diff options
Diffstat (limited to 'macros/latex/contrib/proflycee/tex/proflycee-tools-probas.tex')
-rw-r--r-- | macros/latex/contrib/proflycee/tex/proflycee-tools-probas.tex | 748 |
1 files changed, 748 insertions, 0 deletions
diff --git a/macros/latex/contrib/proflycee/tex/proflycee-tools-probas.tex b/macros/latex/contrib/proflycee/tex/proflycee-tools-probas.tex new file mode 100644 index 0000000000..270e99e3cc --- /dev/null +++ b/macros/latex/contrib/proflycee/tex/proflycee-tools-probas.tex @@ -0,0 +1,748 @@ +% proflycee-tools-probas.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. + +%%------LOISPROBAS +%calculs "simples" +\newcommand\CalcBinomP[3]{%npk + \xintFloatToDecimal{\xintfloateval{binomial(#1,#3)*#2^#3*(1-#2)^(#1-#3)}} +} +\newcommand\CalcBinomC[4]{%npab + \def\BorneInf{#3}\def\BorneSup{#4} + \ifthenelse{\equal{#3}{*}}% + {\def\BorneInf{0}} + {} + \ifthenelse{\equal{#4}{*}}% + {\def\BorneSup{#1}} + {} + \xintFloatToDecimal{\xintfloateval{add(binomial(#1,i)*#2^i*(1-#2)^(#1-i), i=\BorneInf..\BorneSup)}} +} +\newcommand\CalcGeomP[2]{%pk + \xintFloatToDecimal{\xintfloateval{(1-#1)^(#2-1)*(#1)}} +} +\newcommand\CalcGeomC[3]{%pab + \def\BorneInf{#2}\def\BorneSup{#3} + \ifthenelse{\equal{#2}{*}}% + {\def\BorneInf{1}} + {} + \ifthenelse{\equal{#3}{*}}% + {\def\BorneSup{\fpeval{trunc(1/#1*10,0)}}} + {} + \xintFloatToDecimal{\xintfloateval{add((1-#1)^(i-1)*(#1), i=\BorneInf..\BorneSup)}} +} +\newcommand\CalcHypergeomP[4]{%Nnmk + \xintFloatToDecimal{\xintfloateval{binomial(#3,#4)*binomial(#1-#3,#2-#4)/binomial(#1,#2)}} +} +\newcommand\CalcHypergeomC[5]{%Nnmab + \def\BorneInf{#4}\def\BorneSup{#5} + \ifthenelse{\equal{#4}{*}}% + {\def\BorneInf{0}} + {} + \ifthenelse{\equal{#5}{*}}% + {\def\BorneSup{#1}} + {} + \xintFloatToDecimal{\xintfloateval{add(binomial(#3,i)*binomial(#1-#3,#2-i)/binomial(#1,#2), i=\BorneInf..\BorneSup)}} +} +\newcommand\CalcPoissP[2]{%lk + \xintFloatToDecimal{\xintfloateval{exp(-#1)*#1^#2/factorial(#2)}} +} +\newcommand\CalcPoissC[3]{%lab + \def\BorneInf{#2}\def\BorneSup{#3} + \ifthenelse{\equal{#2}{*}}% + {\def\BorneInf{0}} + {} + \ifthenelse{\equal{#3}{*}}% + {\def\BorneSup{10*#1}} + {} + \xintFloatToDecimal{\xintfloateval{add(exp(-#1)*#1^i/factorial(i), i=\BorneInf..\BorneSup)}} +} +%utiles idée de https://tex.stackexchange.com/questions/355574/im-searching-for-a-table-with-cdf-of-standard-normal-distribution +\xintdeffloatvar a_1,a_2,a_3,a_4,a_5,a_6 := +0.0705230784,0.0422820123,0.0092705272,0.0001520143,0.0002765672,0.0000430638; +\xintdeffloatvar rac2inv := sqrt(2)/2 ; +\xintdeffloatfunc erfc(x) := % uniquement pour x positif +((((((a_6*x+a_5)*x+a_4)*x+a_3)*x+a_2)*x+a_1)*x+1)**-16 ; % fin de définition de erfc(x) +\xintdeffloatfunc Phi(z) := (z>=0)?{1 - 0.5 * erfc(rac2inv * z)}{0.5 * erfc(-rac2inv * z)}; + +\newcommand\CalcNormC[4]{%msab + %def des bornes de l'intervalle suivant l'absence de a ou de b... + \def\BorneInf{#3}\def\BorneSup{#4} + \ifthenelse{\equal{#3}{*}}% + {\def\BorneInf{#4-10*#2}} + {} + \ifthenelse{\equal{#4}{*}}% + {\def\BorneSup{#3+10*#2}} + {} + \xintFloatToDecimal{\xintfloateval{Phi((\BorneSup-#1)/#2)-Phi((\BorneInf-#1)/#2)}} +} +%calculs "simples" fiabilite +\newcommand\CalcExpoC[3]{%lab + \def\BorneInf{#2}\def\BorneSup{#3} + \ifthenelse{\equal{#2}{*}}% + {\def\BorneInf{0}} + {} + \ifthenelse{\equal{#3}{*}}% + {\def\BorneSup{100/#1}} + {} + \xintFloatToDecimal{\xintfloateval{exp(-#1*\BorneInf)-exp(-#1*\BorneSup)}} +} + +%calculs formatés +\NewDocumentCommand{\BinomP}{ s O{3} m m m }{%*=sci,2=prec,3=n,4=p,5=k + \IfBooleanTF{#1}% + {% + \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(binomial(#3,#5)*#4^#5*(1-#4)^(#3-#5),#2)}}} + }% + {% + \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(binomial(#3,#5)*#4^#5*(1-#4)^(#3-#5),#2)}}} + } +} + +\NewDocumentCommand{\BinomC}{ s O{3} m m m m }{%*=sci,2=prec,3=n,4=p,5=a,6=b + \def\BorneInf{#5}\def\BorneSup{#6} + \ifthenelse{\equal{#5}{*}}% + {\def\BorneInf{0}} + {} + \ifthenelse{\equal{#6}{*}}% + {\def\BorneSup{#3}} + {} + \IfBooleanTF{#1}% + {% + \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#3,i)*#4^i*(1-#4)^(#3-i), i=\BorneInf..\BorneSup),#2)}}} + }% + {% + \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#3,i)*#4^i*(1-#4)^(#3-i), i=\BorneInf..\BorneSup),#2)}}} + } +} + +\NewDocumentCommand{\GeomP}{ s O{3} m m }{%*=sci,2=prec,3=p,4=k + \IfBooleanTF{#1}% + {% + \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round((1-#3)^(#4-1)*(#3),#2)}}} + }% + {% + \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round((1-#3)^(#4-1)*(#3),#2)}}} + } +} + +\NewDocumentCommand{\GeomC}{ s O{3} m m m }{%*=sci,2=prec,3=p,4=a,5=b + \def\BorneInf{#4}\def\BorneSup{#5} + \ifthenelse{\equal{#4}{*}}% + {\def\BorneInf{1}} + {} + \ifthenelse{\equal{#5}{*}}% + {\def\BorneSup{\fpeval{trunc(1/#3*10,0)}}} + {} + \IfBooleanTF{#1}% + {% + \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add((1-#3)^(i-1)*(#3), i=\BorneInf..\BorneSup),#2)}}} + }% + {% + \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add((1-#3)^(i-1)*(#3), i=\BorneInf..\BorneSup),#2)}}} + } +} + +\NewDocumentCommand{\HypergeomP}{ s O{3} m m m m }{%*=sci,2=prec,3=N,4=n,5=m,6=k + \IfBooleanTF{#1}% + {% + \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(binomial(#5,#6)*binomial(#3-#5,#4-#6)/binomial(#3,#4),#2)}}} + }% + {% + \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(binomial(#5,#6)*binomial(#3-#5,#4-#6)/binomial(#3,#4),#2)}}} + } +} + +\NewDocumentCommand{\HypergeomC}{ s O{3} m m m m m }{%*=sci,2=prec,3=N,4=n,5=m,6=a,7=b + \def\BorneInf{#6}\def\BorneSup{#7} + \ifthenelse{\equal{#6}{*}}% + {\def\BorneInf{0}} + {} + \ifthenelse{\equal{#7}{*}}% + {\def\BorneSup{#3}} + {} + \IfBooleanTF{#1}% + {% + \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#5,i)*binomial(#3-#5,#4-i)/binomial(#3,#4), i=\BorneInf..\BorneSup),#2)}}} + }% + {% + \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#5,i)*binomial(#3-#5,#4-i)/binomial(#3,#4), i=\BorneInf..\BorneSup),#2)}}} + } +} + +\NewDocumentCommand{\PoissonP}{ s O{3} m m }{%*=sci,2=prec,3=lbda,4=k + \IfBooleanTF{#1}% + {% + \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(exp(-#3)*#3^#4/factorial(#4),#2)}}} + }% + {% + \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(exp(-#3)*#3^#4/factorial(#4),#2)}}} + } +} + +\NewDocumentCommand{\PoissonC}{ s O{3} m m m }{%*=ing,2=prec,3=lbda,4=a,5=b + \def\BorneInf{#4}\def\BorneSup{#5} + \ifthenelse{\equal{#4}{*}}% + {\def\BorneInf{0}} + {} + \ifthenelse{\equal{#5}{*}}% + {\def\BorneSup{10*#3}} + {} + \IfBooleanTF{#1}% + {% + \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add(exp(-#3)*#3^i/factorial(i), i=\BorneInf..\BorneSup),#2)}}} + }% + {% + \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add(exp(-#3)*#3^i/factorial(i), i=\BorneInf..\BorneSup),#2)}}} + } +} + +\NewDocumentCommand{\NormaleC}{ s O{3} m m m m }{% + %*=ing,2=prec,3=mu,4=sigma,5=a,6=b + %def des bornes de l'intervalle suivant l'absence de a ou de b... + \def\BorneInf{#5}\def\BorneSup{#6} + \ifthenelse{\equal{#5}{*}}% + {\def\BorneInf{#6-10*#4}} + {} + \ifthenelse{\equal{#6}{*}}% + {\def\BorneSup{#5+10*#4}} + {} + \IfBooleanTF{#1}% + {% + \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(Phi((\BorneSup-#3)/#4)-Phi((\BorneInf-#3)/#4),#2)}}} + }% + {% + \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(Phi((\BorneSup-#3)/#4)-Phi((\BorneInf-#3)/#4),#2)}}} + } +} + +\NewDocumentCommand{\ExpoC}{ s O{3} m m m }{%*=ing,2=prec,3=lbda,4=a,5=b + \def\BorneInf{#4}\def\BorneSup{#5} + \ifthenelse{\equal{#4}{*}}% + {\def\BorneInf{0}} + {} + \ifthenelse{\equal{#5}{*}}% + {\def\BorneSup{100/#3}} + {} + \IfBooleanTF{#1}% + {% + \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(exp(-#3*\BorneInf)-exp(-#3*\BorneSup),#2)}}} + }% + {% + \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintFloatToDecimal{\xintfloateval{round(exp(-#3*\BorneInf)-exp(-#3*\BorneSup),#2)}}}} + } +} + +%%------ARBRESPROBAS +\defKV[PLTIKZARBRE]{% + Unite=\def\PLAPunite{#1},% + EspaceNiveau=\def\PLAPespniv{#1},% + EspaceFeuille=\def\PLAPespfeuille{#1},% + Type=\def\PLAPtype{#1},% + Police=\def\PLAPfont{#1},% + PoliceProbas=\def\PLAPfontproba{#1},% + StyleTrait=\def\PLAPtypetrait{#1},% + EpaisseurTrait=\def\PLAPeptrait{#1} +} + +\setKVdefault[PLTIKZARBRE]{% + Unite=1cm,% + EspaceNiveau=3.25,% + EspaceFeuille=1,% + Type=2x2,% + Police=\normalfont\normalsize,% + PoliceProbas=\normalfont\small,% + InclineProbas=true,% + Fleche=false,% + StyleTrait={},% + EpaisseurTrait=semithick +} + +\NewDocumentCommand\ArbreProbasTikz{ O{} m }{%1=options,2=libellés + \useKVdefault[PLTIKZARBRE]% + \setKV[PLTIKZARBRE]{#1}% + \setsepchar[.]{,./}% + \readlist*\PLARBREDONNES{#2}% + \begin{tikzpicture}[x=\PLAPunite,y=\PLAPunite] + %styles + \tikzstyle{noeud} = [font=\PLAPfont] + \tikzstyle{probas}= [font=\PLAPfontproba] + \ifboolKV[PLTIKZARBRE]{InclineProbas} + {\tikzstyle{PLetiquette}=[pos=0.525,sloped,fill=white]} + {\tikzstyle{PLetiquette}=[pos=0.525,fill=white]} + \ifboolKV[PLTIKZARBRE]{Fleche} + {\tikzstyle{PLfleche}=[->,>=latex,\PLAPtypetrait,\PLAPeptrait]} + {\tikzstyle{PLfleche}=[\PLAPtypetrait,\PLAPeptrait]} + %arbre2x2 + \IfEq{\PLAPtype}{2x2} + {% + \coordinate (R) at ({0*\PLAPespniv},{-1.5*\PLAPespfeuille}) ; + \node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]}; + \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]}; + \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]}; + \node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]}; + \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]}; + \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]}; + \ifstrempty{\PLARBREDONNES[1,2]} + {\draw[PLfleche] (R)--(A11) ;} + {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;} + \ifstrempty{\PLARBREDONNES[2,2]} + {\draw[PLfleche] (A11)--(A21) ;} + {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;} + \ifstrempty{\PLARBREDONNES[3,2]} + {\draw[PLfleche] (A11)--(A22) ;} + {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;} + \ifstrempty{\PLARBREDONNES[4,2]} + {\draw[PLfleche] (R)--(A12) ;} + {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;} + \ifstrempty{\PLARBREDONNES[5,2]} + {\draw[PLfleche] (A12)--(A23) ;} + {\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;} + \ifstrempty{\PLARBREDONNES[6,2]} + {\draw[PLfleche] (A12)--(A24) ;} + {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;} + }{} + %arbre3x2 + \IfEq{\PLAPtype}{3x2} + {% + %sommets + \coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ; + \node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]}; + \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]}; + \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]}; + \node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]}; + \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]}; + \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]}; + \node[noeud] (A13) at ({1*\PLAPespniv},{-4.5*\PLAPespfeuille}) {\PLARBREDONNES[7,1]}; + \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[8,1]}; + \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[9,1]}; + %branches + \ifstrempty{\PLARBREDONNES[1,2]} + {\draw[PLfleche] (R)--(A11) ;} + {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;} + \ifstrempty{\PLARBREDONNES[2,2]} + {\draw[PLfleche] (A11)--(A21) ;} + {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;} + \ifstrempty{\PLARBREDONNES[3,2]} + {\draw[PLfleche] (A11)--(A22) ;} + {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;} + \ifstrempty{\PLARBREDONNES[4,2]} + {\draw[PLfleche] (R)--(A12) ;} + {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;} + \ifstrempty{\PLARBREDONNES[5,2]} + {\draw[PLfleche] (A12)--(A23) ;} + {\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;} + \ifstrempty{\PLARBREDONNES[6,2]} + {\draw[PLfleche] (A12)--(A24) ;} + {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;} + \ifstrempty{\PLARBREDONNES[7,2]} + {\draw[PLfleche] (R)--(A13) ;} + {\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;} + \ifstrempty{\PLARBREDONNES[8,2]} + {\draw[PLfleche] (A13)--(A25) ;} + {\draw[PLfleche] (A13)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;} + \ifstrempty{\PLARBREDONNES[9,2]} + {\draw[PLfleche] (A13)--(A26) ;} + {\draw[PLfleche] (A13)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;} + }{} + %arbre2x3 + \IfEq{\PLAPtype}{2x3} + {% + %sommets + \coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ; + \node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]}; + \node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]}; + \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]}; + \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]}; + \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]}; + \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]}; + \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]}; + \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]}; + %branches + \ifstrempty{\PLARBREDONNES[1,2]} + {\draw[PLfleche] (R)--(A11) ;} + {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;} + \ifstrempty{\PLARBREDONNES[5,2]} + {\draw[PLfleche] (R)--(A12) ;} + {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;} + \ifstrempty{\PLARBREDONNES[2,2]} + {\draw[PLfleche] (A11)--(A21) ;} + {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;} + \ifstrempty{\PLARBREDONNES[3,2]} + {\draw[PLfleche] (A11)--(A22) ;} + {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;} + \ifstrempty{\PLARBREDONNES[4,2]} + {\draw[PLfleche] (A11)--(A23) ;} + {\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;} + \ifstrempty{\PLARBREDONNES[6,2]} + {\draw[PLfleche] (A12)--(A24) ;} + {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;} + \ifstrempty{\PLARBREDONNES[7,2]} + {\draw[PLfleche] (A12)--(A25) ;} + {\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;} + \ifstrempty{\PLARBREDONNES[8,2]} + {\draw[PLfleche] (A12)--(A26) ;} + {\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;} + }{} + %arbre2x3 + \IfEq{\PLAPtype}{3x3} + {% + %sommets + \coordinate (R) at ({0*\PLAPespniv},{-4*\PLAPespfeuille}) ; + \node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]}; + \node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]}; + \node[noeud] (A13) at ({1*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[9,1]}; + \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]}; + \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]}; + \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]}; + \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]}; + \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]}; + \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]}; + \node[noeud] (A27) at ({2*\PLAPespniv},{-6*\PLAPespfeuille}) {\PLARBREDONNES[10,1]}; + \node[noeud] (A28) at ({2*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[11,1]}; + \node[noeud] (A29) at ({2*\PLAPespniv},{-8*\PLAPespfeuille}) {\PLARBREDONNES[12,1]}; + %branches + \ifstrempty{\PLARBREDONNES[1,2]} + {\draw[PLfleche] (R)--(A11) ;} + {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;} + \ifstrempty{\PLARBREDONNES[5,2]} + {\draw[PLfleche] (R)--(A12) ;} + {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;} + \ifstrempty{\PLARBREDONNES[9,2]} + {\draw[PLfleche] (R)--(A13) ;} + {\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;} + %N2 + \ifstrempty{\PLARBREDONNES[2,2]} + {\draw[PLfleche] (A11)--(A21) ;} + {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;} + \ifstrempty{\PLARBREDONNES[3,2]} + {\draw[PLfleche] (A11)--(A22) ;} + {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;} + \ifstrempty{\PLARBREDONNES[4,2]} + {\draw[PLfleche] (A11)--(A23) ;} + {\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;} + \ifstrempty{\PLARBREDONNES[6,2]} + {\draw[PLfleche] (A12)--(A24) ;} + {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;} + \ifstrempty{\PLARBREDONNES[7,2]} + {\draw[PLfleche] (A12)--(A25) ;} + {\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;} + \ifstrempty{\PLARBREDONNES[8,2]} + {\draw[PLfleche] (A12)--(A26) ;} + {\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;} + \ifstrempty{\PLARBREDONNES[10,2]} + {\draw[PLfleche] (A13)--(A27) ;} + {\draw[PLfleche] (A13)--(A27) node[probas,PLetiquette,{\PLARBREDONNES[10,3]}] {{\PLARBREDONNES[10,2]}} ;} + \ifstrempty{\PLARBREDONNES[11,2]} + {\draw[PLfleche] (A13)--(A28) ;} + {\draw[PLfleche] (A13)--(A28) node[probas,PLetiquette,{\PLARBREDONNES[11,3]}] {{\PLARBREDONNES[11,2]}} ;} + \ifstrempty{\PLARBREDONNES[12,2]} + {\draw[PLfleche] (A13)--(A29) ;} + {\draw[PLfleche] (A13)--(A29) node[probas,PLetiquette,{\PLARBREDONNES[12,3]}] {{\PLARBREDONNES[12,2]}} ;} + }{} + \end{tikzpicture} +} + +\NewDocumentEnvironment{EnvArbreProbasTikz}{ O{} m }%1=options,2=libellés +{ + \useKVdefault[PLTIKZARBRE] + \setKV[PLTIKZARBRE]{#1} + \setsepchar[.]{,./}% + \readlist*\PLARBREDONNES{#2} + \begin{tikzpicture}[x=\PLAPunite,y=\PLAPunite] + %styles + \tikzstyle{noeud} = [font=\PLAPfont] + \tikzstyle{probas}= [font=\PLAPfontproba] + \ifboolKV[PLTIKZARBRE]{InclineProbas} + {\tikzstyle{PLetiquette}=[pos=0.525,sloped,fill=white]} + {\tikzstyle{PLetiquette}=[pos=0.525,fill=white]} + \ifboolKV[PLTIKZARBRE]{Fleche} + {\tikzstyle{PLfleche}=[->,>=latex,\PLAPtypetrait,\PLAPeptrait]} + {\tikzstyle{PLfleche}=[\PLAPtypetrait,\PLAPeptrait]} + %arbre2x2 + \IfEq{\PLAPtype}{2x2} + {% + \coordinate (R) at ({0*\PLAPespniv},{-1.5*\PLAPespfeuille}) ; + \node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]}; + \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]}; + \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]}; + \node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]}; + \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]}; + \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]}; + \ifstrempty{\PLARBREDONNES[1,2]} + {\draw[PLfleche] (R)--(A11) ;} + {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;} + \ifstrempty{\PLARBREDONNES[2,2]} + {\draw[PLfleche] (A11)--(A21) ;} + {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;} + \ifstrempty{\PLARBREDONNES[3,2]} + {\draw[PLfleche] (A11)--(A22) ;} + {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;} + \ifstrempty{\PLARBREDONNES[4,2]} + {\draw[PLfleche] (R)--(A12) ;} + {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;} + \ifstrempty{\PLARBREDONNES[5,2]} + {\draw[PLfleche] (A12)--(A23) ;} + {\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;} + \ifstrempty{\PLARBREDONNES[6,2]} + {\draw[PLfleche] (A12)--(A24) ;} + {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;} + }{} + %arbre3x2 + \IfEq{\PLAPtype}{3x2} + {% + %sommets + \coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ; + \node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]}; + \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]}; + \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]}; + \node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]}; + \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]}; + \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]}; + \node[noeud] (A13) at ({1*\PLAPespniv},{-4.5*\PLAPespfeuille}) {\PLARBREDONNES[7,1]}; + \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[8,1]}; + \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[9,1]}; + %branches + \ifstrempty{\PLARBREDONNES[1,2]} + {\draw[PLfleche] (R)--(A11) ;} + {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;} + \ifstrempty{\PLARBREDONNES[2,2]} + {\draw[PLfleche] (A11)--(A21) ;} + {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;} + \ifstrempty{\PLARBREDONNES[3,2]} + {\draw[PLfleche] (A11)--(A22) ;} + {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;} + \ifstrempty{\PLARBREDONNES[4,2]} + {\draw[PLfleche] (R)--(A12) ;} + {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;} + \ifstrempty{\PLARBREDONNES[5,2]} + {\draw[PLfleche] (A12)--(A23) ;} + {\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;} + \ifstrempty{\PLARBREDONNES[6,2]} + {\draw[PLfleche] (A12)--(A24) ;} + {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;} + \ifstrempty{\PLARBREDONNES[7,2]} + {\draw[PLfleche] (R)--(A13) ;} + {\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;} + \ifstrempty{\PLARBREDONNES[8,2]} + {\draw[PLfleche] (A13)--(A25) ;} + {\draw[PLfleche] (A13)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;} + \ifstrempty{\PLARBREDONNES[9,2]} + {\draw[PLfleche] (A13)--(A26) ;} + {\draw[PLfleche] (A13)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;} + }{} + %arbre2x3 + \IfEq{\PLAPtype}{2x3} + {% + %sommets + \coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ; + \node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]}; + \node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]}; + \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]}; + \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]}; + \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]}; + \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]}; + \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]}; + \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]}; + %branches + \ifstrempty{\PLARBREDONNES[1,2]} + {\draw[PLfleche] (R)--(A11) ;} + {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;} + \ifstrempty{\PLARBREDONNES[5,2]} + {\draw[PLfleche] (R)--(A12) ;} + {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;} + \ifstrempty{\PLARBREDONNES[2,2]} + {\draw[PLfleche] (A11)--(A21) ;} + {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;} + \ifstrempty{\PLARBREDONNES[3,2]} + {\draw[PLfleche] (A11)--(A22) ;} + {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;} + \ifstrempty{\PLARBREDONNES[4,2]} + {\draw[PLfleche] (A11)--(A23) ;} + {\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;} + \ifstrempty{\PLARBREDONNES[6,2]} + {\draw[PLfleche] (A12)--(A24) ;} + {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;} + \ifstrempty{\PLARBREDONNES[7,2]} + {\draw[PLfleche] (A12)--(A25) ;} + {\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;} + \ifstrempty{\PLARBREDONNES[8,2]} + {\draw[PLfleche] (A12)--(A26) ;} + {\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;} + }{} + %arbre2x3 + \IfEq{\PLAPtype}{3x3} + {% + %sommets + \coordinate (R) at ({0*\PLAPespniv},{-4*\PLAPespfeuille}) ; + \node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]}; + \node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]}; + \node[noeud] (A13) at ({1*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[9,1]}; + \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]}; + \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]}; + \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]}; + \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]}; + \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]}; + \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]}; + \node[noeud] (A27) at ({2*\PLAPespniv},{-6*\PLAPespfeuille}) {\PLARBREDONNES[10,1]}; + \node[noeud] (A28) at ({2*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[11,1]}; + \node[noeud] (A29) at ({2*\PLAPespniv},{-8*\PLAPespfeuille}) {\PLARBREDONNES[12,1]}; + %branches + \ifstrempty{\PLARBREDONNES[1,2]}{} + {\draw[PLfleche] (R)--(A11) ;} + {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;} + \ifstrempty{\PLARBREDONNES[5,2]}{} + {\draw[PLfleche] (R)--(A12) ;} + {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;} + \ifstrempty{\PLARBREDONNES[9,2]}{} + {\draw[PLfleche] (R)--(A13) ;} + {\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;} + %N2 + \ifstrempty{\PLARBREDONNES[2,2]} + {\draw[PLfleche] (A11)--(A21) ;} + {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;} + \ifstrempty{\PLARBREDONNES[3,2]} + {\draw[PLfleche] (A11)--(A22) ;} + {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;} + \ifstrempty{\PLARBREDONNES[4,2]} + {\draw[PLfleche] (A11)--(A23) ;} + {\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;} + \ifstrempty{\PLARBREDONNES[6,2]} + {\draw[PLfleche] (A12)--(A24) ;} + {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;} + \ifstrempty{\PLARBREDONNES[7,2]} + {\draw[PLfleche] (A12)--(A25) ;} + {\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;} + \ifstrempty{\PLARBREDONNES[8,2]} + {\draw[PLfleche] (A12)--(A26) ;} + {\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;} + \ifstrempty{\PLARBREDONNES[10,2]} + {\draw[PLfleche] (A13)--(A27) ;} + {\draw[PLfleche] (A13)--(A27) node[probas,PLetiquette,{\PLARBREDONNES[10,3]}] {{\PLARBREDONNES[10,2]}} ;} + \ifstrempty{\PLARBREDONNES[11,2]} + {\draw[PLfleche] (A13)--(A28) ;} + {\draw[PLfleche] (A13)--(A28) node[probas,PLetiquette,{\PLARBREDONNES[11,3]}] {{\PLARBREDONNES[11,2]}} ;} + \ifstrempty{\PLARBREDONNES[12,2]} + {\draw[PLfleche] (A13)--(A29) ;} + {\draw[PLfleche] (A13)--(A29) node[probas,PLetiquette,{\PLARBREDONNES[12,3]}] {{\PLARBREDONNES[12,2]}} ;} + }{} + } + { + \end{tikzpicture} +} + +%%------SCHEMASPROBAS +%densites utiles +\def\densnorm#1{1/(sqrt(2*pi))*exp(-0.5*(#1*#1))} +\def\densexpo#1{exp(-#1)} + +\defKV[GRPHPROBCONTINUES]{% + CouleurAire=\def\GRPHPROBcoulsurf{#1},% + CouleurCourbe=\def\GRPHPROBcoulcbe{#1},% + Largeur=\def\GRPHPROBlarg{#1},% + Hauteur=\def\GRPHPROBhauteur{#1} +} + +\setKVdefault[GRPHPROBCONTINUES]{% + CouleurAire=LightGray,% + CouleurCourbe=red,% + Largeur=2,% + Hauteur=1,% + AfficheM=true,% + AfficheCadre=true +} + +\NewDocumentCommand\LoiNormaleGraphe{ O{} D<>{} m m m m }{%1=options,2=optionstikz,3=m,4=s,5=a,6=b + %simplekv + \useKVdefault[GRPHPROBCONTINUES]% + \setKV[GRPHPROBCONTINUES]{#1}% + %unites + \def\UNITEX{\fpeval{\GRPHPROBlarg/8}}\def\UNITEY{\fpeval{\GRPHPROBhauteur/0.5}}% + %bornes + \def\BorneInf{\fpeval{(#5-#3)/#4}}\def\BorneSup{\fpeval{(#6-#3)/#4}}% + \ifthenelse{\equal{#5}{*}}{\def\BorneInf{-4}}{}% + \ifthenelse{\equal{#6}{*}}{\def\BorneSup{4}}{}% + %tikzpicture + \begin{tikzpicture}[x=\UNITEX cm,y=\UNITEY cm,#2] + \ifboolKV[GRPHPROBCONTINUES]{AfficheM}% + {\draw (0,-0.0375) node[font=\tiny,scale={2*\UNITEX}] {#3} ;} + {} + \ifboolKV[GRPHPROBCONTINUES]{AfficheCadre}% + {\draw[Gray] (-4,-0.075) rectangle (4,0.425) ;} + {} + \clip (-4,-0.075) rectangle (4,0.425) ; + \draw[black,semithick,fill=\GRPHPROBcoulsurf] ({\BorneInf},0) -- plot [domain={\BorneInf}:{\BorneSup},samples=100] (\x,{\densnorm{\x}}) -- ({\BorneSup},0) -- cycle; + \draw[thick,->,>=latex] (-4,0)--(4,0) ; + \draw[thick,densely dotted] (0,0)--(0,0.39894) ; + \draw[thick,domain=-4:4,samples=100,\GRPHPROBcoulcbe] plot (\x,{\densnorm{\x}}) ; + \end{tikzpicture} +} + +\NewDocumentCommand\LoiExpoGraphe{ O{} D<>{} m m m }{%1=options,2=optionstikz,3=l,4=a,5=b + %simplekv + \useKVdefault[GRPHPROBCONTINUES]% + \setKV[GRPHPROBCONTINUES]{#1}% + %unites + \def\UNITEX{\fpeval{\GRPHPROBlarg/4}}\def\UNITEY{\fpeval{\GRPHPROBhauteur/1}}% + \def\MOYENNE{\fpeval{trunc(1/#3,0)}}% + %bornes + \def\BorneInf{\fpeval{#3*#4}}\def\BorneSup{\fpeval{#3*#5}}% + \ifthenelse{\equal{#4}{*}}{\def\BorneInf{0}}{}% + \ifthenelse{\equal{#5}{*}}{\def\BorneSup{4}}{}% + %tikzpicture + \begin{tikzpicture}[x=\UNITEX cm,y=\UNITEY cm,#2] + \ifboolKV[GRPHPROBCONTINUES]{AfficheCadre}% + {\draw[Gray] (-0.2,-0.15) rectangle (3.8,0.85) ;} + {} + \clip (-0.2,-0.15) rectangle (3.8,0.85) ; + \draw[black,semithick,fill=\GRPHPROBcoulsurf] ({\BorneInf},0) -- plot [domain={\BorneInf}:{\BorneSup},samples=100] (\x,{0.7*\densexpo{\x}}) -- ({\BorneSup},0) -- cycle; + \ifboolKV[GRPHPROBCONTINUES]{AfficheM}% + {\draw (1,-0.075) node[font=\tiny,scale={\UNITEX}] {\MOYENNE} ; + \draw[thick,densely dotted] (1,0)--(1,{0.7*\densexpo{1}}) ;} + {} + \draw[thick,->,>=latex] (-0.2,0)--(3.8,0) ; + \draw[thick,->,>=latex] (0,-0.15)--(0,0.85) ; + \draw[thick,domain=0:3.8,samples=100,\GRPHPROBcoulcbe] plot (\x,{0.7*\densexpo{\x}}) ; + \end{tikzpicture} +} + +%%------aNp/Cnp +\NewDocumentCommand\CalculAnp{ m m }{%avec et pour xint, p/n + pfactorial(#2-#1,#2) +} + +\NewDocumentCommand\CalculCnp{ m m }{%avec et pour xint, p/n + binomial(#2,#1) +} + +\setKVdefault[anpCnp]{% + Formule=false,% + Notation=false,% + NotationAncien=false +} +\NewDocumentCommand\Arrangement{ s O{} m m }{%p/n + \useKVdefault[anpCnp]% + \setKV[anpCnp]{#2}% + \ifboolKV[anpCnp]{Notation}{A_{#4}^{#3}=}{}% + \ifboolKV[anpCnp]{Formule}{\frac{#4!}{\inteval{#4-#3}!}=}{}% + \IfBooleanTF{#1}% + {\xinteval{\CalculAnp{#3}{#4}}}%non formaté + {\num{\xinteval{\CalculAnp{#3}{#4}}}}%formaté +} +\NewDocumentCommand\Combinaison{ s O{} m m }{%p/n + \useKVdefault[anpCnp]% + \setKV[anpCnp]{#2}% + \ifboolKV[anpCnp]{Notation}{\binom{#4}{#3} =}{}% + \ifboolKV[anpCnp]{NotationAncien}{C_{#4}^{#3}=}{}% + \ifboolKV[anpCnp]{Formule}{\frac{#4!}{#3! \times \inteval{#4-#3}!}=}{}% + \IfBooleanTF{#1}% + {\xinteval{\CalculCnp{#3}{#4}}}%non formaté + {\num{\xinteval{\CalculCnp{#3}{#4}}}}%formaté +} + +\endinput
\ No newline at end of file |