ajout de l'intro a julia
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gergaud
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julia/notebook_Julia.pdf
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julia/notebook_Julia.pdf
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julia/scr-julia/.ipynb_checkpoints/intro-julia-checkpoint.ipynb
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julia/scr-julia/.ipynb_checkpoints/intro-julia-checkpoint.ipynb
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julia/scr-julia/.ipynb_checkpoints/ode-exemple-sol-checkpoint.ipynb
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julia/scr-julia/.ipynb_checkpoints/ode-exemple-sol-checkpoint.ipynb
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julia/scr-julia/cmd.jl
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julia/scr-julia/cmd.jl
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println(ARGS)
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julia/scr-julia/intro-julia.ipynb
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julia/scr-julia/intro-julia.ipynb
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julia/scr-julia/ode-exemple-sol.ipynb
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julia/scr-julia/ode-exemple-sol.ipynb
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julia/scr-julia/prog1.jl
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julia/scr-julia/prog1.jl
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#!/Applications/Julia-1.4.app/Contents/Resources/julia/bin/julia
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function helloworld()
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println("Hello, World!") # Bye bye, MATLAB!
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end
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helloworld()
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@ -7,8 +7,8 @@
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"<center>\n",
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"<h1> TP-Projet d'optimisation numérique </h1>\n",
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"<h1> Année 2020-2021 - 2e année département Sciences du Numérique </h1>\n",
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"<h1> Nom: </h1>\n",
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"<h1> Prénom: </h1> \n",
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"<h1> Noms: </h1>\n",
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"<h1> Prénoms: </h1> \n",
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"</center>"
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]
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},
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@ -26,7 +26,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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@ -34,52 +34,26 @@
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"output_type": "stream",
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"text": [
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f2 au point initial [0.0, 0.0050000000010000005]:\u001b[22m\u001b[39m\n",
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" * xsol = [0.0, 0.0]\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f0 au point initial -1.5707963267948966:\u001b[22m\u001b[39m\n",
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" * xsol = [0.0]\n",
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" * f(xsol) = 0\n",
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" * nb_iters = 0\n",
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" * flag = 0\n",
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" * sol_exacte : [1, 1]\n",
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"hess_f2(xmin) = [2.0 -0.0; -0.0 200.0]\n",
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"cond(H) = 100.0\n",
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" * sol_exacte : -1.5707963267948966\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f2 au point initial [0.0, 0.0050000000010000005]:\u001b[22m\u001b[39m\n",
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" * xsol = [0.0, 0.0]\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f0 au point initial -1.0707963267948966:\u001b[22m\u001b[39m\n",
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" * xsol = [0.0]\n",
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" * f(xsol) = 0\n",
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" * nb_iters = 0\n",
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" * flag = 0\n",
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" * sol_exacte : [1, 1]\n",
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"hess_f2(xmin) = [2.0 -0.0; -0.0 200.0]\n",
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"cond(H) = 100.0\n",
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" * sol_exacte : -1.5707963267948966\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f2 au point initial [0.0, 0.0050000000010000005]:\u001b[22m\u001b[39m\n",
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" * xsol = [0.0, 0.0]\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f0 au point initial 1.5707963267948966:\u001b[22m\u001b[39m\n",
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" * xsol = [0.0]\n",
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" * f(xsol) = 0\n",
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" * nb_iters = 0\n",
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" * flag = 0\n",
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" * sol_exacte : [1, 1]\n",
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"hess_f2(xmin) = [2.0 -0.0; -0.0 200.0]\n",
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"cond(H) = 100.0\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f2 au point initial [0.0, 0.0050000000010000005]:\u001b[22m\u001b[39m\n",
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" * xsol = [0.0, 0.0]\n",
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" * f(xsol) = 0\n",
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" * nb_iters = 0\n",
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" * flag = 0\n",
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" * sol_exacte : [1, 1]\n",
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"hess_f2(xmin) = [2.0 -0.0; -0.0 200.0]\n",
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"cond(H) = 100.0\n",
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"-------------------------------------------------------------------------\n",
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"\u001b[34m\u001b[1mRésultats de : Newton appliqué à f2 au point initial [0.0, 0.0050000000010000005]:\u001b[22m\u001b[39m\n",
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" * xsol = [0.0, 0.0]\n",
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" * f(xsol) = 0\n",
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" * nb_iters = 0\n",
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" * flag = 0\n",
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" * sol_exacte : [1, 1]\n",
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"hess_f2(xmin) = [2.0 -0.0; -0.0 200.0]\n",
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"cond(H) = 100.0\n",
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"[-2.0, 1.0000000002]\n",
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"[-4.000000330961484e-10 -0.0; -0.0 200.0]\n"
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" * sol_exacte : -1.5707963267948966\n"
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]
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}
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],
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@ -111,56 +85,17 @@
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"# la hessienne de la fonction f0\n",
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"hess_f0(x) = -sin(x)\n",
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"sol_exacte = -pi/2\n",
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"x0 = -pi/2+0.5\n",
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"options = []\n",
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"xmin,f_min,flag,nb_iters = Algorithme_De_Newton(f0,grad_f0,hess_f0,x0,options)\n",
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"#my_afficher_resultats(\"Newton\",\"f0\",x0,xmin,f_min,flag,sol_exacte,nb_iters)\n",
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"\n",
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"# Fonction f1\n",
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"# -----------\n",
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"f1(x) = 2*(x[1]+x[2]+x[3]-3)^2 + (x[1]-x[2])^2 + (x[2]-x[3])^2\n",
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"# la gradient de la fonction fct1\n",
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"function grad_f1(x)\n",
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" y1 = 4*(x[1]+x[2]+x[3]-3) + 2*(x[1]-x[2])\n",
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" y2 = 4*(x[1]+x[2]+x[3]-3) - 2*(x[1]-x[2]) +2*(x[2]-x[3])\n",
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" y3 = 4*(x[1]+x[2]+x[3]-3) - 2*(x[2]-x[3])\n",
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" return [y1;y2;y3]\n",
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"end\n",
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"# la hessienne de la fonction fct1\n",
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"hess_f1(x) = [6 2 4;2 8 2;4 2 6]\n",
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"sol_exacte = [1;1;1]\n",
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"options = []\n",
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"x0 = [1; 0; 0]\n",
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"xmin,f_min,flag,nb_iters = Algorithme_De_Newton(f1,grad_f1,hess_f1,x0,options)\n",
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"#my_afficher_resultats(\"Newton\",\"f1\",x0,xmin,f_min,flag,sol_exacte,nb_iters)\n",
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"x0 = [10; 3; -2.2]\n",
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"xmin,f_min,flag,nb_iters = Algorithme_De_Newton(f1,grad_f1,hess_f1,x0,options)\n",
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"#my_afficher_resultats(\"Newton\",\"f1\",x0,xmin,f_min,flag,sol_exacte,nb_iters)\n",
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"\n",
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"f2(x)=100*(x[2]-x[1]^2)^2+(1-x[1])^2\n",
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"grad_f2(x)=[-400*x[1]*(x[2]-x[1]^2)-2*(1-x[1]) ; 200*(x[2]-x[1]^2)]\n",
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"hess_f2(x)=[-400*(x[2]-3*x[1]^2)+2 -400*x[1];-400*x[1] 200]\n",
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"sol_exacte = [1;1]\n",
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"options = []\n",
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"x0 = [-1.2; 1]\n",
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"x0 = sol_exacte\n",
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"xmin,f_min,flag,nb_iters = Algorithme_De_Newton(f2,grad_f2,hess_f2,x0,options)\n",
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"#my_afficher_resultats(\"Newton\",\"f2\",x0,xmin,f_min,flag,sol_exacte,nb_iters)\n",
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"x0 = [10.; 0]\n",
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"xmin,f_min,flag,nb_iters = Algorithme_De_Newton(f2,grad_f2,hess_f2,x0,options)\n",
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"#my_afficher_resultats(\"Newton\",\"f2\",x0,xmin,f_min,flag,sol_exacte,nb_iters)\n",
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"x0 = [0 ; 1/200+1/1.e12]\n",
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"options = [1 ; sqrt(eps()) ; 1e-15]\n",
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"for i in 1:5\n",
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" options[1] = i\n",
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" xmin,f_min,flag,nb_iters = Algorithme_De_Newton(f2,grad_f2,hess_f2,x0,options)\n",
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" my_afficher_resultats(\"Newton\",\"f2\",x0,xmin,f_min,flag,sol_exacte,nb_iters)\n",
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" H = hess_f2(xmin)\n",
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" println(\"hess_f2(xmin) = \",H)\n",
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" println(\"cond(H) = \", cond(H))\n",
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"end\n",
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"println(grad_f2(x0))\n",
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"println(hess_f2(x0))"
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"xmin,f_min,flag,nb_iters = Algorithme_De_Newton(f0,grad_f0,hess_f0,x0,options)\n",
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"my_afficher_resultats(\"Newton\",\"f0\",x0,xmin,f_min,flag,sol_exacte,nb_iters)\n",
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"x0 = -pi/2+0.5\n",
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"xmin,f_min,flag,nb_iters = Algorithme_De_Newton(f0,grad_f0,hess_f0,x0,options)\n",
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"my_afficher_resultats(\"Newton\",\"f0\",x0,xmin,f_min,flag,sol_exacte,nb_iters)\n",
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"x0 = pi/2\n",
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"xmin,f_min,flag,nb_iters = Algorithme_De_Newton(f0,grad_f0,hess_f0,x0,options)\n",
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"my_afficher_resultats(\"Newton\",\"f0\",x0,xmin,f_min,flag,sol_exacte,nb_iters)"
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]
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},
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{
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