109 lines
2.8 KiB
Julia
109 lines
2.8 KiB
Julia
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"""
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Ce fichier contient toutes fonctions utilisés dans les tests des algorithmes :
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- L'algorithme de Newton
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- Les régions de confiance
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- Le Lagrangien augmenté
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"""
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# Les points initiaux
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# pour les problèmes sans contraintes
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struct Pts_sans_contraintes
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x011
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x012
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x021
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x022
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x023
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end
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x011 = [1; 0; 0]
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x012 = [10; 3; -2.2]
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x021 = [-1.2; 1]
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x022 = [10; 0]
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x023 = [0; 1/200 + 1/10^12]
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# les points initiaux utilisés dans les problèmes sans contraintes
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pts1 = Pts_sans_contraintes(x011,x012,x021,x022,x023)
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# pour les problèmes avec contraintes
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struct Pts_avec_contraintes
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x01
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x02
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x03
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x04
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end
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x01 = [0; 1; 1]
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x02 = [0.5; 1.25; 1]
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x03 = [1; 0]
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x04 = [sqrt(3)/2 ;sqrt(3)/2]
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pts2 = Pts_avec_contraintes(x01,x02,x03,x04)
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# Les solutions exactes
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# sol_exacte_fct1 = -hess_fct1(x011)\grad_fct1(zero(similar(x011)))
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sol_exacte_fct1 = [1;1;1]
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sol_exacte_fct2 = [1;1]
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"""
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La première fonction de test
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# Expression
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fct1(x) = 2*(x[1]+x[2]+x[3]-3)^2 + (x[1]-x[2])^2 + (x[2]-x[3])^2
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"""
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fct1(x) = 2*(x[1]+x[2]+x[3]-3)^2 + (x[1]-x[2])^2 + (x[2]-x[3])^2
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# la gradient de la fonction fct1
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function grad_fct1(x)
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y1 = 4*(x[1]+x[2]+x[3]-3) + 2*(x[1]-x[2])
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y2 = 4*(x[1]+x[2]+x[3]-3) - 2*(x[1]-x[2]) +2*(x[2]-x[3])
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y3 = 4*(x[1]+x[2]+x[3]-3) - 2*(x[2]-x[3])
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return [y1;y2;y3]
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end
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# la hessienne de la fonction fct1
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hess_fct1(x) = [6 2 4;2 8 2;4 2 6]
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"""
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La première fonction de test
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# Expression
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fct2(x)=100*(x[2]-x[1]^2)^2+(1-x[1])^2
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"""
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fct2(x)=100*(x[2]-x[1]^2)^2+(1-x[1])^2
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# la gradient de la fonction fct2
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grad_fct2(x)=[-400*x[1]*(x[2]-x[1]^2)-2*(1-x[1]) ; 200*(x[2]-x[1]^2)]
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#la hessienne de la fonction fct2
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hess_fct2(x)=[-400*(x[2]-3*x[1]^2)+2 -400*x[1];-400*x[1] 200]
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# Pour les problèmes avec contraintes
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# solutions
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sol_fct1_augm = [0.5 ; 1.25 ; 0.5]
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sol_fct2_augm = [0.9072339605110892; 0.82275545631455]
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"""
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La première contrainte
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# Expression
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contrainte1(x) = x[1]+x[3]-1
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"""
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contrainte1(x) = x[1]+x[3]-1
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grad_contrainte1(x) = [1 ;0; 1]
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hess_contrainte1(x) = [0 0 0;0 0 0;0 0 0]
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"""
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La deuxième contrainte
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# Expression
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contrainte2(x) = (x[1]^2) + (x[2]^2) -1.5
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"""
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contrainte2(x) = (x[1]^2) + (x[2]^2) -1.5
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grad_contrainte2(x) = [2*x[1] ;2*x[2]]
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hess_contrainte2(x) = [2 0;0 2]
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# Affichage les sorties de l'algorithme des Régions de confiance
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function afficher_resultats(algo,nom_fct,point_init,xmin,fxmin,flag,sol_exacte,nbiters)
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println("-------------------------------------------------------------------------")
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printstyled("Résultats de : "*algo*" appliqué à "*nom_fct*" au point initial "*point_init*" :\n",bold=true,color=:blue)
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println(" * xsol = ",xmin)
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println(" * f(xsol) = ",fxmin)
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println(" * nb_iters = ",nbiters)
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println(" * flag = ",flag)
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println(" * sol_exacte : ", sol_exacte)
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end
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