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diff --git a/Master/texmf-dist/tex/generic/pst-fit/pst-fit.tex b/Master/texmf-dist/tex/generic/pst-fit/pst-fit.tex new file mode 100644 index 00000000000..2336d5c20b3 --- /dev/null +++ b/Master/texmf-dist/tex/generic/pst-fit/pst-fit.tex @@ -0,0 +1,981 @@ +%% $Id: pst-fit.tex 673 2012-04-01 09:50:48Z herbert $ +%% +%% This is file `pst-fit.tex', +%% +%% IMPORTANT NOTICE: +%% +%% Package `pst-fit.tex' +%% +%% Buddy Ledger <buddyledger@gmail.com> +%% Herbert Voss <hvoss@tug.org> +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%% DESCRIPTION: +%% `pst-fit' is a PSTricks package for curve fitting +%% +\csname PSTfitLoaded\endcsname +\let\PSTfitLoaded\endinput +% Requires PSTricks, pst-plot +\ifx\PSTricksLoaded\endinput\else \input pstricks.tex\fi +\ifx\PSTricksAddLoaded\endinput\else\input pstricks-add.tex\fi +\ifx\PSTXKeyLoaded\endinput\else \input pst-xkey \fi +% +\def\fileversion{0.01} +\def\filedate{2012/04/01} +\message{`PST-fit' v\fileversion, \filedate\space (BL,HV)} +% +\edef\PstAtCode{\the\catcode`\@} \catcode`\@=11\relax + +\pst@addfams{pst-fit} +\def\beginplot@ErrorLine{\begin@OpenObj} +\def\endplot@ErrorLine{\psErrorLine@ii} +\def\psErrorLine@ii{% + \addto@pscode{ + \pst@cp % current point + \psline@iii % arc and lineto type + \tx@ErrorLine + }% + \end@OpenObj% +} +% +\def\tx@ErrorLine{ErrorLine } +\pst@def{ErrorLine}<{ + /copypt { dup 3 2 roll dup 4 1 roll exch } def %copy point + NArray n 0 eq not + { n { \psk@relyerr\space 0 eq not + {copypt copypt dup \psk@relyerr\space mul add ArrowA + dup \psk@relyerr\space mul sub + Lineto + copypt dup \psk@relyerr\space mul sub ArrowB L} if + \psk@relxerr\space 0 eq not + {copypt copypt exch dup \psk@relxerr\space mul add exch ArrowA + exch dup \psk@relxerr\space mul sub exch + Lineto + copypt exch dup \psk@relxerr\space mul sub exch ArrowB L pop pop } + { pop pop } ifelse } repeat + } if +}> + +\define@boolkey[psset]{pst-fit}[Pst@]{ScyBase}[true]{}% +\define@boolkey[psset]{pst-fit}[Pst@]{ScxBase}[true]{}% +\psset{ScyBase=true,ScxBase=true} + +\def\pstScalePoints(#1,#2)#3#4{% +% xScale | yScale | xOperator | yOperator +% the operators can be any Postscript code +\pst@def{ScalePoints}<% + /y ED /x ED + /yOper { #4\space y mul #2\space mul } def + /xOper { #3\space x mul #1\space mul } def + counttomark dup dup cvi eq not { exch pop } if + /m exch def /n m 2 div cvi def + n { + #4\space y mul #2\space mul m 1 roll + #3\space x mul #1\space mul m 1 roll + /m m 2 sub + def } repeat>% +} +\def\psLineToXAxis@ii{% +\addto@pscode{\pst@cp \psline@iii \tx@LineToXAxis}% +\end@OpenObj} + +\def\tx@LineToXAxis{LineToXAxis } + +\pst@def{LineToXAxis}<{% +NArray +n 0 eq not + { %n 1 eq { 0 0 /n 2 def } if + %ArrowA + %/n n 2 sub def + %2 copy pop 0 \ifPst@ScyBase yOper \fi moveto Lineto + n { 2 copy 2 copy pop 0 \ifPst@ScyBase yOper \fi 4 2 roll ArrowA Lineto + 2 copy pop 0 \ifPst@ScyBase yOper \fi ArrowB L pop pop + } repeat + %2 copy moveto pop 0 \ifPst@ScyBase yOper \fi + %L + %pop pop +} if}> + +\def\psLineToYAxis@ii{% +\addto@pscode{\pst@cp \psline@iii \tx@LineToYAxis}% +\end@OpenObj} +\def\tx@LineToYAxis{LineToYAxis } +\pst@def{LineToYAxis}<{ +NArray +n 0 eq not + { %n 1 eq { 0 0 /n 2 def } if + %ArrowA + %/n n 2 sub def + %CP 2 copy moveto exch pop 0 \ifPst@ScxBase xOper \fi exch Lineto + n { 2 copy 2 copy exch pop 0 \ifPst@ScxBase xOper \fi exch 4 2 roll ArrowA Lineto + 2 copy exch pop 0 \ifPst@ScxBase xOper \fi exch ArrowB L pop pop + } repeat + %2 copy moveto exch pop 0 \ifPst@ScxBase xOper \fi exch + %L + %pop pop +} if}> +% +%%%%%%PREPAREPOINTS +\define@key[psset]{pst-fit}{plotNoTwo}{\def\psk@plotNoTwo{#1}}% +\define@key[psset]{pst-fit}{plotNoTwoFunc}{\def\psk@plotNoTwoFunc{#1}} %Must operate on two stack elements and return one +\psset{plotNoTwo=0,plotNoTwoFunc=dup mul exch dup mul add sqrt} + +%\def\tx@PreparePoints{PreparePoints } +\pst@def{PreparePoints}<{% + counttomark /m exch def + \ifPsk@xyValues\else % we have only y values + /mm m def + /M m 1 add def + m { mm exch M 2 roll /M M 1 add def /mm mm 1 sub def } repeat + /m m dup add def + \fi + \ifPst@ChangeOrder + /m0 m def + m \psk@plotNoMax\space 1 add div 1 sub cvi { + m0 \psk@plotNoMax\space 1 add roll /m0 m0 \psk@plotNoMax\space 1 add sub def + } repeat + \fi + /n m \psk@plotNoMax\space 1 add div cvi def + \psk@plotNoMax\space 1 gt {% multiple data files? + n { + \psk@plotNoTwo\space 0 gt { + \psk@plotNoMax\space copy + \psk@plotNoMax\space \psk@plotNoTwo\space 1 sub neg roll % x yNo y yNoTwo y [yNo y yNoTwo y] + \psk@plotNoMax\space 1 sub { pop } repeat % x yNo y yNoTwo y yNoTwo + \psk@plotNoMax\space 1 add 1 roll } if + \psk@plotNoMax\space \psk@plotNo\space 1 sub neg roll % x yNo y y y ... + \psk@plotNoMax\space 1 sub { pop } repeat % x [yNoTwo] yNo + \psk@plotNoTwo\space 0 gt { + \psk@plotNoTwoFunc\space } if %x f(yNo,yNoTwo) + /m m \psk@plotNoMax\space 1 sub sub def + m 2 roll + } repeat + } if % no multiple data files +% counttomark /m exch def +% /n m 2 div cvi def + /xMax -99999 def /yMax -99999 def + /xP 0 def /yP 0 def + m copy + n { + /y exch def /x exch def + xMax x lt { /xMax x def } if + yMax y lt {/yMax y def } if + xP x gt { /xP x def } if + yP y gt { /yP y def } if + } repeat +% m 2 roll + \psk@xStep\space 0 gt \psk@yStep\space 0 gt or (\psk@xStart) length 0 gt or + (\psk@yStart) length 0 gt or (\psk@xEnd) length 0 gt or (\psk@yEnd) length 0 gt or { +% + (\psk@xStart) length 0 gt {\psk@xStart\space }{ xP } ifelse /xStart exch def + (\psk@yStart) length 0 gt {\psk@yStart\space }{ yP } ifelse /yStart exch def + (\psk@xEnd) length 0 gt { \psk@xEnd\space }{ xMax } ifelse /xEnd exch def + (\psk@yEnd) length 0 gt { \psk@yEnd\space }{ yMax } ifelse /yEnd exch def + n { + m -2 roll + 2 copy /yVal exch def /xVal exch def + xVal xP ge + yVal yP ge and + xVal xEnd le and + yVal yEnd le and + xVal xStart ge and + yVal yStart ge and { + /xP xP \psk@xStep\space add def + /yP yP \psk@yStep\space add def + }{% + pop pop + /m m 2 sub def + } ifelse + } repeat + }{% + /ncount 0 def + (\psk@nEnd) length 0 gt { \psk@nEnd\space }{ m } ifelse + /nEnd exch def + n { + m -2 roll + \psk@nStep\space 1 gt { + ncount \psk@nStart\space sub \psk@nStep\space mod 0 eq }{ true } ifelse + ncount nEnd le and + ncount \psk@nStart\space ge and not { + pop pop + /m m 2 sub def + } if + /ncount ncount 1 add def + } repeat + } ifelse +}> +% + +\def\beginplot@PrintCoor{\begin@SpecialObj} +\def\endplot@PrintCoor{% + \psPrintCoor@ii %\psk@fillstyle\ifpsshadow\pst@closedshadow\fi% + %\pst@stroke + \end@SpecialObj% +} +\define@key[psset]{pst-fit}{relxerr}{\def\psk@relxerr{#1}} +\define@key[psset]{pst-fit}{relyerr}{\def\psk@relyerr{#1}} +\define@key[psset]{pst-fit}{yShift}{\def\psk@yShift{#1}} +\define@boolkey[psset]{pst-fit}[Pst@]{science}[true]{}% +\psset[pst-fit]{science=false,relxerr=0.1,relyerr=0.1,yShift=0} +%Following is new pst-func.tex key which conflicts with mine. +%Must specify [pst-fit] in psset to correct. +%\define@boolkey[psset]{pst-add}[Pst@]{science}[true]{% +% \ifPst@science\def\psk@Scin{true }\else\def\psk@Scin{false }\fi} + +\def\psPrintCoor@ii{% + \addto@pscode{% + false + \tx@NArray + \pst@number\psxunit + \pst@number\psyunit + \psPrintCoor@iii +}} + +\def\psPrintCoor@iii{% + /mfont { \psk@PSfont\space findfont \psk@fontscale\space scalefont setfont } bind def + /mfontexp { \psk@PSfont findfont \psk@fontscale 1.2 div scalefont setfont } bind def + /s1 { /Symbol findfont \psk@fontscale\space scalefont setfont } bind def + /ttxspc \psk@fontscale\space 4 div def + /txspc ttxspc 4 div def + %pop + /ysc ED + /xsc ED + n 0 eq not {% + n {% + ysc div /Yval ED + xsc div /Xval ED + \ifPst@science + %X Coordinate + Xval 0 gt { Xval log floor }{ Xval 0 lt { Xval -1 mul log floor }{ 0 } ifelse } ifelse + cvi /xcoorexp ED + Xval 10 xcoorexp exp div + \psk@decimals\space -1 gt {% + 10 \psk@decimals\space exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /xcoor ED + %Y Coordinate + Yval 0 gt { Yval log floor }{ Yval 0 lt { Yval -1 mul log floor }{ 0 } ifelse } ifelse + cvi /ycoorexp ED + Yval 10 ycoorexp exp div + \psk@decimals\space -1 gt {% + 10 \psk@decimals\space exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /ycoor exch def + %Prep Strings + xcoorexp \psk@valuewidth\space string cvs /xcoorexp ED + ycoorexp \psk@valuewidth\space string cvs /ycoorexp ED + xcoor \psk@valuewidth\space string cvs /xcoor ED + ycoor \psk@valuewidth\space string cvs /ycoor ED + %X Error + \psk@relxerr\space Xval mul /delx ED \psk@relxerr\space 0 ne {% + delx 0 gt { delx log floor }{ delx 0 lt { delx -1 mul log floor }{ 0 } ifelse } ifelse + cvi /delxexp ED + delx 10 delxexp exp div dup mul sqrt + \psk@decimals\space -1 gt {% + 10 \psk@decimals\space exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /delx ED + %Prep Strings + delxexp \psk@valuewidth\space string cvs /delxexp ED + delx \psk@valuewidth\space string cvs /delx ED } if + %Y Error + \psk@relyerr\space Yval mul /dely ED \psk@relyerr\space 0 ne {% + dely 0 gt { dely log floor }{ dely 0 lt { dely -1 mul log floor }{ 0 } ifelse } ifelse + cvi /delyexp ED + dely 10 delyexp exp div dup mul sqrt + \psk@decimals\space -1 gt {% + 10 \psk@decimals\space exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /dely ED + %Prep Strings + delyexp \psk@valuewidth\space string cvs /delyexp ED + dely \psk@valuewidth\space string cvs /dely ED } if + \else + Xval \psk@decimals\space -1 gt + { 10 \psk@decimals\space exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq {cvi} if /xcoor ED + Yval \psk@decimals\space -1 gt + { 10 \psk@decimals\space exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq {cvi} if /ycoor ED + xcoor \psk@valuewidth\space string cvs /xcoor ED + ycoor \psk@valuewidth\space string cvs /ycoor ED + % + \psk@relxerr\space Xval mul dup mul sqrt + \psk@decimals\space -1 gt + { 10 \psk@decimals\space exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq {cvi} if /delx ED + \psk@relyerr\space Yval mul dup mul sqrt + \psk@decimals\space -1 gt + { 10 \psk@decimals\space exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq {cvi} if /dely ED + delx \psk@valuewidth\space string cvs /delx ED + dely \psk@valuewidth\space string cvs /dely ED + \fi +% + newpath + Xval xsc mul %\psk@xShift\space xsc mul add + Yval ysc mul %\psk@yShift\space ysc mul add + moveto + \Pst@Debug\space 0 gt { + mfont + Xval \psk@valuewidth\space string cvs show (,) show + Yval \psk@valuewidth\space string cvs show } + {s1 (\string\050) show + mfont xcoor show + \ifPst@science + mfont (x) show + mfont (10) show + 0 ttxspc rmoveto mfontexp xcoorexp show + \fi + \psk@relxerr\space 0 ne + { \ifPst@science + 0 ttxspc neg rmoveto s1 (\string\261) show + mfont delx show + mfont (x) show + mfont (10) show + 0 ttxspc rmoveto mfontexp delxexp show + 0 ttxspc neg rmoveto s1 (,) show + \else + s1 (\string\261) show + mfont delx show + s1 (,) show + \fi } + { \ifPst@science + 0 ttxspc neg rmoveto s1 (,) show + \else + s1 (,) show + \fi } ifelse +%start on ycoor + mfont ycoor show + \ifPst@science + mfont (x) show + mfont (10) show + 0 ttxspc rmoveto mfontexp ycoorexp show + \fi + \psk@relyerr\space 0 ne + { \ifPst@science + 0 ttxspc neg rmoveto s1 (\string\261) show + mfont dely show + mfont (x) show + mfont (10) show + 0 ttxspc rmoveto mfontexp delyexp show + 0 ttxspc neg rmoveto s1 (\string\051) show + \else + s1 (\string\261) show + mfont dely show + s1 (\string\051) show + \fi } + { s1 (\string\051) show } ifelse } ifelse + } repeat } if } + +%%%POLY FIT +\define@key[psset]{pst-fit}{EqPos}[{}]{\def\psk@EqPos{#1}} +\define@key[psset]{pst-fit}{MaPos}[{}]{\def\psk@MaPos{#1}}%added Feb3, 2012 Matrix out +\define@key[psset]{pst-fit}{MaScale}[{}]{\def\psk@MaScale{#1}}%added Feb3, 2012 Matrix out +\define@boolkey[psset]{pst-fit}[Pst@]{ShowEq}[true]{}% +\psset{EqPos=,ShowEq=true,MaPos=0 0,MaScale=1} + +\define@key[psset]{pst-fit}{PolyOrder}[{}]{\def\psk@PolyOrder{#1}} +\define@boolkey[psset]{pst-fit}[Pst@]{ReduceOrder}[true]{%these percents are critical removal results in shift to in x-dir +\ifPst@ReduceOrder% +\def\psk@ReduceOrder{true}\else\def\psk@ReduceOrder{false}\fi}% +\define@boolkey[psset]{pst-fit}[Pst@]{PowerFit}[true]{%these percents are critical removal results in shift to in x-dir +\ifPst@PowerFit% +\def\psk@PowerFit{true}\def\psk@LogEFit{false}% +\def\psk@LogTFit{false}\def\psk@ExpFit{false}% +\def\psk@GaussFit{false}\def\psk@CustomFit{false}\def\psk@RecipFit{false}% +\else\def\psk@PowerFit{false}\fi}% +\define@boolkey[psset]{pst-fit}[Pst@]{LogEFit}[true]{% +\ifPst@LogEFit% +\def\psk@PowerFit{false}\def\psk@LogEFit{true}% +\def\psk@LogTFit{false}\def\psk@ExpFit{false}% +\def\psk@GaussFit{false}\def\psk@CustomFit{false}\def\psk@RecipFit{false}% +\else\def\psk@LogEFit{false}\fi}% +\define@boolkey[psset]{pst-fit}[Pst@]{LogTFit}[true]{% +\ifPst@LogTFit% +\def\psk@PowerFit{false}\def\psk@LogEFit{false}% +\def\psk@LogTFit{true}\def\psk@ExpFit{false}% +\def\psk@GaussFit{false}\def\psk@CustomFit{false}\def\psk@RecipFit{false}% +\else\def\psk@LogTFit{false}\fi}% +\define@boolkey[psset]{pst-fit}[Pst@]{ExpFit}[true]{% +\ifPst@ExpFit% +\def\psk@PowerFit{false}\def\psk@LogEFit{false}% +\def\psk@LogTFit{false}\def\psk@ExpFit{true}% +\def\psk@GaussFit{false}\def\psk@CustomFit{false}\def\psk@RecipFit{false}% +\else\def\psk@ExpFit{false}\fi}% +\define@boolkey[psset]{pst-fit}[Pst@]{GaussFit}[true]{% +\ifPst@GaussFit% +\def\psk@PowerFit{false}\def\psk@LogEFit{false}% +\def\psk@LogTFit{false}\def\psk@ExpFit{false}% +\def\psk@GaussFit{true}\def\psk@CustomFit{false}\def\psk@RecipFit{false}% +\else\def\psk@GaussFit{false}\fi}% +\define@boolkey[psset]{pst-fit}[Pst@]{RecipFit}[true]{% +\ifPst@RecipFit% +\def\psk@PowerFit{false}\def\psk@LogEFit{false}% +\def\psk@LogTFit{false}\def\psk@ExpFit{false}% +\def\psk@GaussFit{false}\def\psk@CustomFit{false}\def\psk@RecipFit{true}% +\else\def\psk@RecipFit{false}\fi}% +\define@boolkey[psset]{pst-fit}[Pst@]{CustomFit}[true]{% +\ifPst@CustomFit% +\def\psk@PowerFit{false}\def\psk@LogEFit{false}% +\def\psk@LogTFit{false}\def\psk@ExpFit{false}% +\def\psk@GaussFit{false}\def\psk@CustomFit{true}\def\psk@RecipFit{false}% +\else\def\psk@CustomFit{false}\fi}% +\define@key[psset]{pst-fit}{FXtrans}[{}]{\def\psk@FXtrans{#1}} +\define@key[psset]{pst-fit}{FYtrans}[{}]{\def\psk@FYtrans{#1}} +\define@key[psset]{pst-fit}{RYtrans}[{}]{\def\psk@RYtrans{#1}} +\define@key[psset]{pst-fit}{Yint}[{}]{\def\psk@Yint{#1}} +\define@key[psset]{pst-fit}{CheckZeroX}[{}]{\def\psk@CheckZeroX{#1}} +\define@key[psset]{pst-fit}{CheckZeroY}[{}]{\def\psk@CheckZeroY{#1}} +\psset{PolyOrder=1,ReduceOrder=false,PowerFit=false,LogEFit=false,LogTFit=false,% + ExpFit=false,GaussFit=false,RecipFit=false,CustomFit=false,% + FXtrans=,FYtrans=,RYtrans=,Yint=,CheckZeroX=,CheckZeroY=} + +\def\beginplot@GLLSR{\begin@SpecialObj} +\def\endplot@GLLSR{% + \psGLLSR@ii\psk@fillstyle\ifpsshadow\pst@closedshadow\fi% + \pst@stroke + \end@SpecialObj% +} +\def\psGLLSR@ii{\addto@pscode{false \tx@NArray \psGLLSR@iii }} +\def\psGLLSR@iii{% + %General Fit Model: y = a0 + a1*x + a2*x^2 + ... + an*x^n + %Define Fonts + /mfont { \psk@PSfont\space findfont \psk@fontscale\space scalefont setfont } bind def + /mfontbig { \psk@PSfont\space findfont \psk@fontscale\space 2 mul scalefont setfont } bind def + /mfontexp { \psk@PSfont\space findfont \psk@fontscale\space 2 div scalefont setfont } bind def + mfont + %Default parameters + (\psk@PolyOrder) length 0 gt { \psk@PolyOrder\space /order ED }{ /order 1 def } ifelse + /PolyEq true def + (\psk@Yint) length 0 gt + {\psk@Yint\space /Yint ED /setYint true def /ReduceOrder true def } + { /Yint 0 def /setYint false def /ReduceOrder false def} ifelse + /CheckZeroX false def + /CheckZeroY false def + /FXtrans {1 mul} def + /FYtrans { Yint sub } def + /RYtrans {1 mul} def + /xPr {(x) show} def + %Special Fit Functions (Linear Transforms) + \psk@PowerFit\space { /order 1 def /CheckZeroX true def /CheckZeroY true def /PolyEq false def + /FXtrans {log} def /FYtrans {Yint sub log} def /RYtrans {10 exch exp Yint add} def /ReduceOrder false def } if + \psk@LogTFit\space { /order 1 def /CheckZeroX true def /PolyEq true def + /xPr { (log) show (\string\050) show (x) show (\string\051) show } def + /FXtrans {log} def /FYtrans {1 mul} def /RYtrans {1 mul} def } if % + \psk@LogEFit\space { /order 1 def /CheckZeroX true def /PolyEq true def + /xPr { (ln) show (\string\050) show (x) show (\string\051) show } def + /FXtrans {ln} def /FYtrans {1 mul} def /RYtrans {1 mul} def } if % + \psk@ExpFit\space { /order 1 def /CheckZeroY true def /PolyEq false def + /FXtrans {1 mul} def /FYtrans {Yint sub ln} def /RYtrans {Euler exch exp Yint add} def /ReduceOrder false def } if % + \psk@GaussFit\space { /order 2 def /CheckZeroY true def /PolyEq false def + /FXtrans {1 mul} def /FYtrans {Yint sub ln} def /RYtrans {Euler exch exp Yint add} def /ReduceOrder false def } if % + \psk@RecipFit\space { /order 1 def /CheckZeroX true def /PolyEq true def + /xPr { (\string\050) show (1) show (\string\244) show (x) show (\string\051) show } def + /FXtrans { 1 exch div } def /FYtrans {1 mul} def /RYtrans {1 mul} def } if + \psk@CustomFit\space { /PolyFit false def + (\psk@FXtrans) length 0 gt { {\psk@FXtrans\space} /FXtrans ED } if + (\psk@FYtrans) length 0 gt { {\psk@FYtrans\space} /FYtrans ED } if + (\psk@RYtrans) length 0 gt { {\psk@RYtrans\space} /RYtrans ED } if + (\psk@CheckZeroX) length 0 gt { {\psk@CheckZeroX\space} /CheckZeroX ED } if + (\psk@CheckZeroY) length 0 gt { {\psk@CheckZeroY\space} /CheckZeroY ED } if + (\psk@ReduceOrder) length 0 gt { {\psk@ReduceOrder\space} /ReduceOrder ED } if } if % + %Initialize Arrays + /A order 1 add order 1 add mul array def + /B order 1 add array def + /ai order 1 add array def + %Coordinate Conversion Operators X Y PLU -> Plot Units (pts), X Y RLU -> Real Units (arbitrary) + /PLU {exch \pst@number\psxunit\space mul exch \pst@number\psyunit\space mul } def + /RLU {exch \pst@number\psxunit\space div exch \pst@number\psyunit\space div } def + /PRA { %Inputs: Array [ #rows #cols X Y Scale boolean(print equal sign) boolean(return) ] + %"pra" prefix has been added to all variables to minimize chance of naming conflicts +% /praSc exch def /praYc exch def /praXc exch def +% /praCol exch def /praRow exch def /praARY exch def + /praTemp exch def /praARY exch def + praTemp length 7 eq {% + %praTemp 4 get /praSc exch def + %praTemp 3 get /praYc exch def + %praTemp 2 get /praXc exch def + %praTemp 1 get /praCol exch def + %praTemp 0 get /praRow exch def pop + /tempfontscale \psk@fontscale praTemp 4 get mul def + %/praXc praTemp 2 get \pst@number\psxunit\space mul def + /praYc praTemp 3 get \pst@number\psyunit\space mul def + /praXmax -999999 def + /praYmin 999999 def + /prafont {\psk@PSfont\space findfont tempfontscale scalefont setfont} bind def + /prasym { /Symbol findfont tempfontscale 2 mul scalefont setfont} bind def + prafont + praTemp 2 get \pst@number\psxunit\space mul praTemp 3 get \pst@number\psyunit\space mul moveto + praARY length praTemp 1 get praTemp 0 get mul eq not { (Row x Col > Vector Dim) show }{% + /praXstart praTemp 2 get \pst@number\psxunit\space mul def + 0 1 praTemp 1 get 1 sub {/praj ED + 0 1 praTemp 0 get 1 sub {/prai ED /prak praj praTemp 1 get prai mul add def + praARY prak get \psk@valuewidth string cvs show + currentpoint pop dup praXmax gt { /praXmax ED }{ pop } ifelse + currentpoint pop praXstart sub neg tempfontscale 1.5 mul neg rmoveto + } for + currentpoint exch pop dup praYmin lt { /praYmin ED }{ pop } ifelse + /praXstart praXmax tempfontscale 0.75 mul add def + praXstart praTemp 3 get \pst@number\psyunit\space mul moveto + } for + %Brackets + newpath + praTemp 2 get \pst@number\psxunit\space mul tempfontscale 0.125 mul add + praTemp 3 get \pst@number\psyunit\space mul tempfontscale add moveto + praTemp 2 get \pst@number\psxunit\space mul tempfontscale 0.125 mul sub + praTemp 3 get \pst@number\psyunit\space mul tempfontscale add lineto + praTemp 2 get \pst@number\psxunit\space mul tempfontscale 0.125 mul sub + praYmin tempfontscale add lineto + praTemp 2 get \pst@number\psxunit\space mul tempfontscale 0.125 mul add + praYmin tempfontscale add lineto + stroke + newpath + praXmax tempfontscale 0.125 mul sub + praTemp 3 get \pst@number\psyunit\space mul tempfontscale add moveto + praXmax tempfontscale 0.125 mul add + praTemp 3 get \pst@number\psyunit\space mul tempfontscale add lineto + praXmax tempfontscale 0.125 mul add + praYmin tempfontscale add lineto + praXmax tempfontscale 0.125 mul sub + praYmin tempfontscale add lineto + stroke + praTemp 5 get { + praXmax tempfontscale add + praTemp 3 get \pst@number\psyunit\space mul tempfontscale add praYmin add 2 div moveto + prasym (=) show currentpoint pop /praXmax ED} if + %Left Bracket + praTemp 2 get \pst@number\psxunit\space mul praYmin tempfontscale 2 mul sub moveto %Return to bottom left + %the following are defined for use with cascade calls to PRA + % (Xl,Yb) - Print next matrix below last + % (Xr,Yt) - Print next matrix beside last + % (Xr,Yb) - Print next matrix beside and below last + tx@Dict /praYb known { + praYmin tempfontscale 1.5 mul sub \pst@number\psyunit\space div praYb lt { + /praYb praYmin tempfontscale 1.5 mul sub \pst@number\psyunit\space div def } if } + { /praYb praYmin tempfontscale 1.5 mul sub \pst@number\psyunit\space div def } ifelse + /praYb praYmin tempfontscale 1.5 mul sub \pst@number\psyunit\space div def + % + tx@Dict /praXl known not {/praXl praTemp 2 get def } if + % { praTemp 6 get {/praXl praTemp 2 get def} if } ifelse + tx@Dict /praYt known not {/praYt praTemp 3 get def } + { praTemp 6 get {/praYt praYb def} if } ifelse + % + tx@Dict /praXr known { + praTemp 6 get { /praXr praXl def }{ /praXr praXmax tempfontscale add \pst@number\psxunit\space div def } ifelse }{% + /praXr praXmax tempfontscale add \pst@number\psxunit\space div def } ifelse + \psk@PSfont\space findfont \psk@fontscale\space scalefont setfont } ifelse + }{ \psk@PSfont\space findfont \psk@fontscale\space scalefont setfont + 0 0 moveto (PRA Error Not Enough Parameters) show } ifelse } def + 0 1 A length 1 sub { A exch 0 put } for + 0 1 B length 1 sub { B exch 0 put } for + 0 1 ai length 1 sub { ai exch 0 put } for + %%%%%%%% + %Remove Zero Data (As Required By Transformation Functions) + CheckZeroX CheckZeroY or { + n { /tmpx false def /tmpy false def + CheckZeroY { dup \pst@number\psyunit\space div Yint sub 0 le { /tmpy true def } if } if + CheckZeroX { exch dup \pst@number\psxunit\space div 0 le { /tmpx true def } if exch } if + tmpx tmpy or { pop pop /n n 1 sub def }{ n 2 mul 2 roll } ifelse + } repeat } if + %%% + %%%% + %Determine Max/Min X for Plotting + exch dup dup + \pst@number\psxunit\space div /xEnd ED + \pst@number\psxunit\space div /xStart ED + exch + /ybar 0 def + n { % number of data pairs + dup \pst@number\psyunit\space div ybar add /ybar ED + 2 copy %copy point + \pst@number\psyunit\space div /Yval ED + \pst@number\psxunit\space div /Xval ED + Xval xStart lt { /xStart Xval def } if % find the lowest xi + Xval xEnd gt { /xEnd Xval def } if % find the largest xi + n 2 mul 2 roll %roll the original point to the bottom of the stack + } repeat + ybar n div /ybar ED + %Scale X & Y variables and apply Linear Transform if applicable + n { + \pst@number\psyunit\space div FYtrans + n 2 mul 1 roll + \pst@number\psxunit\space div FXtrans + n 2 mul 1 roll + } repeat + %START ASSEMBLY OF LEAST SQUARES MATRIX + 1 1 order 1 add { /ci exch def + 1 1 ci { /cj exch def + /epk ci cj add 2 sub def + /sum 0 def + n { n 2 mul 1 roll + dup epk exp sum add /sum ED + n 2 mul 1 roll + } repeat + A + ci 1 sub order 1 add mul cj add 1 sub + sum put %i row, j col standard + A + cj 1 sub order 1 add mul ci add 1 sub + sum put %j row, i col reversed + } for + /sum 0 def + 1 1 n { /cl exch def + 2 copy + exch + ci 1 sub exp mul sum add /sum ED + n 2 mul 2 roll + } for + B + ci 1 sub + sum put + } for + \Pst@Debug\space 1 eq { + %A [ order 1 add order 1 add 5 20 0.5 false false ] PRA + A [ order 1 add order 1 add \psk@MaPos\space \psk@MaScale\space true false ] PRA + B [ order 1 add 1 praXr praYt \psk@MaScale\space false true ] PRA + } if + %END OF ASSEMBLE MATRIX + %REDUCE ORDER FOR Y INTERCEPT FOR MODELS WHICH ARE APPROPRIATE + ReduceOrder { + /elemOld { exch 1 sub order 1 add mul add 1 sub } def + /elemNew { exch 2 sub order mul add 2 sub } def + /dummyA order order mul array def + 0 1 dummyA length 1 sub { dummyA exch 0 put } for + /dummyB order array def + 0 1 dummyB length 1 sub { dummyB exch 0 put } for + /ai order array def + 0 1 ai length 1 sub { ai exch 0 put } for + %Translate A to dummyA + 2 1 order 1 add {/ci ED + 2 1 order 1 add {/cj ED + dummyA ci cj elemNew + A ci cj elemOld get + put + } for + dummyB ci 2 sub + B ci 1 sub get + put + } for + /order order 1 sub def %temporarily reduce system order + /A order 1 add order 1 add mul array def 0 1 A length 1 sub {/ci ED A ci dummyA ci get put } for %put dummyA in new A + /B order 1 add array def 0 1 B length 1 sub {/ci ED B ci dummyB ci get put } for %put dummyB in new B + \Pst@Debug\space 1 eq { + A [ order 1 add order 1 add praXr praYt \psk@MaScale\space true false ] PRA + B [ order 1 add 1 praXr praYt \psk@MaScale\space false true ] PRA } if + \tx@GaussSolve + /order order 1 add def %restore system order + /m m 1 add def + % \Pst@Debug\space 1 eq { + %ai [ order 1 add 1 praXr praYt \psk@MaScale\space false false ] PRA } if + /dummyai order 1 add array def + 0 1 dummyai length 1 sub {/ci ED dummyai ci 0 put } for + 0 1 ai length 1 sub {/ci ED dummyai ci 1 add ai ci get put } for + /ai dummyai def + ai 0 Yint put + %ai [ order 2 sub 1 0 0 \psk@MaScale\space true false ] PRA + }{ \tx@GaussSolve } ifelse + %\Pst@Debug\space 1 eq { + %ai [ order 1 add 1 praXr praYt \psk@MaScale\space false false ] PRA } if + %%%%%%%%%%%%%%%%%%%%%%%%%% + %% END SOLVE CURVE FITS %% + %%%%%%%%%%%%%%%%%%%%%%%%%% + %%%%%%%%%%%%%%%%%%%%% + %% PLOT CURVE FITS %% + %%%%%%%%%%%%%%%%%%%%% + newpath + (\psk@xStart) length 0 gt % special start value? + { \psk@xStart\space /xStart ED } if + (\psk@xEnd) length 0 gt % special end value? + { \psk@xEnd\space /xEnd ED } if + /xStep xEnd xStart sub \psk@plotpoints\space div def + /Xnow xStart def + /Ynow 0 def + 1 1 m { /ci exch def ai ci 1 sub get ci 1 sub { Xnow FXtrans mul } repeat Ynow add /Ynow exch def } for + Xnow Ynow RYtrans PLU moveto + \psk@plotpoints\space cvi + { /Xnow Xnow xStep add def + /Ynow 0 def + 1 1 m { /ci exch def ai ci 1 sub get ci 1 sub { Xnow FXtrans mul } repeat Ynow add /Ynow exch def } for + Xnow Ynow RYtrans PLU lineto + } repeat + % + /yminusdot 0 def + /yminusbar 0 def + n { + 2 copy + /Ynow ED + /Xnow ED + /Ydot 0 def + 1 1 m { /ci exch def + ai ci 1 sub get ci 1 sub { Xnow mul } repeat Ydot add /Ydot exch def } for % + Ynow Ydot sub dup mul yminusdot add /yminusdot ED + Ynow ybar sub dup mul yminusbar add /yminusbar ED + n 2 mul 2 roll + } repeat + 1 yminusdot yminusbar div sub /rsquared ED + %%%%%%%%%%%%%%%%%%%%%%%%% + %% END PLOT CURVE FITS %% + %%%%%%%%%%%%%%%%%%%%%%%%% + %%%%%%%%%%%%%%%%%%%%%%%%%%% + %% START PRINT EQUATIONS %% + %%%%%%%%%%%%%%%%%%%%%%%%%%% + \ifPst@ShowEq + % Setup Cursor + (\psk@EqPos) length 0 gt + {\psk@EqPos\space PLU } + {2 -5 PLU } ifelse moveto + % Power Fit Equation % + \psk@PowerFit\space { + 10 ai 0 get exp + \psk@decimals\space -1 gt + { 10 \psk@decimals exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /tmpA exch def + ai 1 get + \psk@decimals\space -1 gt + { 10 \psk@decimals exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /tmpB exch def + (y = ) show + tmpA \psk@valuewidth string cvs show + (x) show + 0 \psk@fontscale 4 div rmoveto + mfontexp tmpB \psk@valuewidth string cvs show mfont + 0 \psk@fontscale 4 div neg rmoveto + setYint Yint 0 ne and { Yint 0 gt { (+) show } if Yint \psk@valuewidth string cvs show } if } if + % Exponential Fit Equation % + \psk@ExpFit\space { + Euler ai 0 get exp + \psk@decimals\space -1 gt + { 10 \psk@decimals exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /tmpA exch def + Euler ai 1 get exp + \psk@decimals\space -1 gt + { 10 \psk@decimals exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /tmpB exch def + (y = ) show + (\string\050) show tmpA \psk@valuewidth string cvs show (\string\051) show + %(e) show + (\string\264) show + %0 \psk@fontscale 4 div rmoveto + %mfontexp tmpB \psk@valuewidth string cvs show + (\string\050) show tmpB \psk@valuewidth string cvs show (\string\051) show + 0 \psk@fontscale 2 div rmoveto + mfontexp (x) show mfont + 0 \psk@fontscale 2 div neg rmoveto + setYint Yint 0 ne and { Yint 0 gt { (+) show } if Yint \psk@valuewidth string cvs show } if} if + % Gaussian Fit Equation % + \psk@GaussFit\space { + /tmpA Euler ai 0 get ai 1 get dup mul 4 div ai 2 get div sub exp def + /tmpB ai 1 get 2 div ai 2 get div def + /tmpC ai 2 get def + tmpA + \psk@decimals\space -1 gt + { 10 \psk@decimals exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /tmpA exch def + tmpB + \psk@decimals\space -1 gt + { 10 \psk@decimals exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /tmpB exch def + tmpC + \psk@decimals\space -1 gt + { 10 \psk@decimals exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /tmpC exch def + (y = ) show + tmpA 30 string cvs show + (e) show + 0 \psk@fontscale 4 div rmoveto + mfontexp tmpC \psk@valuewidth string cvs show + (\string\(x) show + tmpB 0 ne { tmpB 0 ge { (+) show } if tmpB \psk@valuewidth string cvs show } if + (\string\)) show + 0 \psk@fontscale 4 div rmoveto (2) show mfont + 0 \psk@fontscale 2 div neg rmoveto + setYint Yint 0 ne and { Yint 0 gt { (+) show } if Yint \psk@valuewidth string cvs show } if } if + %%%%%%%%%%%%%%% + % Round Coeff % + %%%%%%%%%%%%%%% + 0 1 ai length 1 sub {/ci exch def + ai ci get + \psk@decimals\space -1 gt + { 10 \psk@decimals exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if + ai ci 3 -1 roll put } for + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % Plot Polynomial (including Linear) Fit % + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + PolyEq { (y =) show + 1 1 m { /ci exch def + ai ci 1 sub get 30 string cvs show + ci 1 sub 0 gt { xPr } if + ci 1 sub 1 gt {% + 0 \psk@fontscale 4 div rmoveto ci 1 sub 30 string cvs show + 0 \psk@fontscale 4 div neg rmoveto } if + ci m eq not { ai ci get 0 lt {}{ (+) show } ifelse } if + } for } if + %Print Rsquared + rsquared + \psk@decimals\space -1 gt + { 10 \psk@decimals exp dup 3 1 roll mul round exch div } if + \psk@decimals\space 0 eq { cvi } if /rsquared exch def + \psk@EqPos\space PLU moveto + 0 \psk@fontscale 1.5 mul neg rmoveto + (R) show + 0 \psk@fontscale 2 div rmoveto + mfontexp (2) show mfont + 0 \psk@fontscale 2 div neg rmoveto + ( = ) show + rsquared \psk@valuewidth string cvs show + \fi +} +% +\def\tx@GaussSolve{GaussSolve } +\pst@def{GaussSolve}<{% +%Required Variables +%order,A,B,ai + /er 1 def % + /tol 0.00001 def % + /m order 1 add def %number of equations + /Aout m m mul array def %This is for printing the scaled identity matrix which A becomes + 0 1 Aout length 1 sub { Aout exch 0 put } for + /elem { exch 1 sub m mul add 1 sub } def %Array i j + %DETERMINE SCALE FACTORS + /sc m array def %row scale factors + 0 1 sc length 1 sub { sc exch 0 put } for + 1 1 m { /ci exch def + sc + ci 1 sub + A ci 1 elem get + dup mul sqrt + put + 2 1 m { /cj exch def + A ci cj elem get + dup mul sqrt + sc ci 1 sub get gt {% + sc + ci 1 sub + A ci cj elem get + dup mul sqrt + put } if + } for + % 1 ci mul 1 sc ci 1 sub get 30 string cvs show + } for + %END OF SCALE FACTORS + %CALL ELIMINATE + order 1 ge {% + 1 1 m 1 sub { /ck exch def + %Call Pivot + /p ck def + A ck ck elem get + sc ck 1 sub get div + dup mul sqrt + /big exch def + ck 1 add 1 m {/cii exch def + A cii ck elem get + sc cii 1 sub get div + dup mul sqrt + /dummy exch def + dummy big gt { /big dummy def /p cii def } if + } for + p ck eq not { + ck 1 m {/cjj exch def + A p cjj elem get + /dummy exch def + A p cjj elem + A ck cjj elem get + put + A ck cjj elem + dummy + put + } for + B p 1 sub get + /dummy exch def + B p 1 sub + B ck 1 sub get + put + B ck 1 sub + dummy + put + sc p 1 sub get + /dummy exch def + sc p 1 sub + sc ck 1 sub get + put + sc ck 1 sub + dummy + put + } if + %End Pivot + %Back to Eliminate + A ck ck elem get + sc ck 1 sub get div + dup mul sqrt tol lt { /er -1 def } if + ck 1 add 1 m { /ci exch def + A ci ck elem get + A ck ck elem get div + /factor exch def + %ck 1 add 1 m { /cj exch def + 1 1 m { /cj exch def %Line Changed from above, requires more calcs but allows debugging of matrix ops. + A ci cj elem %index + A ci cj elem get + A ck cj elem get + factor + mul sub %value + put + } for + B ci 1 sub %index + B ci 1 sub get + B ck 1 sub get + factor + mul sub %value + put + } for + } for + \Pst@Debug\space 1 eq { + A [ order 1 add order 1 add praXr praYt \psk@MaScale\space true false ] PRA + B [ order 1 add 1 praXr praYt \psk@MaScale\space false true ] PRA + } if + } if + %Start Back Substitution + %Add Error check for er -1 + ai m 1 sub + B m 1 sub get + A m m elem get + div put + %%%%Added for debug + Aout m m elem + A m m elem get dup div + put + %%%% + order 1 ge {% + m 1 sub -1 1 { /ci exch def + /sum 0 def + ci 1 add 1 m { /cj exch def + A ci cj elem get + ai cj 1 sub get + mul sum add + /sum exch def + } for + ai ci 1 sub + B ci 1 sub get + sum sub + A ci ci elem get + div put + %%%%Added for debug + Aout ci ci elem + A ci ci elem get dup div + put + %%%% + } for + A ck ck elem get + sc ck 1 sub get div + dup mul sqrt tol lt { /er -1 def } if + } if + \Pst@Debug\space 1 eq { + Aout [ order 1 add order 1 add praXr praYt \psk@MaScale\space true false ] PRA + ai [ order 1 add 1 praXr praYt \psk@MaScale\space false false ] PRA } if}> + +% +\catcode`\@=\PstAtCode\relax +% +%% END: pst-fit.tex +\endinput + |