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diff --git a/macros/latex/contrib/xint-regression/tex/xint-regression.sty b/macros/latex/contrib/xint-regression/tex/xint-regression.sty new file mode 100644 index 0000000000..71413005aa --- /dev/null +++ b/macros/latex/contrib/xint-regression/tex/xint-regression.sty @@ -0,0 +1,662 @@ +% Author : C. Pierquet +% licence : Released under the LaTeX Project Public License v1.3c +% or later, see http://www.latex-project.org/lppl.txtf + +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{xint-regression}[2024/06/05 0.1.0 Some classic regressions, with xint] +%0.1.0 Initial version + +%------Packages utiles +\RequirePackage{simplekv} +\RequirePackage{xintexpr} +\RequirePackage{listofitems} +\RequirePackage{xstring} + +%régression linéaire +\defKV[CoefRegLin]{% + coeffa=\def\RegLinCoefa{#1},% + coeffb=\def\RegLinCoefb{#1},% + round=\def\RegLinRound{#1} +} + +\setKVdefault[CoefRegLin]{% + coeffa=linrega,% + coeffb=linregb,% + round={} +} + +\newcommand\xintlinreg[3][]{% + \useKVdefault[CoefRegLin]% + \setKV[CoefRegLin]{#1}% on paramètres les nouvelles clés et on les simplifie + %listes des données + \def\xliste{#2}% + \def\yliste{#3}% + \readlist*\LX{\xliste}% + \readlist*\LY{\yliste}% + %taille des listes + \def\LNB{\inteval{\LXlen}}% + %somme des LX et des LY OK + \xdef\LXSomme{0}% + \xdef\LYSomme{0}% + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LXSomme{\xintfloateval{\LXSomme+(\LX[##1])}}% + \xdef\LYSomme{\xintfloateval{\LYSomme+(\LY[##1])}}% + }% + %moyenne des LX et des LY OK + \xdef\LXmoy{\xintfloateval{\LXSomme/\LNB}}% + \xdef\LYmoy{\xintfloateval{\LYSomme/\LNB}}% + %variance des LX et des LY OK + \xdef\LXvar{0}% + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LXvar{\xintfloateval{\LXvar+(\LX[##1]-(\LXmoy))*(\LX[##1]-(\LXmoy))}}% + } + \xdef\LXvar{\xintfloateval{\LXvar/\LNB}}% + \xdef\LYvar{0}% + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LYvar{\xintfloateval{\LYvar+(\LY[##1]-(\LYmoy))*(\LY[##1]-(\LYmoy))}}% + }% + \xdef\LYvar{\xintfloateval{\LYvar/\LNB}}% + %covariance des XY OK + \xdef\LXYvar{0}% + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LXYvar{\xintfloateval{\LXYvar+(\LX[##1]-(\LXmoy))*(\LY[##1]-(\LYmoy))}}% + }% + \xdef\LXYvar{\xintfloateval{\LXYvar/\LNB}}% + %COEFFS TEMPORAIRES OK + \xdef\tmp@reg@lin@a{\xintfloateval{\LXYvar/\LXvar}}% + \xdef\tmp@reg@lin@b{\xintfloateval{\LYmoy-(\tmp@reg@lin@a)*(\LXmoy)}}% + %STOCKAGE + \IfStrEq{\RegLinRound}{}% + {% + \expandafter\def\csname\RegLinCoefa\endcsname{\tmp@reg@lin@a}% + \expandafter\def\csname\RegLinCoefb\endcsname{\tmp@reg@lin@b}% + }% + {% + \IfSubStr{\RegLinRound}{/}% + {% + \StrCut{\RegLinRound}{/}{\xintarrondisreglina}{\xintarrondisreglinb}% + }% + {% + \xdef\xintarrondisreglina{\RegLinRound}\xdef\xintarrondisreglinb{\RegLinRound}% + }% + \expandafter\def\csname\RegLinCoefa\endcsname{\xintfloateval{round(\tmp@reg@lin@a,\xintarrondisreglina)}}% + \expandafter\def\csname\RegLinCoefb\endcsname{\xintfloateval{round(\tmp@reg@lin@b,\xintarrondisreglinb)}}% + }% +} + + + +%régression quadratique +\defKV[CoeffRegQuad]{% + coeffa=\def\RegQuadCoefa{#1},% + coeffb=\def\RegQuadCoefb{#1},% + coeffc=\def\RegQuadCoefc{#1},% + round=\def\RegQuadRound{#1} +} + +\setKVdefault[CoeffRegQuad]{% + coeffa=quadrega,% + coeffb=quadregb,% + coeffc=quadregc,% + round={} +} + +\newcommand\xintquadreg[3][]{% + \useKVdefault[CoeffRegQuad]% + \setKV[CoeffRegQuad]{#1}% on paramètres les nouvelles clés et on les simplifie + %listes des données + \def\xliste{#2}% + \def\yliste{#3}% + \readlist*\LX{\xliste}% + \readlist*\LY{\yliste}% + %taille des listes + \def\LNB{\inteval{\LXlen}}% + %somme importantes + \xdef\LXSomme{0}% + \xdef\LXCSomme{0}% + \xdef\LYSomme{0}% + \xdef\LXXSomme{0}% + \xdef\LXYSomme{0}% + \xdef\LXXCSomme{0}% + \xdef\LXCXCSomme{0}% + \xdef\LXCYSomme{0}% + %calculs + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LXSomme{\xintfloateval{\LXSomme+(\LX[##1])}}% + \xdef\LXCSomme{\xintfloateval{\LXCSomme+(\LX[##1])^2}}% + }% + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LYSomme{\xintfloateval{\LYSomme+(\LY[##1])}}% + }% + \xdef\LXmoy{\xintfloateval{\LXSomme/\LNB}}% + \xdef\LYmoy{\xintfloateval{\LYSomme/\LNB}}% + \xdef\LXCmoy{\xintfloateval{\LXCSomme/\LNB}}% + %calculs suites + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LXXSomme{\xintfloateval{\LXXSomme+(\LX[##1]-\LXmoy)^2}}% + \xdef\LXYSomme{\xintfloateval{\LXYSomme+(\LX[##1]-\LXmoy)*(\LY[##1]-\LYmoy)}}% + \xdef\LXXCSomme{\xintfloateval{\LXXCSomme+(\LX[##1]-\LXmoy)*((\LX[##1])*(\LX[##1])-\LXCmoy)}}% + \xdef\LXCXCSomme{\xintfloateval{\LXCXCSomme+((\LX[##1])^2-\LXCmoy)^2}}% + \xdef\LXCYSomme{\xintfloateval{\LXCYSomme+((\LX[##1])^2-\LXCmoy)*(\LY[##1]-\LYmoy)}}% + }% + %COEFFS TEMPORAIRES OK + \xdef\tmp@reg@quad@b{\xintfloateval{(\LXYSomme*\LXCXCSomme-\LXCYSomme*\LXXCSomme)/(\LXXSomme*\LXCXCSomme-(\LXXCSomme)^2)}}% + \xdef\tmp@reg@quad@a{\xintfloateval{(\LXCYSomme*\LXXSomme-\LXYSomme*\LXXCSomme)/(\LXXSomme*\LXCXCSomme-(\LXXCSomme)^2)}}% + \xdef\tmp@reg@quad@c{\xintfloateval{\LYmoy-(\tmp@reg@quad@b)*\LXmoy-(\tmp@reg@quad@a)*\LXCmoy}}% + %STOCKAGE + \IfStrEq{\RegQuadRound}{}% + {% + \expandafter\def\csname\RegQuadCoefb\endcsname{\tmp@reg@quad@b}% + \expandafter\def\csname\RegQuadCoefa\endcsname{\tmp@reg@quad@a}% + \expandafter\def\csname\RegQuadCoefc\endcsname{\tmp@reg@quad@c}% + }% + {% + \IfSubStr{\RegQuadRound}{/}% + {% + \StrBefore[1]{\RegQuadRound}{/}[\xintarrondisregquada]% + \StrBetween[1,2]{\RegQuadRound}{/}{/}[\xintarrondisregquadb]% + \StrBehind[2]{\RegQuadRound}{/}[\xintarrondisregquadc]% + }% + {% + \xdef\xintarrondisregquada{\RegQuadRound}% + \xdef\xintarrondisregquadb{\RegQuadRound}% + \xdef\xintarrondisregquadc{\RegQuadRound}% + + }% + \expandafter\def\csname\RegQuadCoefb\endcsname{\xintfloateval{round(\tmp@reg@quad@b,\xintarrondisregquadb)}}% + \expandafter\def\csname\RegQuadCoefa\endcsname{\xintfloateval{round(\tmp@reg@quad@a,\xintarrondisregquada)}}% + \expandafter\def\csname\RegQuadCoefc\endcsname{\xintfloateval{round(\tmp@reg@quad@c,\xintarrondisregquadc)}}% + }% +} + +%régression puissance a*x^b +\defKV[CoeffRegPuiss]{% + coeffa=\def\RegPuissCoefa{#1},% + coeffb=\def\RegPuissCoefb{#1},% + round=\def\RegPuissRound{#1} +} + +\setKVdefault[CoeffRegPuiss]{% + coeffa=powrega,% + coeffb=powregb,% + round={} +} + +\newcommand\xintpowreg[3][]{% + \useKVdefault[CoeffRegPuiss]% + \setKV[CoeffRegPuiss]{#1}% on paramètres les nouvelles clés et on les simplifie + %listes des données + \def\xliste{#2}% + \def\yliste{#3}% + \readlist*\LX{\xliste}% + \readlist*\LY{\yliste}% + %taille des listes + \def\LNB{\inteval{\LXlen}}% + %somme importantes + \xdef\LlnXSomme{0}% + \xdef\LlnYSomme{0}% + \xdef\LlnXlnYSomme{0}% + \xdef\LlncXSomme{0}% + %calculs + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LlnXSomme{\xintfloateval{\LlnXSomme+log(\LX[##1])}}% + \xdef\LlnYSomme{\xintfloateval{\LlnYSomme+log(\LY[##1])}}% + \xdef\LlnXlnYSomme{\xintfloateval{\LlnXlnYSomme+log(\LX[##1])*log(\LY[##1])}}% + \xdef\LlncXSomme{\xintfloateval{\LlncXSomme+(log(\LX[##1]))^2}}% + }% + %COEFFS TEMPORAIRES OK + \xdef\tmp@reg@pow@b{\xintfloateval{(\LNB*\LlnXlnYSomme-\LlnXSomme*\LlnYSomme)/(\LNB*\LlncXSomme-(\LlnXSomme)^2)}}% + \xdef\tmp@reg@pow@a{\xintfloateval{exp(1/\LNB*\LlnYSomme-(\tmp@reg@pow@b)/\LNB*\LlnXSomme)}}% + %STOCKAGE + \IfStrEq{\RegPuissRound}{}% + {% + \expandafter\def\csname\RegPuissCoefb\endcsname{\xintfloateval{\tmp@reg@pow@b}}% + \expandafter\def\csname\RegPuissCoefa\endcsname{\xintfloateval{\tmp@reg@pow@a}}% + }% + {% + \IfSubStr{\RegPuissRound}{/}% + {% + \StrCut{\RegPuissRound}{/}{\xintarrondisregpowa}{\xintarrondisregpowb}% + }% + {% + \xdef\xintarrondisregpowa{\RegPuissRound}\xdef\xintrrondisregpowb{\RegPuissRound}% + }% + \expandafter\def\csname\RegPuissCoefb\endcsname{\xintfloateval{round(\tmp@reg@pow@b,\xintarrondisregpowb)}}% + \expandafter\def\csname\RegPuissCoefa\endcsname{\xintfloateval{round(\tmp@reg@pow@a,\xintarrondisregpowa)}}% + }% +} + +%régression a*b^x +\defKV[CoeffRegExpoAB]{% + coeffa=\def\RegExpoCoefa{#1},% + coeffb=\def\RegExpoCoefb{#1},% + round=\def\RegExpoRound{#1} +} + +\setKVdefault[CoeffRegExpoAB]{% + coeffa=expabrega,% + coeffb=expabregb,% + round={} +} + +\newcommand\xintexpabreg[3][]{% + \useKVdefault[CoeffRegExpoAB]% + \setKV[CoeffRegExpoAB]{#1}% on paramètres les nouvelles clés et on les simplifie + %listes des données + \def\xliste{#2}% + \def\yliste{#3}% + \readlist*\LX{\xliste}% + \readlist*\LY{\yliste}% + %taille des listes + \def\LNB{\inteval{\LXlen}}% + %somme importantes + \xdef\LXlnYSomme{0}% + \xdef\LXSomme{0}% + \xdef\LlnYSomme{0}% + \xdef\LXcSomme{0}% + %calculs + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LXlnYSomme{\xintfloateval{\LXlnYSomme+\LX[##1]*log(\LY[##1])}}% + \xdef\LXSomme{\xintfloateval{\LXSomme+\LX[##1]}}% + \xdef\LlnYSomme{\xintfloateval{\LlnYSomme+log(\LY[##1])}}% + \xdef\LXcSomme{\xintfloateval{\LXcSomme+(\LX[##1])^2}}% + }% + %COEFFS TEMPORAIRES OK + \xdef\tmp@reg@expab@b{\xintfloateval{exp((\LNB*\LXlnYSomme-\LXSomme*\LlnYSomme)/(\LNB*\LXcSomme-(\LXSomme)^2))}}% + \xdef\tmp@reg@expab@a{\xintfloateval{exp(1/\LNB*\LlnYSomme-log(\tmp@reg@expab@b)/\LNB*\LXSomme)}}% + %STOCKAGE + \IfStrEq{\RegExpoRound}{}% + {% + \expandafter\def\csname\RegExpoCoefb\endcsname{\tmp@reg@expab@b}% + \expandafter\def\csname\RegExpoCoefa\endcsname{\tmp@reg@expab@a}% + }% + {% + \IfSubStr{\RegExpoRound}{/}% + {% + \StrCut{\RegExpoRound}{/}{\xintarrondisregexpoaba}{\xintarrondisregexpoabb}% + }% + {% + \xdef\xintarrondisregexpoaba{\RegExpoRound}\xdef\xintarrondisregexpoabb{\RegExpoRound}% + }% + \expandafter\def\csname\RegExpoCoefb\endcsname{\xintfloateval{round(\tmp@reg@expab@b,\xintarrondisregexpoabb)}}% + \expandafter\def\csname\RegExpoCoefa\endcsname{\xintfloateval{round(\tmp@reg@expab@a,\xintarrondisregexpoaba)}}% + }% +} + +%régression a+b/x +\defKV[CoeffRegHyperb]{% + coeffa=\def\RegHyperbCoefa{#1},% + coeffb=\def\RegHyperbCoefb{#1},% + round=\def\RegHyperbRound{#1} +} + +\setKVdefault[CoeffRegHyperb]{% + coeffa=hyprega,% + coeffb=hypregb,% + round={} +} + +\newcommand\xinthypreg[3][]{% + \useKVdefault[CoeffRegHyperb]% + \setKV[CoeffRegHyperb]{#1}% on paramètres les nouvelles clés et on les simplifie + %listes des données + \def\xliste{#2}% + \def\yliste{#3}% + \readlist*\LX{\xliste}% + \readlist*\LY{\yliste}% + %taille des listes + \def\LNB{\inteval{\LXlen}}% + %somme importantes + \xdef\LinvXSomme{0}% + \xdef\LYdivXSomme{0}% + \xdef\LYSomme{0}% + \xdef\LinvXcSomme{0}% + %calculs + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LinvXSomme{\xintfloateval{\LinvXSomme+1/\LX[##1]}}% + \xdef\LYdivXSomme{\xintfloateval{\LYdivXSomme+\LY[##1]/\LX[##1]}}% + \xdef\LYSomme{\xintfloateval{\LYSomme+\LY[##1]}}% + \xdef\LinvXcSomme{\xintfloateval{\LinvXcSomme+1/(\LX[##1])^2}}% + }% + %COEFFS TEMPORAIRES OK + \xdef\tmp@reg@hyp@b{\xintfloateval{(\LNB*\LYdivXSomme-\LinvXSomme*\LYSomme)/(\LNB*\LinvXcSomme-(\LinvXSomme)^2)}}% + \xdef\tmp@reg@hyp@a{\xintfloateval{1/\LNB*\LYSomme-(\tmp@reg@hyp@b)/\LNB*\LinvXSomme}}% + %STOCKAGE + \IfStrEq{\RegHyperbRound}{}% + {% + \expandafter\def\csname\RegHyperbCoefb\endcsname{\tmp@reg@hyp@b}% + \expandafter\def\csname\RegHyperbCoefa\endcsname{\tmp@reg@hyp@a}% + }% + {% + \IfSubStr{\RegHyperbRound}{/}% + {% + \StrCut{\RegHyperbRound}{/}{\xintarrondisreghypa}{\xintarrondisreghypb}% + }% + {% + \xdef\xintarrondisreghypa{\RegHyperbRound}\xdef\xintarrondisreghypb{\RegHyperbRound}% + }% + \expandafter\def\csname\RegHyperbCoefb\endcsname{\xintfloateval{round(\tmp@reg@hyp@b,\xintarrondisreghypb)}}% + \expandafter\def\csname\RegHyperbCoefa\endcsname{\xintfloateval{round(\tmp@reg@hyp@a,\xintarrondisreghypa)}}% + }% +} + +%régression a+b*ln(x) +\defKV[CoeffRegLog]{% + coeffa=\def\RegLogCoefa{#1},% + coeffb=\def\RegLogCoefb{#1},% + round=\def\RegLogRound{#1} +} + +\setKVdefault[CoeffRegLog]{% + coeffa=logrega,% + coeffb=logregb,% + round={} +} + +\newcommand\xintlogreg[3][]{% + \useKVdefault[CoeffRegLog]% + \setKV[CoeffRegLog]{#1}% on paramètres les nouvelles clés et on les simplifie + %listes des données + \def\xliste{#2}% + \def\yliste{#3}% + \readlist*\LX{\xliste}% + \readlist*\LY{\yliste}% + %taille des listes + \def\LNB{\inteval{\LXlen}}% + %somme importantes + \xdef\LYlnXSomme{0}% + \xdef\LlnXSomme{0}% + \xdef\LYSomme{0}% + \xdef\LYlncXSomme{0}% + %calculs + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LYlnXSomme{\xintfloateval{\LYlnXSomme+\LY[##1]*log(\LX[##1])}}% + \xdef\LlnXSomme{\xintfloateval{\LlnXSomme+log(\LX[##1])}}% + \xdef\LYSomme{\xintfloateval{\LYSomme+\LY[##1]}}% + \xdef\LYlncXSomme{\xintfloateval{\LYlncXSomme+log(\LX[##1])^2}}% + }% + %COEFFS TEMPORAIRES OK + \xdef\tmp@reg@log@b{\xintfloateval{(\LNB*\LYlnXSomme-\LlnXSomme*\LYSomme)/(\LNB*\LYlncXSomme-(\LlnXSomme)^2)}}% + \xdef\tmp@reg@log@a{\xintfloateval{1/\LNB*\LYSomme-(\tmp@reg@log@b)/\LNB*\LlnXSomme}}% + %STOCKAGE + \IfStrEq{\RegLogRound}{}% + {% + \expandafter\def\csname\RegLogCoefb\endcsname{\tmp@reg@log@b}% + \expandafter\def\csname\RegLogCoefa\endcsname{\tmp@reg@log@a}% + }% + {% + \IfSubStr{\RegLogRound}{/}% + {% + \StrCut{\RegLogRound}{/}{\xintarrondisregloga}{\xintarrondisreglogb}% + }% + {% + \xdef\xintarrondisregloga{\RegLogRound}\xdef\xintarrondisreglogb{\RegLogRound}% + }% + \expandafter\def\csname\RegLogCoefb\endcsname{\xintfloateval{round(\tmp@reg@log@b,\xintarrondisreglogb)}}% + \expandafter\def\csname\RegLogCoefa\endcsname{\xintfloateval{round(\tmp@reg@log@a,\xintarrondisregloga)}}% + }% +} + +%régression e^(ax+b) +\defKV[CoeffRegExpo]{% + coeffa=\def\RegExpoNCoefa{#1},% + coeffb=\def\RegExpoNCoefb{#1},% + round=\def\RegExpoNRound{#1} +} + +\setKVdefault[CoeffRegExpo]{% + coeffa=exprega,% + coeffb=expregb,% + Alt=false,% + round={} +} + +\newcommand\xintexpreg[3][]{% + \useKVdefault[CoeffRegExpo]% + \setKV[CoeffRegExpo]{#1}% on paramètres les nouvelles clés et on les simplifie + %listes des données + \def\xliste{#2}% + \def\yliste{#3}% + \readlist*\LX{\xliste}% + \readlist*\LY{\yliste}% + %taille des listes + \def\LNB{\inteval{\LXlen}}% + %somme importantes + \xdef\LXlnYSomme{0}% + \xdef\LXSomme{0}% + \xdef\LlnYSomme{0}% + \xdef\LXcSomme{0}% + %calculs + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LXlnYSomme{\xintfloateval{\LXlnYSomme+\LX[##1]*log(\LY[##1])}}% + \xdef\LXSomme{\xintfloateval{\LXSomme+\LX[##1]}}% + \xdef\LlnYSomme{\xintfloateval{\LlnYSomme+log(\LY[##1])}}% + \xdef\LXcSomme{\xintfloateval{\LXcSomme+(\LX[##1])^2}}% + }% + %COEFFS TEMPORAIRES + \xdef\TmpCoeffExpoA{\xintfloateval{(\LNB*\LXlnYSomme-\LXSomme*\LlnYSomme)/(\LNB*\LXcSomme-(\LXSomme)^2)}}% + \xdef\TmpCoeffExpoB{\xintfloateval{1/\LNB*\LlnYSomme-(\TmpCoeffExpoA)/\LNB*\LXSomme}}% + \ifboolKV[CoeffRegExpo]{Alt}% + {% + %STOCKAGE + \IfStrEq{\RegExpoNRound}{}% + {% + \expandafter\def\csname\RegExpoNCoefb\endcsname{\xintfloateval{exp(\TmpCoeffExpoB)}}% + \expandafter\def\csname\RegExpoNCoefa\endcsname{\TmpCoeffExpoA}% + }% + {% + \IfSubStr{\RegExpoNRound}{/}% + {% + \StrCut{\RegExpoNRound}{/}{\xintarrondisregexpoa}{\xintarrondisregexpob}% + }% + {% + \xdef\xintarrondisregexpoa{\RegExpoNRound}\xdef\xintarrondisregexpob{\RegExpoNRound}% + }% + \expandafter\def\csname\RegExpoNCoefb\endcsname{\xintfloateval{round(exp(\TmpCoeffExpoB),\xintarrondisregexpob)}}% + \expandafter\def\csname\RegExpoNCoefa\endcsname{\xintfloateval{round(\TmpCoeffExpoA,\xintarrondisregexpoa)}}% + }% + }% + {% + %STOCKAGE + \IfStrEq{\RegExpoNRound}{}% + {% + \expandafter\def\csname\RegExpoNCoefb\endcsname{\TmpCoeffExpoB}% + \expandafter\def\csname\RegExpoNCoefa\endcsname{\TmpCoeffExpoA}% + }% + {% + \IfSubStr{\RegExpoNRound}{/}% + {% + \StrCut{\RegExpoNRound}{/}{\xintarrondisregexpoa}{\xintarrondisregexpob}% + }% + {% + \xdef\xintarrondisregexpoa{\RegExpoNRound}\xdef\xintarrondisregexpob{\RegExpoNRound}% + }% + \expandafter\def\csname\RegExpoNCoefb\endcsname{\xintfloateval{round(\TmpCoeffExpoB,\xintarrondisregexpob)}}% + \expandafter\def\csname\RegExpoNCoefa\endcsname{\xintfloateval{round(\TmpCoeffExpoA,\xintarrondisregexpoa)}}% + }% + }% +} + +%régression C + b*e^(ax) +\defKV[CoeffRegExpoOff]{% + coeffa=\def\RegExpoOffCoefa{#1},% + coeffb=\def\RegExpoOffCoefb{#1},% + offset=\def\RegExpoOffset{#1},% + round=\def\RegExpoOffRound{#1} +} + +\setKVdefault[CoeffRegExpoOff]{% + coeffa=expregoffa,% + coeffb=expregoffb,% + offset=0,% + round={} +} + +\newcommand\xintexpoffreg[3][]{% + \useKVdefault[CoeffRegExpoOff]% + \setKV[CoeffRegExpoOff]{#1}% on paramètres les nouvelles clés et on les simplifie + %listes des données + \def\xliste{#2}% + \def\yliste{#3}% + \readlist*\LX{\xliste}% + \readlist*\LY{\yliste}% + %taille des listes + \def\LNB{\inteval{\LXlen}}% + %somme importantes + \xdef\LXlnYSomme{0}% + \xdef\LXSomme{0}% + \xdef\LlnYSomme{0}% + \xdef\LXcSomme{0}% + %calculs + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LXlnYSomme{\xintfloateval{\LXlnYSomme+\LX[##1]*log(\LY[##1]-\RegExpoOffset)}}% + \xdef\LXSomme{\xintfloateval{\LXSomme+\LX[##1]}}% + \xdef\LlnYSomme{\xintfloateval{\LlnYSomme+log(\LY[##1]-\RegExpoOffset)}}% + \xdef\LXcSomme{\xintfloateval{\LXcSomme+(\LX[##1])^2}}% + }% + %COEFFS TEMPORAIRES + \xdef\TmpCoeffExpoA{\xintfloateval{(\LNB*\LXlnYSomme-\LXSomme*\LlnYSomme)/(\LNB*\LXcSomme-(\LXSomme)^2)}}% + \xdef\TmpCoeffExpoB{\xintfloateval{1/\LNB*\LlnYSomme-(\TmpCoeffExpoA)/\LNB*\LXSomme}}% + %STOCKAGE + \IfStrEq{\RegExpoOffRound}{}% + {% + \expandafter\def\csname\RegExpoOffCoefb\endcsname{\xintfloateval{exp(\TmpCoeffExpoB)}}% + \expandafter\def\csname\RegExpoOffCoefa\endcsname{\xintfloateval{\TmpCoeffExpoA}}% + }% + {% + \IfSubStr{\RegExpoOffRound}{/}% + {% + \StrCut{\RegExpoOffRound}{/}{\xintarrondisregexpoffa}{\xintarrondisregexpoffb}% + }% + {% + \xdef\xintarrondisregexpoffa{\RegExpoOffRound}\xdef\xintarrondisregexpoffb{\RegExpoOffRound}% + }% + \expandafter\def\csname\RegExpoOffCoefb\endcsname{\xintfloateval{round(exp(\TmpCoeffExpoB),\xintarrondisregexpoffb)}}% + \expandafter\def\csname\RegExpoOffCoefa\endcsname{\xintfloateval{round(\TmpCoeffExpoA,\xintarrondisregexpoffa)}}% + }% +} + +%régression cubique +\defKV[CoeffRegCubic]{% + coeffa=\def\RegCubicCoefa{#1},% + coeffb=\def\RegCubicCoefb{#1},% + coeffc=\def\RegCubicCoefc{#1},% + coeffd=\def\RegCubicCoefd{#1},% + round=\def\RegCubicRound{#1} +} + +\setKVdefault[CoeffRegCubic]{% + coeffa=cubrega,% + coeffb=cubregb,% + coeffc=cubregc,% + coeffd=cubregd,% + round={} +} + +\newcommand\xintcubreg[3][]{% + \useKVdefault[CoeffRegCubic]% + \setKV[CoeffRegCubic]{#1}% on paramètres les nouvelles clés et on les simplifie + %listes des données + \def\xliste{#2}% + \def\yliste{#3}% + \readlist*\LX{\xliste}% + \readlist*\LY{\yliste}% + %taille des listes + \def\LNB{\inteval{\LXlen}}% + %somme importantes + \xdef\LXSomme{0}% + \xdef\LXdSomme{0}% + \xdef\LXtSomme{0}% + \xdef\LXqSomme{0}% + \xdef\LXcSomme{0}% + \xdef\LXsSomme{0}% + \xdef\LYSomme{0}% + \xdef\LXYSomme{0}% + \xdef\LXdYSomme{0}% + \xdef\LXtYSomme{0}% + %calculs + \xintFor* ##1 in {\xintSeq{1}{\LNB}}\do{% + \xdef\LXSomme{\xintfloateval{\LXSomme+\LX[##1]}}% + \xdef\LXdSomme{\xintfloateval{\LXdSomme+(\LX[##1])^2}}% + \xdef\LXtSomme{\xintfloateval{\LXtSomme+(\LX[##1])^3}}% + \xdef\LXqSomme{\xintfloateval{\LXqSomme+(\LX[##1])^4}}% + \xdef\LXcSomme{\xintfloateval{\LXcSomme+(\LX[##1])^5}}% + \xdef\LXsSomme{\xintfloateval{\LXsSomme+(\LX[##1])^6}}% + \xdef\LYSomme{\xintfloateval{\LYSomme+\LY[##1]}}% + \xdef\LXYSomme{\xintfloateval{\LXYSomme+\LX[##1]*\LY[##1]}}% + \xdef\LXdYSomme{\xintfloateval{\LXdYSomme+(\LX[##1])^2*\LY[##1]}}% + \xdef\LXtYSomme{\xintfloateval{\LXtYSomme+(\LX[##1])^3*\LY[##1]}}% + }% + %calculs suites, avec des matrices !! + \def\MatA{\LXtSomme}% + \def\MatB{\LXdSomme}% + \def\MatC{\LXSomme}% + \def\MatD{\LNB}% + \def\MatE{\LXqSomme}% + \def\MatF{\LXtSomme}% + \def\MatG{\LXdSomme}% + \def\MatH{\LXSomme}% + \def\MatI{\LXcSomme}% + \def\MatJ{\LXqSomme}% + \def\MatK{\LXtSomme}% + \def\MatL{\LXdSomme}% + \def\MatM{\LXsSomme}% + \def\MatN{\LXcSomme}% + \def\MatO{\LXqSomme}% + \def\MatP{\LXtSomme}% + \def\MatBA{\LYSomme}% + \def\MatBB{\LXYSomme}% + \def\MatBC{\LXdYSomme}% + \def\MatBD{\LXtYSomme}% + \def\DETMATRICE{\xintfloateval{\MatA*\MatF*\MatK*\MatP-\MatA*\MatF*\MatL*\MatO-\MatA*\MatG*\MatJ*\MatP+\MatA*\MatG*\MatL*\MatN+\MatA*\MatH*\MatJ*\MatO-\MatA*\MatH*\MatK*\MatN-\MatB*\MatE*\MatK*\MatP+\MatB*\MatE*\MatL*\MatO+\MatB*\MatG*\MatI*\MatP-\MatB*\MatG*\MatL*\MatM-\MatB*\MatH*\MatI*\MatO+\MatB*\MatH*\MatK*\MatM+\MatC*\MatE*\MatJ*\MatP-\MatC*\MatE*\MatL*\MatN-\MatC*\MatF*\MatI*\MatP+\MatC*\MatF*\MatL*\MatM+\MatC*\MatH*\MatI*\MatN-\MatC*\MatH*\MatJ*\MatM-\MatD*\MatE*\MatJ*\MatO+\MatD*\MatE*\MatK*\MatN+\MatD*\MatF*\MatI*\MatO-\MatD*\MatF*\MatK*\MatM-\MatD*\MatG*\MatI*\MatN+\MatD*\MatG*\MatJ*\MatM}}% + \def\MatInvA{(\MatF*\MatK*\MatP-\MatF*\MatL*\MatO-\MatG*\MatJ*\MatP+\MatG*\MatL*\MatN+\MatH*\MatJ*\MatO-\MatH*\MatK*\MatN)/\DETMATRICE}% + \def\MatInvB{(-\MatB*\MatK*\MatP+\MatB*\MatL*\MatO+\MatC*\MatJ*\MatP-\MatC*\MatL*\MatN-\MatD*\MatJ*\MatO+\MatD*\MatK*\MatN)/\DETMATRICE}% + \def\MatInvC{(\MatB*\MatG*\MatP-\MatB*\MatH*\MatO-\MatC*\MatF*\MatP+\MatC*\MatH*\MatN+\MatD*\MatF*\MatO-\MatD*\MatG*\MatN)/\DETMATRICE}% + \def\MatInvD{(-\MatB*\MatG*\MatL+\MatB*\MatH*\MatK+\MatC*\MatF*\MatL-\MatC*\MatH*\MatJ-\MatD*\MatF*\MatK+\MatD*\MatG*\MatJ)/\DETMATRICE}% + \def\MatInvE{(-\MatE*\MatK*\MatP+\MatE*\MatL*\MatO+\MatG*\MatI*\MatP-\MatG*\MatL*\MatM-\MatH*\MatI*\MatO+\MatH*\MatK*\MatM)/\DETMATRICE}% + \def\MatInvF{(\MatA*\MatK*\MatP-\MatA*\MatL*\MatO-\MatC*\MatI*\MatP+\MatC*\MatL*\MatM+\MatD*\MatI*\MatO-\MatD*\MatK*\MatM)/\DETMATRICE}% + \def\MatInvG{(-\MatA*\MatG*\MatP+\MatA*\MatH*\MatO+\MatC*\MatE*\MatP-\MatC*\MatH*\MatM-\MatD*\MatE*\MatO+\MatD*\MatG*\MatM)/\DETMATRICE}% + \def\MatInvH{(\MatA*\MatG*\MatL-\MatA*\MatH*\MatK-\MatC*\MatE*\MatL+\MatC*\MatH*\MatI+\MatD*\MatE*\MatK-\MatD*\MatG*\MatI)/\DETMATRICE}% + \def\MatInvI{(\MatE*\MatJ*\MatP-\MatE*\MatL*\MatN-\MatF*\MatI*\MatP+\MatF*\MatL*\MatM+\MatH*\MatI*\MatN-\MatH*\MatJ*\MatM)/\DETMATRICE}% + \def\MatInvJ{(-\MatA*\MatJ*\MatP+\MatA*\MatL*\MatN+\MatB*\MatI*\MatP-\MatB*\MatL*\MatM-\MatD*\MatI*\MatN+\MatD*\MatJ*\MatM)/\DETMATRICE}% + \def\MatInvK{(\MatA*\MatF*\MatP-\MatA*\MatH*\MatN-\MatB*\MatE*\MatP+\MatB*\MatH*\MatM+\MatD*\MatE*\MatN-\MatD*\MatF*\MatM)/\DETMATRICE}% + \def\MatInvL{(-\MatA*\MatF*\MatL+\MatA*\MatH*\MatJ+\MatB*\MatE*\MatL-\MatB*\MatH*\MatI-\MatD*\MatE*\MatJ+\MatD*\MatF*\MatI)/\DETMATRICE}% + \def\MatInvM{(-\MatE*\MatJ*\MatO+\MatE*\MatK*\MatN+\MatF*\MatI*\MatO-\MatF*\MatK*\MatM-\MatG*\MatI*\MatN+\MatG*\MatJ*\MatM)/\DETMATRICE}% + \def\MatInvN{(\MatA*\MatJ*\MatO-\MatA*\MatK*\MatN-\MatB*\MatI*\MatO+\MatB*\MatK*\MatM+\MatC*\MatI*\MatN-\MatC*\MatJ*\MatM)/\DETMATRICE}% + \def\MatInvO{(-\MatA*\MatF*\MatO+\MatA*\MatG*\MatN+\MatB*\MatE*\MatO-\MatB*\MatG*\MatM-\MatC*\MatE*\MatN+\MatC*\MatF*\MatM)/\DETMATRICE}% + \def\MatInvP{(\MatA*\MatF*\MatK-\MatA*\MatG*\MatJ-\MatB*\MatE*\MatK+\MatB*\MatG*\MatI+\MatC*\MatE*\MatJ-\MatC*\MatF*\MatI)/\DETMATRICE}% + %COEFFS TEMPORAIRES OK + \xdef\tmp@reg@cub@a{\xintfloateval{\MatInvA*\MatBA+\MatInvB*\MatBB+\MatInvC*\MatBC+\MatInvD*\MatBD}}% + \xdef\tmp@reg@cub@b{\xintfloateval{\MatInvE*\MatBA+\MatInvF*\MatBB+\MatInvG*\MatBC+\MatInvH*\MatBD}}% + \xdef\tmp@reg@cub@c{\xintfloateval{\MatInvI*\MatBA+\MatInvJ*\MatBB+\MatInvK*\MatBC+\MatInvL*\MatBD}}% + \xdef\tmp@reg@cub@d{\xintfloateval{\MatInvM*\MatBA+\MatInvN*\MatBB+\MatInvO*\MatBC+\MatInvP*\MatBD}}% + %STOCKAGE + \IfStrEq{\RegCubicRound}{}% + {% + \expandafter\def\csname\RegCubicCoefa\endcsname{\tmp@reg@cub@a}% + \expandafter\def\csname\RegCubicCoefb\endcsname{\tmp@reg@cub@b}% + \expandafter\def\csname\RegCubicCoefc\endcsname{\tmp@reg@cub@c}% + \expandafter\def\csname\RegCubicCoefd\endcsname{\tmp@reg@cub@d}% + }% + {% + \IfSubStr{\RegCubicRound}{/}% + {% + \StrBefore[1]{\RegCubicRound}{/}[\xintarrondisregcuba]% + \StrBetween[1,2]{\RegCubicRound}{/}{/}[\xintarrondisregcubb]% + \StrBetween[2,3]{\RegCubicRound}{/}{/}[\xintarrondisregcubc]% + \StrBehind[3]{\RegCubicRound}{/}[\xintarrondisregcubd]% + }% + {% + \xdef\xintarrondisregcuba{\RegCubicRound}% + \xdef\xintarrondisregcubb{\RegCubicRound}% + \xdef\xintarrondisregcubc{\RegCubicRound}% + \xdef\xintarrondisregcubd{\RegCubicRound}% + }% + \expandafter\def\csname\RegCubicCoefa\endcsname{\xintfloateval{round(\tmp@reg@cub@a,\xintarrondisregcuba)}}% + \expandafter\def\csname\RegCubicCoefb\endcsname{\xintfloateval{round(\tmp@reg@cub@b,\xintarrondisregcubb)}}% + \expandafter\def\csname\RegCubicCoefc\endcsname{\xintfloateval{round(\tmp@reg@cub@c,\xintarrondisregcubc)}}% + \expandafter\def\csname\RegCubicCoefd\endcsname{\xintfloateval{round(\tmp@reg@cub@d,\xintarrondisregcubd)}}% + }% +} + +\endinput
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