="function">
663<dt id="GSASIImath.UpdateMCSAxyz">
664<tt class="descclassname">GSASIImath.</tt><tt class="descname">UpdateMCSAxyz</tt><big>(</big><em>Bmat</em>, <em>MCSA</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#UpdateMCSAxyz"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.UpdateMCSAxyz" title="Permalink to this definition">¶</a></dt>
665<dd><p>default doc string</p>
666<table class="docutils field-list" frame="void" rules="none">
667<col class="field-name" />
668<col class="field-body" />
669<tbody valign="top">
670<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
671</tr>
672<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
673</tr>
674</tbody>
675</table>
676</dd></dl>
677
678<dl class="function">
679<dt id="GSASIImath.UpdateRBUIJ">
680<tt class="descclassname">GSASIImath.</tt><tt class="descname">UpdateRBUIJ</tt><big>(</big><em>Bmat</em>, <em>Cart</em>, <em>RBObj</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#UpdateRBUIJ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.UpdateRBUIJ" title="Permalink to this definition">¶</a></dt>
681<dd><p>default doc string</p>
682<table class="docutils field-list" frame="void" rules="none">
683<col class="field-name" />
684<col class="field-body" />
685<tbody valign="top">
686<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
687</tr>
688<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
689</tr>
690</tbody>
691</table>
692</dd></dl>
693
694<dl class="function">
695<dt id="GSASIImath.UpdateRBXYZ">
696<tt class="descclassname">GSASIImath.</tt><tt class="descname">UpdateRBXYZ</tt><big>(</big><em>Bmat</em>, <em>RBObj</em>, <em>RBData</em>, <em>RBType</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#UpdateRBXYZ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.UpdateRBXYZ" title="Permalink to this definition">¶</a></dt>
697<dd><p>default doc string</p>
698<table class="docutils field-list" frame="void" rules="none">
699<col class="field-name" />
700<col class="field-body" />
701<tbody valign="top">
702<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
703</tr>
704<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
705</tr>
706</tbody>
707</table>
708</dd></dl>
709
710<dl class="function">
711<dt id="GSASIImath.ValEsd">
712<tt class="descclassname">GSASIImath.</tt><tt class="descname">ValEsd</tt><big>(</big><em>value</em>, <em>esd=0</em>, <em>nTZ=False</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#ValEsd"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.ValEsd" title="Permalink to this definition">¶</a></dt>
713<dd><p>Format a floating point number with a given level of precision or
714with in crystallographic format with a &#8220;esd&#8221;, as value(esd). If esd is
715negative the number is formatted with the level of significant figures
716appropriate if abs(esd) were the esd, but the esd is not included.
717if the esd is zero, approximately 6 significant figures are printed.
718nTZ=True causes &#8220;extra&#8221; zeros to be removed after the decimal place.
719for example:</p>
720<blockquote>
721<div><ul class="simple">
722<li>&#8220;1.235(3)&#8221; for value=1.2346 &amp; esd=0.003</li>
723<li>&#8220;1.235(3)e4&#8221; for value=12346. &amp; esd=30</li>
724<li>&#8220;1.235(3)e6&#8221; for value=0.12346e7 &amp; esd=3000</li>
725<li>&#8220;1.235&#8221; for value=1.2346 &amp; esd=-0.003</li>
726<li>&#8220;1.240&#8221; for value=1.2395 &amp; esd=-0.003</li>
727<li>&#8220;1.24&#8221; for value=1.2395 &amp; esd=-0.003 with nTZ=True</li>
728<li>&#8220;1.23460&#8221; for value=1.2346 &amp; esd=0.0</li>
729</ul>
730</div></blockquote>
731<table class="docutils field-list" frame="void" rules="none">
732<col class="field-name" />
733<col class="field-body" />
734<tbody valign="top">
735<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
736<li><strong>value</strong> (<em>float</em>) &#8211; number to be formatted</li>
737<li><strong>esd</strong> (<em>float</em>) &#8211; uncertainty or if esd &lt; 0, specifies level of
738precision to be shown e.g. esd=-0.01 gives 2 places beyond decimal</li>
739<li><strong>nTZ</strong> (<em>bool</em>) &#8211; True to remove trailing zeros (default is False)</li>
740</ul>
741</td>
742</tr>
743<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">value(esd) or value as a string</p>
744</td>
745</tr>
746</tbody>
747</table>
748</dd></dl>
749
750<dl class="function">
751<dt id="GSASIImath.Vol2Den">
752<tt class="descclassname">GSASIImath.</tt><tt class="descname">Vol2Den</tt><big>(</big><em>Elements</em>, <em>volume</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#Vol2Den"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.Vol2Den" title="Permalink to this definition">¶</a></dt>
753<dd><p>converts volume to density</p>
754<table class="docutils field-list" frame="void" rules="none">
755<col class="field-name" />
756<col class="field-body" />
757<tbody valign="top">
758<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
759<li><strong>Elements</strong> (<em>dict</em>) &#8211; elements in molecular formula;
760each must contain
761Num: number of atoms in formula
762Mass: at. wt.</li>
763<li><strong>volume</strong> (<em>float</em>) &#8211; molecular volume in A^3</li>
764</ul>
765</td>
766</tr>
767<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">float density: material density in gm/cm^3</p>
768</td>
769</tr>
770</tbody>
771</table>
772</dd></dl>
773
774<dl class="function">
775<dt id="GSASIImath.XScattDen">
776<tt class="descclassname">GSASIImath.</tt><tt class="descname">XScattDen</tt><big>(</big><em>Elements</em>, <em>vol</em>, <em>wave=0.0</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#XScattDen"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.XScattDen" title="Permalink to this definition">¶</a></dt>
777<dd><p>Estimate X-ray scattering density from molecular formula &amp; volume;
778ignores valence, but includes anomalous effects</p>
779<table class="docutils field-list" frame="void" rules="none">
780<col class="field-name" />
781<col class="field-body" />
782<tbody valign="top">
783<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
784<li><strong>Elements</strong> (<em>dict</em>) &#8211; elements in molecular formula;
785each element must contain
786Num: number of atoms in formula
787Z: atomic number</li>
788<li><strong>vol</strong> (<em>float</em>) &#8211; molecular volume in A^3</li>
789<li><strong>wave</strong> (<em>float</em>) &#8211; optional wavelength in A</li>
790</ul>
791</td>
792</tr>
793<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">float rho: scattering density in 10^10cm^-2;
794if wave &gt; 0 the includes f&#8217; contribution</p>
795</td>
796</tr>
797<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">float mu: if wave&gt;0 absorption coeff in cm^-1 ; otherwise 0</p>
798</td>
799</tr>
800</tbody>
801</table>
802</dd></dl>
803
804<dl class="function">
805<dt id="GSASIImath.adjHKLmax">
806<tt class="descclassname">GSASIImath.</tt><tt class="descname">adjHKLmax</tt><big>(</big><em>SGData</em>, <em>Hmax</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#adjHKLmax"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.adjHKLmax" title="Permalink to this definition">¶</a></dt>
807<dd><p>default doc string</p>
808<table class="docutils field-list" frame="void" rules="none">
809<col class="field-name" />
810<col class="field-body" />
811<tbody valign="top">
812<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
813</tr>
814<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
815</tr>
816</tbody>
817</table>
818</dd></dl>
819
820<dl class="function">
821<dt id="GSASIImath.anneal">
822<tt class="descclassname">GSASIImath.</tt><tt class="descname">anneal</tt><big>(</big><em>func</em>, <em>x0</em>, <em>args=()</em>, <em>schedule='fast'</em>, <em>full_output=0</em>, <em>T0=None</em>, <em>Tf=1e-12</em>, <em>maxeval=None</em>, <em>maxaccept=None</em>, <em>maxiter=400</em>, <em>boltzmann=1.0</em>, <em>learn_rate=0.5</em>, <em>feps=1e-06</em>, <em>quench=1.0</em>, <em>m=1.0</em>, <em>n=1.0</em>, <em>lower=-100</em>, <em>upper=100</em>, <em>dwell=50</em>, <em>slope=0.9</em>, <em>ranStart=False</em>, <em>ranRange=0.1</em>, <em>autoRan=False</em>, <em>dlg=None</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#anneal"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.anneal" title="Permalink to this definition">¶</a></dt>
823<dd><p>Minimize a function using simulated annealing.</p>
824<p>Schedule is a schedule class implementing the annealing schedule.
825Available ones are &#8216;fast&#8217;, &#8216;cauchy&#8217;, &#8216;boltzmann&#8217;</p>
826<table class="docutils field-list" frame="void" rules="none">
827<col class="field-name" />
828<col class="field-body" />
829<tbody valign="top">
830<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
831<li><strong>func</strong> (<em>callable</em>) &#8211; f(x, *args)
832Function to be optimized.</li>
833<li><strong>x0</strong> (<em>ndarray</em>) &#8211; Initial guess.</li>
834<li><strong>args</strong> (<em>tuple</em>) &#8211; Extra parameters to <cite>func</cite>.</li>
835<li><strong>schedule</strong> (<em>base_schedule</em>) &#8211; Annealing schedule to use (a class).</li>
836<li><strong>full_output</strong> (<em>bool</em>) &#8211; Whether to return optional outputs.</li>
837<li><strong>T0</strong> (<em>float</em>) &#8211; Initial Temperature (estimated as 1.2 times the largest
838cost-function deviation over random points in the range).</li>
839<li><strong>Tf</strong> (<em>float</em>) &#8211; Final goal temperature.</li>
840<li><strong>maxeval</strong> (<em>int</em>) &#8211; Maximum function evaluations.</li>
841<li><strong>maxaccept</strong> (<em>int</em>) &#8211; Maximum changes to accept.</li>
842<li><strong>maxiter</strong> (<em>int</em>) &#8211; Maximum cooling iterations.</li>
843<li><strong>learn_rate</strong> (<em>float</em>) &#8211; Scale constant for adjusting guesses.</li>
844<li><strong>boltzmann</strong> (<em>float</em>) &#8211; Boltzmann constant in acceptance test
845(increase for less stringent test at each temperature).</li>
846<li><strong>feps</strong> (<em>float</em>) &#8211; Stopping relative error tolerance for the function value in
847last four coolings.</li>
848<li><strong>quench,m,n</strong> (<em>float</em>) &#8211; Parameters to alter fast_sa schedule.</li>
849<li><strong>lower,upper</strong> (<em>float/ndarray</em>) &#8211; Lower and upper bounds on <cite>x</cite>.</li>
850<li><strong>dwell</strong> (<em>int</em>) &#8211; The number of times to search the space at each temperature.</li>
851<li><strong>slope</strong> (<em>float</em>) &#8211; Parameter for log schedule</li>
852<li><strong>ranStart=False</strong> (<em>bool</em>) &#8211; True for set 10% of ranges about x</li>
853</ul>
854</td>
855</tr>
856<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last"><p>(xmin, Jmin, T, feval, iters, accept, retval) where</p>
857<ul>
858<li><p class="first">xmin (ndarray): Point giving smallest value found.</p>
859</li>
860<li><p class="first">Jmin (float): Minimum value of function found.</p>
861</li>
862<li><p class="first">T (float): Final temperature.</p>
863</li>
864<li><p class="first">feval (int): Number of function evaluations.</p>
865</li>
866<li><p class="first">iters (int): Number of cooling iterations.</p>
867</li>
868<li><p class="first">accept (int): Number of tests accepted.</p>
869</li>
870<li><p class="first">retval (int): Flag indicating stopping condition:</p>
871<blockquote>
872<div><ul class="simple">
873<li>0: Points no longer changing</li>
874<li>1: Cooled to final temperature</li>
875<li>2: Maximum function evaluations</li>
876<li>3: Maximum cooling iterations reached</li>
877<li>4: Maximum accepted query locations reached</li>
878<li>5: Final point not the minimum amongst encountered points</li>
879</ul>
880</div></blockquote>
881</li>
882</ul>
883</p>
884</td>
885</tr>
886</tbody>
887</table>
888<p><em>Notes</em>:
889Simulated annealing is a random algorithm which uses no derivative
890information from the function being optimized. In practice it has
891been more useful in discrete optimization than continuous
892optimization, as there are usually better algorithms for continuous
893optimization problems.</p>
894<p>Some experimentation by trying the difference temperature
895schedules and altering their parameters is likely required to
896obtain good performance.</p>
897<p>The randomness in the algorithm comes from random sampling in numpy.
898To obtain the same results you can call numpy.random.seed with the
899same seed immediately before calling scipy.optimize.anneal.</p>
900<p>We give a brief description of how the three temperature schedules
901generate new points and vary their temperature. Temperatures are
902only updated with iterations in the outer loop. The inner loop is
903over xrange(dwell), and new points are generated for
904every iteration in the inner loop. (Though whether the proposed
905new points are accepted is probabilistic.)</p>
906<p>For readability, let d denote the dimension of the inputs to func.
907Also, let x_old denote the previous state, and k denote the
908iteration number of the outer loop. All other variables not
909defined below are input variables to scipy.optimize.anneal itself.</p>
910<p>In the &#8216;fast&#8217; schedule the updates are</p>
911<div class="highlight-python"><div class="highlight"><pre>u ~ Uniform(0, 1, size=d)
912y = sgn(u - 0.5) * T * ((1+ 1/T)**abs(2u-1) -1.0)
913xc = y * (upper - lower)
914x_new = x_old + xc
915
916c = n * exp(-n * quench)
917T_new = T0 * exp(-c * k**quench)
918</pre></div>
919</div>
920<p>In the &#8216;cauchy&#8217; schedule the updates are</p>
921<div class="highlight-python"><div class="highlight"><pre>u ~ Uniform(-pi/2, pi/2, size=d)
922xc = learn_rate * T * tan(u)
923x_new = x_old + xc
924
925T_new = T0 / (1+k)
926</pre></div>
927</div>
928<p>In the &#8216;boltzmann&#8217; schedule the updates are</p>
929<div class="highlight-python"><div class="highlight"><pre>std = minimum( sqrt(T) * ones(d), (upper-lower) / (3*learn_rate) )
930y ~ Normal(0, std, size=d)
931x_new = x_old + learn_rate * y
932
933T_new = T0 / log(1+k)
934</pre></div>
935</div>
936</dd></dl>
937
938<dl class="function">
939<dt id="GSASIImath.calcRamaEnergy">
940<tt class="descclassname">GSASIImath.</tt><tt class="descname">calcRamaEnergy</tt><big>(</big><em>phi</em>, <em>psi</em>, <em>Coeff=</em><span class="optional">[</span><span class="optional">]</span><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#calcRamaEnergy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.calcRamaEnergy" title="Permalink to this definition">¶</a></dt>
941<dd><p>Computes pseudo potential energy from a pair of torsion angles and a
942numerical description of the potential energy surface. Used to create
943penalty function in LS refinement:     
944<span class="math">\(Eval(\phi,\psi) = C[0]*exp(-V/1000)\)</span></p>
945<p>where <span class="math">\(V = -C[3] * (\phi-C[1])^2 - C[4]*(\psi-C[2])^2 - 2*(\phi-C[1])*(\psi-C[2])\)</span></p>
946<table class="docutils field-list" frame="void" rules="none">
947<col class="field-name" />
948<col class="field-body" />
949<tbody valign="top">
950<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
951<li><strong>phi</strong> (<em>float</em>) &#8211; first torsion angle (<span class="math">\(\phi\)</span>)</li>
952<li><strong>psi</strong> (<em>float</em>) &#8211; second torsion angle (<span class="math">\(\psi\)</span>)</li>
953<li><strong>Coeff</strong> (<em>list</em>) &#8211; pseudo potential coefficients</li>
954</ul>
955</td>
956</tr>
957<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">list (sum,Eval): pseudo-potential difference from minimum &amp; value;
958sum is used for penalty function.</p>
959</td>
960</tr>
961</tbody>
962</table>
963</dd></dl>
964
965<dl class="function">
966<dt id="GSASIImath.calcTorsionEnergy">
967<tt class="descclassname">GSASIImath.</tt><tt class="descname">calcTorsionEnergy</tt><big>(</big><em>TOR</em>, <em>Coeff=</em><span class="optional">[</span><span class="optional">]</span><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#calcTorsionEnergy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.calcTorsionEnergy" title="Permalink to this definition">¶</a></dt>
968<dd><p>default doc string</p>
969<table class="docutils field-list" frame="void" rules="none">
970<col class="field-name" />
971<col class="field-body" />
972<tbody valign="top">
973<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
974</tr>
975<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
976</tr>
977</tbody>
978</table>
979</dd></dl>
980
981<dl class="function">
982<dt id="GSASIImath.findOffset">
983<tt class="descclassname">GSASIImath.</tt><tt class="descname">findOffset</tt><big>(</big><em>SGData</em>, <em>A</em>, <em>Fhkl</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#findOffset"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.findOffset" title="Permalink to this definition">¶</a></dt>
984<dd><p>default doc string</p>
985<table class="docutils field-list" frame="void" rules="none">
986<col class="field-name" />
987<col class="field-body" />
988<tbody valign="top">
989<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
990</tr>
991<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
992</tr>
993</tbody>
994</table>
995</dd></dl>
996
997<dl class="function">
998<dt id="GSASIImath.findSSOffset">
999<tt class="descclassname">GSASIImath.</tt><tt class="descname">findSSOffset</tt><big>(</big><em>SGData</em>, <em>SSGData</em>, <em>A</em>, <em>Fhklm</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#findSSOffset"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.findSSOffset" title="Permalink to this definition">¶</a></dt>
1000<dd><p>default doc string</p>
1001<table class="docutils field-list" frame="void" rules="none">
1002<col class="field-name" />
1003<col class="field-body" />
1004<tbody valign="top">
1005<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1006</tr>
1007<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1008</tr>
1009</tbody>
1010</table>
1011</dd></dl>
1012
1013<dl class="function">
1014<dt id="GSASIImath.getAngSig">
1015<tt class="descclassname">GSASIImath.</tt><tt class="descname">getAngSig</tt><big>(</big><em>VA</em>, <em>VB</em>, <em>Amat</em>, <em>SGData</em>, <em>covData={}</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getAngSig"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getAngSig" title="Permalink to this definition">¶</a></dt>
1016<dd><p>default doc string</p>
1017<table class="docutils field-list" frame="void" rules="none">
1018<col class="field-name" />
1019<col class="field-body" />
1020<tbody valign="top">
1021<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1022</tr>
1023<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1024</tr>
1025</tbody>
1026</table>
1027</dd></dl>
1028
1029<dl class="function">
1030<dt id="GSASIImath.getAtomXYZ">
1031<tt class="descclassname">GSASIImath.</tt><tt class="descname">getAtomXYZ</tt><big>(</big><em>atoms</em>, <em>cx</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getAtomXYZ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getAtomXYZ" title="Permalink to this definition">¶</a></dt>
1032<dd><p>default doc string</p>
1033<table class="docutils field-list" frame="void" rules="none">
1034<col class="field-name" />
1035<col class="field-body" />
1036<tbody valign="top">
1037<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1038</tr>
1039<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1040</tr>
1041</tbody>
1042</table>
1043</dd></dl>
1044
1045<dl class="function">
1046<dt id="GSASIImath.getCWgam">
1047<tt class="descclassname">GSASIImath.</tt><tt class="descname">getCWgam</tt><big>(</big><em>ins</em>, <em>pos</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getCWgam"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getCWgam" title="Permalink to this definition">¶</a></dt>
1048<dd><p>get CW peak profile gamma</p>
1049<table class="docutils field-list" frame="void" rules="none">
1050<col class="field-name" />
1051<col class="field-body" />
1052<tbody valign="top">
1053<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
1054<li><strong>ins</strong> (<em>dict</em>) &#8211; instrument parameters with at least &#8216;X&#8217; &amp; &#8216;Y&#8217; 
1055as values only</li>
1056<li><strong>pos</strong> (<em>float</em>) &#8211; 2-theta of peak</li>
1057</ul>
1058</td>
1059</tr>
1060<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">float getCWgam: peak gamma</p>
1061</td>
1062</tr>
1063</tbody>
1064</table>
1065</dd></dl>
1066
1067<dl class="function">
1068<dt id="GSASIImath.getCWgamDeriv">
1069<tt class="descclassname">GSASIImath.</tt><tt class="descname">getCWgamDeriv</tt><big>(</big><em>pos</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getCWgamDeriv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getCWgamDeriv" title="Permalink to this definition">¶</a></dt>
1070<dd><p>get derivatives of CW peak profile gamma wrt X &amp; Y</p>
1071<table class="docutils field-list" frame="void" rules="none">
1072<col class="field-name" />
1073<col class="field-body" />
1074<tbody valign="top">
1075<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>pos</strong> (<em>float</em>) &#8211; 2-theta of peak</td>
1076</tr>
1077<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">list getCWgamDeriv: d(gam)/dX &amp; d(gam)/dY</td>
1078</tr>
1079</tbody>
1080</table>
1081</dd></dl>
1082
1083<dl class="function">
1084<dt id="GSASIImath.getCWsig">
1085<tt class="descclassname">GSASIImath.</tt><tt class="descname">getCWsig</tt><big>(</big><em>ins</em>, <em>pos</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getCWsig"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getCWsig" title="Permalink to this definition">¶</a></dt>
1086<dd><p>get CW peak profile sigma</p>
1087<table class="docutils field-list" frame="void" rules="none">
1088<col class="field-name" />
1089<col class="field-body" />
1090<tbody valign="top">
1091<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
1092<li><strong>ins</strong> (<em>dict</em>) &#8211; instrument parameters with at least &#8216;U&#8217;, &#8216;V&#8217;, &amp; &#8216;W&#8217; 
1093as values only</li>
1094<li><strong>pos</strong> (<em>float</em>) &#8211; 2-theta of peak</li>
1095</ul>
1096</td>
1097</tr>
1098<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">float getCWsig: peak sigma</p>
1099</td>
1100</tr>
1101</tbody>
1102</table>
1103</dd></dl>
1104
1105<dl class="function">
1106<dt id="GSASIImath.getCWsigDeriv">
1107<tt class="descclassname">GSASIImath.</tt><tt class="descname">getCWsigDeriv</tt><big>(</big><em>pos</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getCWsigDeriv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getCWsigDeriv" title="Permalink to this definition">¶</a></dt>
1108<dd><p>get derivatives of CW peak profile sigma wrt U,V, &amp; W</p>
1109<table class="docutils field-list" frame="void" rules="none">
1110<col class="field-name" />
1111<col class="field-body" />
1112<tbody valign="top">
1113<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>pos</strong> (<em>float</em>) &#8211; 2-theta of peak</td>
1114</tr>
1115<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">list getCWsigDeriv: d(sig)/dU, d(sig)/dV &amp; d(sig)/dW</td>
1116</tr>
1117</tbody>
1118</table>
1119</dd></dl>
1120
1121<dl class="function">
1122<dt id="GSASIImath.getDensity">
1123<tt class="descclassname">GSASIImath.</tt><tt class="descname">getDensity</tt><big>(</big><em>generalData</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getDensity"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getDensity" title="Permalink to this definition">¶</a></dt>
1124<dd><p>calculate crystal structure density</p>
1125<table class="docutils field-list" frame="void" rules="none">
1126<col class="field-name" />
1127<col class="field-body" />
1128<tbody valign="top">
1129<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>generalData</strong> (<em>dict</em>) &#8211; The General dictionary in Phase</td>
1130</tr>
1131<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">float density: crystal density in gm/cm^3</td>
1132</tr>
1133</tbody>
1134</table>
1135</dd></dl>
1136
1137<dl class="function">
1138<dt id="GSASIImath.getDistDerv">
1139<tt class="descclassname">GSASIImath.</tt><tt class="descname">getDistDerv</tt><big>(</big><em>Oxyz</em>, <em>Txyz</em>, <em>Amat</em>, <em>Tunit</em>, <em>Top</em>, <em>SGData</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getDistDerv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getDistDerv" title="Permalink to this definition">¶</a></dt>
1140<dd><p>default doc string</p>
1141<table class="docutils field-list" frame="void" rules="none">
1142<col class="field-name" />
1143<col class="field-body" />
1144<tbody valign="top">
1145<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1146</tr>
1147<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1148</tr>
1149</tbody>
1150</table>
1151</dd></dl>
1152
1153<dl class="function">
1154<dt id="GSASIImath.getMass">
1155<tt class="descclassname">GSASIImath.</tt><tt class="descname">getMass</tt><big>(</big><em>generalData</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getMass"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getMass" title="Permalink to this definition">¶</a></dt>
1156<dd><p>Computes mass of unit cell contents</p>
1157<table class="docutils field-list" frame="void" rules="none">
1158<col class="field-name" />
1159<col class="field-body" />
1160<tbody valign="top">
1161<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>generalData</strong> (<em>dict</em>) &#8211; The General dictionary in Phase</td>
1162</tr>
1163<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">float mass: Crystal unit cell mass in AMU.</td>
1164</tr>
1165</tbody>
1166</table>
1167</dd></dl>
1168
1169<dl class="function">
1170<dt id="GSASIImath.getRamaDeriv">
1171<tt class="descclassname">GSASIImath.</tt><tt class="descname">getRamaDeriv</tt><big>(</big><em>XYZ</em>, <em>Amat</em>, <em>Coeff</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getRamaDeriv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getRamaDeriv" title="Permalink to this definition">¶</a></dt>
1172<dd><p>Computes numerical derivatives of torsion angle pair pseudo potential
1173with respect of crystallographic atom coordinates of the 5 atom sequence</p>
1174<table class="docutils field-list" frame="void" rules="none">
1175<col class="field-name" />
1176<col class="field-body" />
1177<tbody valign="top">
1178<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
1179<li><strong>XYZ</strong> (<em>nparray</em>) &#8211; crystallographic coordinates of 5 atoms</li>
1180<li><strong>Amat</strong> (<em>nparray</em>) &#8211; crystal to cartesian transformation matrix</li>
1181<li><strong>Coeff</strong> (<em>list</em>) &#8211; pseudo potential coefficients</li>
1182</ul>
1183</td>
1184</tr>
1185<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">list (deriv) derivatives of pseudopotential with respect to 5 atom
1186crystallographic xyz coordinates.</p>
1187</td>
1188</tr>
1189</tbody>
1190</table>
1191</dd></dl>
1192
1193<dl class="function">
1194<dt id="GSASIImath.getRestAngle">
1195<tt class="descclassname">GSASIImath.</tt><tt class="descname">getRestAngle</tt><big>(</big><em>XYZ</em>, <em>Amat</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getRestAngle"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getRestAngle" title="Permalink to this definition">¶</a></dt>
1196<dd><p>default doc string</p>
1197<table class="docutils field-list" frame="void" rules="none">
1198<col class="field-name" />
1199<col class="field-body" />
1200<tbody valign="top">
1201<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1202</tr>
1203<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1204</tr>
1205</tbody>
1206</table>
1207</dd></dl>
1208
1209<dl class="function">
1210<dt id="GSASIImath.getRestChiral">
1211<tt class="descclassname">GSASIImath.</tt><tt class="descname">getRestChiral</tt><big>(</big><em>XYZ</em>, <em>Amat</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getRestChiral"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getRestChiral" title="Permalink to this definition">¶</a></dt>
1212<dd><p>default doc string</p>
1213<table class="docutils field-list" frame="void" rules="none">
1214<col class="field-name" />
1215<col class="field-body" />
1216<tbody valign="top">
1217<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1218</tr>
1219<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1220</tr>
1221</tbody>
1222</table>
1223</dd></dl>
1224
1225<dl class="function">
1226<dt id="GSASIImath.getRestDeriv">
1227<tt class="descclassname">GSASIImath.</tt><tt class="descname">getRestDeriv</tt><big>(</big><em>Func</em>, <em>XYZ</em>, <em>Amat</em>, <em>ops</em>, <em>SGData</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getRestDeriv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getRestDeriv" title="Permalink to this definition">¶</a></dt>
1228<dd><p>default doc string</p>
1229<table class="docutils field-list" frame="void" rules="none">
1230<col class="field-name" />
1231<col class="field-body" />
1232<tbody valign="top">
1233<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1234</tr>
1235<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1236</tr>
1237</tbody>
1238</table>
1239</dd></dl>
1240
1241<dl class="function">
1242<dt id="GSASIImath.getRestDist">
1243<tt class="descclassname">GSASIImath.</tt><tt class="descname">getRestDist</tt><big>(</big><em>XYZ</em>, <em>Amat</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getRestDist"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getRestDist" title="Permalink to this definition">¶</a></dt>
1244<dd><p>default doc string</p>
1245<table class="docutils field-list" frame="void" rules="none">
1246<col class="field-name" />
1247<col class="field-body" />
1248<tbody valign="top">
1249<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1250</tr>
1251<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1252</tr>
1253</tbody>
1254</table>
1255</dd></dl>
1256
1257<dl class="function">
1258<dt id="GSASIImath.getRestPlane">
1259<tt class="descclassname">GSASIImath.</tt><tt class="descname">getRestPlane</tt><big>(</big><em>XYZ</em>, <em>Amat</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getRestPlane"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getRestPlane" title="Permalink to this definition">¶</a></dt>
1260<dd><p>default doc string</p>
1261<table class="docutils field-list" frame="void" rules="none">
1262<col class="field-name" />
1263<col class="field-body" />
1264<tbody valign="top">
1265<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1266</tr>
1267<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1268</tr>
1269</tbody>
1270</table>
1271</dd></dl>
1272
1273<dl class="function">
1274<dt id="GSASIImath.getRestPolefig">
1275<tt class="descclassname">GSASIImath.</tt><tt class="descname">getRestPolefig</tt><big>(</big><em>ODFln</em>, <em>SamSym</em>, <em>Grid</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getRestPolefig"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getRestPolefig" title="Permalink to this definition">¶</a></dt>
1276<dd><p>default doc string</p>
1277<table class="docutils field-list" frame="void" rules="none">
1278<col class="field-name" />
1279<col class="field-body" />
1280<tbody valign="top">
1281<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1282</tr>
1283<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1284</tr>
1285</tbody>
1286</table>
1287</dd></dl>
1288
1289<dl class="function">
1290<dt id="GSASIImath.getRestPolefigDerv">
1291<tt class="descclassname">GSASIImath.</tt><tt class="descname">getRestPolefigDerv</tt><big>(</big><em>HKL</em>, <em>Grid</em>, <em>SHCoeff</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getRestPolefigDerv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getRestPolefigDerv" title="Permalink to this definition">¶</a></dt>
1292<dd><p>default doc string</p>
1293<table class="docutils field-list" frame="void" rules="none">
1294<col class="field-name" />
1295<col class="field-body" />
1296<tbody valign="top">
1297<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1298</tr>
1299<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1300</tr>
1301</tbody>
1302</table>
1303</dd></dl>
1304
1305<dl class="function">
1306<dt id="GSASIImath.getRestRama">
1307<tt class="descclassname">GSASIImath.</tt><tt class="descname">getRestRama</tt><big>(</big><em>XYZ</em>, <em>Amat</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getRestRama"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getRestRama" title="Permalink to this definition">¶</a></dt>
1308<dd><p>Computes a pair of torsion angles in a 5 atom string</p>
1309<table class="docutils field-list" frame="void" rules="none">
1310<col class="field-name" />
1311<col class="field-body" />
1312<tbody valign="top">
1313<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
1314<li><strong>XYZ</strong> (<em>nparray</em>) &#8211; crystallographic coordinates of 5 atoms</li>
1315<li><strong>Amat</strong> (<em>nparray</em>) &#8211; crystal to cartesian transformation matrix</li>
1316</ul>
1317</td>
1318</tr>
1319<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">list (phi,psi) two torsion angles in degrees</p>
1320</td>
1321</tr>
1322</tbody>
1323</table>
1324</dd></dl>
1325
1326<dl class="function">
1327<dt id="GSASIImath.getRestTorsion">
1328<tt class="descclassname">GSASIImath.</tt><tt class="descname">getRestTorsion</tt><big>(</big><em>XYZ</em>, <em>Amat</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getRestTorsion"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getRestTorsion" title="Permalink to this definition">¶</a></dt>
1329<dd><p>default doc string</p>
1330<table class="docutils field-list" frame="void" rules="none">
1331<col class="field-name" />
1332<col class="field-body" />
1333<tbody valign="top">
1334<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1335</tr>
1336<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1337</tr>
1338</tbody>
1339</table>
1340</dd></dl>
1341
1342<dl class="function">
1343<dt id="GSASIImath.getSyXYZ">
1344<tt class="descclassname">GSASIImath.</tt><tt class="descname">getSyXYZ</tt><big>(</big><em>XYZ</em>, <em>ops</em>, <em>SGData</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getSyXYZ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getSyXYZ" title="Permalink to this definition">¶</a></dt>
1345<dd><p>default doc string</p>
1346<table class="docutils field-list" frame="void" rules="none">
1347<col class="field-name" />
1348<col class="field-body" />
1349<tbody valign="top">
1350<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1351</tr>
1352<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1353</tr>
1354</tbody>
1355</table>
1356</dd></dl>
1357
1358<dl class="function">
1359<dt id="GSASIImath.getTOFalpha">
1360<tt class="descclassname">GSASIImath.</tt><tt class="descname">getTOFalpha</tt><big>(</big><em>ins</em>, <em>dsp</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getTOFalpha"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getTOFalpha" title="Permalink to this definition">¶</a></dt>
1361<dd><p>get TOF peak profile alpha</p>
1362<table class="docutils field-list" frame="void" rules="none">
1363<col class="field-name" />
1364<col class="field-body" />
1365<tbody valign="top">
1366<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
1367<li><strong>ins</strong> (<em>dict</em>) &#8211; instrument parameters with at least &#8216;alpha&#8217;
1368as values only</li>
1369<li><strong>dsp</strong> (<em>float</em>) &#8211; d-spacing of peak</li>
1370</ul>
1371</td>
1372</tr>
1373<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">flaot getTOFalpha: peak alpha</p>
1374</td>
1375</tr>
1376</tbody>
1377</table>
1378</dd></dl>
1379
1380<dl class="function">
1381<dt id="GSASIImath.getTOFalphaDeriv">
1382<tt class="descclassname">GSASIImath.</tt><tt class="descname">getTOFalphaDeriv</tt><big>(</big><em>dsp</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getTOFalphaDeriv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getTOFalphaDeriv" title="Permalink to this definition">¶</a></dt>
1383<dd><p>get derivatives of TOF peak profile beta wrt alpha</p>
1384<table class="docutils field-list" frame="void" rules="none">
1385<col class="field-name" />
1386<col class="field-body" />
1387<tbody valign="top">
1388<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>dsp</strong> (<em>float</em>) &#8211; d-spacing of peak</td>
1389</tr>
1390<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">float getTOFalphaDeriv: d(alp)/d(alpha)</td>
1391</tr>
1392</tbody>
1393</table>
1394</dd></dl>
1395
1396<dl class="function">
1397<dt id="GSASIImath.getTOFbeta">
1398<tt class="descclassname">GSASIImath.</tt><tt class="descname">getTOFbeta</tt><big>(</big><em>ins</em>, <em>dsp</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getTOFbeta"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getTOFbeta" title="Permalink to this definition">¶</a></dt>
1399<dd><p>get TOF peak profile beta</p>
1400<table class="docutils field-list" frame="void" rules="none">
1401<col class="field-name" />
1402<col class="field-body" />
1403<tbody valign="top">
1404<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
1405<li><strong>ins</strong> (<em>dict</em>) &#8211; instrument parameters with at least &#8216;beat-0&#8217;, &#8216;beta-1&#8217; &amp; &#8216;beta-q&#8217;
1406as values only</li>
1407<li><strong>dsp</strong> (<em>float</em>) &#8211; d-spacing of peak</li>
1408</ul>
1409</td>
1410</tr>
1411<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">float getTOFbeta: peak beat</p>
1412</td>
1413</tr>
1414</tbody>
1415</table>
1416</dd></dl>
1417
1418<dl class="function">
1419<dt id="GSASIImath.getTOFbetaDeriv">
1420<tt class="descclassname">GSASIImath.</tt><tt class="descname">getTOFbetaDeriv</tt><big>(</big><em>dsp</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getTOFbetaDeriv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getTOFbetaDeriv" title="Permalink to this definition">¶</a></dt>
1421<dd><p>get derivatives of TOF peak profile beta wrt beta-0, beta-1, &amp; beat-q</p>
1422<table class="docutils field-list" frame="void" rules="none">
1423<col class="field-name" />
1424<col class="field-body" />
1425<tbody valign="top">
1426<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>dsp</strong> (<em>float</em>) &#8211; d-spacing of peak</td>
1427</tr>
1428<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">list getTOFbetaDeriv: d(beta)/d(beat-0), d(beta)/d(beta-1) &amp; d(beta)/d(beta-q)</td>
1429</tr>
1430</tbody>
1431</table>
1432</dd></dl>
1433
1434<dl class="function">
1435<dt id="GSASIImath.getTOFgamma">
1436<tt class="descclassname">GSASIImath.</tt><tt class="descname">getTOFgamma</tt><big>(</big><em>ins</em>, <em>dsp</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getTOFgamma"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getTOFgamma" title="Permalink to this definition">¶</a></dt>
1437<dd><p>get TOF peak profile gamma</p>
1438<table class="docutils field-list" frame="void" rules="none">
1439<col class="field-name" />
1440<col class="field-body" />
1441<tbody valign="top">
1442<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
1443<li><strong>ins</strong> (<em>dict</em>) &#8211; instrument parameters with at least &#8216;X&#8217; &amp; &#8216;Y&#8217;
1444as values only</li>
1445<li><strong>dsp</strong> (<em>float</em>) &#8211; d-spacing of peak</li>
1446</ul>
1447</td>
1448</tr>
1449<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">float getTOFgamma: peak gamma</p>
1450</td>
1451</tr>
1452</tbody>
1453</table>
1454</dd></dl>
1455
1456<dl class="function">
1457<dt id="GSASIImath.getTOFgammaDeriv">
1458<tt class="descclassname">GSASIImath.</tt><tt class="descname">getTOFgammaDeriv</tt><big>(</big><em>dsp</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getTOFgammaDeriv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getTOFgammaDeriv" title="Permalink to this definition">¶</a></dt>
1459<dd><p>get derivatives of TOF peak profile gamma wrt X &amp; Y</p>
1460<table class="docutils field-list" frame="void" rules="none">
1461<col class="field-name" />
1462<col class="field-body" />
1463<tbody valign="top">
1464<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>dsp</strong> (<em>float</em>) &#8211; d-spacing of peak</td>
1465</tr>
1466<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">list getTOFgammaDeriv: d(gam)/dX &amp; d(gam)/dY</td>
1467</tr>
1468</tbody>
1469</table>
1470</dd></dl>
1471
1472<dl class="function">
1473<dt id="GSASIImath.getTOFsig">
1474<tt class="descclassname">GSASIImath.</tt><tt class="descname">getTOFsig</tt><big>(</big><em>ins</em>, <em>dsp</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getTOFsig"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getTOFsig" title="Permalink to this definition">¶</a></dt>
1475<dd><p>get TOF peak profile sigma</p>
1476<table class="docutils field-list" frame="void" rules="none">
1477<col class="field-name" />
1478<col class="field-body" />
1479<tbody valign="top">
1480<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
1481<li><strong>ins</strong> (<em>dict</em>) &#8211; instrument parameters with at least &#8216;sig-0&#8217;, &#8216;sig-1&#8217; &amp; &#8216;sig-q&#8217;
1482as values only</li>
1483<li><strong>dsp</strong> (<em>float</em>) &#8211; d-spacing of peak</li>
1484</ul>
1485</td>
1486</tr>
1487<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">float getTOFsig: peak sigma</p>
1488</td>
1489</tr>
1490</tbody>
1491</table>
1492</dd></dl>
1493
1494<dl class="function">
1495<dt id="GSASIImath.getTOFsigDeriv">
1496<tt class="descclassname">GSASIImath.</tt><tt class="descname">getTOFsigDeriv</tt><big>(</big><em>dsp</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getTOFsigDeriv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getTOFsigDeriv" title="Permalink to this definition">¶</a></dt>
1497<dd><p>get derivatives of TOF peak profile gamma wrt sig-0, sig-1, &amp; sig-q</p>
1498<table class="docutils field-list" frame="void" rules="none">
1499<col class="field-name" />
1500<col class="field-body" />
1501<tbody valign="top">
1502<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>dsp</strong> (<em>float</em>) &#8211; d-spacing of peak</td>
1503</tr>
1504<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">list getTOFsigDeriv: d(sig0/d(sig-0), d(sig)/d(sig-1) &amp; d(sig)/d(sig-q)</td>
1505</tr>
1506</tbody>
1507</table>
1508</dd></dl>
1509
1510<dl class="function">
1511<dt id="GSASIImath.getTorsionDeriv">
1512<tt class="descclassname">GSASIImath.</tt><tt class="descname">getTorsionDeriv</tt><big>(</big><em>XYZ</em>, <em>Amat</em>, <em>Coeff</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getTorsionDeriv"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getTorsionDeriv" title="Permalink to this definition">¶</a></dt>
1513<dd><p>default doc string</p>
1514<table class="docutils field-list" frame="void" rules="none">
1515<col class="field-name" />
1516<col class="field-body" />
1517<tbody valign="top">
1518<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1519</tr>
1520<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1521</tr>
1522</tbody>
1523</table>
1524</dd></dl>
1525
1526<dl class="function">
1527<dt id="GSASIImath.getVCov">
1528<tt class="descclassname">GSASIImath.</tt><tt class="descname">getVCov</tt><big>(</big><em>varyNames</em>, <em>varyList</em>, <em>covMatrix</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getVCov"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getVCov" title="Permalink to this definition">¶</a></dt>
1529<dd><p>obtain variance-covariance terms for a set of variables. NB: the varyList
1530and covMatrix were saved by the last least squares refinement so they must match.</p>
1531<table class="docutils field-list" frame="void" rules="none">
1532<col class="field-name" />
1533<col class="field-body" />
1534<tbody valign="top">
1535<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
1536<li><strong>varyNames</strong> (<em>list</em>) &#8211; variable names to find v-cov matric for</li>
1537<li><strong>varyList</strong> (<em>list</em>) &#8211; full list of all variables in v-cov matrix</li>
1538<li><strong>covMatrix</strong> (<em>nparray</em>) &#8211; full variance-covariance matrix from the last
1539least squares refinement</li>
1540</ul>
1541</td>
1542</tr>
1543<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">nparray vcov: variance-covariance matrix for the variables given
1544in varyNames</p>
1545</td>
1546</tr>
1547</tbody>
1548</table>
1549</dd></dl>
1550
1551<dl class="function">
1552<dt id="GSASIImath.getWave">
1553<tt class="descclassname">GSASIImath.</tt><tt class="descname">getWave</tt><big>(</big><em>Parms</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#getWave"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.getWave" title="Permalink to this definition">¶</a></dt>
1554<dd><p>returns wavelength from Instrument parameters dictionary</p>
1555<table class="docutils field-list" frame="void" rules="none">
1556<col class="field-name" />
1557<col class="field-body" />
1558<tbody valign="top">
1559<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>Parms</strong> (<em>dict</em>) &#8211; Instrument parameters;
1560must contain:
1561Lam: single wavelength
1562or
1563Lam1: Ka1 radiation wavelength</td>
1564</tr>
1565<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">float wave: wavelength</td>
1566</tr>
1567</tbody>
1568</table>
1569</dd></dl>
1570
1571<dl class="function">
1572<dt id="GSASIImath.invQ">
1573<tt class="descclassname">GSASIImath.</tt><tt class="descname">invQ</tt><big>(</big><em>Q</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#invQ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.invQ" title="Permalink to this definition">¶</a></dt>
1574<dd><p>get inverse of quaternion
1575q=r+ai+bj+ck; q* = r-ai-bj-ck</p>
1576</dd></dl>
1577
1578<dl class="function">
1579<dt id="GSASIImath.makeQuat">
1580<tt class="descclassname">GSASIImath.</tt><tt class="descname">makeQuat</tt><big>(</big><em>A</em>, <em>B</em>, <em>C</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#makeQuat"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.makeQuat" title="Permalink to this definition">¶</a></dt>
1581<dd><p>Make quaternion from rotation of A vector to B vector about C axis</p>
1582<table class="docutils field-list" frame="void" rules="none">
1583<col class="field-name" />
1584<col class="field-body" />
1585<tbody valign="top">
1586<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>A,B,C</strong> (<em>np.array</em>) &#8211; Cartesian 3-vectors</td>
1587</tr>
1588<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">quaternion &amp; rotation angle in radians q=r+ai+bj+ck</td>
1589</tr>
1590</tbody>
1591</table>
1592</dd></dl>
1593
1594<dl class="function">
1595<dt id="GSASIImath.mcsaSearch">
1596<tt class="descclassname">GSASIImath.</tt><tt class="descname">mcsaSearch</tt><big>(</big><em>data</em>, <em>RBdata</em>, <em>reflType</em>, <em>reflData</em>, <em>covData</em>, <em>pgbar</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#mcsaSearch"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.mcsaSearch" title="Permalink to this definition">¶</a></dt>
1597<dd><p>default doc string</p>
1598<table class="docutils field-list" frame="void" rules="none">
1599<col class="field-name" />
1600<col class="field-body" />
1601<tbody valign="top">
1602<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1603</tr>
1604<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1605</tr>
1606</tbody>
1607</table>
1608</dd></dl>
1609
1610<dl class="function">
1611<dt id="GSASIImath.normQ">
1612<tt class="descclassname">GSASIImath.</tt><tt class="descname">normQ</tt><big>(</big><em>QA</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#normQ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.normQ" title="Permalink to this definition">¶</a></dt>
1613<dd><p>get length of quaternion &amp; normalize it
1614q=r+ai+bj+ck</p>
1615</dd></dl>
1616
1617<dl class="function">
1618<dt id="GSASIImath.printRho">
1619<tt class="descclassname">GSASIImath.</tt><tt class="descname">printRho</tt><big>(</big><em>SGLaue</em>, <em>rho</em>, <em>rhoMax</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#printRho"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.printRho" title="Permalink to this definition">¶</a></dt>
1620<dd><p>default doc string</p>
1621<table class="docutils field-list" frame="void" rules="none">
1622<col class="field-name" />
1623<col class="field-body" />
1624<tbody valign="top">
1625<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>type</em>) &#8211; description</td>
1626</tr>
1627<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">type name: description</td>
1628</tr>
1629</tbody>
1630</table>
1631</dd></dl>
1632
1633<dl class="function">
1634<dt id="GSASIImath.prodQQ">
1635<tt class="descclassname">GSASIImath.</tt><tt class="descname">prodQQ</tt><big>(</big><em>QA</em>, <em>QB</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#prodQQ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.prodQQ" title="Permalink to this definition">¶</a></dt>
1636<dd><p>Grassman quaternion product
1637QA,QB quaternions; q=r+ai+bj+ck</p>
1638</dd></dl>
1639
1640<dl class="function">
1641<dt id="GSASIImath.prodQVQ">
1642<tt class="descclassname">GSASIImath.</tt><tt class="descname">prodQVQ</tt><big>(</big><em>Q</em>, <em>V</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#prodQVQ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.prodQVQ" title="Permalink to this definition">¶</a></dt>
1643<dd><p>compute the quaternion vector rotation qvq-1 = v&#8217;
1644q=r+ai+bj+ck</p>
1645</dd></dl>
1646
1647<dl class="function">
1648<dt id="GSASIImath.randomAVdeg">
1649<tt class="descclassname">GSASIImath.</tt><tt class="descname">randomAVdeg</tt><big>(</big><em>r0</em>, <em>r1</em>, <em>r2</em>, <em>r3</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#randomAVdeg"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.randomAVdeg" title="Permalink to this definition">¶</a></dt>
1650<dd><p>create random angle (deg),vector from 4 random number in range (-1,1)</p>
1651</dd></dl>
1652
1653<dl class="function">
1654<dt id="GSASIImath.randomQ">
1655<tt class="descclassname">GSASIImath.</tt><tt class="descname">randomQ</tt><big>(</big><em>r0</em>, <em>r1</em>, <em>r2</em>, <em>r3</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#randomQ"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.randomQ" title="Permalink to this definition">¶</a></dt>
1656<dd><p>create random quaternion from 4 random numbers in range (-1,1)</p>
1657</dd></dl>
1658
1659<dl class="function">
1660<dt id="GSASIImath.setPeakparms">
1661<tt class="descclassname">GSASIImath.</tt><tt class="descname">setPeakparms</tt><big>(</big><em>Parms</em>, <em>Parms2</em>, <em>pos</em>, <em>mag</em>, <em>ifQ=False</em>, <em>useFit=False</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#setPeakparms"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.setPeakparms" title="Permalink to this definition">¶</a></dt>
1662<dd><p>set starting peak parameters for single peak fits from plot selection or auto selection</p>
1663<table class="docutils field-list" frame="void" rules="none">
1664<col class="field-name" />
1665<col class="field-body" />
1666<tbody valign="top">
1667<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
1668<li><strong>Parms</strong> (<em>dict</em>) &#8211; instrument parameters dictionary</li>
1669<li><strong>Parms2</strong> (<em>dict</em>) &#8211; table lookup for TOF profile coefficients</li>
1670<li><strong>pos</strong> (<em>float</em>) &#8211; peak position in 2-theta, TOF or Q (ifQ=True)</li>
1671<li><strong>mag</strong> (<em>float</em>) &#8211; peak top magnitude from pick</li>
1672<li><strong>ifQ</strong> (<em>bool</em>) &#8211; True if pos in Q</li>
1673<li><strong>useFit</strong> (<em>bool</em>) &#8211; True if use fitted CW Parms values (not defaults)</li>
1674</ul>
1675</td>
1676</tr>
1677<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">list XY: peak list entry:
1678for CW: [pos,0,mag,1,sig,0,gam,0]
1679for TOF: [pos,0,mag,1,alp,0,bet,0,sig,0,gam,0]
1680NB: mag refinement set by default, all others off</p>
1681</td>
1682</tr>
1683</tbody>
1684</table>
1685</dd></dl>
1686
1687<dl class="function">
1688<dt id="GSASIImath.sortArray">
1689<tt class="descclassname">GSASIImath.</tt><tt class="descname">sortArray</tt><big>(</big><em>data</em>, <em>pos</em>, <em>reverse=False</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#sortArray"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.sortArray" title="Permalink to this definition">¶</a></dt>
1690<dd><p>data is a list of items
1691sort by pos in list; reverse if True</p>
1692</dd></dl>
1693
1694<dl class="function">
1695<dt id="GSASIImath.wavekE">
1696<tt class="descclassname">GSASIImath.</tt><tt class="descname">wavekE</tt><big>(</big><em>wavekE</em><big>)</big><a class="reference internal" href="_modules/GSASIImath.html#wavekE"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GSASIImath.wavekE" title="Permalink to this definition">¶</a></dt>
1697<dd><p>Convert wavelength to energy &amp; vise versa</p>
1698<p>:param float waveKe:wavelength in A or energy in kE</p>
1699<p>:returns float waveKe:the other one</p>
1700</dd></dl>
1701
1702</div>
1703
1704
1705          </div>
1706        </div>
1707      </div>
1708      <div class="sphinxsidebar">
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