source: Tutorials/SeqRefine/ParametricFitting.htm @ 2353

Last change on this file since 2353 was 2353, checked in by vondreele, 7 years ago

combine hml files in certain directories
File size: 123.1 KB
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2xmlns:o="urn:schemas-microsoft-com:office:office"
3xmlns:w="urn:schemas-microsoft-com:office:word"
4xmlns:m="http://schemas.microsoft.com/office/2004/12/omml"
5xmlns="http://www.w3.org/TR/REC-html40" xmlns:ns0="http://macVmlSchemaUri">
6
7<head>
8<meta http-equiv=Content-Type content="text/html; charset=windows-1252">
9<meta name=ProgId content=Word.Document>
10<meta name=Generator content="Microsoft Word 15">
11<meta name=Originator content="Microsoft Word 15">
12<link rel=File-List href="ParametricFitting_files/filelist.xml">
13<link rel=Edit-Time-Data href="ParametricFitting_files/editdata.mso">
14<!--[if !mso]>
15<style>
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22 <o:DocumentProperties>
23  <o:Author>B Toby</o:Author>
24  <o:LastAuthor>Von Dreele</o:LastAuthor>
25  <o:Revision>3</o:Revision>
26  <o:TotalTime>986</o:TotalTime>
27  <o:Created>2014-07-22T21:21:00Z</o:Created>
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38 <o:OfficeDocumentSettings>
39  <o:AllowPNG/>
40 </o:OfficeDocumentSettings>
41</xml><![endif]-->
42<link rel=themeData href="ParametricFitting_files/themedata.thmx">
43<link rel=colorSchemeMapping
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66   <w:SnapToGridInCell/>
67   <w:WrapTextWithPunct/>
68   <w:UseAsianBreakRules/>
69   <w:DontGrowAutofit/>
70   <w:SplitPgBreakAndParaMark/>
71   <w:EnableOpenTypeKerning/>
72   <w:DontFlipMirrorIndents/>
73   <w:OverrideTableStyleHps/>
74   <w:UseFELayout/>
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156  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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161   UnhideWhenUsed="true" QFormat="true" Name="caption"/>
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166  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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171   Name="annotation reference"/>
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173   Name="line number"/>
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175   Name="page number"/>
176  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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184  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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198  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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200  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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202  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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214  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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216  <w:LsdException Locked="false" Priority="10" QFormat="true" Name="Title"/>
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219  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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227  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
228   Name="List Continue"/>
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251   Name="Body Text 2"/>
252  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
253   Name="Body Text 3"/>
254  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
255   Name="Body Text Indent 2"/>
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266  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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270  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
271   Name="E-mail Signature"/>
272  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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275   Name="HTML Bottom of Form"/>
276  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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278  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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282  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
283   Name="HTML Cite"/>
284  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
285   Name="HTML Code"/>
286  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
287   Name="HTML Definition"/>
288  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
289   Name="HTML Keyboard"/>
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297   Name="HTML Variable"/>
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303   Name="No List"/>
304  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
305   Name="Outline List 1"/>
306  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
307   Name="Outline List 2"/>
308  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
309   Name="Outline List 3"/>
310  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
311   Name="Table Simple 1"/>
312  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
313   Name="Table Simple 2"/>
314  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
315   Name="Table Simple 3"/>
316  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
317   Name="Table Classic 1"/>
318  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
319   Name="Table Classic 2"/>
320  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
321   Name="Table Classic 3"/>
322  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
323   Name="Table Classic 4"/>
324  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
325   Name="Table Colorful 1"/>
326  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
327   Name="Table Colorful 2"/>
328  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
329   Name="Table Colorful 3"/>
330  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
331   Name="Table Columns 1"/>
332  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
333   Name="Table Columns 2"/>
334  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
335   Name="Table Columns 3"/>
336  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
337   Name="Table Columns 4"/>
338  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
339   Name="Table Columns 5"/>
340  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
341   Name="Table Grid 1"/>
342  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
343   Name="Table Grid 2"/>
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345   Name="Table Grid 3"/>
346  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
347   Name="Table Grid 4"/>
348  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
349   Name="Table Grid 5"/>
350  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
351   Name="Table Grid 6"/>
352  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
353   Name="Table Grid 7"/>
354  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
355   Name="Table Grid 8"/>
356  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
357   Name="Table List 1"/>
358  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
359   Name="Table List 2"/>
360  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
361   Name="Table List 3"/>
362  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
363   Name="Table List 4"/>
364  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
365   Name="Table List 5"/>
366  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
367   Name="Table List 6"/>
368  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
369   Name="Table List 7"/>
370  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
371   Name="Table List 8"/>
372  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
373   Name="Table 3D effects 1"/>
374  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
375   Name="Table 3D effects 2"/>
376  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
377   Name="Table 3D effects 3"/>
378  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
379   Name="Table Contemporary"/>
380  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
381   Name="Table Elegant"/>
382  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
383   Name="Table Professional"/>
384  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
385   Name="Table Subtle 1"/>
386  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
387   Name="Table Subtle 2"/>
388  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
389   Name="Table Web 1"/>
390  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
391   Name="Table Web 2"/>
392  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
393   Name="Table Web 3"/>
394  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
395   Name="Balloon Text"/>
396  <w:LsdException Locked="false" Priority="59" Name="Table Grid"/>
397  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
398   Name="Table Theme"/>
399  <w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/>
400  <w:LsdException Locked="false" Priority="1" SemiHidden="true" QFormat="true"
401   Name="No Spacing"/>
402  <w:LsdException Locked="false" Priority="60" Name="Light Shading"/>
403  <w:LsdException Locked="false" Priority="61" Name="Light List"/>
404  <w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
405  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
406  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/>
407  <w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
408  <w:LsdException Locked="false" Priority="66" Name="Medium List 2"/>
409  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
410  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
411  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
412  <w:LsdException Locked="false" Priority="70" Name="Dark List"/>
413  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
414  <w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
415  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
416  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
417  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
418  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
419  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
420  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
421  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
422  <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
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424   Name="List Paragraph"/>
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427   Name="Intense Quote"/>
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430  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
431  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
432  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
433  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
434  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
435  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
436  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
437  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
438  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
439  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
440  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
441  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
442  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
443  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
444  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
445  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
446  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
447  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
448  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
449  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
450  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
451  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
452  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
453  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
454  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
455  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
456  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
457  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
458  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
459  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
460  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
461  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
462  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
463  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
464  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
465  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
466  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
467  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
468  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
469  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
470  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
471  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
472  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
473  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
474  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
475  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
476  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
477  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
478  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
479  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
480  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
481  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
482  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
483  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
484  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
485  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
486  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
487  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
488  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
489  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
490  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
491  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
492  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
493  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
494  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
495  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
496  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
497  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
498  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
499  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
500  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
501  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
502  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
503  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
504  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
505  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
506  <w:LsdException Locked="false" Priority="19" QFormat="true"
507   Name="Subtle Emphasis"/>
508  <w:LsdException Locked="false" Priority="21" QFormat="true"
509   Name="Intense Emphasis"/>
510  <w:LsdException Locked="false" Priority="31" QFormat="true"
511   Name="Subtle Reference"/>
512  <w:LsdException Locked="false" Priority="32" QFormat="true"
513   Name="Intense Reference"/>
514  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
515  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
516   UnhideWhenUsed="true" Name="Bibliography"/>
517  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
518   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
519  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
520  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
521  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
522  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
523  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
524  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
525  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
526  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
527  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
528  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
529  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
530  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
531  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
532  <w:LsdException Locked="false" Priority="46"
533   Name="Grid Table 1 Light Accent 1"/>
534  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
535  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
536  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
537  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
538  <w:LsdException Locked="false" Priority="51"
539   Name="Grid Table 6 Colorful Accent 1"/>
540  <w:LsdException Locked="false" Priority="52"
541   Name="Grid Table 7 Colorful Accent 1"/>
542  <w:LsdException Locked="false" Priority="46"
543   Name="Grid Table 1 Light Accent 2"/>
544  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
545  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
546  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
547  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
548  <w:LsdException Locked="false" Priority="51"
549   Name="Grid Table 6 Colorful Accent 2"/>
550  <w:LsdException Locked="false" Priority="52"
551   Name="Grid Table 7 Colorful Accent 2"/>
552  <w:LsdException Locked="false" Priority="46"
553   Name="Grid Table 1 Light Accent 3"/>
554  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
555  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
556  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
557  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
558  <w:LsdException Locked="false" Priority="51"
559   Name="Grid Table 6 Colorful Accent 3"/>
560  <w:LsdException Locked="false" Priority="52"
561   Name="Grid Table 7 Colorful Accent 3"/>
562  <w:LsdException Locked="false" Priority="46"
563   Name="Grid Table 1 Light Accent 4"/>
564  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
565  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
566  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
567  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
568  <w:LsdException Locked="false" Priority="51"
569   Name="Grid Table 6 Colorful Accent 4"/>
570  <w:LsdException Locked="false" Priority="52"
571   Name="Grid Table 7 Colorful Accent 4"/>
572  <w:LsdException Locked="false" Priority="46"
573   Name="Grid Table 1 Light Accent 5"/>
574  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
575  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
576  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
577  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
578  <w:LsdException Locked="false" Priority="51"
579   Name="Grid Table 6 Colorful Accent 5"/>
580  <w:LsdException Locked="false" Priority="52"
581   Name="Grid Table 7 Colorful Accent 5"/>
582  <w:LsdException Locked="false" Priority="46"
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584  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
585  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
586  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
587  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
588  <w:LsdException Locked="false" Priority="51"
589   Name="Grid Table 6 Colorful Accent 6"/>
590  <w:LsdException Locked="false" Priority="52"
591   Name="Grid Table 7 Colorful Accent 6"/>
592  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
593  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
594  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
595  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
596  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
597  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
598  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
599  <w:LsdException Locked="false" Priority="46"
600   Name="List Table 1 Light Accent 1"/>
601  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
602  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
603  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
604  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
605  <w:LsdException Locked="false" Priority="51"
606   Name="List Table 6 Colorful Accent 1"/>
607  <w:LsdException Locked="false" Priority="52"
608   Name="List Table 7 Colorful Accent 1"/>
609  <w:LsdException Locked="false" Priority="46"
610   Name="List Table 1 Light Accent 2"/>
611  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
612  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
613  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
614  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
615  <w:LsdException Locked="false" Priority="51"
616   Name="List Table 6 Colorful Accent 2"/>
617  <w:LsdException Locked="false" Priority="52"
618   Name="List Table 7 Colorful Accent 2"/>
619  <w:LsdException Locked="false" Priority="46"
620   Name="List Table 1 Light Accent 3"/>
621  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
622  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
623  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
624  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
625  <w:LsdException Locked="false" Priority="51"
626   Name="List Table 6 Colorful Accent 3"/>
627  <w:LsdException Locked="false" Priority="52"
628   Name="List Table 7 Colorful Accent 3"/>
629  <w:LsdException Locked="false" Priority="46"
630   Name="List Table 1 Light Accent 4"/>
631  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
632  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
633  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
634  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
635  <w:LsdException Locked="false" Priority="51"
636   Name="List Table 6 Colorful Accent 4"/>
637  <w:LsdException Locked="false" Priority="52"
638   Name="List Table 7 Colorful Accent 4"/>
639  <w:LsdException Locked="false" Priority="46"
640   Name="List Table 1 Light Accent 5"/>
641  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
642  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
643  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
644  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
645  <w:LsdException Locked="false" Priority="51"
646   Name="List Table 6 Colorful Accent 5"/>
647  <w:LsdException Locked="false" Priority="52"
648   Name="List Table 7 Colorful Accent 5"/>
649  <w:LsdException Locked="false" Priority="46"
650   Name="List Table 1 Light Accent 6"/>
651  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
652  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
653  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
654  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
655  <w:LsdException Locked="false" Priority="51"
656   Name="List Table 6 Colorful Accent 6"/>
657  <w:LsdException Locked="false" Priority="52"
658   Name="List Table 7 Colorful Accent 6"/>
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782        mso-style-priority:99;
783        color:purple;
784        mso-themecolor:followedhyperlink;
785        text-decoration:underline;
786        text-underline:single;}
787pre
788        {mso-style-noshow:yes;
789        mso-style-priority:99;
790        mso-style-link:"HTML Preformatted Char";
791        margin:0in;
792        margin-bottom:.0001pt;
793        mso-pagination:widow-orphan;
794        font-size:10.0pt;
795        font-family:"Courier New";
796        mso-fareast-font-family:"Times New Roman";
797        mso-fareast-theme-font:minor-fareast;}
798p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
799        {mso-style-noshow:yes;
800        mso-style-priority:99;
801        mso-style-link:"Balloon Text Char";
802        margin:0in;
803        margin-bottom:.0001pt;
804        mso-pagination:widow-orphan;
805        font-size:9.0pt;
806        font-family:"Lucida Grande";
807        mso-fareast-font-family:"Times New Roman";
808        mso-fareast-theme-font:minor-fareast;
809        mso-fareast-language:JA;}
810p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
811        {mso-style-priority:34;
812        mso-style-unhide:no;
813        mso-style-qformat:yes;
814        margin-top:0in;
815        margin-right:0in;
816        margin-bottom:0in;
817        margin-left:.5in;
818        margin-bottom:.0001pt;
819        mso-add-space:auto;
820        mso-pagination:widow-orphan;
821        font-size:12.0pt;
822        mso-bidi-font-size:10.0pt;
823        font-family:"Times New Roman",serif;
824        mso-fareast-font-family:"Times New Roman";
825        mso-fareast-theme-font:minor-fareast;
826        mso-bidi-font-family:"Times New Roman";
827        mso-bidi-theme-font:minor-bidi;
828        mso-fareast-language:JA;}
829p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
830        {mso-style-priority:34;
831        mso-style-unhide:no;
832        mso-style-qformat:yes;
833        mso-style-type:export-only;
834        margin-top:0in;
835        margin-right:0in;
836        margin-bottom:0in;
837        margin-left:.5in;
838        margin-bottom:.0001pt;
839        mso-add-space:auto;
840        mso-pagination:widow-orphan;
841        font-size:12.0pt;
842        mso-bidi-font-size:10.0pt;
843        font-family:"Times New Roman",serif;
844        mso-fareast-font-family:"Times New Roman";
845        mso-fareast-theme-font:minor-fareast;
846        mso-bidi-font-family:"Times New Roman";
847        mso-bidi-theme-font:minor-bidi;
848        mso-fareast-language:JA;}
849p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
850        {mso-style-priority:34;
851        mso-style-unhide:no;
852        mso-style-qformat:yes;
853        mso-style-type:export-only;
854        margin-top:0in;
855        margin-right:0in;
856        margin-bottom:0in;
857        margin-left:.5in;
858        margin-bottom:.0001pt;
859        mso-add-space:auto;
860        mso-pagination:widow-orphan;
861        font-size:12.0pt;
862        mso-bidi-font-size:10.0pt;
863        font-family:"Times New Roman",serif;
864        mso-fareast-font-family:"Times New Roman";
865        mso-fareast-theme-font:minor-fareast;
866        mso-bidi-font-family:"Times New Roman";
867        mso-bidi-theme-font:minor-bidi;
868        mso-fareast-language:JA;}
869p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
870        {mso-style-priority:34;
871        mso-style-unhide:no;
872        mso-style-qformat:yes;
873        mso-style-type:export-only;
874        margin-top:0in;
875        margin-right:0in;
876        margin-bottom:0in;
877        margin-left:.5in;
878        margin-bottom:.0001pt;
879        mso-add-space:auto;
880        mso-pagination:widow-orphan;
881        font-size:12.0pt;
882        mso-bidi-font-size:10.0pt;
883        font-family:"Times New Roman",serif;
884        mso-fareast-font-family:"Times New Roman";
885        mso-fareast-theme-font:minor-fareast;
886        mso-bidi-font-family:"Times New Roman";
887        mso-bidi-theme-font:minor-bidi;
888        mso-fareast-language:JA;}
889span.Heading1Char
890        {mso-style-name:"Heading 1 Char";
891        mso-style-priority:9;
892        mso-style-unhide:no;
893        mso-style-locked:yes;
894        mso-style-link:"Heading 1";
895        mso-ansi-font-size:18.0pt;
896        mso-bidi-font-size:16.0pt;
897        font-family:"Times New Roman",serif;
898        mso-ascii-font-family:"Times New Roman";
899        mso-fareast-font-family:"Times New Roman";
900        mso-fareast-theme-font:major-fareast;
901        mso-hansi-font-family:"Times New Roman";
902        mso-bidi-font-family:"Times New Roman";
903        mso-bidi-theme-font:major-bidi;
904        font-weight:bold;}
905span.Heading2Char
906        {mso-style-name:"Heading 2 Char";
907        mso-style-noshow:yes;
908        mso-style-priority:9;
909        mso-style-unhide:no;
910        mso-style-locked:yes;
911        mso-style-link:"Heading 2";
912        mso-ansi-font-size:13.0pt;
913        mso-bidi-font-size:13.0pt;
914        font-family:"Calibri",sans-serif;
915        mso-ascii-font-family:Calibri;
916        mso-ascii-theme-font:major-latin;
917        mso-fareast-font-family:"Times New Roman";
918        mso-fareast-theme-font:major-fareast;
919        mso-hansi-font-family:Calibri;
920        mso-hansi-theme-font:major-latin;
921        mso-bidi-font-family:"Times New Roman";
922        mso-bidi-theme-font:major-bidi;
923        color:#4F81BD;
924        mso-themecolor:accent1;
925        font-weight:bold;}
926span.HTMLPreformattedChar
927        {mso-style-name:"HTML Preformatted Char";
928        mso-style-noshow:yes;
929        mso-style-priority:99;
930        mso-style-unhide:no;
931        mso-style-locked:yes;
932        mso-style-link:"HTML Preformatted";
933        font-family:Consolas;
934        mso-ascii-font-family:Consolas;
935        mso-hansi-font-family:Consolas;
936        mso-bidi-font-family:Consolas;}
937span.BalloonTextChar
938        {mso-style-name:"Balloon Text Char";
939        mso-style-noshow:yes;
940        mso-style-priority:99;
941        mso-style-unhide:no;
942        mso-style-locked:yes;
943        mso-style-link:"Balloon Text";
944        mso-ansi-font-size:9.0pt;
945        mso-bidi-font-size:9.0pt;
946        font-family:"Lucida Grande";
947        mso-ascii-font-family:"Lucida Grande";
948        mso-hansi-font-family:"Lucida Grande";
949        mso-bidi-font-family:"Lucida Grande";}
950span.SpellE
951        {mso-style-name:"";
952        mso-spl-e:yes;}
953span.GramE
954        {mso-style-name:"";
955        mso-gram-e:yes;}
956.MsoChpDefault
957        {mso-style-type:export-only;
958        mso-default-props:yes;
959        font-size:10.0pt;
960        mso-ansi-font-size:10.0pt;
961        mso-bidi-font-size:10.0pt;
962        font-family:"Cambria",serif;
963        mso-ascii-font-family:Cambria;
964        mso-ascii-theme-font:minor-latin;
965        mso-fareast-font-family:"Times New Roman";
966        mso-fareast-theme-font:minor-fareast;
967        mso-hansi-font-family:Cambria;
968        mso-hansi-theme-font:minor-latin;
969        mso-bidi-font-family:"Times New Roman";
970        mso-bidi-theme-font:minor-bidi;
971        mso-fareast-language:JA;}
972@page WordSection1
973        {size:8.5in 11.0in;
974        margin:1.0in 1.25in 1.0in 1.25in;
975        mso-header-margin:.5in;
976        mso-footer-margin:.5in;
977        mso-paper-source:0;}
978div.WordSection1
979        {page:WordSection1;}
980 /* List Definitions */
981 @list l0
982        {mso-list-id:109671306;
983        mso-list-type:hybrid;
984        mso-list-template-ids:129770836 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
985@list l0:level1
986        {mso-level-tab-stop:none;
987        mso-level-number-position:left;
988        text-indent:-.25in;}
989@list l0:level2
990        {mso-level-number-format:alpha-lower;
991        mso-level-tab-stop:none;
992        mso-level-number-position:left;
993        text-indent:-.25in;}
994@list l0:level3
995        {mso-level-number-format:roman-lower;
996        mso-level-tab-stop:none;
997        mso-level-number-position:right;
998        text-indent:-9.0pt;}
999@list l0:level4
1000        {mso-level-tab-stop:none;
1001        mso-level-number-position:left;
1002        text-indent:-.25in;}
1003@list l0:level5
1004        {mso-level-number-format:alpha-lower;
1005        mso-level-tab-stop:none;
1006        mso-level-number-position:left;
1007        text-indent:-.25in;}
1008@list l0:level6
1009        {mso-level-number-format:roman-lower;
1010        mso-level-tab-stop:none;
1011        mso-level-number-position:right;
1012        text-indent:-9.0pt;}
1013@list l0:level7
1014        {mso-level-tab-stop:none;
1015        mso-level-number-position:left;
1016        text-indent:-.25in;}
1017@list l0:level8
1018        {mso-level-number-format:alpha-lower;
1019        mso-level-tab-stop:none;
1020        mso-level-number-position:left;
1021        text-indent:-.25in;}
1022@list l0:level9
1023        {mso-level-number-format:roman-lower;
1024        mso-level-tab-stop:none;
1025        mso-level-number-position:right;
1026        text-indent:-9.0pt;}
1027@list l1
1028        {mso-list-id:235746779;
1029        mso-list-type:hybrid;
1030        mso-list-template-ids:129770836 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
1031@list l1:level1
1032        {mso-level-tab-stop:none;
1033        mso-level-number-position:left;
1034        text-indent:-.25in;}
1035@list l1:level2
1036        {mso-level-number-format:alpha-lower;
1037        mso-level-tab-stop:none;
1038        mso-level-number-position:left;
1039        text-indent:-.25in;}
1040@list l1:level3
1041        {mso-level-number-format:roman-lower;
1042        mso-level-tab-stop:none;
1043        mso-level-number-position:right;
1044        text-indent:-9.0pt;}
1045@list l1:level4
1046        {mso-level-tab-stop:none;
1047        mso-level-number-position:left;
1048        text-indent:-.25in;}
1049@list l1:level5
1050        {mso-level-number-format:alpha-lower;
1051        mso-level-tab-stop:none;
1052        mso-level-number-position:left;
1053        text-indent:-.25in;}
1054@list l1:level6
1055        {mso-level-number-format:roman-lower;
1056        mso-level-tab-stop:none;
1057        mso-level-number-position:right;
1058        text-indent:-9.0pt;}
1059@list l1:level7
1060        {mso-level-tab-stop:none;
1061        mso-level-number-position:left;
1062        text-indent:-.25in;}
1063@list l1:level8
1064        {mso-level-number-format:alpha-lower;
1065        mso-level-tab-stop:none;
1066        mso-level-number-position:left;
1067        text-indent:-.25in;}
1068@list l1:level9
1069        {mso-level-number-format:roman-lower;
1070        mso-level-tab-stop:none;
1071        mso-level-number-position:right;
1072        text-indent:-9.0pt;}
1073@list l2
1074        {mso-list-id:584074573;
1075        mso-list-type:hybrid;
1076        mso-list-template-ids:-926633506 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
1077@list l2:level1
1078        {mso-level-tab-stop:none;
1079        mso-level-number-position:left;
1080        text-indent:-.25in;}
1081@list l2:level2
1082        {mso-level-number-format:alpha-lower;
1083        mso-level-tab-stop:none;
1084        mso-level-number-position:left;
1085        text-indent:-.25in;}
1086@list l2:level3
1087        {mso-level-number-format:roman-lower;
1088        mso-level-tab-stop:none;
1089        mso-level-number-position:right;
1090        text-indent:-9.0pt;}
1091@list l2:level4
1092        {mso-level-tab-stop:none;
1093        mso-level-number-position:left;
1094        text-indent:-.25in;}
1095@list l2:level5
1096        {mso-level-number-format:alpha-lower;
1097        mso-level-tab-stop:none;
1098        mso-level-number-position:left;
1099        text-indent:-.25in;}
1100@list l2:level6
1101        {mso-level-number-format:roman-lower;
1102        mso-level-tab-stop:none;
1103        mso-level-number-position:right;
1104        text-indent:-9.0pt;}
1105@list l2:level7
1106        {mso-level-tab-stop:none;
1107        mso-level-number-position:left;
1108        text-indent:-.25in;}
1109@list l2:level8
1110        {mso-level-number-format:alpha-lower;
1111        mso-level-tab-stop:none;
1112        mso-level-number-position:left;
1113        text-indent:-.25in;}
1114@list l2:level9
1115        {mso-level-number-format:roman-lower;
1116        mso-level-tab-stop:none;
1117        mso-level-number-position:right;
1118        text-indent:-9.0pt;}
1119@list l3
1120        {mso-list-id:845174183;
1121        mso-list-type:hybrid;
1122        mso-list-template-ids:129770836 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
1123@list l3:level1
1124        {mso-level-tab-stop:none;
1125        mso-level-number-position:left;
1126        text-indent:-.25in;}
1127@list l3:level2
1128        {mso-level-number-format:alpha-lower;
1129        mso-level-tab-stop:none;
1130        mso-level-number-position:left;
1131        text-indent:-.25in;}
1132@list l3:level3
1133        {mso-level-number-format:roman-lower;
1134        mso-level-tab-stop:none;
1135        mso-level-number-position:right;
1136        text-indent:-9.0pt;}
1137@list l3:level4
1138        {mso-level-tab-stop:none;
1139        mso-level-number-position:left;
1140        text-indent:-.25in;}
1141@list l3:level5
1142        {mso-level-number-format:alpha-lower;
1143        mso-level-tab-stop:none;
1144        mso-level-number-position:left;
1145        text-indent:-.25in;}
1146@list l3:level6
1147        {mso-level-number-format:roman-lower;
1148        mso-level-tab-stop:none;
1149        mso-level-number-position:right;
1150        text-indent:-9.0pt;}
1151@list l3:level7
1152        {mso-level-tab-stop:none;
1153        mso-level-number-position:left;
1154        text-indent:-.25in;}
1155@list l3:level8
1156        {mso-level-number-format:alpha-lower;
1157        mso-level-tab-stop:none;
1158        mso-level-number-position:left;
1159        text-indent:-.25in;}
1160@list l3:level9
1161        {mso-level-number-format:roman-lower;
1162        mso-level-tab-stop:none;
1163        mso-level-number-position:right;
1164        text-indent:-9.0pt;}
1165@list l4
1166        {mso-list-id:1447432924;
1167        mso-list-type:hybrid;
1168        mso-list-template-ids:2060980778 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
1169@list l4:level1
1170        {mso-level-tab-stop:none;
1171        mso-level-number-position:left;
1172        text-indent:-.25in;}
1173@list l4:level2
1174        {mso-level-number-format:alpha-lower;
1175        mso-level-tab-stop:none;
1176        mso-level-number-position:left;
1177        text-indent:-.25in;}
1178@list l4:level3
1179        {mso-level-number-format:roman-lower;
1180        mso-level-tab-stop:none;
1181        mso-level-number-position:right;
1182        text-indent:-9.0pt;}
1183@list l4:level4
1184        {mso-level-tab-stop:none;
1185        mso-level-number-position:left;
1186        text-indent:-.25in;}
1187@list l4:level5
1188        {mso-level-number-format:alpha-lower;
1189        mso-level-tab-stop:none;
1190        mso-level-number-position:left;
1191        text-indent:-.25in;}
1192@list l4:level6
1193        {mso-level-number-format:roman-lower;
1194        mso-level-tab-stop:none;
1195        mso-level-number-position:right;
1196        text-indent:-9.0pt;}
1197@list l4:level7
1198        {mso-level-tab-stop:none;
1199        mso-level-number-position:left;
1200        text-indent:-.25in;}
1201@list l4:level8
1202        {mso-level-number-format:alpha-lower;
1203        mso-level-tab-stop:none;
1204        mso-level-number-position:left;
1205        text-indent:-.25in;}
1206@list l4:level9
1207        {mso-level-number-format:roman-lower;
1208        mso-level-tab-stop:none;
1209        mso-level-number-position:right;
1210        text-indent:-9.0pt;}
1211ol
1212        {margin-bottom:0in;}
1213ul
1214        {margin-bottom:0in;}
1215-->
1216</style>
1217<!--[if gte mso 10]>
1218<style>
1219 /* Style Definitions */
1220 table.MsoNormalTable
1221        {mso-style-name:"Table Normal";
1222        mso-tstyle-rowband-size:0;
1223        mso-tstyle-colband-size:0;
1224        mso-style-noshow:yes;
1225        mso-style-priority:99;
1226        mso-style-parent:"";
1227        mso-padding-alt:0in 5.4pt 0in 5.4pt;
1228        mso-para-margin:0in;
1229        mso-para-margin-bottom:.0001pt;
1230        mso-pagination:widow-orphan;
1231        font-size:10.0pt;
1232        font-family:"Cambria",serif;
1233        mso-ascii-font-family:Cambria;
1234        mso-ascii-theme-font:minor-latin;
1235        mso-hansi-font-family:Cambria;
1236        mso-hansi-theme-font:minor-latin;
1237        mso-fareast-language:JA;}
1238</style>
1239<![endif]-->
1240<meta name=Title content="">
1241<meta name=Keywords content="">
1242<!--[if gte mso 9]><xml>
1243 <o:shapedefaults v:ext="edit" spidmax="1032"/>
1244</xml><![endif]--><!--[if gte mso 9]><xml>
1245 <o:shapelayout v:ext="edit">
1246  <o:idmap v:ext="edit" data="1"/>
1247 </o:shapelayout></xml><![endif]-->
1248</head>
1249
1250<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1251
1252<div class=WordSection1>
1253
1254<h1>Parametric Fitting and Pseudo Variables for Sequential Fits</h1>
1255
1256<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1257
1258<p class=MsoNormal>Once a sequential fit has been performed, any function of
1259the fit parameters from the fit and <i style='mso-bidi-font-style:normal'>their
1260estimated uncertainty</i> (<span class=SpellE>s.u</span>.) can be computed by
1261defining one or more &quot;pseudo-variables&quot;. Note that the covariance
1262matrix from the fit is used to provide appropriate treatment of the correlation
1263in parameters with respect to uncertainty estimation.<span
1264style='mso-spacerun:yes'>  </span>In addition, parametric equations in terms of
1265sample parameters such as temperature and pressure, etc. can be fit to either
1266the parameters from the fit or the pseudo-variables. </p>
1267
1268<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1269
1270<p class=MsoNormal>This tutorial assumes that the steps in the <b
1271style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1272mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin;mso-bidi-font-family:
1273"Times New Roman"'>Sequential refinement of multiple datasets</span></b><span
1274style='mso-bidi-font-family:"Times New Roman"'> tutorial have already been
1275performed. </span>If you have not done so already, start GSAS-II. Some of the
1276pictures in this tutorial are from a Mac OSX machine; these illustrate the
1277differences in menu location from Windows/Linux machines.</p>
1278
1279<h1>Step 1. Open the previous Sequential Fit</h1>
1280
1281<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1282
1283<p class=MsoListParagraphCxSpFirst style='margin-bottom:6.0pt;mso-add-space:
1284auto;text-indent:-.25in;mso-list:l4 level1 lfo2'><![if !supportLists]><span
1285style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1286style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1287</span></span></span><![endif]>Select the<b style='mso-bidi-font-weight:normal'>
1288</b><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1289mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>File/Open
1290Project</span></b> menu item to load file named <span class=SpellE><b
1291style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1292mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>SeqTut.gpx</span></b></span>
1293you created in the previous tutorial.</p>
1294
1295<p class=MsoListParagraphCxSpMiddle style='margin-bottom:6.0pt;mso-add-space:
1296auto;text-indent:-.25in;mso-list:l4 level1 lfo2'><![if !supportLists]><span
1297style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1298style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1299</span></span></span><![endif]>Select the <b style='mso-bidi-font-weight:normal'><span
1300style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1301mso-hansi-theme-font:major-latin'>Sequential results</span></b> item in the
1302data tree. The sequential refinement results data table is displayed, as below.
1303</p>
1304
1305<p class=MsoListParagraphCxSpLast style='margin-bottom:6.0pt;mso-add-space:
1306auto'><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
1307 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
1308 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1309 <v:stroke joinstyle="miter"/>
1310 <v:formulas>
1311  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
1312  <v:f eqn="sum @0 1 0"/>
1313  <v:f eqn="sum 0 0 @1"/>
1314  <v:f eqn="prod @2 1 2"/>
1315  <v:f eqn="prod @3 21600 pixelWidth"/>
1316  <v:f eqn="prod @3 21600 pixelHeight"/>
1317  <v:f eqn="sum @0 0 1"/>
1318  <v:f eqn="prod @6 1 2"/>
1319  <v:f eqn="prod @7 21600 pixelWidth"/>
1320  <v:f eqn="sum @8 21600 0"/>
1321  <v:f eqn="prod @7 21600 pixelHeight"/>
1322  <v:f eqn="sum @10 21600 0"/>
1323 </v:formulas>
1324 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1325 <o:lock v:ext="edit" aspectratio="t"/>
1326</v:shapetype><v:shape id="Picture_x0020_36" o:spid="_x0000_i1053" type="#_x0000_t75"
1327 style='width:525pt;height:262.5pt;visibility:visible;mso-wrap-style:square'>
1328 <v:imagedata src="ParametricFitting_files/image001.png" o:title=""/>
1329</v:shape><![endif]--><![if !vml]><img width=700 height=350
1330src="ParametricFitting_files/image002.png" v:shapes="Picture_x0020_36"><![endif]></span></p>
1331
1332<h1>Step 2. Create a Pseudo Variable</h1>
1333
1334<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1335
1336<p class=MsoNormal>Pseudo-variables allow computation of an arbitrarily defined
1337function of combinations of the variables that are displayed in the sequential
1338refinement table. Any valid Python language expression can be used to define
1339this. While one can plot <i style='mso-bidi-font-style:normal'>a</i>, <i
1340style='mso-bidi-font-style:normal'>b</i> and <i style='mso-bidi-font-style:
1341normal'>c</i> axis lengths by clicking on the appropriate column of the table,
1342to compare them one might want to scale them. Alternately, as will be done
1343here, we will plot the ratio of <i style='mso-bidi-font-style:normal'>b</i> and
1344<i style='mso-bidi-font-style:normal'>c</i>.</p>
1345
1346<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1347
1348<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span
1349style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1350style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1351</span></span></span><![endif]>Click on the <b style='mso-bidi-font-weight:
1352normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1353major-latin;mso-hansi-theme-font:major-latin'>Pseudo <span class=SpellE>Vars</span>/Add</span></b>
1354menu item to create a new pseudo-variable.</p>
1355
1356<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1357
1358<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1359mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_2" o:spid="_x0000_i1052"
1360 type="#_x0000_t75" style='width:159pt;height:45.75pt;visibility:visible;
1361 mso-wrap-style:square'>
1362 <v:imagedata src="ParametricFitting_files/image003.png" o:title=""/>
1363</v:shape><![endif]--><![if !vml]><img width=212 height=61
1364src="ParametricFitting_files/image004.jpg" v:shapes="Picture_x0020_2"><![endif]></span></p>
1365
1366<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1367
1368<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span
1369style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1370style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1371</span></span></span><![endif]>A window opens to define a formula</p>
1372
1373<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1374
1375<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1376mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3" o:spid="_x0000_i1051"
1377 type="#_x0000_t75" style='width:309.75pt;height:152.25pt;visibility:visible;
1378 mso-wrap-style:square'>
1379 <v:imagedata src="ParametricFitting_files/image005.png" o:title="" croptop="4214f"
1380  cropbottom="8982f" cropleft="3852f" cropright="3654f"/>
1381</v:shape><![endif]--><![if !vml]><img width=413 height=203
1382src="ParametricFitting_files/image006.png" v:shapes="Picture_x0020_3"><![endif]></span></p>
1383
1384<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1385
1386<p class=MsoListParagraphCxSpMiddle><!--[if gte vml 1]><v:shape id="Picture_x0020_4"
1387 o:spid="_x0000_s1031" type="#_x0000_t75" style='position:absolute;left:0;
1388 text-align:left;margin-left:178.3pt;margin-top:846.2pt;width:229.5pt;height:86.5pt;
1389 z-index:251658240;visibility:visible;mso-wrap-style:square;
1390 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1391 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1392 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1393 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1394 mso-position-vertical-relative:margin;mso-width-percent:0;
1395 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
1396 <v:imagedata src="ParametricFitting_files/image007.png" o:title=""/>
1397 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1398</v:shape><![endif]--><![if !vml]><img width=306 height=115
1399src="ParametricFitting_files/image008.jpg" align=right hspace=12 v:shapes="Picture_x0020_4"><![endif]>In
1400this window, type a Python expression<b style='mso-bidi-font-weight:normal'>, </b><span
1401style='mso-bidi-font-family:"Times New Roman"'>&quot;</span><b
1402style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1403mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin;mso-bidi-font-family:
1404"Times New Roman"'>b/c</span></b><span style='mso-bidi-font-family:"Times New Roman"'>&quot;,</span>
1405but note that the variables <b style='mso-bidi-font-weight:normal'><span
1406style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1407mso-hansi-theme-font:major-latin'>c</span></b> and <b style='mso-bidi-font-weight:
1408normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1409major-latin;mso-hansi-theme-font:major-latin'>b</span></b> here are arbitrary
1410labels. After entering the formula, press the <b style='mso-bidi-font-weight:
1411normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1412major-latin;mso-hansi-theme-font:major-latin'>Validate</span></b> button or
1413wait a few seconds and the validation will be tested automatically. Note that
1414if you pause too long, while typing, an error message may be displayed as the
1415incomplete formula is found to be invalid. If so, make corrections or keep
1416typing until the entire expression is entered.<span style='mso-spacerun:yes'> 
1417</span>The error message will sometimes show where error is encountered, though
1418not in this case. </p>
1419
1420<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1421
1422<p class=MsoListParagraphCxSpMiddle>When the expression is complete, a new
1423table appears where the arbitrary <b style='mso-bidi-font-weight:normal'><span
1424style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1425mso-hansi-theme-font:major-latin'>c</span></b> and <b style='mso-bidi-font-weight:
1426normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1427major-latin;mso-hansi-theme-font:major-latin'>b</span></b> labels will be
1428assigned.</p>
1429
1430<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1431
1432<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1433mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5" o:spid="_x0000_i1050"
1434 type="#_x0000_t75" style='width:309.75pt;height:152.25pt;visibility:visible;
1435 mso-wrap-style:square'>
1436 <v:imagedata src="ParametricFitting_files/image009.png" o:title="" croptop="4435f"
1437  cropbottom="8537f" cropleft="3852f" cropright="3650f"/>
1438</v:shape><![endif]--><![if !vml]><img width=413 height=203
1439src="ParametricFitting_files/image010.png" v:shapes="Picture_x0020_5"><![endif]></span></p>
1440
1441<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1442
1443<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span
1444style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1445style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1446</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_6"
1447 o:spid="_x0000_s1030" type="#_x0000_t75" style='position:absolute;left:0;
1448 text-align:left;margin-left:37.3pt;margin-top:1143.2pt;width:88.5pt;height:65.5pt;
1449 z-index:251659264;visibility:visible;mso-wrap-style:square;
1450 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1451 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1452 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1453 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1454 mso-position-vertical-relative:margin;mso-width-percent:0;
1455 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
1456 <v:imagedata src="ParametricFitting_files/image011.png" o:title=""/>
1457 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1458</v:shape><![endif]--><![if !vml]><img width=118 height=87
1459src="ParametricFitting_files/image012.jpg" align=right hspace=12 v:shapes="Picture_x0020_6"><![endif]>Assign
1460the label for the numerator by clicking on the menu button next to label <b
1461style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1462mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>;
1463this will bring up a list of variable types, from this select <b
1464style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1465mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Phase</span></b>
1466to bring up a list of phase variables, from that list select variable <b
1467style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1468mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>0::b</span></b>,
1469which is the <i style='mso-bidi-font-style:normal'>b</i> lattice parameter for
1470phase 0 (CuCr<sub>2</sub>O<sub>4</sub>). Repeat this process to select assign
1471to label <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1472mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>c</span></b>
1473variable <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1474mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>0::b</span></b>.</p>
1475
1476<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1477
1478<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1479mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8" o:spid="_x0000_i1049"
1480 type="#_x0000_t75" style='width:315.75pt;height:129pt;visibility:visible;
1481 mso-wrap-style:square'>
1482 <v:imagedata src="ParametricFitting_files/image013.png" o:title="" croptop="4597f"
1483  cropbottom="9873f" cropleft="3348f" cropright="3506f"/>
1484</v:shape><![endif]--><![if !vml]><img width=421 height=172
1485src="ParametricFitting_files/image014.png" v:shapes="Picture_x0020_8"><![endif]></span></p>
1486
1487<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1488
1489<p class=MsoListParagraphCxSpMiddle>As each variable is set, the window shows
1490the value for each variable from the first refinement and when the expression
1491can be evaluated, the value for the expression, evaluated for that first
1492refinement. Only when the expression can be evaluated can the <b
1493style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1494mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>OK</span></b>
1495button be pressed. </p>
1496
1497<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1498
1499<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1500mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9" o:spid="_x0000_i1048"
1501 type="#_x0000_t75" style='width:314.25pt;height:153.75pt;visibility:visible;
1502 mso-wrap-style:square'>
1503 <v:imagedata src="ParametricFitting_files/image015.png" o:title="" croptop="3770f"
1504  cropbottom="8549f" cropleft="3371f" cropright="3424f"/>
1505</v:shape><![endif]--><![if !vml]><img width=419 height=205
1506src="ParametricFitting_files/image016.png" v:shapes="Picture_x0020_9"><![endif]></span></p>
1507
1508<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1509
1510<p class=MsoListParagraphCxSpMiddle>Press<b style='mso-bidi-font-weight:normal'>
1511</b><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1512mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>OK</span></b>
1513to close the window and add the pseudo-variable. Note that a new column appears
1514at the end of the sequential refinement data table. </p>
1515
1516<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1517
1518<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1519mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10" o:spid="_x0000_i1047"
1520 type="#_x0000_t75" style='width:354pt;height:180.75pt;visibility:visible;
1521 mso-wrap-style:square'>
1522 <v:imagedata src="ParametricFitting_files/image017.png" o:title=""/>
1523</v:shape><![endif]--><![if !vml]><img width=472 height=241
1524src="ParametricFitting_files/image018.jpg" v:shapes="Picture_x0020_10"><![endif]></span></p>
1525
1526<p class=MsoListParagraphCxSpMiddle><!--[if gte vml 1]><v:shape id="Picture_x0020_11"
1527 o:spid="_x0000_s1029" type="#_x0000_t75" style='position:absolute;left:0;
1528 text-align:left;margin-left:42.3pt;margin-top:666.2pt;width:93.5pt;height:39pt;
1529 z-index:251660288;visibility:visible;mso-wrap-style:square;
1530 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1531 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1532 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1533 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1534 mso-position-vertical-relative:margin;mso-width-percent:0;
1535 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
1536 <v:imagedata src="ParametricFitting_files/image019.png" o:title=""/>
1537 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1538</v:shape><![endif]--><![if !vml]><img width=125 height=52
1539src="ParametricFitting_files/image020.jpg" align=right hspace=12 v:shapes="Picture_x0020_11"><![endif]>Also
1540note that positioning the mouse above any cell in the table and waiting for a
1541few seconds causes the <span class=SpellE>s.u</span>. to be shown as a tooltip.
1542</p>
1543
1544<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1545
1546<p class=MsoListParagraphCxSpMiddle>Double clicking on the <b style='mso-bidi-font-weight:
1547normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1548major-latin;mso-hansi-theme-font:major-latin'>b/c</span></b> column will cause
1549the pseudo-variable to be plotted:</p>
1550
1551<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1552
1553<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1554mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12" o:spid="_x0000_i1046"
1555 type="#_x0000_t75" style='width:351.75pt;height:303pt;visibility:visible;
1556 mso-wrap-style:square'>
1557 <v:imagedata src="ParametricFitting_files/image021.png" o:title=""/>
1558</v:shape><![endif]--><![if !vml]><img width=469 height=404
1559src="ParametricFitting_files/image022.png" v:shapes="Picture_x0020_12"><![endif]></span></p>
1560
1561<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1562
1563<p class=MsoListParagraphCxSpMiddle>Press the &quot;<b style='mso-bidi-font-weight:
1564normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1565major-latin;mso-hansi-theme-font:major-latin'>s</span></b>&quot; key inside the
1566plot to select<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:
1567normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1568major-latin;mso-hansi-theme-font:major-latin'>Temperature</span></b> as the
1569x-axis. </p>
1570
1571<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1572
1573<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1574mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13" o:spid="_x0000_i1045"
1575 type="#_x0000_t75" style='width:162.75pt;height:156pt;visibility:visible;
1576 mso-wrap-style:square'>
1577 <v:imagedata src="ParametricFitting_files/image023.png" o:title="" croptop="4105f"
1578  cropbottom="8920f" cropleft="6109f" cropright="5911f"/>
1579</v:shape><![endif]--><![if !vml]><img width=217 height=208
1580src="ParametricFitting_files/image024.png" v:shapes="Picture_x0020_13"><![endif]></span></p>
1581
1582<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1583
1584<p class=MsoListParagraphCxSpMiddle>The plot will then appear as below:</p>
1585
1586<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1587
1588<p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US;
1589mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14" o:spid="_x0000_i1044"
1590 type="#_x0000_t75" style='width:353.25pt;height:303.75pt;visibility:visible;
1591 mso-wrap-style:square'>
1592 <v:imagedata src="ParametricFitting_files/image025.png" o:title=""/>
1593</v:shape><![endif]--><![if !vml]><img width=471 height=405
1594src="ParametricFitting_files/image026.jpg" v:shapes="Picture_x0020_14"><![endif]></span></p>
1595
1596<h1>Step 3: Fitting a simple parametric equation to the unit cell volume</h1>
1597
1598<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1599
1600<p class=MsoNormal>In the next few steps we will fit increasingly sophisticated
1601equations of state to different parameters. As a simple example, we can
1602double-click on<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:
1603normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1604major-latin;mso-hansi-theme-font:major-latin'>0::Vol</span></b>, to plot the
1605unit volume for the first phase vs. T, and fit this to a straight line.<span
1606style='mso-spacerun:yes'>  </span></p>
1607
1608<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1609
1610<p class=MsoListParagraphCxSpFirst><span style='mso-fareast-language:EN-US;
1611mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15" o:spid="_x0000_i1043"
1612 type="#_x0000_t75" style='width:356.25pt;height:305.25pt;visibility:visible;
1613 mso-wrap-style:square'>
1614 <v:imagedata src="ParametricFitting_files/image027.png" o:title=""/>
1615</v:shape><![endif]--><![if !vml]><img width=475 height=407
1616src="ParametricFitting_files/image028.jpg" v:shapes="Picture_x0020_15"><![endif]></span></p>
1617
1618<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1619style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1620style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1621</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_16"
1622 o:spid="_x0000_s1028" type="#_x0000_t75" style='position:absolute;left:0;
1623 text-align:left;margin-left:21.8pt;margin-top:891.2pt;width:73pt;height:53pt;
1624 z-index:251661312;visibility:visible;mso-wrap-style:square;
1625 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1626 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1627 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1628 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1629 mso-position-vertical-relative:margin;mso-width-percent:0;
1630 mso-height-percent:0;mso-width-relative:margin;mso-height-relative:margin'>
1631 <v:imagedata src="ParametricFitting_files/image029.png" o:title=""/>
1632 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1633</v:shape><![endif]--><![if !vml]><img width=97 height=71
1634src="ParametricFitting_files/image030.jpg" align=right hspace=12 v:shapes="Picture_x0020_16"><![endif]>Click
1635on the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1636mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Parametric
1637Fit/Add</span></b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1638major-latin;mso-hansi-theme-font:major-latin'> <b style='mso-bidi-font-weight:
1639normal'>equation</b></span> menu item, which opens a window similar to what was
1640used before to create a pseudo-variable, except that here an equation is
1641defined.<span style='mso-spacerun:yes'>  </span></p>
1642
1643<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1644
1645<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1646mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_17" o:spid="_x0000_i1042"
1647 type="#_x0000_t75" style='width:311.25pt;height:152.25pt;visibility:visible;
1648 mso-wrap-style:square'>
1649 <v:imagedata src="ParametricFitting_files/image031.png" o:title="" croptop="4213f"
1650  cropbottom="8982f" cropleft="3490f" cropright="3653f"/>
1651</v:shape><![endif]--><![if !vml]><img width=415 height=203
1652src="ParametricFitting_files/image032.png" v:shapes="Picture_x0020_17"><![endif]></span></p>
1653
1654<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
1655
1656<p class=MsoNormal>We will want to fit the unit cell volume to an equation of
1657form <i style='mso-bidi-font-style:normal'>y = <span class=SpellE>mx+b</span></i>,
1658where y will be the volume and x temperature and m and b will be best fit. </p>
1659
1660<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><o:p>&nbsp;</o:p></b></p>
1661
1662<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><b
1663style='mso-bidi-font-weight:normal'><span style='mso-fareast-font-family:"Times New Roman";
1664mso-bidi-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
1665style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span></b><![endif]>Click
1666the<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:
1667normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1668major-latin;mso-hansi-theme-font:major-latin'>&#8597; </span></b>button to
1669select a dependent variable for &quot;y&quot;. From the phase list, select the
1670unit cell volume for the CuCr<sub>2</sub>O<sub>4</sub> phase, select<b
1671style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
1672style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1673mso-hansi-theme-font:major-latin'>0::Vol</span></b> and then press<b
1674style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
1675style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1676mso-hansi-theme-font:major-latin'>OK</span>.<o:p></o:p></b></p>
1677
1678<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1679
1680<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1681mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_19" o:spid="_x0000_i1041"
1682 type="#_x0000_t75" style='width:314.25pt;height:132pt;visibility:visible;
1683 mso-wrap-style:square'>
1684 <v:imagedata src="ParametricFitting_files/image033.png" o:title="" croptop="3830f"
1685  cropbottom="9359f" cropleft="3705f" cropright="3502f"/>
1686</v:shape><![endif]--><![if !vml]><img width=419 height=176
1687src="ParametricFitting_files/image034.png" v:shapes="Picture_x0020_19"><![endif]></span></p>
1688
1689<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1690mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20" o:spid="_x0000_i1040"
1691 type="#_x0000_t75" style='width:311.25pt;height:155.25pt;visibility:visible;
1692 mso-wrap-style:square'>
1693 <v:imagedata src="ParametricFitting_files/image035.png" o:title="" croptop="3548f"
1694  cropbottom="8549f" cropleft="3611f" cropright="3665f"/>
1695</v:shape><![endif]--><![if !vml]><img width=415 height=207
1696src="ParametricFitting_files/image036.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
1697
1698<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1699
1700<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1701style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1702style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1703</span></span></span><![endif]>Now we enter the equation using Python syntax,
1704which is simply &quot;<b style='mso-bidi-font-weight:normal'><span
1705style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1706mso-hansi-theme-font:major-latin'>m*x + b</span></b>&quot;, note that the use
1707of spaces and the choice of labels is arbitrary. If one were to accidentally
1708leave out the &quot;<span style='font-family:Courier'>*</span>&quot; and typed
1709&quot;<span style='font-family:Courier'>mx</span>&quot; then that would be
1710considered a label, if &quot;<span style='font-family:Courier'>m x</span>&quot;
1711were typed, an error message would be displayed. </p>
1712
1713<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1714
1715<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1716mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21" o:spid="_x0000_i1039"
1717 type="#_x0000_t75" style='width:315.75pt;height:155.25pt;visibility:visible;
1718 mso-wrap-style:square'>
1719 <v:imagedata src="ParametricFitting_files/image037.png" o:title="" croptop="3326f"
1720  cropbottom="8766f" cropleft="3010f" cropright="3419f"/>
1721</v:shape><![endif]--><![if !vml]><img width=421 height=207
1722src="ParametricFitting_files/image038.png" v:shapes="Picture_x0020_21"><![endif]></span></p>
1723
1724<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1725
1726<p class=MsoListParagraphCxSpMiddle>Then press <b style='mso-bidi-font-weight:
1727normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1728major-latin;mso-hansi-theme-font:major-latin'>Validate</span></b> or wait a few
1729seconds and a window changes, as above, allowing assignment of the three new
1730labels (<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1731mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b>,
1732<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1733mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x</span></b>,
1734and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1735mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>).
1736</p>
1737
1738<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1739
1740<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1741style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1742style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1743</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_22"
1744 o:spid="_x0000_s1027" type="#_x0000_t75" style='position:absolute;left:0;
1745 text-align:left;margin-left:43.8pt;margin-top:603.2pt;width:95pt;height:35pt;
1746 z-index:251662336;visibility:visible;mso-wrap-style:square;
1747 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1748 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1749 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1750 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1751 mso-position-vertical-relative:margin;mso-width-percent:0;
1752 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
1753 <v:imagedata src="ParametricFitting_files/image039.png" o:title=""/>
1754 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1755</v:shape><![endif]--><![if !vml]><img width=127 height=47
1756src="ParametricFitting_files/image040.jpg" align=right hspace=12 v:shapes="Picture_x0020_22"><![endif]>Assign
1757<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1758mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>
1759and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1760mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b>
1761as refinable “free” parameters: Click on the <b style='mso-bidi-font-weight:
1762normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1763major-latin;mso-hansi-theme-font:major-latin'>&#8597;</span></b><span
1764style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1765mso-hansi-theme-font:major-latin'> </span>button next to b and select<b
1766style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
1767style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1768mso-hansi-theme-font:major-latin'>Free</span></b>. Then repeat this <span
1769class=SpellE>for<b style='mso-bidi-font-weight:normal'> </b><b
1770style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1771mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b></span>.
1772</p>
1773
1774<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1775mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_23" o:spid="_x0000_i1038"
1776 type="#_x0000_t75" style='width:314.25pt;height:153pt;visibility:visible;
1777 mso-wrap-style:square'>
1778 <v:imagedata src="ParametricFitting_files/image041.png" o:title="" croptop="3992f"
1779  cropbottom="8541f" cropleft="3250f" cropright="3415f"/>
1780</v:shape><![endif]--><![if !vml]><img width=419 height=204
1781src="ParametricFitting_files/image042.png" v:shapes="Picture_x0020_23"><![endif]></span></p>
1782
1783<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1784
1785<p class=MsoListParagraphCxSpMiddle>It is not necessary to change the default
1786variable names, the initial values, or the refine flag. </p>
1787
1788<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1789
1790<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1791style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1792style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1793</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_24"
1794 o:spid="_x0000_s1026" type="#_x0000_t75" style='position:absolute;left:0;
1795 text-align:left;margin-left:24.3pt;margin-top:837.2pt;width:75.5pt;height:26pt;
1796 z-index:251663360;visibility:visible;mso-wrap-style:square;
1797 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1798 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1799 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1800 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1801 mso-position-vertical-relative:margin;mso-width-percent:0;
1802 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
1803 <v:imagedata src="ParametricFitting_files/image043.png" o:title=""/>
1804 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1805</v:shape><![endif]--><![if !vml]><img width=101 height=35
1806src="ParametricFitting_files/image044.jpg" align=right hspace=12 v:shapes="Picture_x0020_24"><![endif]>To
1807set <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1808mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x</span></b>
1809as the temperature, click on the <b style='mso-bidi-font-weight:normal'><span
1810style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1811mso-hansi-theme-font:major-latin'>&#8597;</span></b><span style='font-family:
1812"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
1813major-latin'> </span>button next to <b style='mso-bidi-font-weight:normal'><span
1814style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1815mso-hansi-theme-font:major-latin'>x</span></b>, select<b style='mso-bidi-font-weight:
1816normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family:
1817"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
1818major-latin'>Global</span>,</b> and then select<b style='mso-bidi-font-weight:
1819normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family:
1820"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
1821major-latin'>Temperature</span></b> from the list and click on<b
1822style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
1823style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1824mso-hansi-theme-font:major-latin'>OK</span></b>.</p>
1825
1826<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1827
1828<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span
1829style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1830 id="Picture_x0020_25" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:245.25pt;
1831 height:108.75pt;visibility:visible;mso-wrap-style:square'>
1832 <v:imagedata src="ParametricFitting_files/image045.png" o:title="" croptop="5483f"
1833  cropbottom="10984f" cropleft="4191f" cropright="4159f"/>
1834</v:shape><![endif]--><![if !vml]><img width=327 height=145
1835src="ParametricFitting_files/image046.png" v:shapes="Picture_x0020_25"><![endif]></span></p>
1836
1837<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1838
1839<p class=MsoListParagraphCxSpMiddle>The window then changes, showing the values
1840of the dependent variable and the expression for the first refinement, as
1841below. <span style='mso-spacerun:yes'> </span>Optionally, the values for <b
1842style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1843mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b>
1844and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1845mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>
1846could be changed manually and the displayed value will be updated when <b
1847style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1848mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Validate</span></b>
1849is pressed or after a short delay.</p>
1850
1851<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1852
1853<p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US;
1854mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26" o:spid="_x0000_i1036"
1855 type="#_x0000_t75" style='width:314.25pt;height:153pt;visibility:visible;
1856 mso-wrap-style:square'>
1857 <v:imagedata src="ParametricFitting_files/image047.png" o:title="" croptop="3992f"
1858  cropbottom="8541f" cropleft="3490f" cropright="3294f"/>
1859</v:shape><![endif]--><![if !vml]><img width=419 height=204
1860src="ParametricFitting_files/image048.png" v:shapes="Picture_x0020_26"><![endif]></span></p>
1861
1862<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1863
1864<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1865style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1866style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1867</span></span></span><![endif]>Press the <b style='mso-bidi-font-weight:normal'><span
1868style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1869mso-hansi-theme-font:major-latin'>OK</span></b> button to save this parametric
1870fit. The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1871mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>
1872and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1873mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b>
1874values are then refined and the console shows the results:</p>
1875
1876<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1877style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1878style='mso-list:Ignore'>7.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1879</span></span></span><![endif]><o:p>&nbsp;</o:p></p>
1880
1881<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1882auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'>Fit
1883Results<o:p></o:p></span></b></p>
1884
1885<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1886auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span
1887style='mso-spacerun:yes'>  </span>0::Vol = m*x +b<o:p></o:p></span></b></p>
1888
1889<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1890auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span
1891style='mso-spacerun:yes'>   </span><span class=GramE>x<span
1892style='mso-spacerun:yes'>  </span>=</span> Temperature<o:p></o:p></span></b></p>
1893
1894<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1895auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span
1896style='mso-spacerun:yes'>   </span><span class=GramE>b<span
1897style='mso-spacerun:yes'>  </span>=</span> 561.7722(26)<o:p></o:p></span></b></p>
1898
1899<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1900auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span
1901style='mso-spacerun:yes'>   </span><span class=GramE>m<span
1902style='mso-spacerun:yes'>  </span>=</span> 0.014833(14)<o:p></o:p></span></b></p>
1903
1904<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1905auto'><span style='font-family:Courier'><o:p>&nbsp;</o:p></span></p>
1906
1907<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1908mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27" o:spid="_x0000_i1035"
1909 type="#_x0000_t75" style='width:350.25pt;height:302.25pt;visibility:visible;
1910 mso-wrap-style:square'>
1911 <v:imagedata src="ParametricFitting_files/image049.png" o:title=""/>
1912</v:shape><![endif]--><![if !vml]><img width=467 height=403
1913src="ParametricFitting_files/image050.jpg" v:shapes="Picture_x0020_27"><![endif]></span><span
1914style='font-family:"Cambria",serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1915minor-latin'><o:p></o:p></span></p>
1916
1917<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1918
1919<p class=MsoListParagraphCxSpMiddle>Also, the plot shows the actual values and
1920the fit. Note that while the values are close to a straight line, the
1921deviations are huge compared to the estimated uncertainty values for the unit
1922cell volume (shown as very small error bars, unless the plot is
1923magnified).<span style='mso-spacerun:yes'>  </span>If a linear relationship had
1924been defined as a constraint (as can be done with other software packages) <i>the
1925unit cell parameters would have been forced onto this line with no obvious
1926indication that this was not a correct result.</i> </p>
1927
1928<p class=MsoListParagraphCxSpLast><span style='mso-spacerun:yes'> </span></p>
1929
1930<h1>Step 4: Examples of more complex fitt<span class=Heading1Char><span
1931style='font-weight:normal'>i</span></span>ng equations</h1>
1932
1933<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1934
1935<p class=MsoNormal>Here we will look at how more sophisticated Python
1936capabilities can be used to fit more complex behavior.<span
1937style='mso-spacerun:yes'>  </span></p>
1938
1939<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
1940style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1941style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1942</span></span></span><![endif]>Optionally Double-click on the<b
1943style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
1944style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1945mso-hansi-theme-font:major-latin'>0::c</span> </b>column. Note the changes in
1946the <i style='mso-bidi-font-style:normal'>c</i> unit cell parameter as a
1947function of temperature, as shown below. </p>
1948
1949<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1950
1951<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1952mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28" o:spid="_x0000_i1034"
1953 type="#_x0000_t75" style='width:350.25pt;height:303pt;visibility:visible;
1954 mso-wrap-style:square'>
1955 <v:imagedata src="ParametricFitting_files/image051.png" o:title=""/>
1956</v:shape><![endif]--><![if !vml]><img width=467 height=404
1957src="ParametricFitting_files/image052.jpg" v:shapes="Picture_x0020_28"><![endif]></span></p>
1958
1959<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1960
1961<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
1962style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1963style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1964</span></span></span><![endif]>We will now fit <i style='mso-bidi-font-style:
1965normal'>c</i> as a function of form 1<span class=GramE>/(</span>1 + <span
1966class=SpellE>exp</span>[k(t-t<sub>0</sub>)]). Select the<b style='mso-bidi-font-weight:
1967normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family:
1968"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
1969major-latin'>Parametric Fit/Add</span></b><span style='font-family:"Calibri",sans-serif;
1970mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'> <b
1971style='mso-bidi-font-weight:normal'>equation</b></span> menu item (as before).
1972For the dependent variable, click on<b style='mso-bidi-font-weight:normal'> </b><b
1973style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1974mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Phase</span></b>
1975and then select<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:
1976normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1977major-latin;mso-hansi-theme-font:major-latin'>0::c</span></b>.<span
1978style='mso-spacerun:yes'>  </span></p>
1979
1980<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1981
1982<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
1983style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1984style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1985</span></span></span><![endif]>We then enter expression</p>
1986
1987<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1988
1989<p class=MsoListParagraphCxSpMiddle style='text-indent:.5in'><b
1990style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1991mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b + c / (1+<span
1992class=GramE>math.exp(</span>k*(t-t0)))<o:p></o:p></span></b></p>
1993
1994<p class=MsoListParagraphCxSpMiddle><span style='font-family:"Cambria",serif;
1995mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p>&nbsp;</o:p></span></p>
1996
1997<p class=MsoListParagraphCxSpLast>Note that use of spaces here is arbitrary, but
1998all parentheses are required. Also note that the exponential function [<span
1999class=SpellE>exp</span>(x) or e<sup>x</sup>] is supplied in Python in the math
2000and <span class=SpellE>numpy</span> modules as <span class=SpellE><span
2001class=GramE>math.exp</span></span><span class=GramE>(</span>), <span
2002class=SpellE>numpy.exp</span>(). Either of these can be used as well as the
2003convenience abbreviation of <span class=SpellE><span class=GramE>np.exp</span></span><span
2004class=GramE>(</span>). Further, there are also a small number of common
2005functions that are defined without the prefix for convenience [these include
2006pi, <span class=SpellE><span class=GramE>exp</span></span><span class=GramE>(</span>),
2007<span class=SpellE>sqrt</span>(), <span class=SpellE>sind</span>(), <span
2008class=SpellE>cosd</span>(), <span class=SpellE>tand</span>() where d indicates
2009an argument in degrees.]</p>
2010
2011<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2012
2013<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
2014style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2015style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2016</span></span></span><![endif]>Assign free variables to<b style='mso-bidi-font-weight:
2017normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family:
2018"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
2019major-latin'>b</span>, </b><b style='mso-bidi-font-weight:normal'><span
2020style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2021mso-hansi-theme-font:major-latin'>c</span>, </b><b style='mso-bidi-font-weight:
2022normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2023major-latin;mso-hansi-theme-font:major-latin'>k</span> </b>and<b
2024style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
2025style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2026mso-hansi-theme-font:major-latin'>t0</span></b>, similar as to what was done
2027before. Note that the<b style='mso-bidi-font-weight:normal'> </b>variable name
2028for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2029mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>
2030label was set automatically to <b style='mso-bidi-font-weight:normal'><span
2031style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2032mso-hansi-theme-font:major-latin'>b_1</span></b>. If the same variable name (<b
2033style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2034mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>)
2035was used again here, the same value would be used to fit both equations, which
2036is certainly not what we want here.<span style='mso-spacerun:yes'> 
2037</span>Finally, since this equation is too complex to fit without some
2038reasonable starting values, specify an approximate value, <b style='mso-bidi-font-weight:
2039normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2040major-latin;mso-hansi-theme-font:major-latin'>120</span></b>, for the vicinity
2041of where the <i style='mso-bidi-font-style:normal'>c</i> lattice parameter
2042starts to change (<b style='mso-bidi-font-weight:normal'><span
2043style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2044mso-hansi-theme-font:major-latin'>t0</span></b>) and non-zero values for
2045variables <b>c</b> and <b>k</b>.</p>
2046
2047<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2048
2049<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2050mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40" o:spid="_x0000_i1033"
2051 type="#_x0000_t75" style='width:317.25pt;height:171pt;visibility:visible;
2052 mso-wrap-style:square'>
2053 <v:imagedata src="ParametricFitting_files/image053.png" o:title=""/>
2054</v:shape><![endif]--><![if !vml]><img width=423 height=228
2055src="ParametricFitting_files/image054.jpg" v:shapes="Picture_x0020_40"><![endif]></span></p>
2056
2057<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2058
2059<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
2060style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2061style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2062</span></span></span><![endif]>Optionally, press the <b style='mso-bidi-font-weight:
2063normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2064major-latin;mso-hansi-theme-font:major-latin'>Fit</span></b> button to see if
2065the equation can be refined with starting values of zero for the other three
2066parameters.<span style='mso-spacerun:yes'>  </span>A fit is obtained and is
2067plotted. </p>
2068
2069<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2070
2071<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span
2072style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2073 id="Picture_x0020_41" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:317.25pt;
2074 height:168.75pt;visibility:visible;mso-wrap-style:square'>
2075 <v:imagedata src="ParametricFitting_files/image055.png" o:title=""/>
2076</v:shape><![endif]--><![if !vml]><img width=423 height=225
2077src="ParametricFitting_files/image056.jpg" v:shapes="Picture_x0020_41"><![endif]></span></p>
2078
2079<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2080
2081<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
2082style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2083style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2084</span></span></span><![endif]>Press <b style='mso-bidi-font-weight:normal'><span
2085style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2086mso-hansi-theme-font:major-latin'>OK</span></b> to add this equation to the
2087parametric fits and both equations are refit (and if the label for <b
2088style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2089mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>
2090had not been changed, applying the constraint that <b style='mso-bidi-font-weight:
2091normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2092major-latin;mso-hansi-theme-font:major-latin'>b</span></b> must be the same for
2093both equations.) </p>
2094
2095<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2096
2097<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2098mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32" o:spid="_x0000_i1031"
2099 type="#_x0000_t75" style='width:353.25pt;height:300.75pt;visibility:visible;
2100 mso-wrap-style:square'>
2101 <v:imagedata src="ParametricFitting_files/image057.png" o:title=""/>
2102</v:shape><![endif]--><![if !vml]><img width=471 height=401
2103src="ParametricFitting_files/image058.jpg" v:shapes="Picture_x0020_32"><![endif]></span></p>
2104
2105<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2106
2107<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
2108style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2109style='mso-list:Ignore'>7.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2110</span></span></span><![endif]>We will now try a more complex equation for the
2111same data, where we set the value to <b style='mso-bidi-font-weight:normal'><span
2112style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2113mso-hansi-theme-font:major-latin'>b</span></b> for temperatures less than <b
2114style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2115mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>t0</span></b>
2116and a critical phenomenon formulism [(t-t<sub>0</sub>)<sup>-a</sup>] for
2117temperatures above <b style='mso-bidi-font-weight:normal'><span
2118style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2119mso-hansi-theme-font:major-latin'>t0</span></b>. To do this we use the Python
2120syntax &quot;<b style='mso-bidi-font-weight:normal'><span style='font-family:
2121"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
2122major-latin'>x1 if <span class=SpellE>testexp</span> else x2</span></b>&quot;
2123which is <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2124mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x1</span></b>
2125where the test expression (<span class=SpellE><b style='mso-bidi-font-weight:
2126normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2127major-latin;mso-hansi-theme-font:major-latin'>testexp</span></b></span> here)
2128is <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2129mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>True</span></b>
2130and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2131mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x2</span></b>
2132otherwise. Thus we can use an expression such as:</p>
2133
2134<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span></p>
2135
2136<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
2137auto'><span class=GramE><b style='mso-bidi-font-weight:normal'><span
2138style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2139mso-hansi-theme-font:major-latin'>b</span></b></span><b style='mso-bidi-font-weight:
2140normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2141major-latin;mso-hansi-theme-font:major-latin'> if t &lt;= t0 else b + c *
2142(1-(t-t0)**d)<o:p></o:p></span></b></p>
2143
2144<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
2145auto'><span style='font-family:Courier'><o:p>&nbsp;</o:p></span></p>
2146
2147<p class=MsoListParagraphCxSpMiddle>This may be easier to read with the inclusion
2148of extra parentheses (that have no effect on the execution):<span
2149style='font-family:"Cambria",serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2150minor-latin'><o:p></o:p></span></p>
2151
2152<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2153
2154<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
2155auto'><span class=GramE><b style='mso-bidi-font-weight:normal'><span
2156style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2157mso-hansi-theme-font:major-latin'>b</span></b></span><b style='mso-bidi-font-weight:
2158normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2159major-latin;mso-hansi-theme-font:major-latin'> if (t &lt;= t0) else (b + c *
2160(1-(t-t0)**d))<o:p></o:p></span></b></p>
2161
2162<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
2163auto'><span style='font-family:Courier'><o:p>&nbsp;</o:p></span></p>
2164
2165<p class=MsoListParagraphCxSpMiddle>As before, add an equation (or edit an
2166existing one), set the dependent variable to <b style='mso-bidi-font-weight:
2167normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2168major-latin;mso-hansi-theme-font:major-latin'>0::c</span></b>, enter the
2169expression and assign the free and fixed variables, as before. Set the exponent
2170and the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2171mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>t0</span></b>
2172values to initial values of <b style='mso-bidi-font-weight:normal'><span
2173style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2174mso-hansi-theme-font:major-latin'>-0.025</span></b> and <b style='mso-bidi-font-weight:
2175normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2176major-latin;mso-hansi-theme-font:major-latin'>120</span></b>, respectively, and
2177turn off their refinement flags. Then press <b style='mso-bidi-font-weight:
2178normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2179major-latin;mso-hansi-theme-font:major-latin'>Fit</span></b>.<span
2180style='font-family:"Cambria",serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2181minor-latin'><o:p></o:p></span></p>
2182
2183<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2184mso-no-proof:yes'><o:p>&nbsp;</o:p></span></p>
2185
2186<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2187mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42" o:spid="_x0000_i1030"
2188 type="#_x0000_t75" style='width:315.75pt;height:168.75pt;visibility:visible;
2189 mso-wrap-style:square'>
2190 <v:imagedata src="ParametricFitting_files/image059.png" o:title=""/>
2191</v:shape><![endif]--><![if !vml]><img width=421 height=225
2192src="ParametricFitting_files/image060.jpg" v:shapes="Picture_x0020_42"><![endif]></span></p>
2193
2194<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2195
2196<p class=MsoListParagraphCxSpMiddle>Then turn refinement of <b
2197style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2198mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>t0</span></b>
2199back on and press <b style='mso-bidi-font-weight:normal'><span
2200style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2201mso-hansi-theme-font:major-latin'>OK</span></b>. The resulting fit shows the
2202trends quite well: </p>
2203
2204<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2205
2206<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2207mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35" o:spid="_x0000_i1029"
2208 type="#_x0000_t75" style='width:351pt;height:302.25pt;visibility:visible;
2209 mso-wrap-style:square'>
2210 <v:imagedata src="ParametricFitting_files/image061.png" o:title=""/>
2211</v:shape><![endif]--><![if !vml]><img width=468 height=403
2212src="ParametricFitting_files/image062.jpg" v:shapes="Picture_x0020_35"><![endif]></span></p>
2213
2214<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
2215
2216<h1>Step 5: Fitting to a Pseudo Variable</h1>
2217
2218<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2219
2220<p class=MsoNormal>One can fit a function to a pseudo variable, just as to a
2221direct variable. If we look at the plot shown in Step 2, it appears there are
2222two regions. We can treat the lower range as a power-law growth, <span
2223class=SpellE>T<sup>k</sup></span>, and the upper region as linear (m*T + b). </p>
2224
2225<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2226
2227<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
2228style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2229style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2230</span></span></span><![endif]>As before, add an equation<b style='mso-bidi-font-weight:
2231normal'> </b>(or edit an existing one). For the dependent variable, select<b
2232style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
2233style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2234mso-hansi-theme-font:major-latin'>Global</span></b> to bring up that selection
2235of variables and select<b style='mso-bidi-font-weight:normal'> </b><b
2236style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2237mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b/c</span> </b>and
2238press<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:
2239normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2240major-latin;mso-hansi-theme-font:major-latin'>OK</span>. </b></p>
2241
2242<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2243
2244<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
2245style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2246style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2247</span></span></span><![endif]>Then enter the equation as </p>
2248
2249<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2250
2251<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
2252auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2253mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin;mso-bidi-font-family:
2254"Lucida Grande";color:black'>(o1 + (a1*T<span class=GramE>)*</span>*k) if T
2255&lt; 120 else (o2 + a2*T</span></b><b style='mso-bidi-font-weight:normal'><span
2256style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2257mso-hansi-theme-font:major-latin'>)<o:p></o:p></span></b></p>
2258
2259<p class=MsoListParagraphCxSpMiddle><span style='font-family:"Cambria",serif;
2260mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p>&nbsp;</o:p></span></p>
2261
2262<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
2263style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2264style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2265</span></span></span><![endif]>Assign the free and fixed variables, as shown
2266below. Note that the exponent (<b style='mso-bidi-font-weight:normal'><span
2267style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2268mso-hansi-theme-font:major-latin'>k</span></b>) and scaling factor (<b
2269style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2270mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>a1</span></b>),
2271cannot start as zero<b style='mso-bidi-font-weight:normal'>. </b></p>
2272
2273<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2274
2275<p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US;
2276mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44" o:spid="_x0000_i1028"
2277 type="#_x0000_t75" style='width:332.25pt;height:186pt;visibility:visible;
2278 mso-wrap-style:square'>
2279 <v:imagedata src="ParametricFitting_files/image063.png" o:title=""/>
2280</v:shape><![endif]--><![if !vml]><img width=443 height=248
2281src="ParametricFitting_files/image064.png" v:shapes="Picture_x0020_44"><![endif]></span></p>
2282
2283<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2284
2285<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
2286style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2287style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2288</span></span></span><![endif]>Press the <b style='mso-bidi-font-weight:normal'><span
2289style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2290mso-hansi-theme-font:major-latin'>Fit</span></b> button and note that all the
2291free variables are adjusted </p>
2292
2293<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2294
2295<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2296mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45" o:spid="_x0000_i1027"
2297 type="#_x0000_t75" style='width:333.75pt;height:189pt;visibility:visible;
2298 mso-wrap-style:square'>
2299 <v:imagedata src="ParametricFitting_files/image065.png" o:title=""/>
2300</v:shape><![endif]--><![if !vml]><img width=445 height=252
2301src="ParametricFitting_files/image066.png" v:shapes="Picture_x0020_45"><![endif]></span><span
2302style='mso-spacerun:yes'> </span></p>
2303
2304<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2305
2306<p class=MsoListParagraphCxSpMiddle>Also, that the plotted result is close to
2307the values from the refinement.</p>
2308
2309<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2310
2311<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2312mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48" o:spid="_x0000_i1026"
2313 type="#_x0000_t75" style='width:348.75pt;height:302.25pt;visibility:visible;
2314 mso-wrap-style:square'>
2315 <v:imagedata src="ParametricFitting_files/image067.png" o:title=""/>
2316</v:shape><![endif]--><![if !vml]><img width=465 height=403
2317src="ParametricFitting_files/image068.png" v:shapes="Picture_x0020_48"><![endif]></span></p>
2318
2319<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
2320
2321<p class=MsoNormal style='margin-left:.25in'><o:p>&nbsp;</o:p></p>
2322
2323<p class=MsoNormal>This completes this tutorial on use of Pseudo Variables and
2324parametric fitting. </p>
2325
2326<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2327
2328<h1>Advanced Use: Externally-Defined Functions</h1>
2329
2330<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2331
2332<p class=MsoNormal>The parametric refinement section of GSAS-II is intended to
2333be quite flexible, but for very complex fitting, a user may wish to define a
2334custom Python function. Such a function can be defined in a separate module
2335that will be accessed with a parametric equation (or pseudo variable).</p>
2336
2337<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2338
2339<p class=MsoNormal>As an example of that, if we create a file called <b
2340style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2341mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>fittest.py</span></b>
2342and locate that file in any directory in the Python path (most simply, in the
2343directory where the project file, <span class=SpellE><b style='mso-bidi-font-weight:
2344normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2345major-latin;mso-hansi-theme-font:major-latin'>SeqTut.gpx</span></b></span>, is
2346located) and place a routine <span class=SpellE><b style='mso-bidi-font-weight:
2347normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2348major-latin;mso-hansi-theme-font:major-latin'>fitfxn</span></b></span> in that
2349module:</p>
2350
2351<blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'>
2352
2353<blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><pre><o:p>&nbsp;</o:p></pre><pre><b
2354style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2355mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'># <span
2356class=GramE>file</span> fittest.py<o:p></o:p></span></b></pre><pre><span
2357class=SpellE><span class=GramE><b style='mso-bidi-font-weight:normal'><span
2358style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2359mso-hansi-theme-font:major-latin'>def</span></b></span></span><b
2360style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2361mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'> <span
2362class=SpellE>fitfxn</span>(T,o1,o2,a1,a2,k):<o:p></o:p></span></b></pre><pre><b
2363style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2364mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'>    </span><span
2365class=GramE>if</span> T &lt; 120:<o:p></o:p></span></b></pre><pre><b
2366style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2367mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'>        </span><span
2368class=GramE>return</span> o1 + (a1*T)**k<o:p></o:p></span></b></pre><pre><b
2369style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2370mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'>    </span><span
2371class=GramE>else</span>:<o:p></o:p></span></b></pre><pre><b style='mso-bidi-font-weight:
2372normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2373major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'>        </span><span
2374class=GramE>return</span> o2 + a2*T<o:p></o:p></span></b></pre></blockquote>
2375
2376</blockquote>
2377
2378<p class=MsoNormal>The function <span class=SpellE><b style='mso-bidi-font-weight:
2379normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2380major-latin;mso-hansi-theme-font:major-latin'>fittest.fitfxn</span></b></span>
2381can then be used to duplicate the previous example: </p>
2382
2383<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2384
2385<p class=MsoNormal><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2386 id="Picture_x0020_47" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:315pt;
2387 height:185.25pt;visibility:visible;mso-wrap-style:square'>
2388 <v:imagedata src="ParametricFitting_files/image069.png" o:title="" croptop="3393f"
2389  cropbottom="7847f" cropleft="3471f" cropright="3290f"/>
2390</v:shape><![endif]--><![if !vml]><img width=420 height=247
2391src="ParametricFitting_files/image070.png" v:shapes="Picture_x0020_47"><![endif]></span></p>
2392
2393<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2394
2395<p class=MsoNormal>Note that module <b style='mso-bidi-font-weight:normal'><span
2396style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2397mso-hansi-theme-font:major-latin'>fittest</span></b> is automatically located
2398and loaded, provided it is found in the path. No changes to the standard
2399distributed GSAS-II code are needed. Care to avoid use of a module name already
2400found in GSAS-II or Python is wise.</p>
2401
2402</div>
2403
2404</body>
2405
2406</html>
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