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sequential_refinements [topas wiki]

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sequential_refinements [2018/08/09 08:18] – rowlesmr3sequential_refinements [2022/11/03 15:08] (current) – external edit 127.0.0.1
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 +====== Sequential Refinements ======
 +
 +Sequential refinement is a way of modelling multipattern datasets where the output of the nth dataset is used as the input of the (n+1)th dataset. This example uses data from the [[http://community.dur.ac.uk/john.evans/topas_workshop/tutorial_multitopas.htm|sequential refinement tutorial]] written by John Evans.
 +
 +These macros are written for Topas v6. To do sequential refinements in v<5, an external batch file must be used, as [[http://community.dur.ac.uk/john.evans/topas_workshop/tutorial_multitopas.htm|discussed]].
 +
 +Several macros will be introduced regarding setting up the sequential refinement with the #list command, outputting of refined parameter values, and fast plotting of the data to see how the parameter values change between datasets.
 +
 +A sample input file, taken essentially totally from John's tutorial, is provided at the end.
 +
 +===== Sequential refinement setup =====
 +
 +The macro ''Sequential_Refinement'', sets up the ability to easily run sequential refinements
 +<code topas>
 +macro Sequential_Refinement(numruns, ident)         { Sequential_Refinement(numruns, ident, , INP_File, Run_Number) }
 +macro Sequential_Refinement(numruns, ident, output) { Sequential_Refinement(numruns, ident, output, INP_File, Run_Number) }
 +macro Sequential_Refinement(numruns, ident, output, INPFILE, RUNNUMBER) 'This one would almost never be called directly'
 +{
 +    num_runs numruns
 +
 +    'saves a backup of the original input file'
 +    #if Run_Number == 0;
 +        system_before_save_OUT { copy INPFILE##.inp INPFILE##.backup }
 +    #endif   
 +   
 +    'Save each input file with the run number and some other identifier'
 +    system_before_save_OUT { copy INPFILE##.inp INPFILE##_##RUNNUMBER##_##ident##.inp }
 + 
 +    'copy the output of the nth file and use it as the input for the (n+1)th file'
 +    out_file = Concat(String(INPFILE), ".INP");
 +
 +    'copies the backup back over the final input file at the end of the run so you can restart from where you started'
 +    #if Run_Number == numruns-1;
 +        system_after_save_OUT { copy INPFILE##.backup INPFILE##.inp }
 +    #endif   
 +   
 +    'output every refined parameter with the in-built TOPAS keyword'
 +    'This currently doesn't work for multi-file refinement
 +    #m_ifarg output "" #m_else
 +    out_prm_vals_on_convergence output
 +    #m_endif
 +}
 +</code>
 +
 +''Sequential_Refinement'' does many things
 +  * Initialises the number of runs to refine
 +  * Save a backup of the original input file
 +  * Save each input file as you move down the #list with new filenames containing both the run number and some identifier you provide.
 +  * Copying the output of the nth refinement into the input of the (n+1)th refinement
 +  * Restoring the original input file after the #list has been traversed
 +
 +You would normally use ''Sequential_Refinement(numruns, ident)'' or ''Sequential_Refinement(numruns, ident, output)'' when putting the macro in your input file, as this allows for the automatic entering of the input file name and run number into the macro.
 +
 +===== Output refined values =====
 +
 +Outputting the refined and calculated parameter values is of great importance in order to actually quantify what it is you're refining. Given below are several output macros which provide quite a bit of flexibility in how they can be used. In all cases, the parameter value and error are reported. An example of their implementation is given in the sample input file at the end. In all cases, a value of -1 infers that the parameter doesn't exist for that particular phase.
 +
 +==== Parameter values ====
 +
 +The macro ''Out_Results'' sets up for the output of an arbitrary number of parameters
 +<code topas>
 +macro Out_Results(outFileName)              { Out_Results(outFileName, file, seqno, Get(phase_name)) }
 +macro Out_Results(outFileName, phasename)   { Out_Results(outFileName, file, seqno, phasename)       }
 +macro Out_Results(outFileName, file, seqno) { Out_Results(outFileName, file, seqno, Get(phase_name)) }
 +macro Out_Results(outFileName, file, seqno, phasename) {
 + out outFileName append
 + Out_String("\n")
 + Out_String(file)
 + Out_String("\t")
 + Out_String(seqno)
 + Out_String("\t")
 + load out_record out_fmt out_eqn 
 + {
 + "%s"  = phasename;
 + }
 + load out_record out_fmt out_fmt_err out_eqn 
 +}
 +</code>
 +
 +The ''Out_Results'' macro can be called in many different ways. To output a parameter value, the macro ''O_R'' is used. This macro incorporates some error checking to ensure that it can still operate even when trying to report values for parameters that don't exist. This is good for reporting parameters for multiple structures, where some things may not exist in each structure.
 +<code topas>
 +macro O_R(& value) {
 + "\t%10.9f" "\t%10.9f" 
 + #m_ifarg value #m_code 
 + = If(Prm_There(value),value,-1);
 + #m_else 'it must be a numeral, an eqn, or a Get(), and therefore, should exist'
 + =value;
 + #m_endif
 +}
 +</code>
 +
 +
 +To output all cell parameters, the macro ''O_R_cellprms'' is provided. This macro allows for the outputting, or not, of cell parameters, in order to maintain each type of parameter in the correct column in the output file.
 +<code topas>
 +macro O_R_cellprms(themacroval) {
 + #m_ifarg themacroval "0"
 + "\t%10.9f" "\t%10.9f" = -1.0 ;
 + "\t%10.9f" "\t%10.9f" = -1.0 ;
 + "\t%10.9f" "\t%10.9f" = -1.0 ;
 + "\t%10.9f" "\t%10.9f" = -1.0 ;
 + "\t%10.9f" "\t%10.9f" = -1.0 ;
 + "\t%10.9f" "\t%10.9f" = -1.0 ;
 + "\t%10.9f" "\t%10.9f" = -1.0 ;
 + "\t%10.9f" "\t%10.9f" = -1.0 ;
 + #m_else                 
 + "\t%10.9f" "\t%10.9f" = Get(a);
 + "\t%10.9f" "\t%10.9f" = Get(b);
 + "\t%10.9f" "\t%10.9f" = Get(c);
 + "\t%10.9f" "\t%10.9f" = Get(al);
 + "\t%10.9f" "\t%10.9f" = Get(be);
 + "\t%10.9f" "\t%10.9f" = Get(ga);
 + "\t%10.9f" "\t%10.9f" = Get(cell_volume);
 + "\t%10.9f" "\t%10.9f" = Get(cell_mass);
 + #m_endif
 +}
 +</code>
 +
 +
 +=== Example usage ===
 +The above macros could be used in the following manner
 +<code topas>
 +Out_Results("output.txt") {
 + O_R(csL)
 + O_R(csG)
 + O_R(Get(scale))
 + O_R_cellprms(1)
 + O_R(Get(r_wp))
 +}
 +</code>
 +
 +
 +
 +
 +
 +==== Column headers ====
 +Describing each of the columns is also of importance. The following macros allow for the writing of descriptive text to head each column of data in the output. The parameter and header macros must be manually updated to ensure that they both correspond.
 +
 +Please note the "@" present in the first entry of the header. This is important for the subsequent data processing and plotting.
 +<code topas>
 +macro Out_Header(outFileName) {
 + out outFileName append
 + Out_String("@file\t") 
 + Out_String("seqno\t") 
 + Out_String("phase")
 +}
 +
 +macro O_H(head) {
 + Out_String("\t") Out_String(head)
 + Out_String("\t") Out_String(head##_err)
 +}
 +
 +macro O_H_cellprms {
 + Out_String("\t") Out_String("a")
 + Out_String("\t") Out_String("a_err")
 + Out_String("\t") Out_String("b")
 + Out_String("\t") Out_String("b_err")
 + Out_String("\t") Out_String("c")
 + Out_String("\t") Out_String("c_err")
 + Out_String("\t") Out_String("al")
 + Out_String("\t") Out_String("al_err")
 + Out_String("\t") Out_String("be")
 + Out_String("\t") Out_String("be_err")
 + Out_String("\t") Out_String("ga")
 + Out_String("\t") Out_String("ga_err")
 + Out_String("\t") Out_String("cellVol")
 + Out_String("\t") Out_String("cellVol_err")
 + Out_String("\t") Out_String("cellMass")
 + Out_String("\t") Out_String("cellMass_err")
 +}
 +</code>
 +
 +
 +=== Example usage ===
 +The above macros could be used in the following manner
 +<code topas>
 +Out_Header("output.txt") {
 + O_H(csL)
 + O_H(csG)
 + O_H(scale)
 + O_H_cellprms
 + O_H(r_wp)
 +}
 +</code>
 +
 +==== Reporting calculated values ====
 +Sometimes it is nice to output calculated values, such as LVol. In these cases, the output macros must be written in a robust manner to allow for the potential of some parameters not existing in some structures. 
 +
 +Example calculations of LVol and e0 are given; they can be easily expanded to other calculations. The error checking used allows for the existence of both, either, or none of the parameters, as well as the complete absence of one or the other parameters from the macro call.
 +<code topas>
 +macro LVol_v(csg, csl) 
 +{
 + #m_ifarg csg "" 
 + IF Prm_There(csl) THEN
 + 1 / IB_from_CS(,csl)
 + ELSE
 + -1
 + ENDIF
 + #m_else #m_ifarg csl ""
 + IF Prm_There(csg) THEN
 + 1 / IB_from_CS(csg,)
 + ELSE
 + -1
 + ENDIF
 + #m_else
 + IF And(Prm_There(csg), Prm_There(csl)) THEN
 + 1 / IB_from_CS(csg, csl) 
 + ELSE IF Prm_There(csg) THEN
 + 1 / IB_from_CS(csg,)
 + ELSE IF Prm_There(csl) THEN
 + 1 / IB_from_CS(,csl)
 + ELSE
 + -1
 + ENDIF ENDIF ENDIF
 + #m_endif
 + #m_endif
 +}
 +
 +
 +macro e0_v(strg, strl) 
 +{
 + #m_ifarg strg "" 
 + IF Prm_There(strl) THEN
 + Voigt_FWHM_GL(0, strl) .25 Pi/360
 + ELSE
 + -1
 + ENDIF
 + #m_else #m_ifarg strl ""
 + IF Prm_There(strg) THEN
 + Voigt_FWHM_GL(strg, 0) .25 Pi/360
 + ELSE
 + -1
 + ENDIF
 + #m_else
 + IF And(Prm_There(strg), Prm_There(strl)) THEN
 + Voigt_FWHM_GL(strg, strl) .25 Pi/360
 + ELSE IF Prm_There(strg) THEN
 + Voigt_FWHM_GL(strg, 0) .25 Pi/360
 + ELSE IF Prm_There(strl) THEN
 + Voigt_FWHM_GL(0, strl) .25 Pi/360
 + ELSE
 + -1
 + ENDIF ENDIF ENDIF
 + #m_endif
 + #m_endif
 +}
 +</code>
 +
 +
 +====== Visualising output ======
 +It is almost always preferred to graph the output to ensure that the refinements are behaving themselves. There are many tools to do this. The example given here uses [[http://www.gnuplot.info/|gnuplot]] to plot the data, with a variety of Unix/Linux tools made available through [[https://www.cygwin.com/|cygwin]].
 +
 +In order to use the scripts below, you will need to install cygwin and install gnuplot with the cygwin installation. If you are not comfortable in using cygwin, after you've installed it, there is also a Windows batch file which you can use to automatically run the cygwin scripts to process the data. 
 +
 +There is probably a way to put the scripts in a single location and make them accessible everywhere, but I haven't figured out how to do that in cygwin (only in Windows); you'll need to copy the scripts into each directory you want to use them in.
 +
 +The following script takes the data output from the output macros above, massages it into a format that gnuplot can plot, and produces a multi-page PDF document with a single parameter plotted on each page. This is not a publication-quality graph; it is designed to give feedback as to the validity of the model you are using.
 +
 +This code is saved as ''plotme.sh'', and is used as ''> ./plotme.sh output.txt'', where ''output.txt'' is the name of the output file from Topas.
 +<code bash>
 +#!/bin/bash
 +
 +file=$1
 +tmp="tmp.txt"
 +output="forGnuplot.txt"
 +header=$(head -n1 $file)
 +
 +
 +############################
 +# awk script               #
 +############################
 +read -d '' awkscript << 'EOF'
 +BEGIN { OFS = "\\t" }
 +
 +/^@/ {
 + #save header fields into an array if the line starts with a "@"
 + for (i = 1; i <= NF; ++i)
 + header[i] = $i
 + next
 +}
 +
 +#If we're not on the first line, and the 3rd token of the current line
 +#  is not the same as the third token of the previous line
 +NR > 1 && $3!=p {
 + #output two blank lines if needed
 + if (print_blank) {
 + print "\\n"
 + }
 + print_blank = 1 #this gets set here to get the first line right
 +
 + #print first three headers as-is
 + for (i = 1; i <= 3; ++i)
 + printf("%s%s", header[i], OFS)
 +
 + #prepend column three to remaining headers
 + for (i = 4; i < NF; ++i)
 + printf("%s_%s%s", $3, header[i], OFS)
 + printf("%s_%s%s", $3, header[NF], ORS)
 +}
 +
 +# Otherwise, save value from column 3, and print everything
 +{ p=$3; print }
 +EOF
 +############################
 +# end awk script           #
 +############################
 +
 +
 +
 +#sort the topas output file by the third column, and then sort
 +#  within each sorted section by the second column.
 +# and  then put the header back on the sorted file.
 +#  3rd = phase name, 2nd = seqno. the "n" sorts numerically
 +# Unix stackexchange 52762
 +(head -n1 $file && tail -n +2 $file | sort -k 3,3 -k 2n,2n) > ${tmp}
 +
 +
 +#get the name of the phase and prepend it to the data column header titles
 +#  Unix stackexchange 460246
 +awk "$awkscript" ${tmp} > ${output}
 +
 +
 +#get the number of columns in the data file
 +numcols=$(echo $header | awk '{print NF}')
 +
 +#get the number of phases - count the number of empty lines and divide by two.
 +numphases=$(grep -cvP '\S' ${output})
 +numphases=$((($numphases/2)+1))
 +
 +
 +#if the 5th token ends in '_err', then skip the error columns when plotting
 +amIAnError=$(echo $header | awk '{print $5}')
 +if [[ "$amIAnError" == *\_err ]]; then
 + skipError=2
 +else
 + skipError=1
 +fi
 +
 +
 +rm ${tmp}
 +rm figure.pdf
 +
 +#currently fixed, but will later allow this to be changed through a command line argument
 +xcol=2
 +
 +#plot the data
 +gnuplot <<-EOF
 +set print "-"
 +set encoding iso_8859_1
 +set terminal postscript landscape noenhanced color 16
 +set output "figure.ps"
 +set key autotitle columnhead
 +set key outside
 +set key right above
 +do for [j=0:(${numphases}-1)] { #cycle over all of the data blocks
 + do for [i=4:${numcols}:${skipError}] { #plot from the 4th col to the end, skipping of there are errors
 + do for [k=${xcol}:${xcol}] { #hack to be the xcol variable working
 + stats '${output}' index j every 1:1:0:0:1:0 using i nooutput #get the first value of a column
 + if ( STATS_min == -1 ) { continue; } #if that value == -1, skip that column
 + plot '${output}' index j using k:i with lp title columnhead #plot all the data!
 + }
 + }
 +}
 +!ps2pdf figure.ps figure.pdf
 +EOF
 +</code>
 +
 +
 +If you would prefer to use a Windows batch file, the following file can be run from the Windows command line interface, and calls  cygwin in the background to process the data. 
 +
 +This code is saved as ''plotme.bat'', and is used as ''> plotme output.txt'', where ''output.txt'' is the name of the output file from Topas.
 +<code winbatch>
 +@echo off
 +
 +REM A constant to use later
 +SET cygwin=/cygdrive/
 +
 +REM the folder where the batch file is being run from
 +SET winFolder=%cd%
 +
 +REM replace the \ with / to go from Windows to Unix styles
 +SET unixFolder=%winFolder:\=/%
 +
 +REM change the drive ":" to be a /
 +REM  and prepend the cygwin constant to get the 
 +REM  cygwin directory
 +SET unixFolder=%unixFolder::=%
 +SET "unixFolder=%cygwin%%unixFolder%"
 +
 +REM put the command together to be given to cygwin
 +REM  "replace" is the name of the script to run in cygwin
 +REM "%*" passess all the command line arguments 
 +SET "command=cd %unixFolder%; ./plotme.sh %*"
 +
 +
 +REM actually run the script.
 +@echo on
 +c:\cygwin64\bin\bash --login -c "%command%"
 +</code>
 +
 +
 +
 +
 +====== Sample input file ======
 +This input file and data has been taken directly from John Evans' [[http://community.dur.ac.uk/john.evans/topas_workshop/tutorial_multitopas.htm|tutorial]]
 +
 +<code topas>
 +r_wp  14.7060581 r_exp  9.5411932 r_p  11.0801261 r_wp_dash  24.5432007 r_p_dash  23.5343473 r_exp_dash  15.9234662 weighted_Durbin_Watson  1.50046576 gof  1.54132275
 +
 +iters 100000
 +chi2_convergence_criteria 0.001
 +do_errors
 +
 +#list File_Name Temperature identifier {
 +xye_files\576460-mac-001_reb_0003.xye 30  576460
 +xye_files\576461-mac-001_reb_0003.xye 50  576461
 +xye_files\576462-mac-001_reb_0003.xye 70  576462
 +xye_files\576463-mac-001_reb_0003.xye 90  576463
 +xye_files\576464-mac-001_reb_0003.xye 110 576464
 +xye_files\576465-mac-001_reb_0003.xye 130 576465
 +xye_files\576466-mac-001_reb_0003.xye 150 576466
 +xye_files\576467-mac-001_reb_0003.xye 170 576467
 +xye_files\576468-mac-001_reb_0003.xye 190 576468
 +xye_files\576469-mac-001_reb_0003.xye 210 576469
 +xye_files\576470-mac-001_reb_0003.xye 230 576470
 +xye_files\576471-mac-001_reb_0003.xye 250 576471
 +xye_files\576472-mac-001_reb_0003.xye 270 576472
 +xye_files\576473-mac-001_reb_0003.xye 290 576473
 +xye_files\576474-mac-001_reb_0003.xye 310 576474
 +xye_files\576475-mac-001_reb_0003.xye 330 576475
 +xye_files\576476-mac-001_reb_0003.xye 350 576476
 +xye_files\576477-mac-001_reb_0003.xye 370 576477
 +xye_files\576478-mac-001_reb_0003.xye 400 576478
 +xye_files\576479-mac-001_reb_0003.xye 450 576479
 +xye_files\576480-mac-001_reb_0003.xye 500 576480
 +xye_files\576481-mac-001_reb_0003.xye 550 576481
 +xye_files\576482-mac-001_reb_0003.xye 600 576482
 +xye_files\576483-mac-001_reb_0003.xye 650 576483
 +xye_files\576484-mac-001_reb_0003.xye 700 576484
 +xye_files\576485-mac-001_reb_0003.xye 750 576485
 +xye_files\576486-mac-001_reb_0003.xye 800 576486
 +xye_files\576487-mac-001_reb_0003.xye 850 576487
 +xye_files\576488-mac-001_reb_0003.xye 900 576488
 +xye_files\576489-mac-001_reb_0003.xye 950 576489 
 +}
 +
 +prm !te =Temperature(Run_Number);:50.00000
 +
 +
 +'Here we define all the macros that we need to use for the file names, identifiers.'
 +' Note that they all use Run_Number to scroll through the #list'
 +macro file { File_Name(Run_Number) }
 +macro seqno { Temperature(Run_Number) } 
 +macro ident { identifier(Run_Number) }
 +macro outFileName { output.txt }
 +
 +
 +
 +Sequential_Refinement(30, ident)
 +
 +
 +#define OUTPUT
 +'This single output macro encapsulate all of the desired outputs, allowing it '
 +'  to be easily turned on and off with the above #define'
 +' The Output macro is referred to at the end of the input file '
 +macro Output {
 + 'Only write the header the first time the file is run'
 + #if Run_Number == 0;
 + Out_Header(outFileName)
 + O_H(temp)
 + O_H(th2_zero)
 + O_H(csL)
 + O_H(csG)
 + O_H(strL)
 + O_H(strG)
 + O_H(Al_O_beq)
 + O_H(Si_beq)
 + O_H_cellprms
 + O_H(Lvol)
 + O_H(e0)
 + O_H(density)
 + O_H(LAC)
 + O_H(scale)
 + O_H(wtpct)
 + O_H(RBragg)
 + O_H(Rwp)
 + O_H(Rexp)
 + O_H(gof)
 + #endif
 +
 + 'output the following parameters for each str '
 + ' Yes, there is doubling up on things like R_wp, but '
 + ' this is an expedient way of doing it. '
 + for strs {
 + Out_Results(outFileName) {
 + O_R(te)
 + O_R(zero)
 + O_R(csL)
 + O_R(csG)
 + O_R(strL)
 + O_R(strG)
 + O_R(beq_Al_O)
 + O_R(beq_Si)
 + O_R_cellprms(1)
 + O_R(LVol_v(csG,csL))
 + O_R(e0_v(strG, strL))
 + O_R(Phase_Density_Eqn_g_on_cm3)
 + O_R(Phase_LAC_Eqn_1_on_cm)
 + O_R(Get(scale))
 + O_R(Get(weight_percent))
 + O_R(Get(r_bragg))
 + O_R(Get(r_wp))
 + O_R(Get(r_exp))
 + O_R(Get(gof))
 + }
 + }
 +}
 +
 +
 +
 +xdd file
 + start_X 5
 + finish_X 65
 + x_calculation_step = Yobs_dx_at(Xo);
 + 'lambda derived on peak shape derived on 574646-mac-001_offline.xye on 21/4/2017.xye by John 2016'
 + 'Si zero was -1.69258/1000 degrees'
 + lam ymin_on_ymax 0.00001 la 1.0 lo   0.8257653_8.44468382e-008 lh 0.1
 + LP_Factor( 90) 'change the LP correction  or lh value if required'
 +   prm zero -0.73189` th2_offset = (zero/1000);: -0.000731892355`
 + bkg @  33.8497345` -20.6790085` -0.0215825246`  4.12571439` -7.26100925`  11.085209` -8.51176792`  0.504480555`  5.02091543` -5.47486731`  3.66723328` -2.31323425` -0.875693589`  3.93798196` -3.78164372`  2.5772305` -1.73983838`  0.593683324`
 +
 +    str
 + phase_name Al2O3
 +
 +
 + 'Note the use of local parameters to allow for the same names to be used for the same parameters '
 + ' in different structures. This significantly simplifies the output macro '
 + local csL 441.48490` min 20 max 5000
 + local csG 10000.00000`_LIMIT_MIN_0.3 min 20 max 5000
 + local strL 0.01530` min 0.00001 max 2
 + local strG 0.00011`_LIMIT_MIN_0.0001 min 0.00001 max 2
 +
 +
 +  LVol_FWHM_CS_G_L(1, 281.81513`, 0.89, 392.90767`, ,csG  , ,csL )
 +  e0_from_Strain( 0.00003`, , strG, , strL)
 + Hexagonal(lpa_1  4.759307`, lpc_1  12.992397`)
 + MVW( 611.768, 254.863`, 72.020`)
 + space_group "R-3cH"
 + site Al1 num_posns 12 x 0    y 0 z 0.148 occ Al+3 1 beq beq_Al_O  0.34729` 
 + site O1  num_posns 18 x 0.306 y 0 z 0.25 occ O-2  1 beq beq_Al_O  0.34729`
 + scale  scal_1  6.13160855e-005`
 + r_bragg  2.18302298
 + Phase_Density_g_on_cm3( 3.98592`)
 +
 + str
 + phase_name silicon
 + Cubic(lpa_2  5.431042)
 + MVW( 224.684, 160.195`, 27.980`)
 + space_group "Fd-3mS"
 + site Si1 num_posns 8 x 0 y 0 z 0 occ Si 1 beq beq_Si  0.38226`
 + scale  scal_2  0.000103012159`
 + r_bragg  2.01378994
 + Phase_Density_g_on_cm3( 2.32901`)
 +
 + for strs {
 + 'peak shape derived on 574646-mac-001_offline.xye on 21/4/2017'
 + 'This is a fixed instrumental profile'
 + 'Just use size/strain on your sample'
 + TCHZ_Peak_Type(!pku,-0.00072_0.00002,!pkv, -0.00008_0.00001,!pkw, -0.00080_0.00002,!pkz, 0.00087_0.00002,!pky, 0.01490_0.00011,!pkx, 0.00175_0.00002)
 + Simple_Axial_Model(!axial, 2.12938_0.00228)
 + }
 +
 + #ifdef OUTPUT
 + Output
 + #endif
 +</code>
 +
 +
 +===== Sample data =====
 +
 +The output straight from Topas looks like:
 +<code>
 +@file seqno phase temp temp_err th2_zero th2_zero_err csL csL_err csG csG_err strL strL_err strG strG_err Al_O_beq Al_O_beq_err Si_beq Si_beq_err a a_err b b_err c c_err al al_err be be_err ga ga_err cellVol cellVol_err cellMass cellMass_err Lvol Lvol_err e0 e0_err density density_err LAC LAC_err scale scale_err wtpct wtpct_err RBragg RBragg_err Rwp Rwp_err Rexp Rexp_err gof gof_err
 +xye_files\576460-mac-001_reb_0003.xye 30 Al2O3 30.000000000 0.000000000 -0.740395087 0.034251094 457.056345418 18.647401687 5000.000000000 5836.253245142 0.013722097 0.001656271 0.000010000 0.906905709 0.352918542 0.014508964 0.382080499 0.014808988 4.759301460 0.000009336 4.759301460 0.000009336 12.992385154 0.000041209 90.000000000 0.000000000 90.000000000 0.000000000 120.000000000 0.000000000 254.862504865 0.001285843 611.767656000 0.000000000 289.516481798 12.883985498 0.000029935 0.000297908 3.985932675 0.000020107 20.182163481 0.000101808 0.000061165 0.000000254 72.005379050 0.122017420 2.129176452 0.000000000 14.632201273 0.000000000 9.541193204 0.000000000 1.533581907 0.000000000
 +xye_files\576460-mac-001_reb_0003.xye 30 silicon 30.000000000 0.000000000 -0.740395087 0.034251094 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 0.352918542 0.014508964 0.382080499 0.014808988 5.431041634 0.000005881 5.431041634 0.000005881 5.431041634 0.000005881 90.000000000 0.000000000 90.000000000 0.000000000 90.000000000 0.000000000 160.195162072 0.000520495 224.684000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 2.329014244 0.000007565 24.020119193 0.000078021 0.000103011 0.000000455 27.994620950 0.122017420 2.012050371 0.000000000 14.632201273 0.000000000 9.541193204 0.000000000 1.533581907 0.000000000
 +xye_files\576461-mac-001_reb_0003.xye 50 Al2O3 50.000000000 0.000000000 -0.812397177 0.035303714 464.403780160 19.173135735 5000.000000000 5809.071294680 0.013181063 0.001643816 0.000010000 0.894178127 0.349627634 0.014540330 0.408054377 0.014973569 4.759793589 0.000009383 4.759793589 0.000009383 12.994024245 0.000041209 90.000000000 0.000000000 90.000000000 0.000000000 120.000000000 0.000000000 254.947374482 0.001290043 611.767656000 0.000000000 294.092665429 13.239741734 0.000028754 0.000292552 3.984605795 0.000020159 20.175445026 0.000102072 0.000060399 0.000000252 72.102460855 0.122505922 2.212796335 0.000000000 14.691631182 0.000000000 9.585669178 0.000000000 1.532666203 0.000000000
 +xye_files\576461-mac-001_reb_0003.xye 50 silicon 50.000000000 0.000000000 -0.812397177 0.035303714 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 0.349627634 0.014540330 0.408054377 0.014973569 5.431334617 0.000006056 5.431334617 0.000006056 5.431334617 0.000006056 90.000000000 0.000000000 90.000000000 0.000000000 90.000000000 0.000000000 160.221089130 0.000536020 224.684000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 2.328637362 0.000007788 24.016232245 0.000080322 0.000101248 0.000000451 27.897539145 0.122505922 1.936206569 0.000000000 14.691631182 0.000000000 9.585669178 0.000000000 1.532666203 0.000000000
 +xye_files\576462-mac-001_reb_0003.xye 70 Al2O3 70.000000000 0.000000000 -0.880848871 0.035525317 485.853333685 21.025288239 5000.000000000 5835.183824737 0.015792581 0.001656884 0.000010000 0.916456708 0.331996481 0.014451057 0.420349853 0.014921309 4.760311020 0.000009487 4.760311020 0.000009487 12.995620523 0.000041422 90.000000000 0.000000000 90.000000000 0.000000000 120.000000000 0.000000000 255.034133834 0.001301636 611.767656000 0.000000000 307.438086970 14.503216691 0.000034452 0.000304838 3.983250283 0.000020326 20.168581598 0.000102919 0.000060367 0.000000250 71.922823012 0.122021715 2.292445550 0.000000000 14.548238223 0.000000000 9.559905369 0.000000000 1.521797305 0.000000000
 +xye_files\576462-mac-001_reb_0003.xye 70 silicon 70.000000000 0.000000000 -0.880848871 0.035525317 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 0.331996481 0.014451057 0.420349853 0.014921309 5.431624209 0.000006091 5.431624209 0.000006091 5.431624209 0.000006091 90.000000000 0.000000000 90.000000000 0.000000000 90.000000000 0.000000000 160.246718857 0.000539130 224.684000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 2.328264921 0.000007831 24.012391109 0.000080762 0.000102119 0.000000451 28.077176988 0.122021715 2.151463548 0.000000000 14.548238223 0.000000000 9.559905369 0.000000000 1.521797305 0.000000000
 +xye_files\576463-mac-001_reb_0003.xye 90 Al2O3 90.000000000 0.000000000 -0.703527828 0.035289268 475.605918859 20.342679603 5000.000000000 5897.549999134 0.014390428 0.001668355 0.000010000 0.914911794 0.352004457 0.014676691 0.480279412 0.015330682 4.760897115 0.000009484 4.760897115 0.000009484 12.997435186 0.000041612 90.000000000 0.000000000 90.000000000 0.000000000 120.000000000 0.000000000 255.132558739 0.001304070 611.767656000 0.000000000 301.064960013 14.045940582 0.000031393 0.000302022 3.981713627 0.000020349 20.160800973 0.000103032 0.000059966 0.000000251 71.831369590 0.124216169 2.488148571 0.000000000 14.708246327 0.000000000 9.591345896 0.000000000 1.533491388 0.000000000
 +xye_files\576463-mac-001_reb_0003.xye 90 silicon 90.000000000 0.000000000 -0.703527828 0.035289268 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 0.352004457 0.014676691 0.480279412 0.015330682 5.431969563 0.000006097 5.431969563 0.000006097 5.431969563 0.000006097 90.000000000 0.000000000 90.000000000 0.000000000 90.000000000 0.000000000 160.277287294 0.000539724 224.684000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 2.327820870 0.000007836 24.007811413 0.000080821 0.000101921 0.000000458 28.168630410 0.124216169 1.917091353 0.000000000 14.708246327 0.000000000 9.591345896 0.000000000 1.533491388 0.000000000
 +xye_files\576464-mac-001_reb_0003.xye 110 Al2O3 110.000000000 0.000000000 -0.701583629 0.035318818 480.349448846 20.517785024 5000.000000000 5830.324740872 0.015176590 0.001659493 0.000010000 0.917406941 0.381850116 0.014560194 0.507470746 0.015241752 4.761478894 0.000009443 4.761478894 0.000009443 12.999133546 0.000041549 90.000000000 0.000000000 90.000000000 0.000000000 120.000000000 0.000000000 255.228262771 0.001300156 611.767656000 0.000000000 304.015666103 14.161232126 0.000033108 0.000304387 3.980220587 0.000020272 20.153241191 0.000102646 0.000061035 0.000000252 72.107533398 0.121844748 2.065533571 0.000000000 14.513534949 0.000000000 9.549136409 0.000000000 1.519879320 0.000000000
 +xye_files\576464-mac-001_reb_0003.xye 110 silicon 110.000000000 0.000000000 -0.701583629 0.035318818 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 0.381850116 0.014560194 0.507470746 0.015241752 5.432316833 0.000006122 5.432316833 0.000006122 5.432316833 0.000006122 90.000000000 0.000000000 90.000000000 0.000000000 90.000000000 0.000000000 160.308029204 0.000542026 224.684000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 2.327374469 0.000007867 24.003207489 0.000081134 0.000102346 0.000000455 27.892466602 0.121844748 2.058927699 0.000000000 14.513534949 0.000000000 9.549136409 0.000000000 1.519879320 0.000000000
 +xye_files\576465-mac-001_reb_0003.xye 130 Al2O3 130.000000000 0.000000000 -0.736181437 0.036114760 481.324413199 20.726623111 5000.000000000 5873.782695800 0.015765805 0.001673105 0.000010000 0.931858886 0.379068548 0.014651644 0.511254055 0.015342909 4.762064520 0.000009612 4.762064520 0.000009612 13.000969502 0.000042139 90.000000000 0.000000000 90.000000000 0.000000000 120.000000000 0.000000000 255.327105405 0.001321909 611.767656000 0.000000000 304.622016741 14.308217416 0.000034394 0.000309927 3.978679758 0.000020596 20.145439437 0.000104283 0.000059907 0.000000248 72.020563118 0.122483432 2.073157162 0.000000000 14.503811050 0.000000000 9.600815270 0.000000000 1.510685358 0.000000000
 +xye_files\576465-mac-001_reb_0003.xye 130 silicon 130.000000000 0.000000000 -0.736181437 0.036114760 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 0.379068548 0.014651644 0.511254055 0.015342909 5.432654340 0.000006251 5.432654340 0.000006251 5.432654340 0.000006251 90.000000000 0.000000000 90.000000000 0.000000000 90.000000000 0.000000000 160.337910675 0.000553513 224.684000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 2.326940726 0.000008031 23.998734117 0.000082823 0.000100910 0.000000450 27.979436882 0.122483432 2.302132815 0.000000000 14.503811050 0.000000000 9.600815270 0.000000000 1.510685358 0.000000000
 +xye_files\576466-mac-001_reb_0003.xye 150 Al2O3 150.000000000 0.000000000 -0.635163488 0.036157329 499.236908045 22.525692251 5000.000000000 5909.062839966 0.016637932 0.001695928 0.000010000 0.948028749 0.410719473 0.014885177 0.564343278 0.015578883 4.762667978 0.000009678 4.762667978 0.000009678 13.002850501 0.000042344 90.000000000 0.000000000 90.000000000 0.000000000 120.000000000 0.000000000 255.428771061 0.001330277 611.767656000 0.000000000 315.754622440 15.516606620 0.000036296 0.000316427 3.977096165 0.000020709 20.137421157 0.000104859 0.000060639 0.000000254 71.898486551 0.123772162 2.325527727 0.000000000 14.544761034 0.000000000 9.545510299 0.000000000 1.523727970 0.000000000
 +xye_files\576466-mac-001_reb_0003.xye 150 silicon 150.000000000 0.000000000 -0.635163488 0.036157329 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 0.410719473 0.014885177 0.564343278 0.015578883 5.433020158 0.000006302 5.433020158 0.000006302 5.433020158 0.000006302 90.000000000 0.000000000 90.000000000 0.000000000 90.000000000 0.000000000 160.370302768 0.000558121 224.684000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 2.326470723 0.000008094 23.993886778 0.000083479 0.000102784 0.000000461 28.101513449 0.123772162 1.862890550 0.000000000 14.544761034 0.000000000 9.545510299 0.000000000 1.523727970 0.000000000
 +xye_files\576467-mac-001_reb_0003.xye 170 Al2O3 170.000000000 0.000000000 -0.590086622 0.035728812 453.762581191 18.832182354 5000.000000000 6005.106591983 0.013262418 0.001704684 0.000010000 0.938671943 0.413333194 0.015046985 0.611639106 0.015903846 4.763309482 0.000009674 4.763309482 0.000009674 13.004715379 0.000042513 90.000000000 0.000000000 90.000000000 0.000000000 120.000000000 0.000000000 255.534228924 0.001332419 611.767656000 0.000000000 287.464236568 13.024492832 0.000028932 0.000307294 3.975454835 0.000020726 20.129110531 0.000104941 0.000059743 0.000000252 71.831432519 0.125089853 2.300890720 0.000000000 14.638001041 0.000000000 9.601475435 0.000000000 1.524557464 0.000000000
 +xye_files\576467-mac-001_reb_0003.xye 170 silicon 170.000000000 0.000000000 -0.590086622 0.035728812 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 0.413333194 0.015046985 0.611639106 0.015903846 5.433385998 0.000006287 5.433385998 0.000006287 5.433385998 0.000006287 90.000000000 0.000000000 90.000000000 0.000000000 90.000000000 0.000000000 160.402701270 0.000556862 224.684000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 2.326000818 0.000008073 23.989040438 0.000083257 0.000101623 0.000000460 28.168567481 0.125089853 2.206670581 0.000000000 14.638001041 0.000000000 9.601475435 0.000000000 1.524557464 0.000000000
 +xye_files\576468-mac-001_reb_0003.xye 190 Al2O3 190.000000000 0.000000000 -0.555840481 0.036545211 486.968859310 21.540165789 5000.000000000 5934.572845638 0.015283316 0.001700448 0.000010000 0.943067770 0.409043523 0.015009272 0.599686824 0.015906226 4.763945854 0.000009689 4.763945854 0.000009689 13.006662915 0.000042439 90.000000000 0.000000000 90.000000000 0.000000000 120.000000000 0.000000000 255.640789615 0.001333070 611.767656000 0.000000000 308.131578414 14.849829691 0.000033341 0.000313037 3.973797716 0.000020719 20.120719961 0.000104905 0.000059801 0.000000252 71.864040181 0.124818793 2.480488544 0.000000000 14.584574024 0.000000000 9.570391793 0.000000000 1.523926537 0.000000000
 +xye_files\576468-mac-001_reb_0003.xye 190 silicon 190.000000000 0.000000000 -0.555840481 0.036545211 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 0.409043523 0.015009272 0.599686824 0.015906226 5.433764885 0.000006376 5.433764885 0.000006376 5.433764885 0.000006376 90.000000000 0.000000000 90.000000000 0.000000000 90.000000000 0.000000000 160.436259758 0.000564788 224.684000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 2.325514287 0.000008184 23.984022645 0.000084406 0.000101578 0.000000460 28.135959819 0.124818793 2.048403943 0.000000000 14.584574024 0.000000000 9.570391793 0.000000000 1.523926537 0.000000000
 +xye_files\576469-mac-001_reb_0003.xye 210 Al2O3 210.000000000 0.000000000 -0.539994383 0.035720625 524.784239486 25.071437281 5000.000000000 5959.118009091 0.018798767 0.001716238 0.000010000 0.973833586 0.396436028 0.014981987 0.643849127 0.016009905 4.764583443 0.000009770 4.764583443 0.000009770 13.008603262 0.000042772 90.000000000 0.000000000 90.000000000 0.000000000 120.000000000 0.000000000 255.747369202 0.001344351 611.767656000 0.000000000 331.607712627 17.238954179 0.000041011 0.000327895 3.972141684 0.000020876 20.112334897 0.000105705 0.000059208 0.000000249 71.843645119 0.124749760 2.366026678 0.000000000 14.530574512 0.000000000 9.613881168 0.000000000 1.511416072 0.000000000
 +xye_files\576469-mac-001_reb_0003.xye 210 silicon 210.000000000 0.000000000 -0.539994383 0.035720625 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 0.396436028 0.014981987 0.643849127 0.016009905 5.434133194 0.000006290 5.434133194 0.000006290 5.434133194 0.000006290 90.000000000 0.000000000 90.000000000 0.000000000 90.000000000 0.000000000 160.468885803 0.000557290 224.684000000 0.000000000 -1.000000000 0.000000000 -1.000000000 0.000000000 2.325041471 0.000008072 23.979146287 0.000083252 0.000100693 0.000000456 28.156354881 0.124749760 2.249226762 0.000000000 14.530574512 0.000000000 9.613881168 0.000000000 1.511416072 0.000000000
 +xye_files\576470-mac-001_reb_0003.xye 230 Al2O3 230.000000000 0.000000000 -0.602201960 0.036026591 476.949364242 20.800670227 5000.000000000 6008.348691468 0.015686520 0.001721346 0.000010000 0.965496459 0.454899400 0.015107205 0.662714936 0.016045773 4.765202339 0.000009769 4.765202339 0.000009769 13.010538402 0.000042797 90.000000000 0.000000000 90.000000000 0.000000000 120.000000000 0.000000000 255.851868646 0.001344936 611.767656000 0.000000000 301.900750276 14.365870176 0.000034221 0.000321010 3.970519313 0.000020868 20.104120270 0.000105664 0.000060367 0.000000253 72.127859367 0.123927445 2.364320116 0.000000000 14.503697518 0.000000000 9.577692663 0.000000000 1.514320623 0.000000000
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 +</code>
 +
 +
 +Once the data has gone through the gnuplot script, it looks like
 +<code>
 +@file seqno phase Al2O3_temp Al2O3_temp_err Al2O3_th2_zero Al2O3_th2_zero_err Al2O3_csL Al2O3_csL_err Al2O3_csG Al2O3_csG_err Al2O3_strL Al2O3_strL_err Al2O3_strG Al2O3_strG_err Al2O3_Al_O_beq Al2O3_Al_O_beq_err Al2O3_Si_beq Al2O3_Si_beq_err Al2O3_a Al2O3_a_err Al2O3_b Al2O3_b_err Al2O3_c Al2O3_c_err Al2O3_al Al2O3_al_err Al2O3_be Al2O3_be_err Al2O3_ga Al2O3_ga_err Al2O3_cellVol Al2O3_cellVol_err Al2O3_cellMass Al2O3_cellMass_err Al2O3_Lvol Al2O3_Lvol_err Al2O3_e0 Al2O3_e0_err Al2O3_density Al2O3_density_err Al2O3_LAC Al2O3_LAC_err Al2O3_scale Al2O3_scale_err Al2O3_wtpct Al2O3_wtpct_err Al2O3_RBragg Al2O3_RBragg_err Al2O3_Rwp Al2O3_Rwp_err Al2O3_Rexp Al2O3_Rexp_err Al2O3_gof Al2O3_gof_err
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 +</code>
 +
 +The produced PDF file looks like [[https://cloudstor.aarnet.edu.au/plus/s/A7KpkVGtjzpSV7f|this]].
 +
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