source: Tutorials/SeqParametric/ParametricFitting.htm @ 2349

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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
1354class=SpellE>Vars</span>/Add Formula</span></b>
1355menu item to create a new pseudo-variable.</p>
1356
1357<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1358
1359<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1360mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_2" o:spid="_x0000_i1052"
1361 type="#_x0000_t75" style='width:159pt;height:45.75pt;visibility:visible;
1362 mso-wrap-style:square'>
1363 <v:imagedata src="ParametricFitting_files/image003.png" o:title=""/>
1364</v:shape><![endif]--><![if !vml]><img width=212 height=61
1365src="ParametricFitting_files/image004.jpg" v:shapes="Picture_x0020_2"><![endif]></span></p>
1366
1367<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1368
1369<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span
1370style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1371style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1372</span></span></span><![endif]>A window opens to define a formula</p>
1373
1374<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1375
1376<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1377mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3" o:spid="_x0000_i1051"
1378 type="#_x0000_t75" style='width:309.75pt;height:152.25pt;visibility:visible;
1379 mso-wrap-style:square'>
1380 <v:imagedata src="ParametricFitting_files/image005.png" o:title="" croptop="4214f"
1381  cropbottom="8982f" cropleft="3852f" cropright="3654f"/>
1382</v:shape><![endif]--><![if !vml]><img width=413 height=203
1383src="ParametricFitting_files/image006.png" v:shapes="Picture_x0020_3"><![endif]></span></p>
1384
1385<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1386
1387<p class=MsoListParagraphCxSpMiddle><!--[if gte vml 1]><v:shape id="Picture_x0020_4"
1388 o:spid="_x0000_s1031" type="#_x0000_t75" style='position:absolute;left:0;
1389 text-align:left;margin-left:178.3pt;margin-top:846.2pt;width:229.5pt;height:86.5pt;
1390 z-index:251658240;visibility:visible;mso-wrap-style:square;
1391 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1392 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1393 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1394 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1395 mso-position-vertical-relative:margin;mso-width-percent:0;
1396 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
1397 <v:imagedata src="ParametricFitting_files/image007.png" o:title=""/>
1398 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1399</v:shape><![endif]--><![if !vml]><img width=306 height=115
1400src="ParametricFitting_files/image008.jpg" align=right hspace=12 v:shapes="Picture_x0020_4"><![endif]>In
1401this window, type a Python expression<b style='mso-bidi-font-weight:normal'>, </b><span
1402style='mso-bidi-font-family:"Times New Roman"'>&quot;</span><b
1403style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1404mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin;mso-bidi-font-family:
1405"Times New Roman"'>b/c</span></b><span style='mso-bidi-font-family:"Times New Roman"'>&quot;,</span>
1406but note that the variables <b style='mso-bidi-font-weight:normal'><span
1407style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1408mso-hansi-theme-font:major-latin'>c</span></b> and <b style='mso-bidi-font-weight:
1409normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1410major-latin;mso-hansi-theme-font:major-latin'>b</span></b> here are arbitrary
1411labels. After entering the formula, press the <b style='mso-bidi-font-weight:
1412normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1413major-latin;mso-hansi-theme-font:major-latin'>Validate</span></b> button or
1414wait a few seconds and the validation will be tested automatically. Note that
1415if you pause too long, while typing, an error message may be displayed as the
1416incomplete formula is found to be invalid. If so, make corrections or keep
1417typing until the entire expression is entered.<span style='mso-spacerun:yes'> 
1418</span>The error message will sometimes show where error is encountered, though
1419not in this case. </p>
1420
1421<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1422
1423<p class=MsoListParagraphCxSpMiddle>When the expression is complete, a new
1424table appears where the arbitrary <b style='mso-bidi-font-weight:normal'><span
1425style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1426mso-hansi-theme-font:major-latin'>c</span></b> and <b style='mso-bidi-font-weight:
1427normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1428major-latin;mso-hansi-theme-font:major-latin'>b</span></b> labels will be
1429assigned.</p>
1430
1431<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1432
1433<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1434mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5" o:spid="_x0000_i1050"
1435 type="#_x0000_t75" style='width:309.75pt;height:152.25pt;visibility:visible;
1436 mso-wrap-style:square'>
1437 <v:imagedata src="ParametricFitting_files/image009.png" o:title="" croptop="4435f"
1438  cropbottom="8537f" cropleft="3852f" cropright="3650f"/>
1439</v:shape><![endif]--><![if !vml]><img width=413 height=203
1440src="ParametricFitting_files/image010.png" v:shapes="Picture_x0020_5"><![endif]></span></p>
1441
1442<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1443
1444<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span
1445style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1446style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1447</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_6"
1448 o:spid="_x0000_s1030" type="#_x0000_t75" style='position:absolute;left:0;
1449 text-align:left;margin-left:37.3pt;margin-top:1143.2pt;width:88.5pt;height:65.5pt;
1450 z-index:251659264;visibility:visible;mso-wrap-style:square;
1451 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1452 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1453 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1454 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1455 mso-position-vertical-relative:margin;mso-width-percent:0;
1456 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
1457 <v:imagedata src="ParametricFitting_files/image011.png" o:title=""/>
1458 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1459</v:shape><![endif]--><![if !vml]><img width=118 height=87
1460src="ParametricFitting_files/image012.jpg" align=right hspace=12 v:shapes="Picture_x0020_6"><![endif]>Assign
1461the label for the numerator by clicking on the menu button next to label <b
1462style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1463mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>;
1464this will bring up a list of variable types, from this select <b
1465style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1466mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Phase</span></b>
1467to bring up a list of phase variables, from that list select variable <b
1468style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1469mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>0::b</span></b>,
1470which is the <i style='mso-bidi-font-style:normal'>b</i> lattice parameter for
1471phase 0 (CuCr<sub>2</sub>O<sub>4</sub>). Repeat this process to select assign
1472to label <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1473mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>c</span></b>
1474variable <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1475mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>0::b</span></b>.</p>
1476
1477<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1478
1479<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1480mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8" o:spid="_x0000_i1049"
1481 type="#_x0000_t75" style='width:315.75pt;height:129pt;visibility:visible;
1482 mso-wrap-style:square'>
1483 <v:imagedata src="ParametricFitting_files/image013.png" o:title="" croptop="4597f"
1484  cropbottom="9873f" cropleft="3348f" cropright="3506f"/>
1485</v:shape><![endif]--><![if !vml]><img width=421 height=172
1486src="ParametricFitting_files/image014.png" v:shapes="Picture_x0020_8"><![endif]></span></p>
1487
1488<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1489
1490<p class=MsoListParagraphCxSpMiddle>As each variable is set, the window shows
1491the value for each variable from the first refinement and when the expression
1492can be evaluated, the value for the expression, evaluated for that first
1493refinement. Only when the expression can be evaluated can the <b
1494style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1495mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>OK</span></b>
1496button be pressed. </p>
1497
1498<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1499
1500<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1501mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9" o:spid="_x0000_i1048"
1502 type="#_x0000_t75" style='width:314.25pt;height:153.75pt;visibility:visible;
1503 mso-wrap-style:square'>
1504 <v:imagedata src="ParametricFitting_files/image015.png" o:title="" croptop="3770f"
1505  cropbottom="8549f" cropleft="3371f" cropright="3424f"/>
1506</v:shape><![endif]--><![if !vml]><img width=419 height=205
1507src="ParametricFitting_files/image016.png" v:shapes="Picture_x0020_9"><![endif]></span></p>
1508
1509<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1510
1511<p class=MsoListParagraphCxSpMiddle>Press<b style='mso-bidi-font-weight:normal'>
1512</b><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1513mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>OK</span></b>
1514to close the window and add the pseudo-variable. Note that a new column appears
1515at the end of the sequential refinement data table. </p>
1516
1517<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1518
1519<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1520mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10" o:spid="_x0000_i1047"
1521 type="#_x0000_t75" style='width:354pt;height:180.75pt;visibility:visible;
1522 mso-wrap-style:square'>
1523 <v:imagedata src="ParametricFitting_files/image017.png" o:title=""/>
1524</v:shape><![endif]--><![if !vml]><img width=472 height=241
1525src="ParametricFitting_files/image018.jpg" v:shapes="Picture_x0020_10"><![endif]></span></p>
1526
1527<p class=MsoListParagraphCxSpMiddle><!--[if gte vml 1]><v:shape id="Picture_x0020_11"
1528 o:spid="_x0000_s1029" type="#_x0000_t75" style='position:absolute;left:0;
1529 text-align:left;margin-left:42.3pt;margin-top:666.2pt;width:93.5pt;height:39pt;
1530 z-index:251660288;visibility:visible;mso-wrap-style:square;
1531 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1532 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1533 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1534 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1535 mso-position-vertical-relative:margin;mso-width-percent:0;
1536 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
1537 <v:imagedata src="ParametricFitting_files/image019.png" o:title=""/>
1538 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1539</v:shape><![endif]--><![if !vml]><img width=125 height=52
1540src="ParametricFitting_files/image020.jpg" align=right hspace=12 v:shapes="Picture_x0020_11"><![endif]>Also
1541note that positioning the mouse above any cell in the table and waiting for a
1542few seconds causes the <span class=SpellE>s.u</span>. to be shown as a tooltip.
1543</p>
1544
1545<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1546
1547<p class=MsoListParagraphCxSpMiddle>Double clicking on the <b style='mso-bidi-font-weight:
1548normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1549major-latin;mso-hansi-theme-font:major-latin'>b/c</span></b> column will cause
1550the pseudo-variable to be plotted:</p>
1551
1552<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1553
1554<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1555mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12" o:spid="_x0000_i1046"
1556 type="#_x0000_t75" style='width:351.75pt;height:303pt;visibility:visible;
1557 mso-wrap-style:square'>
1558 <v:imagedata src="ParametricFitting_files/image021.png" o:title=""/>
1559</v:shape><![endif]--><![if !vml]><img width=469 height=404
1560src="ParametricFitting_files/image022.png" v:shapes="Picture_x0020_12"><![endif]></span></p>
1561
1562<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1563
1564<p class=MsoListParagraphCxSpMiddle>Press the &quot;<b style='mso-bidi-font-weight:
1565normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1566major-latin;mso-hansi-theme-font:major-latin'>s</span></b>&quot; key inside the
1567plot to select<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:
1568normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1569major-latin;mso-hansi-theme-font:major-latin'>Temperature</span></b> as the
1570x-axis. </p>
1571
1572<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1573
1574<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1575mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13" o:spid="_x0000_i1045"
1576 type="#_x0000_t75" style='width:162.75pt;height:156pt;visibility:visible;
1577 mso-wrap-style:square'>
1578 <v:imagedata src="ParametricFitting_files/image023.png" o:title="" croptop="4105f"
1579  cropbottom="8920f" cropleft="6109f" cropright="5911f"/>
1580</v:shape><![endif]--><![if !vml]><img width=217 height=208
1581src="ParametricFitting_files/image024.png" v:shapes="Picture_x0020_13"><![endif]></span></p>
1582
1583<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1584
1585<p class=MsoListParagraphCxSpMiddle>The plot will then appear as below:</p>
1586
1587<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1588
1589<p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US;
1590mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14" o:spid="_x0000_i1044"
1591 type="#_x0000_t75" style='width:353.25pt;height:303.75pt;visibility:visible;
1592 mso-wrap-style:square'>
1593 <v:imagedata src="ParametricFitting_files/image025.png" o:title=""/>
1594</v:shape><![endif]--><![if !vml]><img width=471 height=405
1595src="ParametricFitting_files/image026.jpg" v:shapes="Picture_x0020_14"><![endif]></span></p>
1596
1597<h1>Step 3: Fitting a simple parametric equation to the unit cell volume</h1>
1598
1599<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1600
1601<p class=MsoNormal>In the next few steps we will fit increasingly sophisticated
1602equations of state to different parameters. As a simple example, we can
1603double-click on<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:
1604normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1605major-latin;mso-hansi-theme-font:major-latin'>0::Vol</span></b>, to plot the
1606unit volume for the first phase vs. T, and fit this to a straight line.<span
1607style='mso-spacerun:yes'>  </span></p>
1608
1609<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1610
1611<p class=MsoListParagraphCxSpFirst><span style='mso-fareast-language:EN-US;
1612mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15" o:spid="_x0000_i1043"
1613 type="#_x0000_t75" style='width:356.25pt;height:305.25pt;visibility:visible;
1614 mso-wrap-style:square'>
1615 <v:imagedata src="ParametricFitting_files/image027.png" o:title=""/>
1616</v:shape><![endif]--><![if !vml]><img width=475 height=407
1617src="ParametricFitting_files/image028.jpg" v:shapes="Picture_x0020_15"><![endif]></span></p>
1618
1619<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1620style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1621style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1622</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_16"
1623 o:spid="_x0000_s1028" type="#_x0000_t75" style='position:absolute;left:0;
1624 text-align:left;margin-left:21.8pt;margin-top:891.2pt;width:73pt;height:53pt;
1625 z-index:251661312;visibility:visible;mso-wrap-style:square;
1626 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1627 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1628 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1629 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1630 mso-position-vertical-relative:margin;mso-width-percent:0;
1631 mso-height-percent:0;mso-width-relative:margin;mso-height-relative:margin'>
1632 <v:imagedata src="ParametricFitting_files/image029.png" o:title=""/>
1633 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1634</v:shape><![endif]--><![if !vml]><img width=97 height=71
1635src="ParametricFitting_files/image030.jpg" align=right hspace=12 v:shapes="Picture_x0020_16"><![endif]>Click
1636on the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1637mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Parametric
1638Fit/Add</span></b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1639major-latin;mso-hansi-theme-font:major-latin'> <b style='mso-bidi-font-weight:
1640normal'>equation</b></span> menu item, which opens a window similar to what was
1641used before to create a pseudo-variable, except that here an equation is
1642defined.<span style='mso-spacerun:yes'>  </span></p>
1643
1644<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1645
1646<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1647mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_17" o:spid="_x0000_i1042"
1648 type="#_x0000_t75" style='width:311.25pt;height:152.25pt;visibility:visible;
1649 mso-wrap-style:square'>
1650 <v:imagedata src="ParametricFitting_files/image031.png" o:title="" croptop="4213f"
1651  cropbottom="8982f" cropleft="3490f" cropright="3653f"/>
1652</v:shape><![endif]--><![if !vml]><img width=415 height=203
1653src="ParametricFitting_files/image032.png" v:shapes="Picture_x0020_17"><![endif]></span></p>
1654
1655<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
1656
1657<p class=MsoNormal>We will want to fit the unit cell volume to an equation of
1658form <i style='mso-bidi-font-style:normal'>y = <span class=SpellE>mx+b</span></i>,
1659where y will be the volume and x temperature and m and b will be best fit. </p>
1660
1661<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><o:p>&nbsp;</o:p></b></p>
1662
1663<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><b
1664style='mso-bidi-font-weight:normal'><span style='mso-fareast-font-family:"Times New Roman";
1665mso-bidi-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
1666style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span></b><![endif]>Click
1667the<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:
1668normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1669major-latin;mso-hansi-theme-font:major-latin'>&#8597; </span></b>button to
1670select a dependent variable for &quot;y&quot;. From the phase list, select the
1671unit cell volume for the CuCr<sub>2</sub>O<sub>4</sub> phase, select<b
1672style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
1673style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1674mso-hansi-theme-font:major-latin'>0::Vol</span></b> and then press<b
1675style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
1676style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1677mso-hansi-theme-font:major-latin'>OK</span>.<o:p></o:p></b></p>
1678
1679<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1680
1681<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1682mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_19" o:spid="_x0000_i1041"
1683 type="#_x0000_t75" style='width:314.25pt;height:132pt;visibility:visible;
1684 mso-wrap-style:square'>
1685 <v:imagedata src="ParametricFitting_files/image033.png" o:title="" croptop="3830f"
1686  cropbottom="9359f" cropleft="3705f" cropright="3502f"/>
1687</v:shape><![endif]--><![if !vml]><img width=419 height=176
1688src="ParametricFitting_files/image034.png" v:shapes="Picture_x0020_19"><![endif]></span></p>
1689
1690<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1691mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20" o:spid="_x0000_i1040"
1692 type="#_x0000_t75" style='width:311.25pt;height:155.25pt;visibility:visible;
1693 mso-wrap-style:square'>
1694 <v:imagedata src="ParametricFitting_files/image035.png" o:title="" croptop="3548f"
1695  cropbottom="8549f" cropleft="3611f" cropright="3665f"/>
1696</v:shape><![endif]--><![if !vml]><img width=415 height=207
1697src="ParametricFitting_files/image036.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
1698
1699<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1700
1701<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1702style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1703style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1704</span></span></span><![endif]>Now we enter the equation using Python syntax,
1705which is simply &quot;<b style='mso-bidi-font-weight:normal'><span
1706style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1707mso-hansi-theme-font:major-latin'>m*x + b</span></b>&quot;, note that the use
1708of spaces and the choice of labels is arbitrary. If one were to accidentally
1709leave out the &quot;<span style='font-family:Courier'>*</span>&quot; and typed
1710&quot;<span style='font-family:Courier'>mx</span>&quot; then that would be
1711considered a label, if &quot;<span style='font-family:Courier'>m x</span>&quot;
1712were typed, an error message would be displayed. </p>
1713
1714<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1715
1716<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1717mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21" o:spid="_x0000_i1039"
1718 type="#_x0000_t75" style='width:315.75pt;height:155.25pt;visibility:visible;
1719 mso-wrap-style:square'>
1720 <v:imagedata src="ParametricFitting_files/image037.png" o:title="" croptop="3326f"
1721  cropbottom="8766f" cropleft="3010f" cropright="3419f"/>
1722</v:shape><![endif]--><![if !vml]><img width=421 height=207
1723src="ParametricFitting_files/image038.png" v:shapes="Picture_x0020_21"><![endif]></span></p>
1724
1725<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1726
1727<p class=MsoListParagraphCxSpMiddle>Then press <b style='mso-bidi-font-weight:
1728normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1729major-latin;mso-hansi-theme-font:major-latin'>Validate</span></b> or wait a few
1730seconds and a window changes, as above, allowing assignment of the three new
1731labels (<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1732mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b>,
1733<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1734mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x</span></b>,
1735and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1736mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>).
1737</p>
1738
1739<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1740
1741<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1742style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1743style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1744</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_22"
1745 o:spid="_x0000_s1027" type="#_x0000_t75" style='position:absolute;left:0;
1746 text-align:left;margin-left:43.8pt;margin-top:603.2pt;width:95pt;height:35pt;
1747 z-index:251662336;visibility:visible;mso-wrap-style:square;
1748 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1749 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1750 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1751 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1752 mso-position-vertical-relative:margin;mso-width-percent:0;
1753 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
1754 <v:imagedata src="ParametricFitting_files/image039.png" o:title=""/>
1755 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1756</v:shape><![endif]--><![if !vml]><img width=127 height=47
1757src="ParametricFitting_files/image040.jpg" align=right hspace=12 v:shapes="Picture_x0020_22"><![endif]>Assign
1758<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1759mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>
1760and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1761mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b>
1762as refinable “free” parameters: Click on the <b style='mso-bidi-font-weight:
1763normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1764major-latin;mso-hansi-theme-font:major-latin'>&#8597;</span></b><span
1765style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1766mso-hansi-theme-font:major-latin'> </span>button next to b and select<b
1767style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
1768style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1769mso-hansi-theme-font:major-latin'>Free</span></b>. Then repeat this <span
1770class=SpellE>for<b style='mso-bidi-font-weight:normal'> </b><b
1771style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1772mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b></span>.
1773</p>
1774
1775<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1776mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_23" o:spid="_x0000_i1038"
1777 type="#_x0000_t75" style='width:314.25pt;height:153pt;visibility:visible;
1778 mso-wrap-style:square'>
1779 <v:imagedata src="ParametricFitting_files/image041.png" o:title="" croptop="3992f"
1780  cropbottom="8541f" cropleft="3250f" cropright="3415f"/>
1781</v:shape><![endif]--><![if !vml]><img width=419 height=204
1782src="ParametricFitting_files/image042.png" v:shapes="Picture_x0020_23"><![endif]></span></p>
1783
1784<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1785
1786<p class=MsoListParagraphCxSpMiddle>It is not necessary to change the default
1787variable names, the initial values, or the refine flag. </p>
1788
1789<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1790
1791<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1792style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1793style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1794</span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_24"
1795 o:spid="_x0000_s1026" type="#_x0000_t75" style='position:absolute;left:0;
1796 text-align:left;margin-left:24.3pt;margin-top:837.2pt;width:75.5pt;height:26pt;
1797 z-index:251663360;visibility:visible;mso-wrap-style:square;
1798 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
1799 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
1800 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
1801 mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
1802 mso-position-vertical-relative:margin;mso-width-percent:0;
1803 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
1804 <v:imagedata src="ParametricFitting_files/image043.png" o:title=""/>
1805 <w:wrap type="square" anchorx="margin" anchory="margin"/>
1806</v:shape><![endif]--><![if !vml]><img width=101 height=35
1807src="ParametricFitting_files/image044.jpg" align=right hspace=12 v:shapes="Picture_x0020_24"><![endif]>To
1808set <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1809mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x</span></b>
1810as the temperature, click on the <b style='mso-bidi-font-weight:normal'><span
1811style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1812mso-hansi-theme-font:major-latin'>&#8597;</span></b><span style='font-family:
1813"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
1814major-latin'> </span>button next to <b style='mso-bidi-font-weight:normal'><span
1815style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1816mso-hansi-theme-font:major-latin'>x</span></b>, select<b style='mso-bidi-font-weight:
1817normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family:
1818"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
1819major-latin'>Global</span>,</b> and then select<b style='mso-bidi-font-weight:
1820normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family:
1821"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
1822major-latin'>Temperature</span></b> from the list and click on<b
1823style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
1824style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1825mso-hansi-theme-font:major-latin'>OK</span></b>.</p>
1826
1827<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1828
1829<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span
1830style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1831 id="Picture_x0020_25" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:245.25pt;
1832 height:108.75pt;visibility:visible;mso-wrap-style:square'>
1833 <v:imagedata src="ParametricFitting_files/image045.png" o:title="" croptop="5483f"
1834  cropbottom="10984f" cropleft="4191f" cropright="4159f"/>
1835</v:shape><![endif]--><![if !vml]><img width=327 height=145
1836src="ParametricFitting_files/image046.png" v:shapes="Picture_x0020_25"><![endif]></span></p>
1837
1838<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1839
1840<p class=MsoListParagraphCxSpMiddle>The window then changes, showing the values
1841of the dependent variable and the expression for the first refinement, as
1842below. <span style='mso-spacerun:yes'> </span>Optionally, the values for <b
1843style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1844mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b>
1845and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1846mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>
1847could be changed manually and the displayed value will be updated when <b
1848style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1849mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Validate</span></b>
1850is pressed or after a short delay.</p>
1851
1852<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1853
1854<p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US;
1855mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26" o:spid="_x0000_i1036"
1856 type="#_x0000_t75" style='width:314.25pt;height:153pt;visibility:visible;
1857 mso-wrap-style:square'>
1858 <v:imagedata src="ParametricFitting_files/image047.png" o:title="" croptop="3992f"
1859  cropbottom="8541f" cropleft="3490f" cropright="3294f"/>
1860</v:shape><![endif]--><![if !vml]><img width=419 height=204
1861src="ParametricFitting_files/image048.png" v:shapes="Picture_x0020_26"><![endif]></span></p>
1862
1863<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1864
1865<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1866style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1867style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1868</span></span></span><![endif]>Press the <b style='mso-bidi-font-weight:normal'><span
1869style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1870mso-hansi-theme-font:major-latin'>OK</span></b> button to save this parametric
1871fit. The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1872mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>
1873and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1874mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b>
1875values are then refined and the console shows the results:</p>
1876
1877<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
1878style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1879style='mso-list:Ignore'>7.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1880</span></span></span><![endif]><o:p>&nbsp;</o:p></p>
1881
1882<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1883auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'>Fit
1884Results<o:p></o:p></span></b></p>
1885
1886<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1887auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span
1888style='mso-spacerun:yes'>  </span>0::Vol = m*x +b<o:p></o:p></span></b></p>
1889
1890<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1891auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span
1892style='mso-spacerun:yes'>   </span><span class=GramE>x<span
1893style='mso-spacerun:yes'>  </span>=</span> Temperature<o:p></o:p></span></b></p>
1894
1895<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1896auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span
1897style='mso-spacerun:yes'>   </span><span class=GramE>b<span
1898style='mso-spacerun:yes'>  </span>=</span> 561.7722(26)<o:p></o:p></span></b></p>
1899
1900<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1901auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span
1902style='mso-spacerun:yes'>   </span><span class=GramE>m<span
1903style='mso-spacerun:yes'>  </span>=</span> 0.014833(14)<o:p></o:p></span></b></p>
1904
1905<p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space:
1906auto'><span style='font-family:Courier'><o:p>&nbsp;</o:p></span></p>
1907
1908<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1909mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27" o:spid="_x0000_i1035"
1910 type="#_x0000_t75" style='width:350.25pt;height:302.25pt;visibility:visible;
1911 mso-wrap-style:square'>
1912 <v:imagedata src="ParametricFitting_files/image049.png" o:title=""/>
1913</v:shape><![endif]--><![if !vml]><img width=467 height=403
1914src="ParametricFitting_files/image050.jpg" v:shapes="Picture_x0020_27"><![endif]></span><span
1915style='font-family:"Cambria",serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1916minor-latin'><o:p></o:p></span></p>
1917
1918<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1919
1920<p class=MsoListParagraphCxSpMiddle>Also, the plot shows the actual values and
1921the fit. Note that while the values are close to a straight line, the
1922deviations are huge compared to the estimated uncertainty values for the unit
1923cell volume (shown as very small error bars, unless the plot is
1924magnified).<span style='mso-spacerun:yes'>  </span>If a linear relationship had
1925been defined as a constraint (as can be done with other software packages) <i>the
1926unit cell parameters would have been forced onto this line with no obvious
1927indication that this was not a correct result.</i> </p>
1928
1929<p class=MsoListParagraphCxSpLast><span style='mso-spacerun:yes'> </span></p>
1930
1931<h1>Step 4: Examples of more complex fitt<span class=Heading1Char><span
1932style='font-weight:normal'>i</span></span>ng equations</h1>
1933
1934<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1935
1936<p class=MsoNormal>Here we will look at how more sophisticated Python
1937capabilities can be used to fit more complex behavior.<span
1938style='mso-spacerun:yes'>  </span></p>
1939
1940<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
1941style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1942style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1943</span></span></span><![endif]>Optionally Double-click on the<b
1944style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
1945style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
1946mso-hansi-theme-font:major-latin'>0::c</span> </b>column. Note the changes in
1947the <i style='mso-bidi-font-style:normal'>c</i> unit cell parameter as a
1948function of temperature, as shown below. </p>
1949
1950<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1951
1952<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
1953mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28" o:spid="_x0000_i1034"
1954 type="#_x0000_t75" style='width:350.25pt;height:303pt;visibility:visible;
1955 mso-wrap-style:square'>
1956 <v:imagedata src="ParametricFitting_files/image051.png" o:title=""/>
1957</v:shape><![endif]--><![if !vml]><img width=467 height=404
1958src="ParametricFitting_files/image052.jpg" v:shapes="Picture_x0020_28"><![endif]></span></p>
1959
1960<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1961
1962<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
1963style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1964style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1965</span></span></span><![endif]>We will now fit <i style='mso-bidi-font-style:
1966normal'>c</i> as a function of form 1<span class=GramE>/(</span>1 + <span
1967class=SpellE>exp</span>[k(t-t<sub>0</sub>)]). Select the<b style='mso-bidi-font-weight:
1968normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family:
1969"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
1970major-latin'>Parametric Fit/Add</span></b><span style='font-family:"Calibri",sans-serif;
1971mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'> <b
1972style='mso-bidi-font-weight:normal'>equation</b></span> menu item (as before).
1973For the dependent variable, click on<b style='mso-bidi-font-weight:normal'> </b><b
1974style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1975mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Phase</span></b>
1976and then select<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:
1977normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1978major-latin;mso-hansi-theme-font:major-latin'>0::c</span></b>.<span
1979style='mso-spacerun:yes'>  </span></p>
1980
1981<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1982
1983<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
1984style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
1985style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1986</span></span></span><![endif]>We then enter expression</p>
1987
1988<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
1989
1990<p class=MsoListParagraphCxSpMiddle style='text-indent:.5in'><b
1991style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1992mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b + c / (1+<span
1993class=GramE>math.exp(</span>k*(t-t0)))<o:p></o:p></span></b></p>
1994
1995<p class=MsoListParagraphCxSpMiddle><span style='font-family:"Cambria",serif;
1996mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p>&nbsp;</o:p></span></p>
1997
1998<p class=MsoListParagraphCxSpLast>Note that use of spaces here is arbitrary, but
1999all parentheses are required. Also note that the exponential function [<span
2000class=SpellE>exp</span>(x) or e<sup>x</sup>] is supplied in Python in the math
2001and <span class=SpellE>numpy</span> modules as <span class=SpellE><span
2002class=GramE>math.exp</span></span><span class=GramE>(</span>), <span
2003class=SpellE>numpy.exp</span>(). Either of these can be used as well as the
2004convenience abbreviation of <span class=SpellE><span class=GramE>np.exp</span></span><span
2005class=GramE>(</span>). Further, there are also a small number of common
2006functions that are defined without the prefix for convenience [these include
2007pi, <span class=SpellE><span class=GramE>exp</span></span><span class=GramE>(</span>),
2008<span class=SpellE>sqrt</span>(), <span class=SpellE>sind</span>(), <span
2009class=SpellE>cosd</span>(), <span class=SpellE>tand</span>() where d indicates
2010an argument in degrees.]</p>
2011
2012<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2013
2014<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
2015style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2016style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2017</span></span></span><![endif]>Assign free variables to<b style='mso-bidi-font-weight:
2018normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family:
2019"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
2020major-latin'>b</span>, </b><b style='mso-bidi-font-weight:normal'><span
2021style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2022mso-hansi-theme-font:major-latin'>c</span>, </b><b style='mso-bidi-font-weight:
2023normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2024major-latin;mso-hansi-theme-font:major-latin'>k</span> </b>and<b
2025style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
2026style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2027mso-hansi-theme-font:major-latin'>t0</span></b>, similar as to what was done
2028before. Note that the<b style='mso-bidi-font-weight:normal'> </b>variable name
2029for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2030mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>
2031label was set automatically to <b style='mso-bidi-font-weight:normal'><span
2032style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2033mso-hansi-theme-font:major-latin'>b_1</span></b>. If the same variable name (<b
2034style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2035mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>)
2036was used again here, the same value would be used to fit both equations, which
2037is certainly not what we want here.<span style='mso-spacerun:yes'> 
2038</span>Finally, since this equation is too complex to fit without some
2039reasonable starting values, specify an approximate value, <b style='mso-bidi-font-weight:
2040normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2041major-latin;mso-hansi-theme-font:major-latin'>120</span></b>, for the vicinity
2042of where the <i style='mso-bidi-font-style:normal'>c</i> lattice parameter
2043starts to change (<b style='mso-bidi-font-weight:normal'><span
2044style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2045mso-hansi-theme-font:major-latin'>t0</span></b>) and non-zero values for
2046variables <b>c</b> and <b>k</b>.</p>
2047
2048<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2049
2050<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2051mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40" o:spid="_x0000_i1033"
2052 type="#_x0000_t75" style='width:317.25pt;height:171pt;visibility:visible;
2053 mso-wrap-style:square'>
2054 <v:imagedata src="ParametricFitting_files/image053.png" o:title=""/>
2055</v:shape><![endif]--><![if !vml]><img width=423 height=228
2056src="ParametricFitting_files/image054.jpg" v:shapes="Picture_x0020_40"><![endif]></span></p>
2057
2058<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2059
2060<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
2061style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2062style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2063</span></span></span><![endif]>Optionally, press the <b style='mso-bidi-font-weight:
2064normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2065major-latin;mso-hansi-theme-font:major-latin'>Fit</span></b> button to see if
2066the equation can be refined with starting values of zero for the other three
2067parameters.<span style='mso-spacerun:yes'>  </span>A fit is obtained and is
2068plotted. </p>
2069
2070<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2071
2072<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span
2073style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2074 id="Picture_x0020_41" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:317.25pt;
2075 height:168.75pt;visibility:visible;mso-wrap-style:square'>
2076 <v:imagedata src="ParametricFitting_files/image055.png" o:title=""/>
2077</v:shape><![endif]--><![if !vml]><img width=423 height=225
2078src="ParametricFitting_files/image056.jpg" v:shapes="Picture_x0020_41"><![endif]></span></p>
2079
2080<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2081
2082<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
2083style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2084style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2085</span></span></span><![endif]>Press <b style='mso-bidi-font-weight:normal'><span
2086style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2087mso-hansi-theme-font:major-latin'>OK</span></b> to add this equation to the
2088parametric fits and both equations are refit (and if the label for <b
2089style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2090mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>
2091had not been changed, applying the constraint that <b style='mso-bidi-font-weight:
2092normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2093major-latin;mso-hansi-theme-font:major-latin'>b</span></b> must be the same for
2094both equations.) </p>
2095
2096<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2097
2098<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2099mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32" o:spid="_x0000_i1031"
2100 type="#_x0000_t75" style='width:353.25pt;height:300.75pt;visibility:visible;
2101 mso-wrap-style:square'>
2102 <v:imagedata src="ParametricFitting_files/image057.png" o:title=""/>
2103</v:shape><![endif]--><![if !vml]><img width=471 height=401
2104src="ParametricFitting_files/image058.jpg" v:shapes="Picture_x0020_32"><![endif]></span></p>
2105
2106<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2107
2108<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span
2109style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2110style='mso-list:Ignore'>7.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2111</span></span></span><![endif]>We will now try a more complex equation for the
2112same data, where we set the value to <b style='mso-bidi-font-weight:normal'><span
2113style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2114mso-hansi-theme-font:major-latin'>b</span></b> for temperatures less than <b
2115style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2116mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>t0</span></b>
2117and a critical phenomenon formulism [(t-t<sub>0</sub>)<sup>-a</sup>] for
2118temperatures above <b style='mso-bidi-font-weight:normal'><span
2119style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2120mso-hansi-theme-font:major-latin'>t0</span></b>. To do this we use the Python
2121syntax &quot;<b style='mso-bidi-font-weight:normal'><span style='font-family:
2122"Calibri",sans-serif;mso-ascii-theme-font:major-latin;mso-hansi-theme-font:
2123major-latin'>x1 if <span class=SpellE>testexp</span> else x2</span></b>&quot;
2124which is <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2125mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x1</span></b>
2126where the test expression (<span class=SpellE><b style='mso-bidi-font-weight:
2127normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2128major-latin;mso-hansi-theme-font:major-latin'>testexp</span></b></span> here)
2129is <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2130mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>True</span></b>
2131and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2132mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x2</span></b>
2133otherwise. Thus we can use an expression such as:</p>
2134
2135<p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span></p>
2136
2137<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
2138auto'><span class=GramE><b style='mso-bidi-font-weight:normal'><span
2139style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2140mso-hansi-theme-font:major-latin'>b</span></b></span><b style='mso-bidi-font-weight:
2141normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2142major-latin;mso-hansi-theme-font:major-latin'> if t &lt;= t0 else b + c *
2143(1-(t-t0)**d)<o:p></o:p></span></b></p>
2144
2145<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
2146auto'><span style='font-family:Courier'><o:p>&nbsp;</o:p></span></p>
2147
2148<p class=MsoListParagraphCxSpMiddle>This may be easier to read with the inclusion
2149of extra parentheses (that have no effect on the execution):<span
2150style='font-family:"Cambria",serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2151minor-latin'><o:p></o:p></span></p>
2152
2153<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2154
2155<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
2156auto'><span class=GramE><b style='mso-bidi-font-weight:normal'><span
2157style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2158mso-hansi-theme-font:major-latin'>b</span></b></span><b style='mso-bidi-font-weight:
2159normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2160major-latin;mso-hansi-theme-font:major-latin'> if (t &lt;= t0) else (b + c *
2161(1-(t-t0)**d))<o:p></o:p></span></b></p>
2162
2163<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
2164auto'><span style='font-family:Courier'><o:p>&nbsp;</o:p></span></p>
2165
2166<p class=MsoListParagraphCxSpMiddle>As before, add an equation (or edit an
2167existing one), set the dependent variable to <b style='mso-bidi-font-weight:
2168normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2169major-latin;mso-hansi-theme-font:major-latin'>0::c</span></b>, enter the
2170expression and assign the free and fixed variables, as before. Set the exponent
2171and the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2172mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>t0</span></b>
2173values to initial values of <b style='mso-bidi-font-weight:normal'><span
2174style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2175mso-hansi-theme-font:major-latin'>-0.025</span></b> and <b style='mso-bidi-font-weight:
2176normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2177major-latin;mso-hansi-theme-font:major-latin'>120</span></b>, respectively, and
2178turn off their refinement flags. Then press <b style='mso-bidi-font-weight:
2179normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2180major-latin;mso-hansi-theme-font:major-latin'>Fit</span></b>.<span
2181style='font-family:"Cambria",serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2182minor-latin'><o:p></o:p></span></p>
2183
2184<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2185mso-no-proof:yes'><o:p>&nbsp;</o:p></span></p>
2186
2187<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2188mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42" o:spid="_x0000_i1030"
2189 type="#_x0000_t75" style='width:315.75pt;height:168.75pt;visibility:visible;
2190 mso-wrap-style:square'>
2191 <v:imagedata src="ParametricFitting_files/image059.png" o:title=""/>
2192</v:shape><![endif]--><![if !vml]><img width=421 height=225
2193src="ParametricFitting_files/image060.jpg" v:shapes="Picture_x0020_42"><![endif]></span></p>
2194
2195<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2196
2197<p class=MsoListParagraphCxSpMiddle>Then turn refinement of <b
2198style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2199mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>t0</span></b>
2200back on and press <b style='mso-bidi-font-weight:normal'><span
2201style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2202mso-hansi-theme-font:major-latin'>OK</span></b>. The resulting fit shows the
2203trends quite well: </p>
2204
2205<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2206
2207<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2208mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35" o:spid="_x0000_i1029"
2209 type="#_x0000_t75" style='width:351pt;height:302.25pt;visibility:visible;
2210 mso-wrap-style:square'>
2211 <v:imagedata src="ParametricFitting_files/image061.png" o:title=""/>
2212</v:shape><![endif]--><![if !vml]><img width=468 height=403
2213src="ParametricFitting_files/image062.jpg" v:shapes="Picture_x0020_35"><![endif]></span></p>
2214
2215<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
2216
2217<h1>Step 5: Fitting to a Pseudo Variable</h1>
2218
2219<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2220
2221<p class=MsoNormal>One can fit a function to a pseudo variable, just as to a
2222direct variable. If we look at the plot shown in Step 2, it appears there are
2223two regions. We can treat the lower range as a power-law growth, <span
2224class=SpellE>T<sup>k</sup></span>, and the upper region as linear (m*T + b). </p>
2225
2226<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2227
2228<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
2229style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2230style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2231</span></span></span><![endif]>As before, add an equation<b style='mso-bidi-font-weight:
2232normal'> </b>(or edit an existing one). For the dependent variable, select<b
2233style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span
2234style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2235mso-hansi-theme-font:major-latin'>Global</span></b> to bring up that selection
2236of variables and select<b style='mso-bidi-font-weight:normal'> </b><b
2237style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2238mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b/c</span> </b>and
2239press<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:
2240normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2241major-latin;mso-hansi-theme-font:major-latin'>OK</span>. </b></p>
2242
2243<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2244
2245<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
2246style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2247style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2248</span></span></span><![endif]>Then enter the equation as </p>
2249
2250<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2251
2252<p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space:
2253auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2254mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin;mso-bidi-font-family:
2255"Lucida Grande";color:black'>(o1 + (a1*T<span class=GramE>)*</span>*k) if T
2256&lt; 120 else (o2 + a2*T</span></b><b style='mso-bidi-font-weight:normal'><span
2257style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2258mso-hansi-theme-font:major-latin'>)<o:p></o:p></span></b></p>
2259
2260<p class=MsoListParagraphCxSpMiddle><span style='font-family:"Cambria",serif;
2261mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p>&nbsp;</o:p></span></p>
2262
2263<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
2264style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2265style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2266</span></span></span><![endif]>Assign the free and fixed variables, as shown
2267below. Note that the exponent (<b style='mso-bidi-font-weight:normal'><span
2268style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2269mso-hansi-theme-font:major-latin'>k</span></b>) and scaling factor (<b
2270style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2271mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>a1</span></b>),
2272cannot start as zero<b style='mso-bidi-font-weight:normal'>. </b></p>
2273
2274<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2275
2276<p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US;
2277mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44" o:spid="_x0000_i1028"
2278 type="#_x0000_t75" style='width:332.25pt;height:186pt;visibility:visible;
2279 mso-wrap-style:square'>
2280 <v:imagedata src="ParametricFitting_files/image063.png" o:title=""/>
2281</v:shape><![endif]--><![if !vml]><img width=443 height=248
2282src="ParametricFitting_files/image064.png" v:shapes="Picture_x0020_44"><![endif]></span></p>
2283
2284<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2285
2286<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span
2287style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span
2288style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2289</span></span></span><![endif]>Press the <b style='mso-bidi-font-weight:normal'><span
2290style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2291mso-hansi-theme-font:major-latin'>Fit</span></b> button and note that all the
2292free variables are adjusted </p>
2293
2294<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2295
2296<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2297mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45" o:spid="_x0000_i1027"
2298 type="#_x0000_t75" style='width:333.75pt;height:189pt;visibility:visible;
2299 mso-wrap-style:square'>
2300 <v:imagedata src="ParametricFitting_files/image065.png" o:title=""/>
2301</v:shape><![endif]--><![if !vml]><img width=445 height=252
2302src="ParametricFitting_files/image066.png" v:shapes="Picture_x0020_45"><![endif]></span><span
2303style='mso-spacerun:yes'> </span></p>
2304
2305<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2306
2307<p class=MsoListParagraphCxSpMiddle>Also, that the plotted result is close to
2308the values from the refinement.</p>
2309
2310<p class=MsoListParagraphCxSpMiddle><o:p>&nbsp;</o:p></p>
2311
2312<p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US;
2313mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48" o:spid="_x0000_i1026"
2314 type="#_x0000_t75" style='width:348.75pt;height:302.25pt;visibility:visible;
2315 mso-wrap-style:square'>
2316 <v:imagedata src="ParametricFitting_files/image067.png" o:title=""/>
2317</v:shape><![endif]--><![if !vml]><img width=465 height=403
2318src="ParametricFitting_files/image068.png" v:shapes="Picture_x0020_48"><![endif]></span></p>
2319
2320<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
2321
2322<p class=MsoNormal style='margin-left:.25in'><o:p>&nbsp;</o:p></p>
2323
2324<p class=MsoNormal>This completes this tutorial on use of Pseudo Variables and
2325parametric fitting. </p>
2326
2327<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2328
2329<h1>Advanced Use: Externally-Defined Functions</h1>
2330
2331<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2332
2333<p class=MsoNormal>The parametric refinement section of GSAS-II is intended to
2334be quite flexible, but for very complex fitting, a user may wish to define a
2335custom Python function. Such a function can be defined in a separate module
2336that will be accessed with a parametric equation (or pseudo variable).</p>
2337
2338<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2339
2340<p class=MsoNormal>As an example of that, if we create a file called <b
2341style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2342mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>fittest.py</span></b>
2343and locate that file in any directory in the Python path (most simply, in the
2344directory where the project file, <span class=SpellE><b style='mso-bidi-font-weight:
2345normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2346major-latin;mso-hansi-theme-font:major-latin'>SeqTut.gpx</span></b></span>, is
2347located) and place a routine <span class=SpellE><b style='mso-bidi-font-weight:
2348normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2349major-latin;mso-hansi-theme-font:major-latin'>fitfxn</span></b></span> in that
2350module:</p>
2351
2352<blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'>
2353
2354<blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><pre><o:p>&nbsp;</o:p></pre><pre><b
2355style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2356mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'># <span
2357class=GramE>file</span> fittest.py<o:p></o:p></span></b></pre><pre><span
2358class=SpellE><span class=GramE><b style='mso-bidi-font-weight:normal'><span
2359style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2360mso-hansi-theme-font:major-latin'>def</span></b></span></span><b
2361style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2362mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'> <span
2363class=SpellE>fitfxn</span>(T,o1,o2,a1,a2,k):<o:p></o:p></span></b></pre><pre><b
2364style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2365mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'>    </span><span
2366class=GramE>if</span> T &lt; 120:<o:p></o:p></span></b></pre><pre><b
2367style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2368mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'>        </span><span
2369class=GramE>return</span> o1 + (a1*T)**k<o:p></o:p></span></b></pre><pre><b
2370style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2371mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'>    </span><span
2372class=GramE>else</span>:<o:p></o:p></span></b></pre><pre><b style='mso-bidi-font-weight:
2373normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2374major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'>        </span><span
2375class=GramE>return</span> o2 + a2*T<o:p></o:p></span></b></pre></blockquote>
2376
2377</blockquote>
2378
2379<p class=MsoNormal>The function <span class=SpellE><b style='mso-bidi-font-weight:
2380normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2381major-latin;mso-hansi-theme-font:major-latin'>fittest.fitfxn</span></b></span>
2382can then be used to duplicate the previous example: </p>
2383
2384<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2385
2386<p class=MsoNormal><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2387 id="Picture_x0020_47" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:315pt;
2388 height:185.25pt;visibility:visible;mso-wrap-style:square'>
2389 <v:imagedata src="ParametricFitting_files/image069.png" o:title="" croptop="3393f"
2390  cropbottom="7847f" cropleft="3471f" cropright="3290f"/>
2391</v:shape><![endif]--><![if !vml]><img width=420 height=247
2392src="ParametricFitting_files/image070.png" v:shapes="Picture_x0020_47"><![endif]></span></p>
2393
2394<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2395
2396<p class=MsoNormal>Note that module <b style='mso-bidi-font-weight:normal'><span
2397style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:major-latin;
2398mso-hansi-theme-font:major-latin'>fittest</span></b> is automatically located
2399and loaded, provided it is found in the path. No changes to the standard
2400distributed GSAS-II code are needed. Care to avoid use of a module name already
2401found in GSAS-II or Python is wise.</p>
2402
2403</div>
2404
2405</body>
2406
2407</html>
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