- Timestamp:
- Jul 22, 2014 3:45:19 PM (11 years ago)
- Location:
- trunk
- Files:
-
- 2 deleted
- 6 edited
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TabularUnified trunk/GSASIIElem.py ¶
r1413 r1428 21 21 import atmdata 22 22 23 getElSym = lambda sym: sym.split('+')[0].split('-')[0] 23 getElSym = lambda sym: sym.split('+')[0].split('-')[0].capitalize() 24 24 def GetFormFactorCoeff(El): 25 25 """Read X-ray form factor coefficients from `atomdata.py` file -
TabularUnified trunk/GSASIIpwdGUI.py ¶
r1418 r1428 2476 2476 ElList = subst['Elements'].keys() 2477 2477 for El in ElList: 2478 Info = G2elem.GetAtomInfo(El.strip(). upper())2478 Info = G2elem.GetAtomInfo(El.strip().capitalize()) 2479 2479 Info.update(subst['Elements'][El]) 2480 2480 data['Substances'][name]['Elements'][El] = Info … … 2573 2573 if dlg.ShowModal() == wx.ID_OK: 2574 2574 for El in dlg.Elem: 2575 El = El.strip(). upper()2575 El = El.strip().capitalize() 2576 2576 Info = G2elem.GetAtomInfo(El) 2577 2577 Info.update({'Num':1}) … … 3763 3763 El = PE.Elem 3764 3764 if El not in ElList and El != 'None': 3765 ElemSym = El.strip(). upper()3765 ElemSym = El.strip().capitalize() 3766 3766 FpMu = G2elem.FPcalc(G2elem.GetXsectionCoeff(ElemSym), keV) 3767 3767 ElData = G2elem.GetFormFactorCoeff(ElemSym)[0] -
TabularUnified trunk/help/Fitting Small Angle Scattering Data.htm ¶
r1351 r1428 25 25 <o:Author>Von Dreele</o:Author> 26 26 <o:LastAuthor>Von Dreele</o:LastAuthor> 27 <o:Revision> 5</o:Revision>28 <o:TotalTime>207 4</o:TotalTime>27 <o:Revision>6</o:Revision> 28 <o:TotalTime>2076</o:TotalTime> 29 29 <o:Created>2014-05-01T13:58:00Z</o:Created> 30 <o:LastSaved>2014-0 5-03T16:24:00Z</o:LastSaved>31 <o:Pages> 10</o:Pages>30 <o:LastSaved>2014-07-22T15:10:00Z</o:LastSaved> 31 <o:Pages>9</o:Pages> 32 32 <o:Words>1444</o:Words> 33 33 <o:Characters>8234</o:Characters> … … 883 883 <div class=WordSection1> 884 884 885 <h1><strong> <span style='mso-bidi-font-weight:normal'>Fitting Small Angle X-Ray886 Data Alumina Powder</span><o:p></o:p></strong></h1>885 <h1><strong>Fitting</strong><strong><span style='mso-bidi-font-weight:normal'> 886 Small Angle X-Ray Data Alumina Powder</span><o:p></o:p></strong></h1> 887 887 888 888 <p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'>In 889 889 this tutorial you will fit small angle scattering data for an alumina polishing 890 powder using data from a constant wavelength synchrotron X-ray USAXS instrument.891 You will use both a lognormal distribution of spherical particles model and a 892 unified <span class=SpellE>Guinier-Porod</span> model. The data were collected 893 from <span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin; 894 m so-bidi-font-weight:bold;mso-bidi-font-style:italic'>powders spread onto895 s ticky tape and covered with another layer of the same tape. The data were896 corrected for background using data collected from two layers of sticky tape. 897 However, the sample thickness is not</span> accurately known <span890 powder using data from a constant wavelength synchrotron X-ray USAXS 891 instrument. You will use both a lognormal distribution of spherical particles 892 model and a unified <span class=SpellE>Guinier-Porod</span> model. The data 893 were collected from <span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font: 894 minor-latin;mso-bidi-font-weight:bold;mso-bidi-font-style:italic'>powders 895 spread onto sticky tape and covered with another layer of the same tape. The 896 data were corrected for background using data collected from two layers of 897 sticky tape. However, the sample thickness is not</span> accurately known <span 898 898 style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin; 899 899 mso-bidi-font-weight:bold;mso-bidi-font-style:italic'>so the data are not … … 944 944 minor-latin'> to find the file</span>; you will have to select the <b 945 945 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; 946 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file (*.*)</span></b>947 filter to see it.</p>946 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file 947 (*.*)</span></b> filter to see it.</p> 948 948 949 949 <p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span … … 1036 1036 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof: 1037 1037 yes'><span style='mso-element:field-begin'></span><span 1038 style='mso-spacerun:yes'> </span>REF _Ref386699439 \h 1039 style='mso-spacerun:yes'> </span>\* MERGEFORMAT <span style='mso-element:field-separator'></span></span></b><![endif]--><b1038 style='mso-spacerun:yes'> </span>REF _Ref386699439 \h<span 1039 style='mso-spacerun:yes'> </span>\* MERGEFORMAT <span style='mso-element:field-separator'></span></span></b><![endif]--><b 1040 1040 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; 1041 1041 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Step 4 … … 1149 1149 mso-hansi-theme-font:minor-latin'>Size Distribution</span></b> tutorial, you 1150 1150 would know that there were two populations of particles in the sample. One had 1151 a mean diameter of ~1300A and the other had a mean diameter of ~150A. You will also1152 need something to describe the very lowest Q portion of the data. Do <b1151 a mean diameter of ~1300A and the other had a mean diameter of ~150A. You will 1152 also need something to describe the very lowest Q portion of the data. Do <b 1153 1153 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; 1154 1154 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models/Add</span></b> … … 1373 1373 <p class=MsoNormal><o:p> </o:p></p> 1374 1374 1375 <p class=MsoNormal>Finally, you can refine these coefficients to find the best 1376 fitto the data. As a beginner, Id start by refining just the two <span1375 <p class=MsoNormal>Finally, you can refine these coefficients to find the best fit 1376 to the data. As a beginner, Id start by refining just the two <span 1377 1377 class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family: 1378 1378 "Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: … … 1649 1649 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; 1650 1650 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Mean</span></b> 1651 values obtained earlier. Also note that this model makes no reference to the 1652 substancecontrast used earlier (the <b style='mso-bidi-font-weight:normal'><span1651 values obtained earlier. Also note that this model makes no reference to the substance 1652 contrast used earlier (the <b style='mso-bidi-font-weight:normal'><span 1653 1653 style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; 1654 1654 mso-hansi-theme-font:minor-latin'>Size Distribution</span></b> plot will not -
TabularUnified trunk/help/ParametricFitting.htm ¶
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987 896 mso-level-tab-stop:none; … … 997 906 <style> 998 907 /* Style Definitions */ 999 table.MsoNormalTable908 table.MsoNormalTable 1000 909 {mso-style-name:"Table Normal"; 1001 910 mso-tstyle-rowband-size:0; … … 1009 918 mso-pagination:widow-orphan; 1010 919 font-size:10.0pt; 1011 font-family: Cambria;920 font-family:"Cambria","serif"; 1012 921 mso-ascii-font-family:Cambria; 1013 922 mso-ascii-theme-font:minor-latin; … … 1016 925 mso-fareast-language:JA;} 1017 926 </style> 1018 <![endif]--><!--[if gte mso 9]><xml> 1019 <o:shapedefaults v:ext="edit" spidmax="1033"/> 927 <![endif]--> 928 <meta name=Title content=""> 929 <meta name=Keywords content=""> 930 <!--[if gte mso 9]><xml> 931 <o:shapedefaults v:ext="edit" spidmax="1032"/> 1020 932 </xml><![endif]--><!--[if gte mso 9]><xml> 1021 933 <o:shapelayout v:ext="edit"> … … 1035 947 the fit parameters from the fit and <i style='mso-bidi-font-style:normal'>their 1036 948 estimated uncertainty</i> (<span class=SpellE>s.u</span>.) can be computed by 1037 defining one or more "pseudo-variables"(Pseudo <span class=SpellE>Vars</span>)949 defining one or more "pseudo-variables" (Pseudo <span class=SpellE>Vars</span>) 1038 950 Note that the covariance matrix from the fit is used to provide appropriate 1039 treatment the correlation in parameters with respect to uncertainty1040 estimation.<span style= "mso-spacerun:yes"> </span>In addition, parametric1041 equations in terms of sample parameters such as temperature and pressure, etc. can1042 be fit to either the parameters from the fit or the Pseudo Vars. </p>951 treatment of the correlation in parameters with respect to uncertainty 952 estimation.<span style='mso-spacerun:yes'> </span>In addition, parametric 953 equations in terms of sample parameters such as temperature and pressure, etc. 954 can be fit to either the parameters from the fit or the Pseudo Vars. </p> 1043 955 1044 956 <p class=MsoNormal><o:p> </o:p></p> … … 1046 958 <p class=MsoNormal>This tutorial assumes that the steps in the <span 1047 959 style='mso-bidi-font-family:"Times New Roman"'><a href="SequentialTutorial.htm">Sequential 1048 refinement of multiple datasets</a> tutorial have already been performed. <o:p></o:p></span></p> 1049 1050 <p class=MsoNormal><span style='mso-bidi-font-family:"Times New Roman"'><o:p> </o:p></span></p> 1051 1052 <h2>Step 1. Open the previous Sequential Fit</h2> 960 refinement of multiple datasets</a> tutorial have already been performed. </span>If 961 you have not done so already, <a href="Starting%20GSAS.htm">start GSAS-II</a>. 962 Some of the pictures in this tutorial are from a Mac OSX machine; these 963 illustrate the differences in menu location from Windows/Linux machines.<o:p></o:p></p> 964 965 <h1><span class=GramE>Step 1.</span> Open the previous Sequential Fit</h1> 1053 966 1054 967 <p class=MsoNormal><o:p> </o:p></p> 1055 968 1056 <p class=MsoListParagraph style='margin-bottom:6.0pt;text-indent:-.25in; 1057 mso-list:l6 level1 lfo1'><![if !supportLists]><span style='mso-fareast-font-family: 1058 Cambria;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:Cambria; 1059 mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>1.<span 1060 style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]>Start 1061 GSAS-II</p> 1062 1063 <p class=MsoListParagraph style='margin-bottom:6.0pt;text-indent:-.25in; 1064 mso-list:l6 level1 lfo1'><![if !supportLists]><span style='mso-fareast-font-family: 1065 Cambria;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:Cambria; 1066 mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>2.<span 1067 style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><b 1068 style='mso-bidi-font-weight:normal'>Click on the File/Open Project</b> menu 1069 item to load file named <span class=SpellE><span style='font-family:Courier'>SeqTut.gpx</span></span>. 969 <p class=MsoListParagraphCxSpFirst style='margin-bottom:6.0pt;mso-add-space: 970 auto;text-indent:-.25in;mso-list:l4 level1 lfo2'><![if !supportLists]><span 971 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 972 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> 973 </span></span></span><![endif]>Select the<b style='mso-bidi-font-weight:normal'> 974 </b><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; 975 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>File/Open 976 Project</span></b> menu item to load file named <span class=SpellE><b 977 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; 978 mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>SeqTut.gpx</span></b></span>. 1070 979 </p> 1071 980 1072 <p class=MsoListParagraph style='margin-bottom:6.0pt;text-indent:-.25in; 1073 mso-list:l6 level1 lfo1'><![if !supportLists]><span style='mso-fareast-font-family: 1074 Cambria;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:Cambria; 1075 mso-bidi-theme-font:minor-latin'><span style='mso-list:Ignore'>3.<span 1076 style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><b 1077 style='mso-bidi-font-weight:normal'>Click on the Sequential results </b>item in 1078 the data tree. The sequential refinement results data table is displayed, as 1079 below. </p> 1080 1081 <p class=MsoListParagraph style='margin-bottom:6.0pt'><span style='mso-fareast-language: 1082 EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype id="_x0000_t75" 1083 coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" 1084 filled="f" stroked="f"> 981 <p class=MsoListParagraphCxSpMiddle style='margin-bottom:6.0pt;mso-add-space: 982 auto;text-indent:-.25in;mso-list:l4 level1 lfo2'><![if !supportLists]><span 983 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 984 style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> 985 </span></span></span><![endif]>Select the <b style='mso-bidi-font-weight:normal'><span 986 style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; 987 mso-hansi-theme-font:major-latin'>Sequential results</span></b> item in the 988 data tree. The sequential refinement results data table is displayed, as below. 989 </p> 990 991 <p class=MsoListParagraphCxSpLast style='margin-bottom:6.0pt;mso-add-space: 992 auto'><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype 993 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" 994 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> 1085 995 <v:stroke joinstyle="miter"/> 1086 996 <v:formulas> … … 1100 1010 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> 1101 1011 <o:lock v:ext="edit" aspectratio="t"/> 1102 </v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_i1053" type="#_x0000_t75" 1103 style='width:358pt;height:181pt;visibility:visible;mso-wrap-style:square'> 1104 <v:imagedata src="ParametricFitting_files/image001.png" o:title="" croptop="2940f" 1105 cropbottom="7530f" cropleft="2593f" cropright="2770f"/> 1106 </v:shape><![endif]--><![if !vml]><img border=0 width=360 height=183 1107 src="ParametricFitting_files/image002.png" v:shapes="Picture_x0020_1"><![endif]></span></p> 1108 1109 <h2>Step 2. Create a Pseudo <span class=SpellE>Var</span></h2> 1012 </v:shapetype><v:shape id="Picture_x0020_36" o:spid="_x0000_i1053" type="#_x0000_t75" 1013 style='width:525pt;height:262.5pt;visibility:visible;mso-wrap-style:square'> 1014 <v:imagedata src="ParametricFitting_files/image069.png" o:title=""/> 1015 </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350 1016 src="ParametricFitting_files/image069.png" v:shapes="Picture_x0020_36"><![endif]></span></p> 1017 1018 <h1>Step 2. Create a Pseudo <span class=SpellE>Var</span></h1> 1110 1019 1111 1020 <p class=MsoNormal><o:p> </o:p></p> … … 1116 1025 expression can be used to define this. While one can plot <i style='mso-bidi-font-style: 1117 1026 normal'>a</i>, <i style='mso-bidi-font-style:normal'>b</i> and <i 1118 style='mso-bidi-font-style:normal'>c</i> axis lengths by clicking on the appropriate 1119 column of the table, to compare them one might want to scale them. Alternately, 1120 as will be done here, we will plot the ratio of <i style='mso-bidi-font-style: 1121 normal'>b</i> and <i style='mso-bidi-font-style:normal'>c</i>.</p> 1027 style='mso-bidi-font-style:normal'>c</i> axis lengths by clicking on the 1028 appropriate column of the table, to compare them one might want to scale them. 1029 Alternately, as will be done here, we will plot the ratio of <i 1030 style='mso-bidi-font-style:normal'>b</i> and <i style='mso-bidi-font-style: 1031 normal'>c</i>.</p> 1122 1032 1123 1033 <p class=MsoNormal><o:p> </o:p></p> 1124 1034 1125 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l2 level1 lfo2'><![if !supportLists]><span 1126 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1127 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1128 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> 1035 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span 1036 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1037 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> 1129 1038 </span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Click on 1130 1039 the Pseudo <span class=SpellE>Vars</span>/Add</b> menu item to create a new … … 1135 1044 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1136 1045 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_2" o:spid="_x0000_i1052" 1137 type="#_x0000_t75" style='width:159pt;height:4 6pt;visibility:visible;1046 type="#_x0000_t75" style='width:159pt;height:45.75pt;visibility:visible; 1138 1047 mso-wrap-style:square'> 1139 1048 <v:imagedata src="ParametricFitting_files/image003.png" o:title=""/> 1140 </v:shape><![endif]--><![if !vml]><img border=0 width=161 height=48 1141 src="ParametricFitting_files/image004.png" v:shapes="Picture_x0020_2"><![endif]></span></p> 1142 1143 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1144 1145 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo2'><![if !supportLists]><span 1146 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1147 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1148 style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> 1049 </v:shape><![endif]--><![if !vml]><img border=0 width=212 height=61 1050 src="ParametricFitting_files/image072.jpg" v:shapes="Picture_x0020_2"><![endif]></span></p> 1051 1052 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1053 1054 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span 1055 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1056 style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> 1149 1057 </span></span></span><![endif]>A window opens to define a formula</p> 1150 1058 … … 1153 1061 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1154 1062 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3" o:spid="_x0000_i1051" 1155 type="#_x0000_t75" style='width:3 10pt;height:152pt;visibility:visible;1063 type="#_x0000_t75" style='width:309.75pt;height:152.25pt;visibility:visible; 1156 1064 mso-wrap-style:square'> 1157 1065 <v:imagedata src="ParametricFitting_files/image005.png" o:title="" croptop="4214f" 1158 1066 cropbottom="8982f" cropleft="3852f" cropright="3654f"/> 1159 </v:shape><![endif]--><![if !vml]><img border=0 width= 312 height=1541160 src="ParametricFitting_files/image0 06.png" v:shapes="Picture_x0020_3"><![endif]></span></p>1067 </v:shape><![endif]--><![if !vml]><img border=0 width=413 height=203 1068 src="ParametricFitting_files/image073.png" v:shapes="Picture_x0020_3"><![endif]></span></p> 1161 1069 1162 1070 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1163 1071 1164 1072 <p class=MsoListParagraphCxSpMiddle><!--[if gte vml 1]><v:shape id="Picture_x0020_4" 1165 o:spid="_x0000_s103 2" type="#_x0000_t75" style='position:absolute;left:0;1073 o:spid="_x0000_s1031" type="#_x0000_t75" style='position:absolute;left:0; 1166 1074 text-align:left;margin-left:178.3pt;margin-top:846.2pt;width:229.5pt;height:86.5pt; 1167 1075 z-index:251658240;visibility:visible;mso-wrap-style:square; 1168 mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; 1076 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; 1077 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; 1169 1078 mso-wrap-distance-bottom:0;mso-position-horizontal:right; 1170 1079 mso-position-horizontal-relative:margin;mso-position-vertical:absolute; 1171 mso-position-vertical-relative:margin'> 1080 mso-position-vertical-relative:margin;mso-width-percent:0; 1081 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'> 1172 1082 <v:imagedata src="ParametricFitting_files/image007.png" o:title=""/> 1173 1083 <w:wrap type="square" anchorx="margin" anchory="margin"/> 1174 </v:shape><![endif]--><![if !vml]><img width= 232 height=891175 src="ParametricFitting_files/image0 08.png" align=right hspace=9v:shapes="Picture_x0020_4"><![endif]>In1176 this window, <b style='mso-bidi-font-weight:normal'>type a Python expression, "b/c",</b>1177 but note that the variables <b style='mso-bidi-font-weight:normal'>c</b> and <b 1178 style='mso-bidi-font-weight:normal'>b</b> here are arbitrary labels. After 1179 entering the formula, <b style='mso-bidi-font-weight:normal'>press the Validate 1180 button</b> or wait a few seconds and the validation will be tested 1181 automatically. Note that if you pause too long, while typing, an error message 1182 may be displayed as the incomplete formula is found to be invalid. If so, make1183 corrections or keep typing until the entire expression is entered. <span 1184 style="mso-spacerun:yes"> </span>The error message will sometimes show 1185 where error is encountered, though not in this case. </p>1084 </v:shape><![endif]--><![if !vml]><img width=306 height=115 1085 src="ParametricFitting_files/image074.jpg" align=right hspace=12 v:shapes="Picture_x0020_4"><![endif]>In 1086 this window, <b style='mso-bidi-font-weight:normal'>type a Python expression, 1087 "b/c",</b> but note that the variables <b style='mso-bidi-font-weight: 1088 normal'>c</b> and <b style='mso-bidi-font-weight:normal'>b</b> here are 1089 arbitrary labels. After entering the formula, <b style='mso-bidi-font-weight: 1090 normal'>press the Validate button</b> or wait a few seconds and the validation 1091 will be tested automatically. Note that if you pause too long, while typing, an 1092 error message may be displayed as the incomplete formula is found to be 1093 invalid. If so, make corrections or keep typing until the entire expression is 1094 entered.<span style='mso-spacerun:yes'> </span>The error message will 1095 sometimes show where error is encountered, though not in this case. </p> 1186 1096 1187 1097 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1195 1105 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1196 1106 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5" o:spid="_x0000_i1050" 1197 type="#_x0000_t75" style='width:3 10pt;height:152pt;visibility:visible;1107 type="#_x0000_t75" style='width:309.75pt;height:152.25pt;visibility:visible; 1198 1108 mso-wrap-style:square'> 1199 1109 <v:imagedata src="ParametricFitting_files/image009.png" o:title="" croptop="4435f" 1200 1110 cropbottom="8537f" cropleft="3852f" cropright="3650f"/> 1201 </v:shape><![endif]--><![if !vml]><img border=0 width=312 height=154 1202 src="ParametricFitting_files/image010.png" v:shapes="Picture_x0020_5"><![endif]></span></p> 1203 1204 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1205 1206 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo2'><![if !supportLists]><span 1207 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1208 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1209 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> 1111 </v:shape><![endif]--><![if !vml]><img border=0 width=413 height=203 1112 src="ParametricFitting_files/image075.png" v:shapes="Picture_x0020_5"><![endif]></span></p> 1113 1114 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1115 1116 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span 1117 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1118 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> 1210 1119 </span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_6" 1211 o:spid="_x0000_s103 1" type="#_x0000_t75" style='position:absolute;left:0;1120 o:spid="_x0000_s1030" type="#_x0000_t75" style='position:absolute;left:0; 1212 1121 text-align:left;margin-left:37.3pt;margin-top:1143.2pt;width:88.5pt;height:65.5pt; 1213 1122 z-index:251659264;visibility:visible;mso-wrap-style:square; 1214 mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; 1123 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; 1124 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; 1215 1125 mso-wrap-distance-bottom:0;mso-position-horizontal:right; 1216 1126 mso-position-horizontal-relative:margin;mso-position-vertical:absolute; 1217 mso-position-vertical-relative:margin'> 1127 mso-position-vertical-relative:margin;mso-width-percent:0; 1128 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'> 1218 1129 <v:imagedata src="ParametricFitting_files/image011.png" o:title=""/> 1219 1130 <w:wrap type="square" anchorx="margin" anchory="margin"/> 1220 </v:shape><![endif]--><![if !vml]><img width= 91 height=681221 src="ParametricFitting_files/image0 12.png" align=right hspace=9v:shapes="Picture_x0020_6"><![endif]>Assign1131 </v:shape><![endif]--><![if !vml]><img width=118 height=87 1132 src="ParametricFitting_files/image076.jpg" align=right hspace=12 v:shapes="Picture_x0020_6"><![endif]>Assign 1222 1133 the label for the numerator by <b style='mso-bidi-font-weight:normal'>clicking 1223 1134 on the menu button next to label b</b>; this will bring up a list of variable 1224 types, from this <b style='mso-bidi-font-weight:normal'>select Phase</b> to 1225 bringup a list of phase variables, from that list <b style='mso-bidi-font-weight:1135 types, from this <b style='mso-bidi-font-weight:normal'>select Phase</b> to bring 1136 up a list of phase variables, from that list <b style='mso-bidi-font-weight: 1226 1137 normal'>select variable </b><b style='mso-bidi-font-weight:normal'><span 1227 style='font-family:Courier'>0<span class=GramE>::</span>b</span>,</b> which is 1228 the <i style='mso-bidi-font-style:normal'>b</i> lattice parameter for phase 0 1229 (CuCr<sub>2</sub>O<sub>4</sub>). Repeat this process to select <b 1230 style='mso-bidi-font-weight:normal'>assign to label c variable </b><b 1231 style='mso-bidi-font-weight:normal'><span style='font-family:Courier'>0<span 1232 class=GramE>::</span>b</span></b>.</p> 1138 style='font-family:Courier'>0::b</span>,</b> which is the <i style='mso-bidi-font-style: 1139 normal'>b</i> lattice parameter for phase 0 (CuCr<sub>2</sub>O<sub>4</sub>). 1140 Repeat this process to select <b style='mso-bidi-font-weight:normal'>assign to 1141 label c variable </b><b style='mso-bidi-font-weight:normal'><span 1142 style='font-family:Courier'>0::b</span></b>.</p> 1233 1143 1234 1144 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1236 1146 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1237 1147 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8" o:spid="_x0000_i1049" 1238 type="#_x0000_t75" style='width:31 6pt;height:129pt;visibility:visible;1148 type="#_x0000_t75" style='width:315.75pt;height:129pt;visibility:visible; 1239 1149 mso-wrap-style:square'> 1240 1150 <v:imagedata src="ParametricFitting_files/image013.png" o:title="" croptop="4597f" 1241 1151 cropbottom="9873f" cropleft="3348f" cropright="3506f"/> 1242 </v:shape><![endif]--><![if !vml]><img border=0 width= 318 height=1311243 src="ParametricFitting_files/image0 14.png" v:shapes="Picture_x0020_8"><![endif]></span></p>1152 </v:shape><![endif]--><![if !vml]><img border=0 width=421 height=172 1153 src="ParametricFitting_files/image077.png" v:shapes="Picture_x0020_8"><![endif]></span></p> 1244 1154 1245 1155 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1255 1165 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1256 1166 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9" o:spid="_x0000_i1048" 1257 type="#_x0000_t75" style='width:314 pt;height:154pt;visibility:visible;1167 type="#_x0000_t75" style='width:314.25pt;height:153.75pt;visibility:visible; 1258 1168 mso-wrap-style:square'> 1259 1169 <v:imagedata src="ParametricFitting_files/image015.png" o:title="" croptop="3770f" 1260 1170 cropbottom="8549f" cropleft="3371f" cropright="3424f"/> 1261 </v:shape><![endif]--><![if !vml]><img border=0 width= 316 height=1561262 src="ParametricFitting_files/image0 16.png" v:shapes="Picture_x0020_9"><![endif]></span></p>1171 </v:shape><![endif]--><![if !vml]><img border=0 width=419 height=205 1172 src="ParametricFitting_files/image078.png" v:shapes="Picture_x0020_9"><![endif]></span></p> 1263 1173 1264 1174 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1272 1182 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1273 1183 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10" o:spid="_x0000_i1047" 1274 type="#_x0000_t75" style='width:354pt;height:18 1pt;visibility:visible;1184 type="#_x0000_t75" style='width:354pt;height:180.75pt;visibility:visible; 1275 1185 mso-wrap-style:square'> 1276 1186 <v:imagedata src="ParametricFitting_files/image017.png" o:title="" croptop="2743f" 1277 1187 cropbottom="7533f" cropleft="2917f" cropright="3097f"/> 1278 </v:shape><![endif]--><![if !vml]><img border=0 width= 356 height=1831279 src="ParametricFitting_files/image0 18.png" v:shapes="Picture_x0020_10"><![endif]></span></p>1188 </v:shape><![endif]--><![if !vml]><img border=0 width=472 height=241 1189 src="ParametricFitting_files/image079.png" v:shapes="Picture_x0020_10"><![endif]></span></p> 1280 1190 1281 1191 <p class=MsoListParagraphCxSpMiddle><!--[if gte vml 1]><v:shape id="Picture_x0020_11" 1282 o:spid="_x0000_s10 30" type="#_x0000_t75" style='position:absolute;left:0;1192 o:spid="_x0000_s1029" type="#_x0000_t75" style='position:absolute;left:0; 1283 1193 text-align:left;margin-left:42.3pt;margin-top:666.2pt;width:93.5pt;height:39pt; 1284 1194 z-index:251660288;visibility:visible;mso-wrap-style:square; 1285 mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; 1195 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; 1196 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; 1286 1197 mso-wrap-distance-bottom:0;mso-position-horizontal:right; 1287 1198 mso-position-horizontal-relative:margin;mso-position-vertical:absolute; 1288 mso-position-vertical-relative:margin'> 1199 mso-position-vertical-relative:margin;mso-width-percent:0; 1200 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'> 1289 1201 <v:imagedata src="ParametricFitting_files/image019.png" o:title=""/> 1290 1202 <w:wrap type="square" anchorx="margin" anchory="margin"/> 1291 </v:shape><![endif]--><![if !vml]><img width= 96 height=411292 src="ParametricFitting_files/image0 20.png" align=right hspace=9v:shapes="Picture_x0020_11"><![endif]>Also1203 </v:shape><![endif]--><![if !vml]><img width=125 height=52 1204 src="ParametricFitting_files/image080.jpg" align=right hspace=12 v:shapes="Picture_x0020_11"><![endif]>Also 1293 1205 note that positioning the mouse above any cell in the table and waiting for a 1294 few <span class=GramE>seconds</span> causes the <span class=SpellE>s.u</span>. <span1295 class=GramE>to</span> be shown as a tooltip.</p>1206 few seconds causes the <span class=SpellE>s.u</span>. to be shown as a tooltip. 1207 </p> 1296 1208 1297 1209 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1298 1210 1299 1211 <p class=MsoListParagraphCxSpMiddle><b style='mso-bidi-font-weight:normal'>Double 1300 clicking on the column</b> will cause the pseudo <span class=SpellE>var</span> to1301 be plotted:</p>1212 clicking on the column</b> will cause the pseudo <span class=SpellE>var</span> 1213 to be plotted:</p> 1302 1214 1303 1215 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1305 1217 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1306 1218 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12" o:spid="_x0000_i1046" 1307 type="#_x0000_t75" style='width:35 2pt;height:303pt;visibility:visible;1219 type="#_x0000_t75" style='width:351.75pt;height:303pt;visibility:visible; 1308 1220 mso-wrap-style:square'> 1309 1221 <v:imagedata src="ParametricFitting_files/image021.png" o:title="" croptop="2107f" 1310 1222 cropbottom="4939f" cropleft="3133f" cropright="3309f"/> 1311 </v:shape><![endif]--><![if !vml]><img border=0 width= 354 height=3051312 src="ParametricFitting_files/image0 22.png" v:shapes="Picture_x0020_12"><![endif]></span></p>1223 </v:shape><![endif]--><![if !vml]><img border=0 width=469 height=404 1224 src="ParametricFitting_files/image081.png" v:shapes="Picture_x0020_12"><![endif]></span></p> 1313 1225 1314 1226 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1315 1227 1316 1228 <p class=MsoListParagraphCxSpMiddle><b style='mso-bidi-font-weight:normal'>Press 1317 the "s" key</b> inside the plot to <b style='mso-bidi-font-weight:normal'>select1318 Temperature</b> as the x-axis. </p>1229 the "s" key</b> inside the plot to <b style='mso-bidi-font-weight: 1230 normal'>select Temperature</b> as the x-axis. </p> 1319 1231 1320 1232 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1322 1234 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1323 1235 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13" o:spid="_x0000_i1045" 1324 type="#_x0000_t75" style='width:16 3pt;height:156pt;visibility:visible;1236 type="#_x0000_t75" style='width:162.75pt;height:156pt;visibility:visible; 1325 1237 mso-wrap-style:square'> 1326 1238 <v:imagedata src="ParametricFitting_files/image023.png" o:title="" croptop="4105f" 1327 1239 cropbottom="8920f" cropleft="6109f" cropright="5911f"/> 1328 </v:shape><![endif]--><![if !vml]><img border=0 width= 165 height=1581329 src="ParametricFitting_files/image0 24.png" v:shapes="Picture_x0020_13"><![endif]></span></p>1240 </v:shape><![endif]--><![if !vml]><img border=0 width=217 height=208 1241 src="ParametricFitting_files/image082.png" v:shapes="Picture_x0020_13"><![endif]></span></p> 1330 1242 1331 1243 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1337 1249 <p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US; 1338 1250 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14" o:spid="_x0000_i1044" 1339 type="#_x0000_t75" style='width:353 pt;height:304pt;visibility:visible;1251 type="#_x0000_t75" style='width:353.25pt;height:303.75pt;visibility:visible; 1340 1252 mso-wrap-style:square'> 1341 1253 <v:imagedata src="ParametricFitting_files/image025.png" o:title="" croptop="1859f" 1342 1254 cropbottom="5066f" cropleft="3024f" cropright="3203f"/> 1343 </v:shape><![endif]--><![if !vml]><img border=0 width= 355 height=3061344 src="ParametricFitting_files/image0 26.png" v:shapes="Picture_x0020_14"><![endif]></span></p>1255 </v:shape><![endif]--><![if !vml]><img border=0 width=471 height=405 1256 src="ParametricFitting_files/image083.png" v:shapes="Picture_x0020_14"><![endif]></span></p> 1345 1257 1346 1258 <h2>Step 3: Fitting a simple parametric equation to the unit cell volume</h2> … … 1351 1263 equations of state to different parameters. As a simple example, we can <b 1352 1264 style='mso-bidi-font-weight:normal'>double-click on </b><b style='mso-bidi-font-weight: 1353 normal'><span style='font-family:Courier'>0<span class=GramE>::</span><span 1354 class=SpellE>Vol</span></span></b>, to plot the unit volume for the first phase 1355 vs. T, and fit this to a straight line. <span 1356 style="mso-spacerun:yes"> </span></p> 1265 normal'><span style='font-family:Courier'>0::<span class=SpellE>Vol</span></span></b>, 1266 to plot the unit volume for the first phase vs. T, and fit this to a straight 1267 line.<span style='mso-spacerun:yes'> </span></p> 1357 1268 1358 1269 <p class=MsoNormal><o:p> </o:p></p> … … 1360 1271 <p class=MsoListParagraphCxSpFirst><span style='mso-fareast-language:EN-US; 1361 1272 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15" o:spid="_x0000_i1043" 1362 type="#_x0000_t75" style='width:356 pt;height:305pt;visibility:visible;1273 type="#_x0000_t75" style='width:356.25pt;height:305.25pt;visibility:visible; 1363 1274 mso-wrap-style:square'> 1364 1275 <v:imagedata src="ParametricFitting_files/image027.png" o:title="" croptop="2107f" 1365 1276 cropbottom="4567f" cropleft="3024f" cropright="2769f"/> 1366 </v:shape><![endif]--><![if !vml]><img border=0 width=358 height=307 1367 src="ParametricFitting_files/image028.png" v:shapes="Picture_x0020_15"><![endif]></span></p> 1368 1369 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span 1370 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1371 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1372 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> 1277 </v:shape><![endif]--><![if !vml]><img border=0 width=475 height=407 1278 src="ParametricFitting_files/image084.png" v:shapes="Picture_x0020_15"><![endif]></span></p> 1279 1280 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span 1281 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1282 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> 1373 1283 </span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_16" 1374 o:spid="_x0000_s102 9" type="#_x0000_t75" style='position:absolute;left:0;1284 o:spid="_x0000_s1028" type="#_x0000_t75" style='position:absolute;left:0; 1375 1285 text-align:left;margin-left:21.8pt;margin-top:891.2pt;width:73pt;height:53pt; 1376 1286 z-index:251661312;visibility:visible;mso-wrap-style:square; … … 1383 1293 <v:imagedata src="ParametricFitting_files/image029.png" o:title=""/> 1384 1294 <w:wrap type="square" anchorx="margin" anchory="margin"/> 1385 </v:shape><![endif]--><![if !vml]><img width= 75 height=551386 src="ParametricFitting_files/image0 30.png" align=right hspace=9v:shapes="Picture_x0020_16"><![endif]><b1295 </v:shape><![endif]--><![if !vml]><img width=97 height=71 1296 src="ParametricFitting_files/image085.jpg" align=right hspace=12 v:shapes="Picture_x0020_16"><![endif]><b 1387 1297 style='mso-bidi-font-weight:normal'>Click on the Parametric Fit/Add</b> <b 1388 1298 style='mso-bidi-font-weight:normal'>equation</b> menu item, which opens a 1389 1299 window similar to what was used before to create a Pseudo <span class=SpellE>var</span>, 1390 except that here an equation is defined. <span1391 style="mso-spacerun:yes"> </span></p>1300 except that here an equation is defined.<span style='mso-spacerun:yes'> 1301 </span></p> 1392 1302 1393 1303 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1395 1305 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1396 1306 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_17" o:spid="_x0000_i1042" 1397 type="#_x0000_t75" style='width:311 pt;height:152pt;visibility:visible;1307 type="#_x0000_t75" style='width:311.25pt;height:152.25pt;visibility:visible; 1398 1308 mso-wrap-style:square'> 1399 1309 <v:imagedata src="ParametricFitting_files/image031.png" o:title="" croptop="4213f" 1400 1310 cropbottom="8982f" cropleft="3490f" cropright="3653f"/> 1401 </v:shape><![endif]--><![if !vml]><img border=0 width= 313 height=1541402 src="ParametricFitting_files/image0 32.png" v:shapes="Picture_x0020_17"><![endif]></span></p>1311 </v:shape><![endif]--><![if !vml]><img border=0 width=415 height=203 1312 src="ParametricFitting_files/image086.png" v:shapes="Picture_x0020_17"><![endif]></span></p> 1403 1313 1404 1314 <p class=MsoListParagraphCxSpLast><o:p> </o:p></p> … … 1410 1320 <p class=MsoNormal><b style='mso-bidi-font-weight:normal'><o:p> </o:p></b></p> 1411 1321 1412 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><b 1413 style='mso-bidi-font-weight:normal'><span style='mso-fareast-font-family:Cambria; 1414 mso-fareast-theme-font:minor-latin;mso-bidi-font-family:Cambria;mso-bidi-theme-font: 1415 minor-latin'><span style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> 1416 </span></span></span></b><![endif]><b style='mso-bidi-font-weight:normal'>Click 1417 the menu button</b> to select a dependent variable for "y". From the phase list, 1418 select the unit cell volume for the CuCr<sub>2</sub>O<sub>4</sub> phase, <b 1419 style='mso-bidi-font-weight:normal'>click on </b><b style='mso-bidi-font-weight: 1420 normal'><span style='font-family:Courier'>0<span class=GramE>::</span><span 1421 class=SpellE>Vol</span></span></b> and then <b style='mso-bidi-font-weight: 1422 normal'>press OK.<o:p></o:p></b></p> 1322 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><b 1323 style='mso-bidi-font-weight:normal'><span style='mso-fareast-font-family:"Times New Roman"; 1324 mso-bidi-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span 1325 style='font:7.0pt "Times New Roman"'> </span></span></span></b><![endif]><b 1326 style='mso-bidi-font-weight:normal'>Click the menu button</b> to select a 1327 dependent variable for "y". From the phase list, select the unit cell 1328 volume for the CuCr<sub>2</sub>O<sub>4</sub> phase, <b style='mso-bidi-font-weight: 1329 normal'>click on </b><b style='mso-bidi-font-weight:normal'><span 1330 style='font-family:Courier'>0::<span class=SpellE>Vol</span></span></b> and 1331 then <b style='mso-bidi-font-weight:normal'>press OK.<o:p></o:p></b></p> 1423 1332 1424 1333 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1426 1335 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1427 1336 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_19" o:spid="_x0000_i1041" 1428 type="#_x0000_t75" style='width:314 pt;height:132pt;visibility:visible;1337 type="#_x0000_t75" style='width:314.25pt;height:132pt;visibility:visible; 1429 1338 mso-wrap-style:square'> 1430 1339 <v:imagedata src="ParametricFitting_files/image033.png" o:title="" croptop="3830f" 1431 1340 cropbottom="9359f" cropleft="3705f" cropright="3502f"/> 1432 </v:shape><![endif]--><![if !vml]><img border=0 width= 316 height=1341433 src="ParametricFitting_files/image0 34.png" v:shapes="Picture_x0020_19"><![endif]></span></p>1341 </v:shape><![endif]--><![if !vml]><img border=0 width=419 height=176 1342 src="ParametricFitting_files/image087.png" v:shapes="Picture_x0020_19"><![endif]></span></p> 1434 1343 1435 1344 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1436 1345 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20" o:spid="_x0000_i1040" 1437 type="#_x0000_t75" style='width:311 pt;height:155pt;visibility:visible;1346 type="#_x0000_t75" style='width:311.25pt;height:155.25pt;visibility:visible; 1438 1347 mso-wrap-style:square'> 1439 1348 <v:imagedata src="ParametricFitting_files/image035.png" o:title="" croptop="3548f" 1440 1349 cropbottom="8549f" cropleft="3611f" cropright="3665f"/> 1441 </v:shape><![endif]--><![if !vml]><img border=0 width=313 height=157 1442 src="ParametricFitting_files/image036.png" v:shapes="Picture_x0020_20"><![endif]></span></p> 1443 1444 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1445 1446 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span 1447 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1448 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1449 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> 1350 </v:shape><![endif]--><![if !vml]><img border=0 width=415 height=207 1351 src="ParametricFitting_files/image088.png" v:shapes="Picture_x0020_20"><![endif]></span></p> 1352 1353 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1354 1355 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span 1356 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1357 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> 1450 1358 </span></span></span><![endif]>Now we <b style='mso-bidi-font-weight:normal'>enter 1451 the equation</b> using Python syntax, which is simply "<b style='mso-bidi-font-weight:1452 normal'><span style='font-family:Courier'>m*x + b</span></b>", note that the 1453 use of spaces and the choice of labels is arbitrary. If one were to accidentally 1454 leave out the "<span style='font-family:Courier'>*</span>" and typed "<span 1455 style='font-family:Courier'>mx</span>" then that would be considered a label, 1456 if "<span style='font-family:Courier'>m x</span>" were typed, an error message 1457 w ould be displayed. </p>1359 the equation</b> using Python syntax, which is simply "<b 1360 style='mso-bidi-font-weight:normal'><span style='font-family:Courier'>m*x + b</span></b>", 1361 note that the use of spaces and the choice of labels is arbitrary. If one were 1362 to accidentally leave out the "<span style='font-family:Courier'>*</span>" 1363 and typed "<span style='font-family:Courier'>mx</span>" then that 1364 would be considered a label, if "<span style='font-family:Courier'>m x</span>" 1365 were typed, an error message would be displayed. </p> 1458 1366 1459 1367 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1461 1369 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1462 1370 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21" o:spid="_x0000_i1039" 1463 type="#_x0000_t75" style='width:31 6pt;height:155pt;visibility:visible;1371 type="#_x0000_t75" style='width:315.75pt;height:155.25pt;visibility:visible; 1464 1372 mso-wrap-style:square'> 1465 1373 <v:imagedata src="ParametricFitting_files/image037.png" o:title="" croptop="3326f" 1466 1374 cropbottom="8766f" cropleft="3010f" cropright="3419f"/> 1467 </v:shape><![endif]--><![if !vml]><img border=0 width= 318 height=1571468 src="ParametricFitting_files/image0 38.png" v:shapes="Picture_x0020_21"><![endif]></span></p>1375 </v:shape><![endif]--><![if !vml]><img border=0 width=421 height=207 1376 src="ParametricFitting_files/image089.png" v:shapes="Picture_x0020_21"><![endif]></span></p> 1469 1377 1470 1378 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1476 1384 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1477 1385 1478 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span 1479 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1480 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1481 style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'> 1386 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span 1387 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1388 style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'> 1482 1389 </span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_22" 1483 o:spid="_x0000_s102 8" type="#_x0000_t75" style='position:absolute;left:0;1390 o:spid="_x0000_s1027" type="#_x0000_t75" style='position:absolute;left:0; 1484 1391 text-align:left;margin-left:43.8pt;margin-top:603.2pt;width:95pt;height:35pt; 1485 1392 z-index:251662336;visibility:visible;mso-wrap-style:square; 1486 mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; 1393 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; 1394 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; 1487 1395 mso-wrap-distance-bottom:0;mso-position-horizontal:right; 1488 1396 mso-position-horizontal-relative:margin;mso-position-vertical:absolute; 1489 mso-position-vertical-relative:margin'> 1397 mso-position-vertical-relative:margin;mso-width-percent:0; 1398 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'> 1490 1399 <v:imagedata src="ParametricFitting_files/image039.png" o:title=""/> 1491 1400 <w:wrap type="square" anchorx="margin" anchory="margin"/> 1492 </v:shape><![endif]--><![if !vml]><img width= 97 height=371493 src="ParametricFitting_files/image0 40.png" align=right hspace=9v:shapes="Picture_x0020_22"><![endif]>Assign1401 </v:shape><![endif]--><![if !vml]><img width=127 height=47 1402 src="ParametricFitting_files/image090.jpg" align=right hspace=12 v:shapes="Picture_x0020_22"><![endif]>Assign 1494 1403 b and m as refinable parameters: <b style='mso-bidi-font-weight:normal'>Click 1495 1404 on the menu button</b> next to b and <b style='mso-bidi-font-weight:normal'>select … … 1498 1407 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1499 1408 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_23" o:spid="_x0000_i1038" 1500 type="#_x0000_t75" style='width:314 pt;height:153pt;visibility:visible;1409 type="#_x0000_t75" style='width:314.25pt;height:153pt;visibility:visible; 1501 1410 mso-wrap-style:square'> 1502 1411 <v:imagedata src="ParametricFitting_files/image041.png" o:title="" croptop="3992f" 1503 1412 cropbottom="8541f" cropleft="3250f" cropright="3415f"/> 1504 </v:shape><![endif]--><![if !vml]><img border=0 width= 316 height=1551505 src="ParametricFitting_files/image0 42.png" v:shapes="Picture_x0020_23"><![endif]></span></p>1413 </v:shape><![endif]--><![if !vml]><img border=0 width=419 height=204 1414 src="ParametricFitting_files/image091.png" v:shapes="Picture_x0020_23"><![endif]></span></p> 1506 1415 1507 1416 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1512 1421 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1513 1422 1514 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span 1515 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1516 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1517 style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'> 1423 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span 1424 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1425 style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'> 1518 1426 </span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_24" 1519 o:spid="_x0000_s102 7" type="#_x0000_t75" style='position:absolute;left:0;1427 o:spid="_x0000_s1026" type="#_x0000_t75" style='position:absolute;left:0; 1520 1428 text-align:left;margin-left:24.3pt;margin-top:837.2pt;width:75.5pt;height:26pt; 1521 1429 z-index:251663360;visibility:visible;mso-wrap-style:square; 1522 mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; 1430 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; 1431 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; 1523 1432 mso-wrap-distance-bottom:0;mso-position-horizontal:right; 1524 1433 mso-position-horizontal-relative:margin;mso-position-vertical:absolute; 1525 mso-position-vertical-relative:margin'> 1434 mso-position-vertical-relative:margin;mso-width-percent:0; 1435 mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'> 1526 1436 <v:imagedata src="ParametricFitting_files/image043.png" o:title=""/> 1527 1437 <w:wrap type="square" anchorx="margin" anchory="margin"/> 1528 </v:shape><![endif]--><![if !vml]><img width= 78 height=281529 src="ParametricFitting_files/image0 44.png" align=right hspace=9v:shapes="Picture_x0020_24"><![endif]>To1438 </v:shape><![endif]--><![if !vml]><img width=101 height=35 1439 src="ParametricFitting_files/image092.jpg" align=right hspace=12 v:shapes="Picture_x0020_24"><![endif]>To 1530 1440 set x as the temperature, <b style='mso-bidi-font-weight:normal'>click on the 1531 1441 menu button</b> next to x, <b style='mso-bidi-font-weight:normal'>select … … 1535 1445 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1536 1446 1537 <p class=MsoListParagraphCxSpMiddle><span 1538 style="mso-spacerun:yes"> </span><span style='mso-fareast-language:EN-US; 1539 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_25" o:spid="_x0000_i1037" 1540 type="#_x0000_t75" style='width:245pt;height:109pt;visibility:visible; 1541 mso-wrap-style:square'> 1447 <p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span 1448 style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1449 id="Picture_x0020_25" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:245.25pt; 1450 height:108.75pt;visibility:visible;mso-wrap-style:square'> 1542 1451 <v:imagedata src="ParametricFitting_files/image045.png" o:title="" croptop="5483f" 1543 1452 cropbottom="10984f" cropleft="4191f" cropright="4159f"/> 1544 </v:shape><![endif]--><![if !vml]><img border=0 width= 247 height=1111545 src="ParametricFitting_files/image0 46.png" v:shapes="Picture_x0020_25"><![endif]></span></p>1453 </v:shape><![endif]--><![if !vml]><img border=0 width=327 height=145 1454 src="ParametricFitting_files/image093.png" v:shapes="Picture_x0020_25"><![endif]></span></p> 1546 1455 1547 1456 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1548 1457 1549 1458 <p class=MsoListParagraphCxSpMiddle>The window then changes, showing the values 1550 of the dependent variable and the expression for the first refinement, as below.<span1551 style="mso-spacerun:yes"> </span>Optionally, the values for m and b could1552 b e changed manually and the displayed value will be updated when Validate is1553 pressed or after a short delay.</p>1459 of the dependent variable and the expression for the first refinement, as 1460 below.<span style='mso-spacerun:yes'> </span>Optionally, the values for m and 1461 b could be changed manually and the displayed value will be updated when 1462 Validate is pressed or after a short delay.</p> 1554 1463 1555 1464 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1557 1466 <p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US; 1558 1467 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26" o:spid="_x0000_i1036" 1559 type="#_x0000_t75" style='width:314 pt;height:153pt;visibility:visible;1468 type="#_x0000_t75" style='width:314.25pt;height:153pt;visibility:visible; 1560 1469 mso-wrap-style:square'> 1561 1470 <v:imagedata src="ParametricFitting_files/image047.png" o:title="" croptop="3992f" 1562 1471 cropbottom="8541f" cropleft="3490f" cropright="3294f"/> 1563 </v:shape><![endif]--><![if !vml]><img border=0 width= 316 height=1551564 src="ParametricFitting_files/image0 48.png" v:shapes="Picture_x0020_26"><![endif]></span></p>1472 </v:shape><![endif]--><![if !vml]><img border=0 width=419 height=204 1473 src="ParametricFitting_files/image094.png" v:shapes="Picture_x0020_26"><![endif]></span></p> 1565 1474 1566 1475 <p class=MsoNormal><o:p> </o:p></p> 1567 1476 1568 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span 1569 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1570 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1571 style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'> 1477 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span 1478 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1479 style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'> 1572 1480 </span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Press the 1573 1481 OK button</b> to save this parametric fit. The b and m values are then refined … … 1578 1486 1579 1487 <p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space: 1580 auto'><span style='font-family:Courier'><span 1581 style="mso-spacerun:yes"> </span><span class=GramE>::</span>m<span 1582 style="mso-spacerun:yes"> </span>=-0.4476(5)<o:p></o:p></span></p>1488 auto'><span style='font-family:Courier'><span style='mso-spacerun:yes'> 1489 </span>:<span class=GramE>:m</span><span style='mso-spacerun:yes'> </span>= 1490 -0.4476(5)<o:p></o:p></span></p> 1583 1491 1584 1492 <p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space: 1585 auto'><span style='font-family:Courier'><span 1586 style="mso-spacerun:yes"> </span><span class=GramE>::</span>b<span 1587 style="mso-spacerun:yes"> </span>=577.73(8)<o:p></o:p></span></p>1493 auto'><span style='font-family:Courier'><span style='mso-spacerun:yes'> 1494 </span>:<span class=GramE>:b</span><span style='mso-spacerun:yes'> </span>= 1495 577.73(8)<o:p></o:p></span></p> 1588 1496 1589 1497 <p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space: … … 1592 1500 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1593 1501 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27" o:spid="_x0000_i1035" 1594 type="#_x0000_t75" style='width:350 pt;height:302pt;visibility:visible;1502 type="#_x0000_t75" style='width:350.25pt;height:302.25pt;visibility:visible; 1595 1503 mso-wrap-style:square'> 1596 1504 <v:imagedata src="ParametricFitting_files/image049.png" o:title="" croptop="2231f" 1597 1505 cropbottom="5061f" cropleft="3133f" cropright="3524f"/> 1598 </v:shape><![endif]--><![if !vml]><img border=0 width=352 height=304 1599 src="ParametricFitting_files/image050.png" v:shapes="Picture_x0020_27"><![endif]></span></p> 1506 </v:shape><![endif]--><![if !vml]><img border=0 width=467 height=403 1507 src="ParametricFitting_files/image095.png" v:shapes="Picture_x0020_27"><![endif]></span><span 1508 style='font-family:"Cambria","serif";mso-ascii-theme-font:minor-latin; 1509 mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> 1600 1510 1601 1511 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1602 1512 1603 1513 <p class=MsoListParagraphCxSpMiddle>Also, a plot shows the actual values and 1604 the fit. Note that while the values are close to a straight line, the deviations1605 are huge compared to the estimated uncertainty values for the unit cell volume 1606 (shown as very small error bars, unless the plot is magnified). <span 1607 style="mso-spacerun:yes"> </span>If a linear relationship had been defined1608 as a constraint (as can be done with other software packages) <I>the unit cell 1609 parameters would have been forced onto this line with no obvious indication 1610 that this was not a correct result.</I> </p>1611 1612 <p class=MsoListParagraphCxSpLast><span style= "mso-spacerun:yes"> </span></p>1514 the fit. Note that while the values are close to a straight line, the 1515 deviations are huge compared to the estimated uncertainty values for the unit 1516 cell volume (shown as very small error bars, unless the plot is 1517 magnified).<span style='mso-spacerun:yes'> </span>If a linear relationship had 1518 been defined as a constraint (as can be done with other software packages) <i>the 1519 unit cell parameters would have been forced onto this line with no obvious 1520 indication that this was not a correct result.</i> </p> 1521 1522 <p class=MsoListParagraphCxSpLast><span style='mso-spacerun:yes'> </span></p> 1613 1523 1614 1524 <h2>Step 4: Examples of more complex fitting equations</h2> … … 1616 1526 <p class=MsoNormal><o:p> </o:p></p> 1617 1527 1618 <p class=MsoNormal>Here we will look at how more sophisticated Python capabilities 1619 can be used to fit more complex behavior. <span 1620 style="mso-spacerun:yes"> </span></p> 1621 1622 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span 1623 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1624 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1625 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> 1528 <p class=MsoNormal>Here we will look at how more sophisticated Python 1529 capabilities can be used to fit more complex behavior.<span 1530 style='mso-spacerun:yes'> </span></p> 1531 1532 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span 1533 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1534 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> 1626 1535 </span></span></span><![endif]>Optionally <b style='mso-bidi-font-weight:normal'>Double-click 1627 1536 on the </b><b style='mso-bidi-font-weight:normal'><span style='font-family: 1628 Courier'>0 <span class=GramE>::</span>c</span> column</b>. Note the changes in1629 the <i style='mso-bidi-font-style:normal'>c</i> unit cell parameter as a 1630 function of temperature, as shown below.</p>1537 Courier'>0::c</span> column</b>. Note the changes in the <i style='mso-bidi-font-style: 1538 normal'>c</i> unit cell parameter as a function of temperature, as shown below. 1539 </p> 1631 1540 1632 1541 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1634 1543 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1635 1544 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28" o:spid="_x0000_i1034" 1636 type="#_x0000_t75" style='width:350 pt;height:303pt;visibility:visible;1545 type="#_x0000_t75" style='width:350.25pt;height:303pt;visibility:visible; 1637 1546 mso-wrap-style:square'> 1638 1547 <v:imagedata src="ParametricFitting_files/image051.png" o:title="" croptop="658f" 1639 1548 cropbottom="2861f" cropleft="1709f" cropright="1878f"/> 1640 </v:shape><![endif]--><![if !vml]><img border=0 width=352 height=305 1641 src="ParametricFitting_files/image052.png" v:shapes="Picture_x0020_28"><![endif]></span></p> 1642 1643 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1644 1645 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span 1646 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1647 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1648 style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> 1549 </v:shape><![endif]--><![if !vml]><img border=0 width=467 height=404 1550 src="ParametricFitting_files/image096.png" v:shapes="Picture_x0020_28"><![endif]></span></p> 1551 1552 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1553 1554 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span 1555 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1556 style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> 1649 1557 </span></span></span><![endif]>We will now fit <i style='mso-bidi-font-style: 1650 normal'>c</i> as a function of form 1/(1 + <span class=SpellE><span 1651 class=GramE>exp</span></span><span class=GramE>[</span>k(t-t<sub>0</sub>)]). <b 1652 style='mso-bidi-font-weight:normal'>Click on the Parametric Fit/Add</b> <b 1653 style='mso-bidi-font-weight:normal'>equation</b> menu item (as before). For the 1654 dependent variable, <b style='mso-bidi-font-weight:normal'>click on Phase</b> 1655 and then <b style='mso-bidi-font-weight:normal'>select </b><b style='mso-bidi-font-weight: 1656 normal'><span style='font-family:Courier'>0<span class=GramE>::</span>c</span></b>. 1657 <span style="mso-spacerun:yes"> </span></p> 1658 1659 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1660 1661 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span 1662 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1663 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1664 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> 1558 normal'>c</i> as a function of form 1<span class=GramE>/(</span>1 + <span 1559 class=SpellE>exp</span>[k(t-t<sub>0</sub>)]). <b style='mso-bidi-font-weight: 1560 normal'>Click on the Parametric Fit/Add</b> <b style='mso-bidi-font-weight: 1561 normal'>equation</b> menu item (as before). For the dependent variable, <b 1562 style='mso-bidi-font-weight:normal'>click on Phase</b> and then <b 1563 style='mso-bidi-font-weight:normal'>select </b><b style='mso-bidi-font-weight: 1564 normal'><span style='font-family:Courier'>0::c</span></b>.<span 1565 style='mso-spacerun:yes'> </span></p> 1566 1567 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1568 1569 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span 1570 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1571 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> 1665 1572 </span></span></span><![endif]>We then <b style='mso-bidi-font-weight:normal'>enter 1666 1573 expression</b></p> … … 1668 1575 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1669 1576 1670 <p class=MsoListParagraphCxSpMiddle style='text-indent:.5in'><span class=GramE><span1671 style='font-family:Courier'>b </span></span><span style='font-family:Courier'> +1672 c / (1+math.exp(k*(t-t0)))<o:p></o:p></span></p> 1673 1674 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p>1577 <p class=MsoListParagraphCxSpMiddle style='text-indent:.5in'><span 1578 style='font-family:Courier'>b + c / (1+<span class=GramE>math.exp(</span>k*(t-t0)))<o:p></o:p></span></p> 1579 1580 <p class=MsoListParagraphCxSpMiddle><span style='font-family:"Cambria","serif"; 1581 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p> </o:p></span></p> 1675 1582 1676 1583 <p class=MsoListParagraphCxSpLast>Note that use of spaces here are arbitrary, 1677 1584 but all parentheses are required. Also note that the exponential function [<span 1678 class=SpellE><span class=GramE>exp</span></span><span class=GramE>(</span>x) or 1679 e<sup>x</sup>] is supplied in Python in the math and <span class=SpellE>numpy</span> 1680 modules as <span class=SpellE>math.exp</span>(), <span class=SpellE>numpy.exp</span>(). 1681 Both of these can be used as well as the convenience abbreviation of <span 1682 class=SpellE><span class=GramE>np.exp</span></span><span class=GramE>(</span>). 1683 Further, there are also a small number of common functions that are defined 1684 without the prefix for convenience [these include pi, <span class=SpellE><span 1685 class=GramE>exp</span></span><span class=GramE>(</span>), <span class=SpellE>sqrt</span>(), 1686 <span class=SpellE>sind</span>(), <span class=SpellE>cosd</span>(), <span 1687 class=SpellE>tand</span>() where d indicates an argument in degrees.]<o:p></o:p></p> 1585 class=SpellE>exp</span>(x) or e<sup>x</sup>] is supplied in Python in the math 1586 and <span class=SpellE>numpy</span> modules as <span class=SpellE><span 1587 class=GramE>math.exp</span></span><span class=GramE>(</span>), <span 1588 class=SpellE>numpy.exp</span>(). Both of these can be used as well as the 1589 convenience abbreviation of <span class=SpellE><span class=GramE>np.exp</span></span><span 1590 class=GramE>(</span>). Further, there are also a small number of common 1591 functions that are defined without the prefix for convenience [these include 1592 pi, <span class=SpellE><span class=GramE>exp</span></span><span class=GramE>(</span>), 1593 <span class=SpellE>sqrt</span>(), <span class=SpellE>sind</span>(), <span 1594 class=SpellE>cosd</span>(), <span class=SpellE>tand</span>() where d indicates 1595 an argument in degrees.]</p> 1688 1596 1689 1597 <p class=MsoNormal><o:p> </o:p></p> 1690 1598 1691 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span 1692 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1693 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1694 style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'> 1599 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span 1600 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1601 style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'> 1695 1602 </span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Assign 1696 1603 free variables to b, c, k and t0</b>, similar as to what was done before. Note … … 1698 1605 style='font-family:Courier'>b</span> label was set automatically to <span 1699 1606 style='font-family:Courier'>b_1</span>. If the same variable name (<span 1700 style='font-family:Courier'>b</span>) <span class=GramE>was</span> used again 1701 here, the same value would be used to fit both equations, which is certainly 1702 not what we want here. <span style="mso-spacerun:yes"> </span>Finally, 1703 since this equation is too complex to fit without some reasonable starting 1704 values, specify an approximate value for the vicinity of where <i 1705 style='mso-bidi-font-style:normal'>c</i> starts to change, <b style='mso-bidi-font-weight: 1706 normal'>enter 120 for </b><b style='mso-bidi-font-weight:normal'><span 1707 style='font-family:Courier'>t0</span>.</b></p> 1607 style='font-family:Courier'>b</span>) was used again here, the same value would 1608 be used to fit both equations, which is certainly not what we want here.<span 1609 style='mso-spacerun:yes'> </span>Finally, since this equation is too complex 1610 to fit without some reasonable starting values, specify an approximate value 1611 for the vicinity of where <i style='mso-bidi-font-style:normal'>c</i> starts to 1612 change, <b style='mso-bidi-font-weight:normal'>enter 120 for </b><b 1613 style='mso-bidi-font-weight:normal'><span style='font-family:Courier'>t0</span>.</b></p> 1708 1614 1709 1615 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1711 1617 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1712 1618 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40" o:spid="_x0000_i1033" 1713 type="#_x0000_t75" style='width:317 pt;height:171pt;visibility:visible;1619 type="#_x0000_t75" style='width:317.25pt;height:171pt;visibility:visible; 1714 1620 mso-wrap-style:square'> 1715 1621 <v:imagedata src="ParametricFitting_files/image053.png" o:title="" croptop="3272f" 1716 1622 cropbottom="7856f" cropleft="3218f" cropright="3436f"/> 1717 </v:shape><![endif]--><![if !vml]><img border=0 width=319 height=173 1718 src="ParametricFitting_files/image054.png" v:shapes="Picture_x0020_40"><![endif]></span></p> 1719 1720 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1721 1722 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span 1723 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1724 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1725 style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'> 1623 </v:shape><![endif]--><![if !vml]><img border=0 width=423 height=228 1624 src="ParametricFitting_files/image097.png" v:shapes="Picture_x0020_40"><![endif]></span></p> 1625 1626 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1627 1628 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span 1629 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1630 style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'> 1726 1631 </span></span></span><![endif]>Optionally, <b style='mso-bidi-font-weight:normal'>press 1727 1632 the Fit button</b> to see if the equation can be refined with starting values 1728 of zero for the other three parameters.<span style= "mso-spacerun:yes"> 1633 of zero for the other three parameters.<span style='mso-spacerun:yes'> 1729 1634 </span>A fit is obtained and is plotted. </p> 1730 1635 1731 1636 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1732 1637 1733 <p class=MsoListParagraphCxSpMiddle><span 1734 style="mso-spacerun:yes"> </span><span style='mso-fareast-language:EN-US; 1735 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_41" o:spid="_x0000_i1032" 1736 type="#_x0000_t75" style='width:317pt;height:169pt;visibility:visible; 1737 mso-wrap-style:square'> 1638 <p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span 1639 style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1640 id="Picture_x0020_41" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:317.25pt; 1641 height:168.75pt;visibility:visible;mso-wrap-style:square'> 1738 1642 <v:imagedata src="ParametricFitting_files/image055.png" o:title="" croptop="3477f" 1739 1643 cropbottom="8265f" cropleft="3218f" cropright="3436f"/> 1740 </v:shape><![endif]--><![if !vml]><img border=0 width=319 height=171 1741 src="ParametricFitting_files/image056.png" v:shapes="Picture_x0020_41"><![endif]></span></p> 1742 1743 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1744 1745 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span 1746 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1747 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1748 style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'> 1644 </v:shape><![endif]--><![if !vml]><img border=0 width=423 height=225 1645 src="ParametricFitting_files/image098.png" v:shapes="Picture_x0020_41"><![endif]></span></p> 1646 1647 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1648 1649 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span 1650 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1651 style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'> 1749 1652 </span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Press OK</b> 1750 1653 to add this equation to the parametric fits and both equations are refit (and … … 1756 1659 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1757 1660 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32" o:spid="_x0000_i1031" 1758 type="#_x0000_t75" style='width:353 pt;height:301pt;visibility:visible;1661 type="#_x0000_t75" style='width:353.25pt;height:300.75pt;visibility:visible; 1759 1662 mso-wrap-style:square'> 1760 1663 <v:imagedata src="ParametricFitting_files/image057.png" o:title="" croptop="2602f" 1761 1664 cropbottom="4943f" cropleft="3024f" cropright="3097f"/> 1762 </v:shape><![endif]--><![if !vml]><img border=0 width=355 height=303 1763 src="ParametricFitting_files/image058.png" v:shapes="Picture_x0020_32"><![endif]></span></p> 1764 1765 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1766 1767 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo6'><![if !supportLists]><span 1768 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1769 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1770 style='mso-list:Ignore'>7.<span style='font:7.0pt "Times New Roman"'> 1665 </v:shape><![endif]--><![if !vml]><img border=0 width=471 height=401 1666 src="ParametricFitting_files/image099.png" v:shapes="Picture_x0020_32"><![endif]></span></p> 1667 1668 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1669 1670 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span 1671 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1672 style='mso-list:Ignore'>7.<span style='font:7.0pt "Times New Roman"'> 1771 1673 </span></span></span><![endif]>We will now try a more complex equation for the 1772 1674 same data, where we set the value to <span style='font-family:Courier'>b</span> 1773 for temperatures less than <span style='font-family:Courier'>t0</span> and a critical1774 phenomenon formulism [(t-t<sub>0</sub>)<sup>-a</sup>] for temperatures above <span 1775 style='font-family:Courier'>t0</span>. To do this we use the Python syntax "<span1776 s tyle='font-family:Courier'>x1 if <span class=SpellE>testexp</span> else x2</span>"1777 which is <span style='font-family:Courier'>x1</span> where the test expression (<span 1778 class=SpellE><span style='font-family:Courier'>testexp</span></span> here) is <span 1779 style='font-family:Courier'>True</span> and <span style='font-family:Courier'>x2</span> 1780 elsewhere. Thus we can use an expression such as:</p> 1781 1782 <p class=MsoListParagraphCxSpMiddle><span 1783 style="mso-spacerun:yes"> </span></p>1675 for temperatures less than <span style='font-family:Courier'>t0</span> and a 1676 critical phenomenon formulism [(t-t<sub>0</sub>)<sup>-a</sup>] for temperatures 1677 above <span style='font-family:Courier'>t0</span>. To do this we use the Python 1678 syntax "<span style='font-family:Courier'>x1 if <span class=SpellE>testexp</span> 1679 else x2</span>" which is <span style='font-family:Courier'>x1</span> where 1680 the test expression (<span class=SpellE><span style='font-family:Courier'>testexp</span></span> 1681 here) is <span style='font-family:Courier'>True</span> and <span 1682 style='font-family:Courier'>x2</span> elsewhere. Thus we can use an expression 1683 such as:</p> 1684 1685 <p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span></p> 1784 1686 1785 1687 <p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space: … … 1791 1693 1792 1694 <p class=MsoListParagraphCxSpMiddle>This may be easier to read with the 1793 inclusion of extra parentheses (that have no effect on the execution):</p> 1695 inclusion of extra parentheses (that have no effect on the execution):<span 1696 style='font-family:"Cambria","serif";mso-ascii-theme-font:minor-latin; 1697 mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> 1794 1698 1795 1699 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1804 1708 <p class=MsoListParagraphCxSpMiddle>As before, <b style='mso-bidi-font-weight: 1805 1709 normal'>add an equation </b>(or edit an existing one), <b style='mso-bidi-font-weight: 1806 normal'>set the dependent variable</b> to <span style='font-family:Courier'>0<span 1807 class=GramE>::</span>c</span>, <b style='mso-bidi-font-weight:normal'>enter the 1808 expression</b> and <b style='mso-bidi-font-weight:normal'>assign the free and 1809 fixed variables</b>, as before. <b style='mso-bidi-font-weight:normal'>Set the 1810 exponent and the t0</b> values to initial values of -0.025 and 120, respectively, 1811 and turn off their refinement flags. Then <b style='mso-bidi-font-weight:normal'>press 1812 Fit.</b></p> 1710 normal'>set the dependent variable</b> to <span style='font-family:Courier'>0::c</span>, 1711 <b style='mso-bidi-font-weight:normal'>enter the expression</b> and <b 1712 style='mso-bidi-font-weight:normal'>assign the free and fixed variables</b>, as 1713 before. <b style='mso-bidi-font-weight:normal'>Set the exponent and the t0</b> 1714 values to initial values of -0.025 and 120, respectively, and turn off their 1715 refinement flags. Then <b style='mso-bidi-font-weight:normal'>press Fit.</b><span 1716 style='font-family:"Cambria","serif";mso-ascii-theme-font:minor-latin; 1717 mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> 1813 1718 1814 1719 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; … … 1817 1722 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1818 1723 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42" o:spid="_x0000_i1030" 1819 type="#_x0000_t75" style='width:31 6pt;height:169pt;visibility:visible;1724 type="#_x0000_t75" style='width:315.75pt;height:168.75pt;visibility:visible; 1820 1725 mso-wrap-style:square'> 1821 1726 <v:imagedata src="ParametricFitting_files/image059.png" o:title="" croptop="3691f" 1822 1727 cropbottom="7919f" cropleft="2889f" cropright="3536f"/> 1823 </v:shape><![endif]--><![if !vml]><img border=0 width= 318 height=1711824 src="ParametricFitting_files/image 060.png" v:shapes="Picture_x0020_42"><![endif]></span></p>1728 </v:shape><![endif]--><![if !vml]><img border=0 width=421 height=225 1729 src="ParametricFitting_files/image100.png" v:shapes="Picture_x0020_42"><![endif]></span></p> 1825 1730 1826 1731 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1834 1739 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1835 1740 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35" o:spid="_x0000_i1029" 1836 type="#_x0000_t75" style='width:351pt;height:302 pt;visibility:visible;1741 type="#_x0000_t75" style='width:351pt;height:302.25pt;visibility:visible; 1837 1742 mso-wrap-style:square'> 1838 1743 <v:imagedata src="ParametricFitting_files/image061.png" o:title="" croptop="2354f" 1839 1744 cropbottom="4937f" cropleft="3349f" cropright="3198f"/> 1840 </v:shape><![endif]--><![if !vml]><img border=0 width= 353 height=3041841 src="ParametricFitting_files/image 062.png" v:shapes="Picture_x0020_35"><![endif]></span></p>1745 </v:shape><![endif]--><![if !vml]><img border=0 width=468 height=403 1746 src="ParametricFitting_files/image101.png" v:shapes="Picture_x0020_35"><![endif]></span></p> 1842 1747 1843 1748 <p class=MsoListParagraphCxSpLast><o:p> </o:p></p> … … 1855 1760 <p class=MsoNormal><o:p> </o:p></p> 1856 1761 1857 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l4 level1 lfo7'><![if !supportLists]><span 1858 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1859 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1860 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> 1762 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span 1763 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1764 style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> 1861 1765 </span></span></span><![endif]>As before, <b style='mso-bidi-font-weight:normal'>add 1862 1766 an equation </b>(or edit an existing one). For the dependent variable, <b … … 1867 1771 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1868 1772 1869 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l4 level1 lfo7'><![if !supportLists]><span 1870 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1871 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1872 style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> 1773 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span 1774 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1775 style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> 1873 1776 </span></span></span><![endif]>Then <b style='mso-bidi-font-weight:normal'>enter 1874 1777 the equation</b> as </p> … … 1878 1781 <p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space: 1879 1782 auto'><span style='font-family:Courier;mso-bidi-font-family:"Lucida Grande"; 1880 color:black'>( <span class=GramE>o1</span> + (a1*T)**k) if T < 120 else (o2 +1783 color:black'>(o1 + (a1*T<span class=GramE>)*</span>*k) if T < 120 else (o2 + 1881 1784 a2*T</span><span style='font-family:Courier'>)<o:p></o:p></span></p> 1882 1785 1883 <p class=MsoListParagraphCxSpMiddle>< o:p> </o:p></p>1884 1885 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l4 level1 lfo7'><![if !supportLists]><span 1886 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1887 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span1888 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> 1786 <p class=MsoListParagraphCxSpMiddle><span style='font-family:"Cambria","serif"; 1787 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p> </o:p></span></p> 1788 1789 <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span 1790 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1791 style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> 1889 1792 </span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Assign 1890 the free and fixed variables</b>, as shown below. Note that the exponent (k) and1891 scaling factor (a1<span class=GramE>),</span> cannot start as zero<b1793 the free and fixed variables</b>, as shown below. Note that the exponent (k) 1794 and scaling factor (a1<span class=GramE>),</span> cannot start as zero<b 1892 1795 style='mso-bidi-font-weight:normal'>. </b></p> 1893 1796 … … 1896 1799 <p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US; 1897 1800 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44" o:spid="_x0000_i1028" 1898 type="#_x0000_t75" style='width:332 pt;height:186pt;visibility:visible;1801 type="#_x0000_t75" style='width:332.25pt;height:186pt;visibility:visible; 1899 1802 mso-wrap-style:square'> 1900 1803 <v:imagedata src="ParametricFitting_files/image063.png" o:title="" croptop="3190f" 1901 1804 cropbottom="8105f" cropleft="3416f" cropright="3246f"/> 1902 </v:shape><![endif]--><![if !vml]><img border=0 width= 334 height=1881903 src="ParametricFitting_files/image 064.png" v:shapes="Picture_x0020_44"><![endif]></span></p>1805 </v:shape><![endif]--><![if !vml]><img border=0 width=443 height=248 1806 src="ParametricFitting_files/image102.png" v:shapes="Picture_x0020_44"><![endif]></span></p> 1904 1807 1905 1808 <p class=MsoNormal><o:p> </o:p></p> 1906 1809 1907 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l4 level1 lfo7'><![if !supportLists]><span 1908 style='mso-fareast-font-family:Cambria;mso-fareast-theme-font:minor-latin; 1909 mso-bidi-font-family:Cambria;mso-bidi-theme-font:minor-latin'><span 1910 style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'> 1810 <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span 1811 style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span 1812 style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'> 1911 1813 </span></span></span><![endif]><b style='mso-bidi-font-weight:normal'>Press the 1912 1814 Fit button</b> and note that all the free variables are adjusted </p> … … 1916 1818 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1917 1819 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45" o:spid="_x0000_i1027" 1918 type="#_x0000_t75" style='width:33 4pt;height:189pt;visibility:visible;1820 type="#_x0000_t75" style='width:333.75pt;height:189pt;visibility:visible; 1919 1821 mso-wrap-style:square'> 1920 1822 <v:imagedata src="ParametricFitting_files/image065.png" o:title="" croptop="2815f" 1921 1823 cropbottom="7542f" cropleft="3074f" cropright="3244f"/> 1922 </v:shape><![endif]--><![if !vml]><img border=0 width= 336 height=1911923 src="ParametricFitting_files/image 066.png" v:shapes="Picture_x0020_45"><![endif]></span><span1924 style= "mso-spacerun:yes"> </span></p>1925 1926 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1927 1928 <p class=MsoListParagraphCxSpMiddle>Also, that the plotted result is close to the1929 values from the refinement.</p>1824 </v:shape><![endif]--><![if !vml]><img border=0 width=445 height=252 1825 src="ParametricFitting_files/image103.png" v:shapes="Picture_x0020_45"><![endif]></span><span 1826 style='mso-spacerun:yes'> </span></p> 1827 1828 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> 1829 1830 <p class=MsoListParagraphCxSpMiddle>Also, that the plotted result is close to 1831 the values from the refinement.</p> 1930 1832 1931 1833 <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> … … 1933 1835 <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; 1934 1836 mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48" o:spid="_x0000_i1026" 1935 type="#_x0000_t75" style='width:34 9pt;height:302pt;visibility:visible;1837 type="#_x0000_t75" style='width:348.75pt;height:302.25pt;visibility:visible; 1936 1838 mso-wrap-style:square'> 1937 1839 <v:imagedata src="ParametricFitting_files/image067.png" o:title="" croptop="2231f" 1938 1840 cropbottom="5061f" cropleft="3350f" cropright="3415f"/> 1939 </v:shape><![endif]--><![if !vml]><img border=0 width= 351 height=3041940 src="ParametricFitting_files/image 068.png" v:shapes="Picture_x0020_48"><![endif]></span></p>1841 </v:shape><![endif]--><![if !vml]><img border=0 width=465 height=403 1842 src="ParametricFitting_files/image104.png" v:shapes="Picture_x0020_48"><![endif]></span></p> 1941 1843 1942 1844 <p class=MsoListParagraphCxSpLast><o:p> </o:p></p> … … 1955 1857 <p class=MsoNormal>The parametric refinement section of GSAS-II is intended to 1956 1858 be quite flexible, but for very complex fitting, a user may wish to define a 1957 custom Python function. Such a function can be defined in a separate 1958 module that will be accessed with a parametric equation (or pseudo 1959 var).</p> 1859 custom Python function. Such a function can be defined in a separate module 1860 that will be accessed with a parametric equation (or pseudo var).</p> 1960 1861 1961 1862 <p class=MsoNormal><o:p> </o:p></p> 1962 1863 1963 <p class=MsoNormal>As an example of that, if we create a file called 1964 <span class=SpellE><span style='font-family:Courier'>fittest.py</span></span> 1965 and locate that file in any directory in the Python path (most simply, 1966 in the directory where the project file, 1967 <span class=SpellE><span 1968 style='font-family:Courier'>SeqTut.gpx</span></span>, 1969 is located) and place a routine <span class=SpellE><span 1970 style='font-family:Courier'>fitfxn</span></span> in that module:</p> 1971 1972 <blockquote><blockquote><PRE> 1973 # file fittest.py 1974 def fitfxn(T,o1,o2,a1,a2,k): 1975 if T < 120: 1976 return o1 + (a1*T)**k 1977 else: 1978 return o2 + a2*T 1979 </PRE></blockquote></blockquote> 1864 <p class=MsoNormal>As an example of that, if we create a file called <span 1865 style='font-family:Courier'>fittest.py</span> and locate that file in any 1866 directory in the Python path (most simply, in the directory where the project 1867 file, <span class=SpellE><span style='font-family:Courier'>SeqTut.gpx</span></span>, 1868 is located) and place a routine <span class=SpellE><span style='font-family: 1869 Courier'>fitfxn</span></span> in that module:</p> 1870 1871 <blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'> 1872 1873 <blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><pre><o:p> </o:p></pre><pre># file fittest.py</pre><pre>def fitfxn(T,o1,o2,a1,a2,k):</pre><pre><span style='mso-spacerun:yes'> </span>if T < 120:</pre><pre><span style='mso-spacerun:yes'> </span>return o1 + (a1*T)**k</pre><pre><span style='mso-spacerun:yes'> </span>else:</pre><pre><span style='mso-spacerun:yes'> </span>return o2 + a2*T</pre></blockquote> 1874 1875 </blockquote> 1980 1876 1981 1877 <p class=MsoNormal>The function <span class=SpellE><span style='font-family: … … 1987 1883 <p class=MsoNormal><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1988 1884 id="Picture_x0020_47" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:315pt; 1989 height:185 pt;visibility:visible;mso-wrap-style:square'>1885 height:185.25pt;visibility:visible;mso-wrap-style:square'> 1990 1886 <v:imagedata src="ParametricFitting_files/image070.png" o:title="" croptop="3393f" 1991 1887 cropbottom="7847f" cropleft="3471f" cropright="3290f"/> 1992 </v:shape><![endif]--><![if !vml]><img border=0 width= 317 height=1871993 src="ParametricFitting_files/image 071.png" v:shapes="Picture_x0020_47"><![endif]></span></p>1888 </v:shape><![endif]--><![if !vml]><img border=0 width=420 height=247 1889 src="ParametricFitting_files/image105.png" v:shapes="Picture_x0020_47"><![endif]></span></p> 1994 1890 1995 1891 <p class=MsoNormal><o:p> </o:p></p> 1996 1892 1997 <p class=MsoNormal>Note that module <span class=SpellE><span style='font-family: 1998 Courier'>fittest</span></span> is automatically located and loaded, 1999 provided it is found in the path. No changes to the standard 2000 distributed GSAS-II code are needed. Care to avoid use of a module name 2001 already found in GSAS-II or Python is wise.</p> 1893 <p class=MsoNormal>Note that module <span style='font-family:Courier'>fittest</span> 1894 is automatically located and loaded, provided it is found in the path. No 1895 changes to the standard distributed GSAS-II code are needed. Care to avoid use 1896 of a module name already found in GSAS-II or Python is wise.</p> 2002 1897 2003 1898 </div> -
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