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+% proflycee-tools-stats.tex
+% Copyright 2023 Cédric Pierquet
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+
+%%------RegressionLinéaire
+%calcul des paramètres
+\defKV[coeffreglin]{%
+ NomCoeffa=\def\RegLinCoeffa{#1},%
+ NomCoeffb=\def\RegLinCoeffb{#1},%
+ NomCoeffr=\def\RegLinCoeffr{#1},%
+ NomCoeffrd=\def\RegLinCoeffrd{#1},%
+ NomXmin=\def\RegLinCoeffXmin{#1},%
+ NomXmax=\def\RegLinCoeffXmax{#1}
+}
+
+\setKVdefault[coeffreglin]{%
+ NomCoeffa=COEFFa,%
+ NomCoeffb=COEFFb,%
+ NomCoeffr=COEFFr,%
+ NomCoeffrd=COEFFrd,%
+ NomXmin=LXmin,%
+ NomXmax=LXmax
+}
+
+\newcommand\CalculsRegLin[3][]{%
+ \useKVdefault[coeffreglin]%
+ \setKV[coeffreglin]{#1}% on paramètres les nouvelles clés et on les simplifie
+ %xmin et xmax
+ \expandafter\def\csname\RegLinCoeffXmin\endcsname{\fpeval{min(#2)}}
+ \expandafter\def\csname\RegLinCoeffXmax\endcsname{\fpeval{max(#2)}}
+ %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}
+ \foreach \i in {1,2,...,\LNB}{
+ \xdef\LXSomme{\fpeval{\LXSomme+\LX[\i]}}
+ }
+ \foreach \i in {1,2,...,\LNB}{
+ \xdef\LYSomme{\fpeval{\LYSomme+\LY[\i]}}
+ }
+ %moyenne des LX et des LY OK
+ \xdef\LXmoy{\fpeval{\LXSomme/\LNB}}
+ \xdef\LYmoy{\fpeval{\LYSomme/\LNB}}
+ %variance des LX et des LY OK
+ \xdef\LXvar{0}
+ \foreach \i in {1,2,...,\LNB}{
+ \xdef\LXvar{\fpeval{\LXvar+(\LX[\i]-\LXmoy)*(\LX[\i]-\LXmoy)}}
+ }
+ \xdef\LXvar{\fpeval{\LXvar/\LNB}}
+ \xdef\LYvar{0}
+ \foreach \i in {1,2,...,\LNB}{
+ \xdef\LYvar{\fpeval{\LYvar+(\LY[\i]-\LYmoy)*(\LY[\i]-\LYmoy)}}
+ }
+ \xdef\LYvar{\fpeval{\LYvar/\LNB}}
+ %covariance des XY OK
+ \xdef\LXYvar{0}
+ \foreach \i in {1,2,...,\LNB}{
+ \xdef\LXYvar{\fpeval{\LXYvar+(\LX[\i]-\LXmoy)*(\LY[\i]-\LYmoy)}}
+ }
+ \xdef\LXYvar{\fpeval{\LXYvar/\LNB}}
+ %COEFFS OK
+ \expandafter\def\csname\RegLinCoeffa\endcsname{\fpeval{\LXYvar/\LXvar}}
+ \expandafter\def\csname\RegLinCoeffb\endcsname{\fpeval{\LYmoy-\csname\RegLinCoeffa\endcsname*\LXmoy}}
+ \expandafter\def\csname\RegLinCoeffr\endcsname{\fpeval{\LXYvar/sqrt(\LXvar*\LYvar)}}
+ \expandafter\def\csname\RegLinCoeffrd\endcsname{\fpeval{\csname\RegLinCoeffr\endcsname*\csname\RegLinCoeffr\endcsname}}
+}
+
+%pour un nuage en TiKz
+\defKV[nuagereglin]{%
+ Couleur=\def\RegLinNuageCouleur{#1},%
+ Taille=\def\RegLinNuageTaille{#1},
+ Ox=\def\RegLinNuageOx{#1},%
+ Oy=\def\RegLinNuageOy{#1},%
+}
+
+\setKVdefault[nuagereglin]{%
+ Couleur=teal,%
+ Taille=2pt,%
+ Ox=0,%
+ Oy=0
+}
+
+\newcommand\PointsRegLin[3][]{%
+ \useKVdefault[nuagereglin]
+ \setKV[nuagereglin]{#1}% on paramètres les nouvelles clés et on les simplifie
+ \def\xliste{#2}
+ \def\yliste{#3}
+ \readlist*\LX{\xliste}
+ \readlist*\LY{\yliste}
+ %taille des listes
+ \def\LNB{\inteval{\LXlen}}
+ \foreach \i in {1,2,...,\LNB} {\filldraw[\RegLinNuageCouleur] ({\LX[\i]-\RegLinNuageOx},{\LY[\i]-\RegLinNuageOy}) circle[radius=\RegLinNuageTaille] ;}
+}
+
+\NewDocumentEnvironment{StatsTikz}{ O{} }
+{%
+ \begin{tikzpicture}[#1]
+ }%
+ {%
+ \end{tikzpicture}%
+}
+
+%%------BOITES MOUSTACHES
+\defKV[boiteamoustaches]{%
+ Couleur=\def\BaMCouleur{#1},%
+ Elevation=\def\BaMElevation{#1},%
+ Hauteur=\def\BaMHauteur{#1},%
+ Moyenne=\def\BaMMoyenne{#1},%
+ Epaisseur=\def\BaMEpaisseur{#1},%
+ Remplir=\def\BaMRemplissage{#1}
+}
+
+\setKVdefault[boiteamoustaches]{%
+ Couleur=black,%
+ Elevation=1,%
+ Hauteur=1,%
+ AffMoyenne=false,%
+ Epaisseur=thick,%
+ Pointilles=false,%
+ Valeurs=false,%
+ Remplir=white
+}
+
+\defKV[boiteamoustachesaxe]{%
+ Min=\def\BaMAxeMin{#1},%
+ Max=\def\BaMAxeMax{#1},%
+ Elargir=\def\BaMAxeElarg{#1},%
+ Epaisseur=\def\BaMAxeEpaisseur{#1},%
+ Valeurs=\def\BaMAxeValeurs{#1}
+}
+
+\setKVdefault[boiteamoustachesaxe]{%
+ Elargir=0.05,%
+ Epaisseur=thick,%
+ AffValeurs=false
+}
+
+\newcommand\BoiteMoustachesAxe[1][]{
+ \useKVdefault[boiteamoustachesaxe]
+ \setKV[boiteamoustachesaxe]{#1}
+ \def\BaMaxelargeur{\fpeval{\BaMAxeMax-\BaMAxeMin}}
+ \def\BaMaxexmin{\fpeval{\BaMAxeMin-\BaMAxeElarg*\BaMaxelargeur}}
+ \def\BaMaxexmax{\fpeval{\BaMAxeMax+\BaMAxeElarg*\BaMaxelargeur}}
+ \draw[\BaMAxeEpaisseur,->,>=latex] (\BaMaxexmin,0) -- (\BaMaxexmax,0) ;
+ \ifboolKV[boiteamoustachesaxe]{AffValeurs}
+ {\foreach \x in \BaMAxeValeurs \draw[\BaMAxeEpaisseur] (\x,3pt)--(\x,-3pt) node[below=3pt] {\num{\x}} ;}
+ {}
+}
+
+\newcommand\BoiteMoustaches[2][]{
+ \useKVdefault[boiteamoustaches]
+ \setKV[boiteamoustaches]{#1}
+ \setsepchar[.]{/}%
+ \readlist*\BaMListeparams{#2}%
+ \itemtomacro\BaMListeparams[1]\BaMmin%
+ \itemtomacro\BaMListeparams[2]\BaMqu%
+ \itemtomacro\BaMListeparams[3]\BaMmed%
+ \itemtomacro\BaMListeparams[4]\BaMqt%
+ \itemtomacro\BaMListeparams[5]\BaMmax%
+ \draw[draw,\BaMEpaisseur,\BaMCouleur,fill=\BaMRemplissage] ({\BaMqu},{\BaMElevation-0.5*\BaMHauteur}) rectangle ({\BaMqt},{\BaMElevation+0.5*\BaMHauteur}) ;
+ \draw[\BaMEpaisseur,\BaMCouleur] (\BaMmin,{\BaMElevation-0.5*\BaMHauteur})--(\BaMmin,{\BaMElevation+0.5*\BaMHauteur}) (\BaMmax,{\BaMElevation-0.5*\BaMHauteur})--(\BaMmax,{\BaMElevation+0.5*\BaMHauteur}) (\BaMmed,{\BaMElevation-0.5*\BaMHauteur})--(\BaMmed,{\BaMElevation+0.5*\BaMHauteur});
+ \draw[\BaMEpaisseur,\BaMCouleur] ({\BaMmin},{\BaMElevation})--({\BaMqu},{\BaMElevation}) ({\BaMqt},{\BaMElevation})--({\BaMmax},{\BaMElevation}) ;
+ \ifboolKV[boiteamoustaches]{AffMoyenne}
+ {\filldraw[\BaMCouleur] ({\BaMMoyenne},{\BaMElevation}) circle[radius=2.5pt] ;}
+ {}
+ \ifboolKV[boiteamoustaches]{Pointilles}
+ {
+ \draw[\BaMEpaisseur,densely dashed] (\BaMmin,{\BaMElevation-0.5*\BaMHauteur}) -- (\BaMmin,0) ;
+ \draw[\BaMEpaisseur,densely dashed] (\BaMqu,{\BaMElevation-0.5*\BaMHauteur}) -- (\BaMqu,0) ;
+ \draw[\BaMEpaisseur,densely dashed] (\BaMmed,{\BaMElevation-0.5*\BaMHauteur}) -- (\BaMmed,0) ;
+ \draw[\BaMEpaisseur,densely dashed] (\BaMqt,{\BaMElevation-0.5*\BaMHauteur}) -- (\BaMqt,0) ;
+ \draw[\BaMEpaisseur,densely dashed] (\BaMmax,{\BaMElevation-0.5*\BaMHauteur}) -- (\BaMmax,0) ;
+ }
+ {}
+ \ifboolKV[boiteamoustaches]{Valeurs}
+ {
+ \filldraw (\BaMmin,0) circle[radius=2pt] node[below=4pt] {\num{\BaMmin}} ;
+ \filldraw (\BaMqu,0) circle[radius=2pt] node[below=4pt] {\num{\BaMqu}} ;
+ \filldraw (\BaMmed,0) circle[radius=2pt] node[below=4pt] {\num{\BaMmed}} ;
+ \filldraw (\BaMqt,0) circle[radius=2pt] node[below=4pt] {\num{\BaMqt}} ;
+ \filldraw (\BaMmax,0) circle[radius=2pt] node[below=4pt] {\num{\BaMmax}} ;
+ }
+ {}
+}
+
+\endinput \ No newline at end of file