TP_Reseau_Notebook_9.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Travaux pratiques sur les réseaux d'eau"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Données et fonctions du problème"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On charge dans l'environnement :\n",
    "1. les fonctions de Python qui seront utilisées,\n",
    "2. les données du problème,\n",
    "3. les fonctions utilitaires du problème."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import random\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Probleme_R import *\n",
    "from Structures_N import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Visualg import Visualg\n",
    "from Verification import Verification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  On charge les prototypes d'algorithmes d'optimisation :\n",
    "\n",
    "* **Gradient_F** : algorithme de gradient à pas fixe,\n",
    "* **Newton_F** : algorithme de Newton à pas fixe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Gradient_F(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "    \n",
    "    iter_max = 10000\n",
    "    gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "\n",
    "    critere_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "    \n",
    "    x = x0\n",
    "\n",
    "    ##### Boucle sur les iterations\n",
    "\n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        critere, gradient = Oracle(x)\n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "\n",
    "        # Direction de descente\n",
    "        direction = -gradient\n",
    "        \n",
    "        # Backracking Line search for step size\n",
    "        #gradient_step = BacktrackingLineSearch(x,critere,gradient,direction)\n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "\n",
    "        \n",
    "        critere_list.append(critere)\n",
    "    \n",
    "    ##### Resultats de l'optimisation\n",
    "\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "    \n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "\n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt, gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Newton_F(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy.linalg import norm\n",
    "    from numpy.linalg import solve\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables    \n",
    "    \n",
    "    iter_max = 100\n",
    "    gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    critere_list = []\n",
    "\n",
    "    time_start = process_time()\n",
    "    \n",
    "    x = x0\n",
    "\n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        critere, gradient, hessien = Oracle(x)\n",
    "\n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "        \n",
    "        # Direction de descente\n",
    "        direction = - solve(hessien, gradient)\n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "        critere_list.append(critere)\n",
    "   \n",
    "    ##### Resultats de l'optimisation\n",
    "    \n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "    \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I. Résolution du problème primal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from HydrauliqueP import HydrauliqueP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.a On écrit les oracles pour le problème primal d'optimisation :\n",
    "\n",
    "* **OraclePG** : calcul de la fonction et du gradient,\n",
    "* **OraclePH** : calcul de la fonction du gradient et du Hessien."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ q=q^{(0)}+B q_{c} $  \n",
    "  \n",
    "$ z=r \\bullet q \\bullet|q| $\n",
    "  \n",
    "$ \\nabla F\\left(q_{C}\\right)=B^{\\top}(r \\bullet q \\bullet|q|)+B^{\\top} A_{r}^{\\top} p_{r} $  \n",
    "\n",
    "$ F\\left(q_{C}\\right) = \\frac{1}{3}\\langle q, r \\bullet q \\bullet|q|\\rangle+\\left\\langle p_{r}, A_{r} q\\right\\rangle $\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OraclePG(qc):\n",
    "    \n",
    "    gradient =B.transpose()@(r*(q0+B@qc)*abs(q0+B@qc))+B.transpose()@Ar.transpose()@pr\n",
    "    critere = dot(q0+B@qc, r*(q0+B@qc)*abs(q0+B@qc))/3 + dot(pr, Ar@(q0+B@qc))\n",
    "    \n",
    "    return critere, gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\nabla^{2} F\\left(q_{c}\\right)=2B^{T} \\operatorname{diag}(\\mathrm{r} \\cdot|q| ) \\mathrm{B} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OraclePH(qc):\n",
    "    q = q0 + B@qc \n",
    "    M =2 * np.diag(r * abs(q))\n",
    "    temp = B.T.dot(M)\n",
    "    hessien = temp.dot(B)\n",
    "    critere, gradient= OraclePG(qc)\n",
    "    # ---> A COMPLETER\n",
    "    # ---> A COMPLETER\n",
    "    \n",
    "    return critere, gradient, hessien"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On teste la validité des oracles en résolvant le problème :\n",
    "\n",
    "* **OraclePG** avec la méthode du gradient à pas fixe,\n",
    "* **OraclePH** avec la méthode de Newton à pas fixe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT A PAS FIXE\n",
      "\n",
      "Iteration : 4153\n",
      "Temps CPU : 0.203125\n",
      "Critere optimal : -3.734007048043509\n",
      "Norme du gradient : 9.972572575530274e-07\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 1.1102230246251565e-16\n",
      "Sur les pressions : 9.97252397216819e-07\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT A PAS FIXE\")\n",
    "copt, gopt, xopt,gnl_GF, gsl_GF, cl_GF = Gradient_F(OraclePG, x0, 0.0005)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Input variables  \n",
    "  1. $ gradient \\ list$: array containing the norm of the gradient  of the criterion at each iteration of the optimization algorithm.  \n",
    "  2. $ step \\ list $: array containing the length of the gradient step at each iteration.\n",
    "  3. $ criterere \\ list$: array containing the value of the criterion "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DE NEWTON A PAS FIXE\n",
      "\n",
      "Iteration : 6\n",
      "Temps CPU : 0.0\n",
      "Critere optimal : -3.7340070480435745\n",
      "Norme du gradient : 3.5901372117748724e-11\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 2.220446049250313e-16\n",
      "Sur les pressions : 2.092482784266103e-11\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE NEWTON A PAS FIXE\")\n",
    "copt, gopt, xopt,gnl_NF, gsl_NF, cl_NF  = Newton_F(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient descending algorithm with optimal stepsize by exact line search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exact line search  \n",
    "$$ t=\\operatorname{argmin}_{s \\geq 0} f(x+s \\Delta x) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import line_search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def F(x):\n",
    "    #print(\"in F\",x)\n",
    "    return dot(q0+B@x, r*(q0+B@x)*abs(q0+B@x))/3 + dot(pr, Ar@(q0+B@x))\n",
    "\n",
    "def G(x):\n",
    "    #print(\"in G\",x)\n",
    "    return B.transpose()@(r*(q0+B@x)*abs(q0+B@x))+B.transpose()@Ar.transpose()@pr\n",
    "def Exact_line_earch(F,G,x0,direction):\n",
    "    #print(F)\n",
    "    #print(G)\n",
    "    #critere = dot(q0+B@qc, r*(q0+B@qc)*abs(q0+B@qc))/3 + dot(pr, Ar@(q0+B@qc))\n",
    "    #gradient = B.transpose()@(r*(q0+B@qc)*abs(q0+B@qc))+B.transpose()@Ar.transpose()@pr\n",
    "    start_point = x0\n",
    "    search_direction = direction\n",
    "    #print(x0)\n",
    "    #print(x0.shape)\n",
    "    #print(gradient)\n",
    "    #print(gradient.shape)\n",
    "    res = line_search(F, G, start_point,  search_direction, maxiter = 10 )\n",
    "    return res\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Gradient_L(F,G,Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "    \n",
    "    iter_max = 10000\n",
    "    gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "\n",
    "    critere_list = []\n",
    "    x_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "    \n",
    "    x = x0\n",
    "\n",
    "    ##### Boucle sur les iterations\n",
    "\n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        critere, gradient = Oracle(x)\n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "\n",
    "        # Direction de descente\n",
    "        direction = -gradient\n",
    "        \n",
    "        # Exact Line search for step size\n",
    "        if k > 0:\n",
    "            res = Exact_line_earch(F,G,x,direction)\n",
    "            \n",
    "            #print(res)\n",
    "            if res[0] is not None:\n",
    "                gradient_step = res[0]\n",
    "                \n",
    "                \n",
    "            else:\n",
    "                gradient_step  =  gradient_step_list[-1]\n",
    "                #print(k)\n",
    "                #print(gradient_step)\n",
    "                \n",
    "        #gradient_step = BacktrackingLineSearch(x,critere,gradient,direction)\n",
    "        #print()\n",
    "        # Mise a jour des variables\n",
    "        x_list.append(x)\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "\n",
    "        \n",
    "        critere_list.append(critere)\n",
    "    \n",
    "    ##### Resultats de l'optimisation\n",
    "\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "    \n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "\n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt, gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT A PAS OPT\n",
      "\n",
      "Iteration : 1156\n",
      "Temps CPU : 0.5625\n",
      "Critere optimal : -3.7340070480435177\n",
      "Norme du gradient : 9.001106101064337e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 5.551115123125783e-17\n",
      "Sur les pressions : 8.99114135921586e-07\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT A PAS OPT\")\n",
    "copt, gopt, xopt,gnl_GF, gsl_GF, cl_GF = Gradient_L(F,G,OraclePG, x0, 0.0005)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient descending algorithm with optimal stepsize by Wolf algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Notation   \n",
    "$ x^{k}$  \n",
    "$g^{k}$ : $ \\nabla f(x) $  \n",
    "$ d^{k}$ : $ \\Delta x^{k} $  \n",
    "$ \\alpha^{(k)} $: $t^{k}$\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- condition  \n",
    "$$ f\\left(x^{(k)}+\\alpha^{(k)} d^{(k)}\\right) \\leq f\\left(x^{(k)}\\right)+\\omega_{1} \\alpha^{(k)} g^{(k)^{\\top}} d^{(k)} $$  \n",
    "$ \\Leftrightarrow $  \n",
    "$$ f(x^{k}+t^{k} \\Delta x^{k})>f(x^{k})+ t^{k} \\nabla f(x^{k})^{T} \\Delta x^{k} $$  \n",
    "$$ \\left(\\nabla f\\left(x^{(k)}+\\alpha^{(k)} d^{(k)}\\right)\\right)^{\\top} d^{(k)} \\geq \\omega_{2} g^{(k)^{\\top}} d^{(k)} $$  \n",
    "where $ 0<\\omega_{1}<\\omega_{2}<1 $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Wolfe(alpha, x, D, Oracle):\n",
    "    \n",
    "    from numpy import dot\n",
    "    from numpy import inf\n",
    "    from numpy.linalg import norm\n",
    "\n",
    "    ##### Coefficients de la recherche lineaire\n",
    "    \n",
    "    omega_1 = 0.1\n",
    "    omega_2 = 0.9\n",
    "    \n",
    "    alpha_min = 0\n",
    "    alpha_max = inf\n",
    "    \n",
    "    ok = 0\n",
    "    dltx = 0.00000001\n",
    "\n",
    "    ##### Algorithme de Fletcher-Lemarechal\n",
    "    \n",
    "    # Appel de l'oracle au point initial\n",
    "    #print(Oracle)\n",
    "    res = Oracle(x)\n",
    "    critere = res[0]\n",
    "    gradient = res[1]\n",
    "    \n",
    "    # Initialisation de l'algorithme\n",
    "    alpha_n = alpha\n",
    "    xn = x\n",
    "    \n",
    "    # Boucle de calcul du pas\n",
    "    # xn represente le point pour la valeur courante du pas,\n",
    "    # xp represente le point pour la valeur precedente du pas.\n",
    "    while ok == 0:\n",
    "        \n",
    "        # Point precedent pour tester l'indistinguabilite\n",
    "        xp = xn\n",
    "        \n",
    "        # Point actuel\n",
    "        xn = x + alpha_n*D\n",
    "        #print(\"xn: \",xn)\n",
    "        \n",
    "        # Calculation of Wolfe conditions\n",
    "        \n",
    "        # f(x^k+t^k d^k) gradient_f(x^k+t^k d^k)\n",
    "        \n",
    "        res_n = Oracle(xn)\n",
    "        critere_n = res_n[0]\n",
    "        gradient_n = res_n[1]\n",
    "        \n",
    "        #print(\"critere_n\",critere_n)\n",
    "        #print(\"gradient_n\",gradient_n)\n",
    "        # condition 1\n",
    "        condition1 = (critere_n <= critere+omega_1*alpha_n*gradient.transpose()@D)\n",
    "        \n",
    "        # condition 2\n",
    "        #print(critere_n.transpose())\n",
    "        #print(D)\n",
    "        condition2 = (gradient_n.transpose()@D >= omega_2*gradient.transpose()@D)\n",
    "        \n",
    "        # ---> To be completed ...\n",
    "        # ---> To be completed ...\n",
    "        \n",
    "        # Test of Wolfe conditions\n",
    "        #\n",
    "        # - If both Wolfe conditions are true,\n",
    "        # set ok = 1: we then exit the while loop\n",
    "        if condition1 and condition2:\n",
    "            \n",
    "            ok = 1\n",
    "            \n",
    "        \n",
    "        # - Otherwise, modify the value of alphan and loop back\n",
    "        else:\n",
    "            if not condition1:\n",
    "                alpha_max = alpha_n\n",
    "                alpha_n = 1/2 * (alpha_min+alpha_max)\n",
    "            if not condition2:\n",
    "                alpha_min = alpha_n\n",
    "                if alpha_max == inf:\n",
    "                    alpha_n = 2*alpha_min\n",
    "                else:\n",
    "                    alpha_n = 1/2 * (alpha_min+alpha_max)\n",
    "        \n",
    "            \n",
    "            \n",
    "        # ---> To be completed ...\n",
    "        # ---> To be completed ...\n",
    "        \n",
    "        # Test d'indistinguabilite\n",
    "        if norm(xn - xp) < dltx:\n",
    "            ok = 2\n",
    "\n",
    "    return alpha_n, ok"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Gradient_V(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "\n",
    "    iter_max = 1000\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    critere_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "\n",
    "    x = x0\n",
    "\n",
    "    ##### Boucle sur les iterations\n",
    "\n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        # ---> A COMPLETER\n",
    "        # ---> A COMPLETER\n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        critere, gradient = Oracle(x)\n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "\n",
    "        # Direction de descente\n",
    "        direction = -gradient\n",
    "        \n",
    "        # conditions de Wolfe for step size\n",
    "        res = Wolfe(default_gradient_step, x, direction, Oracle)\n",
    "        gradient_step = res[0]\n",
    "        #print(\"gradient_n\",gradient_step)\n",
    "        # Mise a jour des variables\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "\n",
    "        \n",
    "        critere_list.append(critere)\n",
    "    ##### Resultats de l'optimisation\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "    \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT A PAS VARIABLE\n",
      "\n",
      "Iteration : 305\n",
      "Temps CPU : 0.21875\n",
      "Critere optimal : -3.734007048043516\n",
      "Norme du gradient : 8.824249639753445e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 1.5265566588595902e-16\n",
      "Sur les pressions : 8.643453458523354e-07\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT A PAS VARIABLE\")\n",
    "copt, gopt, xopt,gnl_GV, gsl_GV, cl_GV = Gradient_V(OraclePG, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conjugation gradient descending algorithm with fixed stepsize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ d^{(k)}=\\left\\{\\begin{array}{ll}-g^{(1)} & \\text { si } k=1 \\\\ -g^{(k)}+\\beta^{(k)} d^{(k-1)} & \\text { sinon }\\end{array}\\right. $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\beta^{(k)}=\\frac{g^{(k)^{\\top}}\\left(g^{(k)}-g^{(k-1)}\\right)}{\\| g^{(k-1) \\|^{2}}} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PolakRibiere(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy import dot\n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "\n",
    "    iter_max = 10000\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    gradient_list = []\n",
    "    critere_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "\n",
    "    x = x0\n",
    "    \n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        critere, gradient = Oracle(x)\n",
    "        \n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "        \n",
    "        # Formule de Polak-Ribi`ere for Direction de descente\n",
    "        if k == 0:\n",
    "            direction = -gradient\n",
    "        else:\n",
    "            #print(\"k:\", k)\n",
    "            #print(\"gradient_list: \",gradient_list)\n",
    "            #print(\"gradient_norm_list:\",gradient_norm_list)\n",
    "            beta = gradient.transpose()@(gradient - gradient_list[-1])/(gradient_norm_list[-1] * gradient_norm_list[-1])\n",
    "            direction = -gradient + beta*direction\n",
    "\n",
    "        # conditions de Wolfe for step size\n",
    "        #res = Wolfe(default_gradient_step, x, direction, Oracle)\n",
    "        #gradient_step = res[0]\n",
    "        gradient_step =  default_gradient_step\n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "        gradient_list.append(gradient)\n",
    "\n",
    "        \n",
    "        critere_list.append(critere)\n",
    "    \n",
    "    # Resultat de l'optimisation\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "        \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT CONJUGUE\n",
      "\n",
      "Iteration : 3934\n",
      "Temps CPU : 0.234375\n",
      "Critere optimal : -3.7340070480435035\n",
      "Norme du gradient : 9.999390940892962e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 1.942890293094024e-16\n",
      "Sur les pressions : 9.99933886913773e-07\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT CONJUGUE\")\n",
    "copt, gopt, xopt,gnl_GC, gsl_GC, cl_GC = PolakRibiere(OraclePG, x0, 0.0005)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conjugation gradient descending algorithm with optimal stepsize by Wolf algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PolakRibiereV(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy import dot\n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "\n",
    "    iter_max = 1000\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    gradient_list = []\n",
    "    critere_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "\n",
    "    x = x0\n",
    "    \n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        critere, gradient = Oracle(x)\n",
    "        \n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "        \n",
    "        # Formule de Polak-Ribi`ere for Direction de descente\n",
    "        if k == 0:\n",
    "            direction = -gradient\n",
    "        else:\n",
    "            #print(\"k:\", k)\n",
    "            #print(\"gradient_list: \",gradient_list)\n",
    "            #print(\"gradient_norm_list:\",gradient_norm_list)\n",
    "            beta = gradient.transpose()@(gradient - gradient_list[-1])/(gradient_norm_list[-1] * gradient_norm_list[-1])\n",
    "            direction = -gradient + beta*direction\n",
    "\n",
    "        # conditions de Wolfe for step size\n",
    "        res = Wolfe(default_gradient_step, x, direction, Oracle)\n",
    "        gradient_step = res[0]\n",
    "        #gradient_step =  default_gradient_step\n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "        gradient_list.append(gradient)\n",
    "\n",
    "        \n",
    "        critere_list.append(critere)\n",
    "    \n",
    "    # Resultat de l'optimisation\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "        \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT CONJUGUE\n",
      "\n",
      "Iteration : 200\n",
      "Temps CPU : 0.125\n",
      "Critere optimal : -3.7340070480435497\n",
      "Norme du gradient : 8.034522796359891e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 1.1102230246251565e-16\n",
      "Sur les pressions : 5.184952871495341e-07\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT CONJUGUE\")\n",
    "copt, gopt, xopt,gnl_GC, gsl_GC, cl_GC = PolakRibiereV(OraclePG, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conjugation gradient descending algorithm with optimal stepsize by exact line search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PolakRibiereL(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy import dot\n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "\n",
    "    iter_max = 1000\n",
    "    gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    gradient_list = []\n",
    "    critere_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "\n",
    "    x = x0\n",
    "    \n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        critere, gradient = Oracle(x)\n",
    "        \n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "        \n",
    "        # Formule de Polak-Ribi`ere for Direction de descente\n",
    "        if k == 0:\n",
    "            direction = -gradient\n",
    "        else:\n",
    "            #print(\"k:\", k)\n",
    "            #print(\"gradient_list: \",gradient_list)\n",
    "            #print(\"gradient_norm_list:\",gradient_norm_list)\n",
    "            beta = gradient.transpose()@(gradient - gradient_list[-1])/(gradient_norm_list[-1] * gradient_norm_list[-1])\n",
    "            direction = -gradient + beta*direction\n",
    "\n",
    "        # conditions de Wolfe for step size\n",
    "        #res = Wolfe(default_gradient_step, x, direction, Oracle)\n",
    "        #gradient_step = res[0]\n",
    "        \n",
    "        # Exact Line search for step size\n",
    "        if k > 0:\n",
    "            res = Exact_line_earch(F,G,x,direction)\n",
    "            \n",
    "            #print(res)\n",
    "            if res[0] is not None:\n",
    "                gradient_step = res[0]\n",
    "                \n",
    "                \n",
    "            else:\n",
    "                gradient_step  =  gradient_step_list[-1]\n",
    "                print(k)\n",
    "                print(gradient_step)    \n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "        gradient_list.append(gradient)\n",
    "\n",
    "        \n",
    "        critere_list.append(critere)\n",
    "    \n",
    "    # Resultat de l'optimisation\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "        \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT CONJUGUE\n",
      "2\n",
      "0.0012360066446066337\n",
      "7\n",
      "0.001052321420485765\n",
      "8\n",
      "0.001052321420485765\n",
      "9\n",
      "0.001052321420485765\n",
      "10\n",
      "0.001052321420485765\n",
      "11\n",
      "0.001052321420485765\n",
      "12\n",
      "0.001052321420485765\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\linesearch.py:327: LineSearchWarning: The line search algorithm did not converge\n",
      "  warn('The line search algorithm did not converge', LineSearchWarning)\n",
      "<ipython-input-66-18bce864a96b>:43: RuntimeWarning: overflow encountered in matmul\n",
      "  beta = gradient.transpose()@(gradient - gradient_list[-1])/(gradient_norm_list[-1] * gradient_norm_list[-1])\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\linesearch.py:287: RuntimeWarning: invalid value encountered in multiply\n",
      "  return f(xk + alpha * pk, *args)\n",
      "<ipython-input-33-ad96acd04c62>:3: RuntimeWarning: invalid value encountered in matmul\n",
      "  return dot(q0+B@x, r*(q0+B@x)*abs(q0+B@x))/3 + dot(pr, Ar@(q0+B@x))\n",
      "<ipython-input-33-ad96acd04c62>:7: RuntimeWarning: invalid value encountered in matmul\n",
      "  return B.transpose()@(r*(q0+B@x)*abs(q0+B@x))+B.transpose()@Ar.transpose()@pr\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\linesearch.py:477: LineSearchWarning: The line search algorithm did not converge\n",
      "  warn('The line search algorithm did not converge', LineSearchWarning)\n",
      "<ipython-input-7-1052a0dc5e65>:4: RuntimeWarning: invalid value encountered in matmul\n",
      "  critere = dot(q0+B@qc, r*(q0+B@qc)*abs(q0+B@qc))/3 + dot(pr, Ar@(q0+B@qc))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Iteration : 999\n",
      "Temps CPU : 0.453125\n",
      "Critere optimal : nan\n",
      "Norme du gradient : nan\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : nan\n",
      "Sur les pressions : nan\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT CONJUGUE\")\n",
    "copt, gopt, xopt,gnl_GC, gsl_GC, cl_GC = PolakRibiereL(OraclePG, x0, 0.0005)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quasi Newton method with fixed stepsize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ d^{(k)}=-W^{(k)} g^{(k)} $  \n",
    "$ \\delta_{x}^{(k)}=x^{(k)}-x^{(k-1)} $  \n",
    "$ \\delta_{g}^{(k)}=g^{(k)}-g^{(k-1)} $  \n",
    "$ W^{(k)}=\\left(I-\\frac{\\delta_{x}^{(k)} \\delta_{g}^{(k)} \\top}{\\delta_{g}^{(k)^{\\top}} \\delta_{x}^{(k)}}\\right) W^{(k-1)}\\left(I-\\frac{\\delta_{g}^{(k)} \\delta_{x}^{(k)} \\top}{\\delta_{g}^{(k)^{\\top}} \\delta_{x}^{(k)}}\\right)+\\frac{\\left.\\delta_{x}^{(k)} \\delta_{x}^{(k)}\\right)^{\\top}}{\\delta_{g}^{(k)} \\delta_{x}^{(k)}} $  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BFGS(Oracle, x0, alpha0):\n",
    "    import numpy as np\n",
    "    from numpy.linalg import solve\n",
    "    from numpy import dot\n",
    "    from numpy import eye\n",
    "    from numpy import outer\n",
    "    from numpy import vdot\n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "\n",
    "    iter_max = 250\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    gradient_list = []\n",
    "    critere_list = []\n",
    "    x_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "\n",
    "    x = x0\n",
    "    I = eye(len(x0))\n",
    "    \n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        res = Oracle(x)\n",
    "        critere = res[0]\n",
    "        gradient = res[1]\n",
    "        #hessien = res[2]\n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "                # Valeur du critere et du gradient\n",
    "        \n",
    "        # Direction de descente\n",
    "        #direction_n = - solve(hessien, gradient)\n",
    "        #print(\"direction_n\",direction_n)\n",
    "        \n",
    "        # Formule de BFGS inverse for Direction de descente\n",
    "        #print(\"k:\",k)\n",
    "        if k == 0:\n",
    "            Wk = I \n",
    "            #print(\"Wk\",Wk)\n",
    "        else:\n",
    "            #print(\"gradient\",gradient)\n",
    "            #print(\"gradient_list[-1]\",gradient_list[-1])\n",
    "            delta_xk = np.array([list(x - x_list[-1])]).transpose()\n",
    "            delta_gk = np.array([list(gradient - gradient_list[-1])]).transpose()\n",
    "            \n",
    "            #print(\"delta_xk\",delta_xk)\n",
    "            #print(\"delta_gk\",delta_gk)\n",
    "            \n",
    "            #print(\"(delta_xk@delta_gk.transpose())\",(delta_xk@delta_gk.transpose()))\n",
    "            \n",
    "            A = I - np.multiply(delta_xk,delta_gk.transpose())/(delta_gk.transpose()@delta_xk)\n",
    "            B = I - np.multiply(delta_gk,delta_xk.transpose())/(delta_gk.transpose()@delta_xk)\n",
    "            C = (np.multiply(delta_xk,delta_xk.transpose()))/(delta_gk.transpose()@delta_xk)\n",
    "            #print(\"A:\",A)\n",
    "            #print(\"B:\",B)\n",
    "            #print(\"C:\",C)\n",
    "                        \n",
    "            Wk = A@Wk@B + C\n",
    "\n",
    "\n",
    "            #print(\"Wk\",Wk)\n",
    "            #print(\"Hessien\", hessien)\n",
    "        direction = -Wk@gradient\n",
    "        #print(\"direction\",direction)\n",
    "        \n",
    "        # Direction de descente\n",
    "        #direction = - solve(hessien, gradient)\n",
    "        \n",
    "        # conditions de Wolfe for step size\n",
    "        #res = Wolfe(default_gradient_step, x, direction, Oracle)\n",
    "        #gradient_step = res[0]\n",
    "        \n",
    "        gradient_step =  default_gradient_step\n",
    "\n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x_list.append(x)\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "        gradient_list.append(gradient)\n",
    "        critere_list.append(critere)\n",
    "    \n",
    "    # Resultat de l'optimisation\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "        \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DE QUASI-NEWTON\n",
      "\n",
      "Iteration : 249\n",
      "Temps CPU : 0.046875\n",
      "Critere optimal : nan\n",
      "Norme du gradient : nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-71-dff377ab0e14>:65: RuntimeWarning: overflow encountered in multiply\n",
      "  A = I - np.multiply(delta_xk,delta_gk.transpose())/(delta_gk.transpose()@delta_xk)\n",
      "<ipython-input-71-dff377ab0e14>:65: RuntimeWarning: overflow encountered in matmul\n",
      "  A = I - np.multiply(delta_xk,delta_gk.transpose())/(delta_gk.transpose()@delta_xk)\n",
      "<ipython-input-71-dff377ab0e14>:65: RuntimeWarning: invalid value encountered in matmul\n",
      "  A = I - np.multiply(delta_xk,delta_gk.transpose())/(delta_gk.transpose()@delta_xk)\n",
      "<ipython-input-71-dff377ab0e14>:66: RuntimeWarning: overflow encountered in multiply\n",
      "  B = I - np.multiply(delta_gk,delta_xk.transpose())/(delta_gk.transpose()@delta_xk)\n",
      "<ipython-input-71-dff377ab0e14>:66: RuntimeWarning: overflow encountered in matmul\n",
      "  B = I - np.multiply(delta_gk,delta_xk.transpose())/(delta_gk.transpose()@delta_xk)\n",
      "<ipython-input-71-dff377ab0e14>:66: RuntimeWarning: invalid value encountered in matmul\n",
      "  B = I - np.multiply(delta_gk,delta_xk.transpose())/(delta_gk.transpose()@delta_xk)\n",
      "<ipython-input-71-dff377ab0e14>:67: RuntimeWarning: overflow encountered in matmul\n",
      "  C = (np.multiply(delta_xk,delta_xk.transpose()))/(delta_gk.transpose()@delta_xk)\n",
      "<ipython-input-71-dff377ab0e14>:67: RuntimeWarning: invalid value encountered in matmul\n",
      "  C = (np.multiply(delta_xk,delta_xk.transpose()))/(delta_gk.transpose()@delta_xk)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : nan\n",
      "Sur les pressions : nan\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE QUASI-NEWTON\")\n",
    "copt, gopt, xopt,gnl_QN, gsl_QN, cl_QN = BFGS(OraclePG, x0, 1)\n",
    "#copt, gopt, xopt = Newton_N(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quasi Newton method with optimal stepsize by Wolf algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BFGS_V(Oracle, x0, alpha0):\n",
    "    import numpy as np\n",
    "    from numpy.linalg import solve\n",
    "    from numpy import dot\n",
    "    from numpy import eye\n",
    "    from numpy import outer\n",
    "    from numpy import vdot\n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "\n",
    "    iter_max = 250\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    gradient_list = []\n",
    "    critere_list = []\n",
    "    x_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "\n",
    "    x = x0\n",
    "    I = eye(len(x0))\n",
    "    \n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        res = Oracle(x)\n",
    "        critere = res[0]\n",
    "        gradient = res[1]\n",
    "        #hessien = res[2]\n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "                # Valeur du critere et du gradient\n",
    "        \n",
    "        # Direction de descente\n",
    "        #direction_n = - solve(hessien, gradient)\n",
    "        #print(\"direction_n\",direction_n)\n",
    "        \n",
    "        # Formule de BFGS inverse for Direction de descente\n",
    "        #print(\"k:\",k)\n",
    "        if k == 0:\n",
    "            Wk = I \n",
    "            #print(\"Wk\",Wk)\n",
    "        else:\n",
    "            #print(\"gradient\",gradient)\n",
    "            #print(\"gradient_list[-1]\",gradient_list[-1])\n",
    "            delta_xk = np.array([list(x - x_list[-1])]).transpose()\n",
    "            delta_gk = np.array([list(gradient - gradient_list[-1])]).transpose()\n",
    "            \n",
    "            #print(\"delta_xk\",delta_xk)\n",
    "            #print(\"delta_gk\",delta_gk)\n",
    "            \n",
    "            #print(\"(delta_xk@delta_gk.transpose())\",(delta_xk@delta_gk.transpose()))\n",
    "            \n",
    "            A = I - np.multiply(delta_xk,delta_gk.transpose())/(delta_gk.transpose()@delta_xk)\n",
    "            B = I - np.multiply(delta_gk,delta_xk.transpose())/(delta_gk.transpose()@delta_xk)\n",
    "            C = (np.multiply(delta_xk,delta_xk.transpose()))/(delta_gk.transpose()@delta_xk)\n",
    "            #print(\"A:\",A)\n",
    "            #print(\"B:\",B)\n",
    "            #print(\"C:\",C)\n",
    "                        \n",
    "            Wk = A@Wk@B + C\n",
    "\n",
    "\n",
    "            #print(\"Wk\",Wk)\n",
    "            #print(\"Hessien\", hessien)\n",
    "        direction = -Wk@gradient\n",
    "        #print(\"direction\",direction)\n",
    "        \n",
    "        # Direction de descente\n",
    "        #direction = - solve(hessien, gradient)\n",
    "        \n",
    "        # conditions de Wolfe for step size\n",
    "        res = Wolfe(default_gradient_step, x, direction, Oracle)\n",
    "        gradient_step = res[0]\n",
    "        \n",
    "        #gradient_step =  default_gradient_step\n",
    "\n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x_list.append(x)\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "        gradient_list.append(gradient)\n",
    "        critere_list.append(critere)\n",
    "    \n",
    "    # Resultat de l'optimisation\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "        \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DE QUASI-NEWTON\n",
      "\n",
      "Iteration : 20\n",
      "Temps CPU : 0.0\n",
      "Critere optimal : -3.734007048043578\n",
      "Norme du gradient : 1.0471479076221681e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 1.8041124150158794e-16\n",
      "Sur les pressions : 8.926470584924573e-08\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE QUASI-NEWTON\")\n",
    "copt, gopt, xopt,gnl_QN, gsl_QN, cl_QN = BFGS_V(OraclePG, x0, 1)\n",
    "#copt, gopt, xopt = Newton_N(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quasi Newton method with optimal stepsize by exact line search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BFGS_L(Oracle, x0, alpha0):\n",
    "    import numpy as np\n",
    "    from numpy.linalg import solve\n",
    "    from numpy import dot\n",
    "    from numpy import eye\n",
    "    from numpy import outer\n",
    "    from numpy import vdot\n",
    "    from numpy.linalg import norm\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables\n",
    "\n",
    "    iter_max = 250\n",
    "    gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    gradient_list = []\n",
    "    critere_list = []\n",
    "    x_list = []\n",
    "    \n",
    "    time_start = process_time()\n",
    "\n",
    "    x = x0\n",
    "    I = eye(len(x0))\n",
    "    \n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        \n",
    "        # Valeur du critere et du gradient\n",
    "        res = Oracle(x)\n",
    "        critere = res[0]\n",
    "        gradient = res[1]\n",
    "        #hessien = res[2]\n",
    "        \n",
    "        # Test de convergence\n",
    "        gradient_norm = norm(gradient)\n",
    "        if gradient_norm <= threshold:\n",
    "            break\n",
    "                # Valeur du critere et du gradient\n",
    "        \n",
    "        # Direction de descente\n",
    "        #direction_n = - solve(hessien, gradient)\n",
    "        #print(\"direction_n\",direction_n)\n",
    "        \n",
    "        # Formule de BFGS inverse for Direction de descente\n",
    "        #print(\"k:\",k)\n",
    "        if k == 0:\n",
    "            Wk = I \n",
    "            #print(\"Wk\",Wk)\n",
    "        else:\n",
    "            #print(\"gradient\",gradient)\n",
    "            #print(\"gradient_list[-1]\",gradient_list[-1])\n",
    "            delta_xk = np.array([list(x - x_list[-1])]).transpose()\n",
    "            delta_gk = np.array([list(gradient - gradient_list[-1])]).transpose()\n",
    "            \n",
    "            #print(\"delta_xk\",delta_xk)\n",
    "            #print(\"delta_gk\",delta_gk)\n",
    "            \n",
    "            #print(\"(delta_xk@delta_gk.transpose())\",(delta_xk@delta_gk.transpose()))\n",
    "            \n",
    "            A = I - np.multiply(delta_xk,delta_gk.transpose())/(delta_gk.transpose()@delta_xk)\n",
    "            B = I - np.multiply(delta_gk,delta_xk.transpose())/(delta_gk.transpose()@delta_xk)\n",
    "            C = (np.multiply(delta_xk,delta_xk.transpose()))/(delta_gk.transpose()@delta_xk)\n",
    "            #print(\"A:\",A)\n",
    "            #print(\"B:\",B)\n",
    "            #print(\"C:\",C)\n",
    "                        \n",
    "            Wk = A@Wk@B + C\n",
    "\n",
    "\n",
    "            #print(\"Wk\",Wk)\n",
    "            #print(\"Hessien\", hessien)\n",
    "        direction = -Wk@gradient\n",
    "        #print(\"direction\",direction)\n",
    "        \n",
    "        # Direction de descente\n",
    "        #direction = - solve(hessien, gradient)\n",
    "        \n",
    "        # Exact Line search for step size\n",
    "        if k > 0:\n",
    "            res = Exact_line_earch(F,G,x,direction)\n",
    "            \n",
    "            #print(res)\n",
    "            if res[0] is not None:\n",
    "                gradient_step = res[0]\n",
    "                \n",
    "                \n",
    "            else:\n",
    "                gradient_step  =  gradient_step_list[-1]\n",
    "                print(k)\n",
    "                print(gradient_step)    \n",
    "        \n",
    "        \n",
    "        #gradient_step =  default_gradient_step\n",
    "\n",
    "        \n",
    "        # Mise a jour des variables\n",
    "        x_list.append(x)\n",
    "        x = x + (gradient_step*direction)\n",
    "        \n",
    "        # Evolution du gradient, du pas, et du critere\n",
    "        gradient_norm_list.append(gradient_norm)\n",
    "        gradient_step_list.append(gradient_step)\n",
    "        gradient_list.append(gradient)\n",
    "        critere_list.append(critere)\n",
    "    \n",
    "    # Resultat de l'optimisation\n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "        \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt,gradient_norm_list, gradient_step_list, critere_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DE QUASI-NEWTON\n",
      "2\n",
      "1.0\n",
      "4\n",
      "1.0\n",
      "5\n",
      "1.0\n",
      "6\n",
      "1.0\n",
      "7\n",
      "1.0\n",
      "8\n",
      "1.0\n",
      "9\n",
      "1.0\n",
      "\n",
      "Iteration : 249\n",
      "Temps CPU : 0.125\n",
      "Critere optimal : nan\n",
      "Norme du gradient : nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\linesearch.py:327: LineSearchWarning: The line search algorithm did not converge\n",
      "  warn('The line search algorithm did not converge', LineSearchWarning)\n",
      "<ipython-input-33-ad96acd04c62>:3: RuntimeWarning: overflow encountered in multiply\n",
      "  return dot(q0+B@x, r*(q0+B@x)*abs(q0+B@x))/3 + dot(pr, Ar@(q0+B@x))\n",
      "<ipython-input-33-ad96acd04c62>:7: RuntimeWarning: overflow encountered in multiply\n",
      "  return B.transpose()@(r*(q0+B@x)*abs(q0+B@x))+B.transpose()@Ar.transpose()@pr\n",
      "<ipython-input-33-ad96acd04c62>:7: RuntimeWarning: invalid value encountered in matmul\n",
      "  return B.transpose()@(r*(q0+B@x)*abs(q0+B@x))+B.transpose()@Ar.transpose()@pr\n",
      "<ipython-input-7-1052a0dc5e65>:3: RuntimeWarning: invalid value encountered in matmul\n",
      "  gradient =B.transpose()@(r*(q0+B@qc)*abs(q0+B@qc))+B.transpose()@Ar.transpose()@pr\n",
      "<ipython-input-7-1052a0dc5e65>:4: RuntimeWarning: overflow encountered in multiply\n",
      "  critere = dot(q0+B@qc, r*(q0+B@qc)*abs(q0+B@qc))/3 + dot(pr, Ar@(q0+B@qc))\n",
      "<ipython-input-82-35117a7d4359>:67: RuntimeWarning: overflow encountered in multiply\n",
      "  C = (np.multiply(delta_xk,delta_xk.transpose()))/(delta_gk.transpose()@delta_xk)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\linesearch.py:477: LineSearchWarning: The line search algorithm did not converge\n",
      "  warn('The line search algorithm did not converge', LineSearchWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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DHxrZL+tw3sRJy8zMXvfgK8uZtXwjV4wdTuvSwksRhReRmZllorKqmh8/OofDDu7M2Uf2yTqcWrXK9wolDQG+CnSNiA+m0zoCvwR2ApOBp2ouY2Zm2brn+QoWrN7Crz8+kpISZR1OrRpV05J0i6SVkqbXmD5O0mxJ8yRdDRAR8yNifI1VvB+4OyI+Dby3jmXMzCwj23dV8bO/z+Xo/t04/fBeWYdTp8Y2D04ExuVOkFQK3ACcBYwALpA0oo7X9wOWpI+r9j5MMzNrSnc8s5hlG7Zz1ZnlSIVZy4JGJq2ImAKsrTF5FDAvrTXtBO4EzqljFRUkiavRZQJImiBpqqSpq1atauzLzMxsL2zZUckNj83j7UN7cOLQsqzDqdf+DMToyxu1J0gSU19JPSTdCBwj6Zp03r3AByT9H/CXOpZ5k4i4KSJGRsTInj177keoZmZWl1ueWMCaLTv54hnlWYfSoP0ZiFFb/TEiYg1wcY2JW4BP1lj2YszMLFPrt+7kpinzGTuiN8cMOCjrcBq0PzWtCqB/zvN+wLL9C8fMzA6kG/81n807K7nyjOFZh9Io+5O0ngOGSRosqQ1wPnB/fsIyM7OmtnLjdib+ewHnHNWHww7uknU4jdLYIe+TSH5bVS6pQtL4iKgELgMeBmYBd0XEjKYL1czM8un6x+ZRWRV8/vTiqGVBI/u0IuKCOqY/BDyU14jMzKzJLVm7lUnPLubc4/ozqKxj1uE0mi/jZGbWAv3073Mpkbj81GFZh7JXnLTMzFqYuSs2cd8LFXzixEEc3LVd1uHsFSctM7MW5sePzqFDm1ZcfMqhWYey15y0zMxakJcr1vPX6a9x0cmD6d6xTdbh7DUnLTOzFuS6R+ZwUIfWjD9pcNah7BMnLTOzFuLp+WuYMmcVl4wZSud2rbMOZ584aZmZtQARwXUPz6Z3l7Z87ISBWYezz5y0zMxagMmzVzF10TouP20Y7VqXZh3OPnPSMjNr5qqrg//38GwGdO/AuSP7N/yCAuakZWbWzD34ynJmLd/IFWOH07q0uE/7xR29mZnVq7Kqmh8/Oofy3p05+6g+WYez35y0zMyasXuer2DB6i1cecZwSktquw1icXHSMjNrprbvquJnf5/LUf27MXZE76zDyQsnLTOzZuqOZxazbMN2rjqzHKn4a1ngpGVm1ixt2VHJDY/N48RDe/D2oWVZh5M3TlpmZs3QrU8uYM2WnXzpzPKsQ8krJy0zs2Zm/dad/GrKfMaO6M0xAw7KOpy8ctIyM2tmfjVlPpt3VHLlGcOzDiXvWh2IQiQNAK4HVgNzIuL7kkqAbwFdgKkR8dsDEYuZWXO2ctN2bn1yAecc1YfDDu6SdTh5t881LUm3SFopaXqN6eMkzZY0T9LV6eThwIMR8SlgRDrtHKAvsAuo2Nc4zMzsDTf8cx6VVcHnT29+tSzYv+bBicC43AmSSoEbgLNIktMFkkYALwDnS/on8Fi6eDnwVERcAXx2P+IwMzNgydqt3PHsYs49rj+DyjpmHU6T2OekFRFTgLU1Jo8C5kXE/IjYCdxJUqP6JPCNiDgVeHe6bAWwLn1cVVsZkiZImipp6qpVq/Y1VDOzFuFn/5iLJC4/dVjWoTSZfA/E6AssyXlekU77G3C5pBuBhem8e4EzJf0CmFLbyiLipogYGREje/bsmedQzcyaj7krNnHv8xV84oSBHNy1XdbhNJl8D8So7SfXERHTgQ/WmLgVGJ/n8s3MWqQfPzqH9q1L+eyYoVmH0qTyXdOqAHJv1tIPWJbnMszMLMfLFev56/TXuOjkIXTv2CbrcJpUvpPWc8AwSYMltQHOB+7PcxlmZpbjukfm0K1Day46eXDWoTS5/RnyPgl4CiiXVCFpfERUApcBDwOzgLsiYkZ+QjUzs5qenr+GKXNWccmYQ+ncrnXW4TS5fe7TiogL6pj+EPDQPkdkZmaNEhFc9/Bsendpy8dPGJR1OAeEL+NkZlakJs9exdRF6/jcqcNo17o063AOCCctM7MiVF0d/PDh2Qzo3oFzR/Zv+AXNhJOWmVkRemj6cmYu38gVY4fTplXLOZW3nC01M2smKquq+fEjcyjv3Zmzj+qTdTgHlJOWmVmRuff5pcxfvYUrzxhOaUlt13Rovpy0zMyKyI7KKn769zkc1b8bY0f0zjqcA85Jy8ysiNzxzGKWbdjOVWeWI7WsWhY4aZmZFY0tOyq54bF5nHhoD94+tCzrcDLhpGVmViRufXIBqzfv5ItnlmcdSmactMzMisD6rTv51ZT5nH54b9424KCsw8mMk5aZWRH41ZT5bN5RyZVnDM86lEw5aZmZFbiVm7Zz65MLeO9RfTj8kC5Zh5MpJy0zswJ3wz/nsasq+MLpLbuWBU5aZmYFbcnardzx7GLOHdmfQWUdsw4nc05aZmYF7Gf/mIskLj9taNahFAQnLTOzAvXSkvXc+3wFHz9+IId0bZ91OAXBScvMrABt2LaLS+94nkO6tudzpw7LOpyCsc93LjYzs6YREVx190u8tmE7f7z4BLp2aJ11SAXjgCQtSScDH0nLGxERJ0oaAnwV6BoRHzwQcZiZFYOJ/17IwzNW8LV3H84xLfiHxLXZ5+ZBSbdIWilpeo3p4yTNljRP0tUAEfF4RFwMPAD8Np02PyLG70/wZmbNzcsV6/nuQ7M4/fBejD9pcNbhFJz96dOaCIzLnSCpFLgBOAsYAVwgaUTOIh8GJu1HmWZmzdbufqxendtx3YeOapFXcW/IPietiJgCrK0xeRQwL61F7QTuBM4BkDQA2BARGxtbhqQJkqZKmrpq1ap9DdXMrOBFBFff8zLL12/n5xccQ7cObbIOqSDle/RgX2BJzvOKdBrAeODW3TMk9ZB0I3CMpGtqW1lE3BQRIyNiZM+ePfMcqplZ4bjtqUX8dfprXDWunGMHuh+rLvkeiFFbXTYAIuIbe0yMWANcnOfyzcyKzisVG/jOg7M47bBeXHTSkKzDKWj5rmlVAP1znvcDluW5DDOzZmPj9qQfq6xTG6770FGUlLgfqz75TlrPAcMkDZbUBjgfuD/PZZiZNQsRwTX3vMLS9dv4xYeP4aCO7sdqyP4MeZ8EPAWUS6qQND4iKoHLgIeBWcBdETEjP6GamTUvv396EQ++spwvnVnOsQO7Zx1OUdjnPq2IuKCO6Q8BD+1zRGZmLcD0pRv41gOzeGd5Tyac7H6sxvK1B83MDrBNaT9W945t+NG5R7sfay/42oNmZgdQRHDNva9QsW4bd044nu7ux9orrmmZmR1Atz+zmAdeXs6VZwznuEHux9pbTlpmZgfIjGUb+N8HZnLK8J5c/I5Dsw6nKDlpmZkdAJu27+KyO17goA6t+fG5/j3WvnKflplZE4sIvnLfdBat2cKdE06gR6e2WYdUtFzTMjNrYpOeXcJfXlrGlWeUM2qw+7H2h5OWmVkTmrlsI9f+ZQYnDyvjs6e4H2t/OWmZmTWRzTsqueyO5zmoQ2t+cp5/j5UP7tMyM2sCEcFX73uFhWu2MOnTx1Pmfqy8cE3LzKwJ/OG5Jfz5xWVcMXY4o4f0yDqcZsNJy8wsz2Yt38g37k/6sS4ZMzTrcJoVJy0zszzasqOSS+94nq7t3Y/VFNynZWaWJxHB1/40nYWrt3D7Re7HagquaZmZ5ckfp1Zw3wtL+fzpwznhUPdjNQUnLTOzPHj1tY38z5+n8/ahPbj0ne7HaipOWmZm+2nLjkouvf15urRvzU/PO4ZS92M1GfdpmZnth4jgf/40nfmrt3D7+NH07Ox+rKZ0QGpaksZIelzSjZLGpNNKJH1H0i8kfeJAxGFmlm9/nFbBvS8s5b9PG8aJQ8uyDqfZ2+ekJekWSSslTa8xfZyk2ZLmSbo6nRzAZqAdUJFOOwfoC+zKmWZmVjTmrNjE1/88nRMP7cHnTh2WdTgtwv7UtCYC43InSCoFbgDOAkYAF0gaATweEWcBXwa+mS5eDjwVEVcAn92POMzMDritOyu55Pbn6dS2NT89/2j3Yx0g+5y0ImIKsLbG5FHAvIiYHxE7gTuBcyKiOp2/Dtjd4FuRPgeo2tc4zMyy8PU/z+A/qzbzs/OPplfndlmH02LkeyBGX2BJzvMKYLSk9wNnAt2A69N59wK/kHQyMKW2lUmaAEwAGDBgQJ5DNTPbN3dPq+DuaRVcftow3u5+rAMq30mrtvpxRMS9JEkqd+JWYHx9K4uIm4CbAEaOHBn5CtLMbF/NXbGJ//nTdI4f0p3/Ps39WAdavkcPVgD9c573A5bluQwzs0xs21nFpXc8T8e2pfz8fP8eKwv5TlrPAcMkDZbUBjgfuD/PZZiZZeIb909n7srN/OS8o+nVxf1YWdifIe+TgKeAckkVksZHRCVwGfAwMAu4KyJm5CdUM7Ps3Pt8BXdNreCydw7l5GE9sw6nxdrnPq2IuKCO6Q8BD+1zRGZmBWbeyk189b7pjB7sfqys+dqDZmb12Laziktvf4EObUr5+QXH0KrUp80s+dqDZmb1uPb+GcxZuYnffnIUvd2PlTl/ZTAzq8N9L1Twh6lLuGTMobxjuPuxCoGTlplZLeat3MxX75vOqEHd+cLpw7MOx1JOWmZmNWzfVcVldzxPu9buxyo07tMyM6vhm3+ZwauvbWLiJ4/j4K7uxyok/vpgZpbjzy8uZdKzS/jsmEMZU94r63CsBictM7PU/FWb+cq9rzBy4EFcOdb9WIXIScvMjKQf69I7XqBNqxJ+8WH3YxUq92mZmQH/+8BMZi3fyK0XHschXdtnHY7VwV8lzKzFu/+lZdzxzGI+c8oQ3nmY+7EKmZOWmbVoC1Zv4Zp7XubYgQfxxTPKsw7HGuCkZWYt1vZdVVx6+/O0blXCLy44htbuxyp47tMysxbr2w/OZObyjdxy4Uj6dHM/VjHw1woza5EeeHkZv396MZ95xxBOPax31uFYIzlpmVmLs3D1Fq6+5xXeNqAbXzzT/VjFxEnLzFqUDVt3cekdz1NaIn7x4be5H6vIuE/LzJq9inVbeXTmCh6duYJnF6ylsjr4zcdH0tf9WEXHScvMmp2IYMayjTySJqpZyzcCMKxXJya8YwjveushHNG3a8ZR2r44YElLUkdgCvCNiHhA0hDgq0DXiPjggYrDzJqnnZXVPLNgDY/OXMHfZ65g2YbtlAiOHXgQX33X4Zw+ojeDyzpmHabtp31OWpJuAd4DrIyII3KmjwN+BpQCv4mI76ezvgzctXu5iJgPjJd0977GYGYt26btu5g8exWPzlzBY7NXsml7Je1al3DysJ58fuxwTjusFz06tc06TMuj/alpTQSuB27bPUFSKXADMBaoAJ6TdD/QB5gJ+MY0ZrZflm/Yxt9nruCRmSt4ev4adlUFPTq24awjDmbsiIM5aWgZ7duUZh2mNZF9TloRMUXSoBqTRwHz0loUku4EzgE6AR2BEcA2SQ9FRHVDZUiaAEwAGDBgwL6GamZFLCJ49bVNrw+keGXpBgCGlHXkU28fzNgRvTlmwEGUlijjSO1AyHefVl9gSc7zCmB0RFwGIOlCYHVEVEvqAXwHOEbSNRHxvZori4ibgJsARo4cGXmO1cwKVGVVNc8uXJv0T81awZK125Dg6P7d+PK4wxg7ojdDe3XKOkzLQL6TVm1fdV5PNhExMefxGuDiPJdvZkVqy45KpsxJ+qf+8epKNmzbRZtWJZw0tIxLxgzltMN70auzexhaunwnrQqgf87zfsCyPJdhZs3Eyo3b+fuslTw68zWe/M8adlZW061Da047vBdnjOjNycN60rGtf5ljb8j30fAcMEzSYGApcD7w4TyXYWZFKiKYt3Lz67+fenHJegAGdO/Ax44fyNgRvRk58CDfNdjqtD9D3icBY4AySRUkv7+6WdJlwMMkQ95viYgZeYnUzIpSVXUwbdE6Hp35Go/OXMHCNVsBOLJfV754xnDGjjiY4b07IXkghTVsf0YPXlDH9IeAh/Y5IjMrett2VvH43Df6p9Zu2UnrUnHCoWWMP3kIYw/vzcFd3T9le8+NxWaWF6s37+Cfs1byyMwVPDFvFdt3VdO5XStOPawXY0f05pThPencrnXWYVqRc9Iys/1SWVXNtx6YyW1PLyIC+nZrz/nHDWDsiJO6eisAACAASURBVN6MGtzdV1G3vHLSMrN9tmn7Li694wWmzFnFR48fwAWjBjDikC7un7Im46RlZvukYt1Wxk+cyn9WbeYHH3gr5x3nq9ZY03PSMrO99tKS9Yz/7VR2VFbx20+N4u1Dy7IOyVoIJy0z2yt/m76cz//hRco6tWXSp0czrHfnrEOyFsRJy8waJSL49ePz+d5fX+Xo/t349cdHUubbftgB5qRlZg3aVVXN1/88g0nPLuY9Rx7CdR86inatffsPO/CctMysXhu37+LS25/n8bmrufSdh3Ll2HJKfBsQy4iTlpnVacnarXxq4nMsWL2F//fBIzl3ZP+GX2TWhJy0zKxWLyxex6dvm8rOympuGz+KEw/1CEHLnpOWmb3JQ68s5wt/eJHeXdpx54TjfMNFKxhOWmb2uojgxn/N5wd/e5VjBx7ETR87lh4eIWgFxEnLzIBkhODX7pvOH6Yu4b1H9eH/ffBIjxC0guOkZWZs2LaLS26fxpPz1nD5qUP5wtjhvn6gFSQnLbMWbsnarXxy4nMsWrOFH33oKD5wbL+sQzKrk5OWWQs2bdE6Jtw2lcrq4HfjR3P8kB5Zh2RWLyctsxbqgZeXccVdL3FI13bccuFxHNrTIwSt8B2QpCXpfcC7gV7ADRHxiKQS4FtAF2BqRPz2QMRi1tJFBL+c/B9++PBsjht0EL/62Ei6d2yTdVhmjbLPtxSVdIuklZKm15g+TtJsSfMkXQ0QEX+KiE8DFwLnpYueA/QFdgEV+xqHmTXezspqrrr7ZX748Gzed3Qffn/RaCcsKyr7cx/sicC43AmSSoEbgLOAEcAFkkbkLPK1dD5AOfBURFwBfHY/4jCzRtiwdRefuOVZ/jitgs+fPoyfnHc0bVt5SLsVl31uHoyIKZIG1Zg8CpgXEfMBJN0JnCNpFvB94K8R8Xy6bAWwM31cVVsZkiYAEwAGDPBdUc321aI1W/jkxOeoWLuNn5x3FP91jEcIWnHKd59WX2BJzvMKYDTwOeB0oKukoRFxI3Av8AtJJwNTaltZRNwE3AQwcuTIyHOsZi3C1IVrmfC7aVRH8PuLRjNqcPesQzLbZ/lOWrX9GjEi4ufAz2tM3AqMz3P5Zpbjzy8u5Ut3v0zfbu255cLjGFzWMeuQzPZLvpNWBZB774J+wLI8l2FmDYgIrv/nPH706BxGDe7Orz56LAd5wIU1A/lOWs8BwyQNBpYC5wMfznMZZlaPHZVVXHPvK9z7/FLef0xfvveBt3rAhTUb+5y0JE0CxgBlkiqAb0TEzZIuAx4GSoFbImJGXiI1swat37qTCb+bxrML1nLF2OF87tShvoagNSv7M3rwgjqmPwQ8tM8Rmdk+Wbg6GSG4dN02fnb+0ZxzdN+sQzLLO1/GyawZeG7hWibcNhWAOz49mpGDPELQmicnLbMi96cXlnLV3S/T76BkhOAgjxC0ZsxJy6xIRQQ/+8dcfvr3uRw/pDs3fvRYunXwCEFr3py0zIrQjsoqrr7nFe57YSkfPLYf3/2vt9Km1f5clc2sODhpmRWZdVt28pnfTePZhWv50pnlXDLmUI8QtBbDScusiMxftZlPTXyOZRu284sLjuHso/pkHZLZAeWkZVYknpm/hs/8fholEpM+PZpjB3qEoLU8TlpmReDe5yv48j0vM6B7B269cBQDenTIOiSzTDhpmRWwiOAnj87h5/+cx4mH9uD/PnIsXTu0zjoss8w4aVmLsKOyigdeWs7tzyxizZadtCoRrUtLaF1aQqtS0bqkhNatRKuSElqXpv9bldC6RMn83cuWiFalJbQpTf63KhVtcqa3TpdtVZq89vX1p8sk6yzJWWfO6/aYXsKuquQuw/e/tIxzR/bj2+/zCEEzJy1r1tZs3sHtzyzmd08vYtWmHQzr1Ymj+3ejsirYVVXNrqpqKquTxzt2VbO5qpJdVUFldTW70mUq0+c7K5NlK6uCnVXVB2wbrhpXzmdP8QhBM3DSsmZqzopN3PLEAu57YSk7Kqs5ZXhPxn9oMCcPK8vLyT8iqKqO1xPerqqgsqqaXdXp/9enBbuqq9lVWd2IZdNEWV39elI9blB33jG8Zx72iFnz4KRlzUZE8K85q7j5iQU8Pnc1bVuV8P639WP8SYMY2qtzXsuSkmbDVqXQrrVv+2F2oDhpWdHbvquK+15Yyi1PLGDuys306tyWL54xnA+PHkh33/jQrFlx0rKitXLjdn739CJuf2Yxa7fs5C19uvDjc4/iPUf28YAFs2bKScuKzoxlG7j5iQX85aVlVFYHpx/em/EnDWb04O4erGDWzDlpWVGorg7+8epKbn5iPk/PX0uHNqV8ZPRALjxxkG/FYdaCOGlZQduyo5K7p1Vw65MLWLhmK327tecr7zqM844bQNf2/pGtWUtzQJKWpCHAV4GuEfHBuqaZ7bZs/TZ++++FTHp2MRu3V3LMgG588cxyxr3lYFqVur/KrKXa56Ql6RbgPcDKiDgiZ/o44GdAKfCbiPh+RMwHxku6e/dytU0ze2HxOm5+YgF/nf4aAOOOOJjxJw3mbQMOyjgyMysE+1PTmghcD9y2e4KkUuAGYCxQATwn6f6ImLk/QVrzVllVzcMzVnDzE/N5fvF6OrdrxfiTBvOJEwfRt1v7rMMzswKyz0krIqZIGlRj8ihgXlqLQtKdwDmAk5a9ycbtu/jDs0uY+O+FLF2/jYE9OnDt2SP44Mj+dGrr7lYze7N8nxn6AktynlcAoyX1AL4DHCPpmoj4Xm3Taq5M0gRgAsCAAQPyHKplZdGaLdz65EL+OHUJW3ZWMXpwd75x9ghOO7w3pSUesm5mdct30qrtjBMRsQa4uMbEN02r5YU3ATcBjBw5MvIVpB14EcGzC9Zy8xMLeHTWClqViLOP7MOnThrMEX27Zh2emRWJfCetCqB/zvN+wLI8l9FsbdtZxdPz1zB59kpeWbqBbh3aUNapDT07t6Vnp7aUpf97dk7+OrVtVfA/pt1ZWc2Dryzj5icWMH3pRg7q0JpLxwzlYycMpHeXdlmHZ2ZFJt9J6zlgmKTBwFLgfODDeS6jWVm4eguTZ6/ksdmreHr+GnZUVtOudQlH9uvGyk3bmbFsA2s276Sy+s0VzbatSl5PYDWTWln6v1f6uH2bA3tR13VbdnLHs4u57amFrNi4g6G9OvHd/3or/3VM3wMei5k1H/sz5H0SMAYok1QBfCMibpZ0GfAwyZD3WyJiRl4ibSa276rimQVreezVlfxrzioWrN4CwJCyjnx49ADeWd6LUYO773Hl8OrqYP22XazatINVm3awenPyf9XmN54vXruVaYvWsXbrTqKWhtRObVvlJLc2e9TYynIe9+jYdr+u2zdv5WZueXIB9z5fwfZd1Zw8rIwffOBI3jGsJyXurzKz/aSo7QxXgEaOHBlTp07NOox9snjNVibPWcnk2av4939Ws31XNW1blXDioT0YU96LMeU9GdgjP5ciqqyqZu2WnaxMk9rqnOS2R8LbtION2ytrXUe3Dq3fVGOrrTbXvWMbSktERPDEvNXc/MQCJs9eRZtWJfzX0X351EmDKT84v7cEMbPmT9K0iBhZ2zyPK24COyqreHbBWh57dRWT56xk/qqkNjWwRwfOP24AY8p7cvyQHk1yH6ZWpSX06tKOXo3oL9q+q4o1W3a+nsRqJrXVm3fwUsV6Vm7cwbZdVW96fYmge8e2tCkVyzZsp6xTW75w+nA+cvwAyjq1zfu2mZk5aeXJkrVbmTxnFf+avZIn561h264q2rQq4fghPfjY8QMZU96LwQV2Ydd2rUvp2619o37Au2VH5R4JLbcWt2HbLr5Q3ov3Ht2Htq3cX2VmTcdJax/trKzmuYVrXx9EMW/lZgD6d2/Ph0b2Y0x5T04YUtZsBh10bNuKjm1b5a0Z08xsXzhp7YVl67cxefYqHpu9kn/PW82WnVW0KS1h9JDunH9cf955WC+GlHUs+GHoZmbFykmrHruqqpm6cB2TZyeDKGav2ARA327ted8xfXlneS9OOLQHHX3JITOzA8Jn2xpe27A9bfJL+qY276ikdak4blB3vnrs4Ywp78nQXp1cmzIzy0CLT1q7qqp5ftE6Js9ZxWOvruTV15LaVJ+u7Tj7qD6MKe/J24eW+QKuZmYFoEWeiVdu3M7kOauYPHslj89dzabtlbQqESMHHcQ1Zx3GmPJeDO/t2pSZWaFpMUlr+tIN/HX6ch57dRUzl28EoHeXtrz7rYe8Xpvq3M63bzczK2QtJmk9+Mpybpoyn2MHHsRV48p5Z3kvDju4s2tTZmZFpMUkrYtOGszFpxxK1/auTZmZFasWk7R6+LJCZmZFb98v521mZnaAOWmZmVnRcNIyM7Oi4aRlZmZFw0nLzMyKhpOWmZkVDSctMzMrGk5aZmZWNBQRWcfQKJJWAYv2czVlwOo8hHMgFFOsUFzxOtam4VibTjHFm49YB0ZEz9pmFE3SygdJUyNiZNZxNEYxxQrFFa9jbRqOtekUU7xNHaubB83MrGg4aZmZWdFoaUnrpqwD2AvFFCsUV7yOtWk41qZTTPE2aawtqk/LzMyKW0uraZmZWRFz0jIzs6LRYpKWpHGSZkuaJ+nqrOOpi6RbJK2UND3rWBoiqb+kxyTNkjRD0n9nHVNdJLWT9Kykl9JYv5l1TA2RVCrpBUkPZB1LQyQtlPSKpBclTc06nvpI6ibpbkmvpsfuCVnHVBtJ5en+3P23UdLns46rLpK+kH62pkuaJKldk5TTEvq0JJUCc4CxQAXwHHBBRMzMNLBaSHoHsBm4LSKOyDqe+kg6BDgkIp6X1BmYBryvQPergI4RsVlSa+AJ4L8j4umMQ6uTpCuAkUCXiHhP1vHUR9JCYGREFPwPYCX9Fng8In4jqQ3QISLWZx1XfdJz2FJgdETs70UW8k5SX5LP1IiI2CbpLuChiJiY77JaSk1rFDAvIuZHxE7gTuCcjGOqVURMAdZmHUdjRMTyiHg+fbwJmAX0zTaq2kVic/q0dfpXsN/YJPUD3g38JutYmhNJXYB3ADcDRMTOQk9YqdOA/xRiwsrRCmgvqRXQAVjWFIW0lKTVF1iS87yCAj25FitJg4BjgGeyjaRuaXPbi8BK4NGIKNhYgZ8CVwHVWQfSSAE8ImmapAlZB1OPIcAq4Na06fU3kjpmHVQjnA9MyjqIukTEUuA6YDGwHNgQEY80RVktJWmplmkF+y272EjqBNwDfD4iNmYdT10ioioijgb6AaMkFWTzq6T3ACsjYlrWseyFt0fE24CzgEvTZu5C1Ap4G/B/EXEMsAUo2D5ugLQJ873AH7OOpS6SDiJpvRoM9AE6SvpoU5TVUpJWBdA/53k/mqjq2tKk/UP3ALdHxL1Zx9MYaXPQZGBcxqHU5e3Ae9N+ojuBUyX9PtuQ6hcRy9L/K4H7SJrkC1EFUJFTy76bJIkVsrOA5yNiRdaB1ON0YEFErIqIXcC9wIlNUVBLSVrPAcMkDU6/tZwP3J9xTEUvHdxwMzArIn6cdTz1kdRTUrf0cXuSD9mr2UZVu4i4JiL6RcQgkmP1nxHRJN9a80FSx3QgDmlT2xlAQY5+jYjXgCWSytNJpwEFN3Cohgso4KbB1GLgeEkd0vPCaSR93HnXqilWWmgiolLSZcDDQClwS0TMyDisWkmaBIwByiRVAN+IiJuzjapObwc+BryS9hUBfCUiHsowprocAvw2HYVVAtwVEQU/lLxI9AbuS85VtALuiIi/ZRtSvT4H3J5+gZ0PfDLjeOokqQPJqOfPZB1LfSLiGUl3A88DlcALNNHlnFrEkHczM2seWkrzoJmZNQNOWmZmVjSctMzMrGg4aZmZWdFw0jIzs6LhpGVmZkXDScvMzIqGk5aZmRUNJy0zMysaTlpmZlY0nLTMzKxoOGmZmVnRcNKyfSZpTHol+oJTMzZJMySNyTCkZktSSBqa53VuljQkn+vcy/JPljQ7q/Ktbk5azYikhZK2pR/4FZJuTe8q3OJFxFsiYvL+rkfStYV+Q8bmICI6RcR8AEkTJX27KcurmXgj4vGIKK/vNZYNJ63m5+yI6ERyN9bjgK9lHM9+k9Qi7vuWlea+f5v79rU0TlrNVEQsBf4KHCHpIEkPSFolaV36uN/uZSVdKGm+pE2SFkj6SG3rlNQ+/da7TtJMkqSYO7+PpHvSchZIuryu+CT1kPQXSRslPSfp25KeyJkfki6VNBeYm077maQl6WumSTp5L2JbKOn09HGJpKsl/UfSGkl3SeqezhuUlv0JSYslrZb01XTeOOArwHlpbfalOrZt97o3SZop6b9y5u1RU8spr9YTq6T+ku5N9+kaSdfnbMPXJC2StFLSbZK6pvPe1GxbY/uvlXS3pN9L2ghcKGmUpKnpvl0hqc47UUv6kqTlkpZJ+lSNeW0lXZfuuxWSblRyp2gklaXH3npJayU9LqnWc9Dumo+kCcBHgKvSff6XdH6dx1o92/dUWvZySdcruQkkkqakL30pLeO8mvtQ0uGSJqevnyHpvTnzJkq6QdKD6Xv+jKRD03mS9JP0Pdog6WVJR9S1b60RIsJ/zeQPWAicnj7uD8wAvgX0AD4AdAA6A38E/pQu1xHYCJSnzw8B3lLH+r8PPA50T9c/HahI55UA04CvA22AISR3hT2zjnXdmf51AEYAS4AncuYH8GhaVvt02kfTbWkFXAm8BrRrKLZa9s3ngaeBfkBb4FfApHTeoLTsXwPtgaOAHcDh6fxrgd838D58COiT7pPzgC3AIbW9Pqe8VrWspxR4CfhJ+j61A05K530KmJfu507AvcDv0nljcre9lu2/FtgFvC+NsT3wFPCxdH4n4Pg6tm0csAI4Io3pjjT+oen8nwL3p+9DZ+AvwPfSed8DbgRap38nk96ItpZyctc5Efh2zrx6j7U6tu9Y4HiSY2cQya3gP19beTX3YRrrPJIvLG2AU4FNvPGZmQisBUal678duDOdd2YaazdAwOG7jwX/7eN5LusA/JfHNzM5MW0G1gOLgF+SnvBrLHc0sC593DFd/gO1LVvjdfOBcTnPJ+R8sEcDi2ssfw1way3rKU1PKuU5077Nm5PWqQ3Esw44qqHYcvbN7pP2LOC0nHmHpPHsPqEF0C9n/rPA+enja2kgadUS54vAObW9nvqT1gnAqjrm/QO4JOd5ec42vH7CrWP7rwWm1Jg/BfgmUNbAttwCfD/n+fA0/qHpSXkLcGiNbViQPv5f4M/kJId6yqkvadV7rNW2fbWs//PAfbWVlz5/fR+SJNfXgJKc+ZOAa3Pi+03OvHcBr6aPTwXmkCTMkvpi8l/j/tw82Py8LyK6RcTAiLgkIrZJ6iDpV2lT0kaSE1Q3SaURsYWkNnAxsDxt4jisjnX3IakR7bYo5/FAoE/afLJe0nqSb6a9a1lPT5KTa+66ltSy3B7TJF0paVbazLIe6AqUNSK2mgYC9+XEOQuoqhHrazmPt5LUPhpF0sclvZiz/iNy4twb/YFFEVFZy7w+7LmNi0j2aW37uzY19/d4kgT0qpLm2vfU8br69nNPkprztJxt/1s6HeCHJDWWR5Q0R1/dyFhrasyxVvPYGZ42Tb6Wfga+S+Pfkz7Akoiozpm2COib87zW4yUi/glcD9wArJB0k6QujSzXauGk1TJcSfJNfHREdAHekU4XQEQ8HBFjSWocr5I0jdVmOcmJdLcBOY+XkHyj7pbz1zki3lXLelYBlSTNc7v1r2W52P1ASf/Vl4FzgYMiohuwYfc2NBBbTUuAs2rE2i6SfsCGRH0zJQ0k2X+XAT3SOKfnxLmF5MS+28ENxDmgjv6uZSQn790GkOzTFTXLkFTKG4mj1u2IiLkRcQHQC/gBcLekjrWUW99+Xg1sI2le3r1fu0YyMIiI2BQRV0bEEOBs4ApJp9Wx7XXGSuOOtZqv+T+SY3tY+hn4Cm+8Jw1ZBvSv0f82AGjM8UJE/DwijgXeQvLF4EuNLNdq4aTVMnQmOZmsVzLg4Bu7Z0jqLem96QlqB0nzYlUd67kLuEbJwI5+wOdy5j0LbJT0ZSWDIkolHSHpuJoriYgqkj6Ya9Na4GHAxxuxDZWkzWWSvg7kfmOtL7aabgS+kyYYJPWUdE4D5e+2AhhU1wACkubWSONE0idJalq7vQi8Q9IAJQMnrqmnrGdJksT3JXWU1E7S29N5k4AvSBqs5GcN3wX+kNbK5gDtJL1bUmuSEaRt69soSR+V1DOtTaxPJ9d2HNxFMrBhhKQO5BxL6Wt/DfxEUq90vX0lnZk+fk86uEIk/ahVdZRR0wqSfqvc/dKoYy1H57TMzenx9tkGysj1DMkXgasktVbye7+zSfpk6yXpOEmj0/dhC7Cdxm2z1cFJq2X4KUln9GqSAQh/y5lXQlITW0bSmXwKcEkd6/kmSbPIAuAR4He7Z6SJ6GyS/rIFaVm/IWnCq81l6bzX0vVMIkmadXmYZDTknDSG7ezZBFRnbLX4GclggUckbSLZJ6PrWT7XH9P/ayQ9X3NmRMwEfkQysGEF8FbgyZz5jwJ/AF4m6aB/oK6CcvbpUGAxUEHSlAtJ39LvSJp6F5Dsj8+lr9tA8h7+hqQ2sCV9bX3GATMkbSbZP+dHxPZaYvoryfH0T5Kmvn/WWOTL6fSn02a4v5PU8gGGpc83k+yfX0bjfjt3MzAibQr80z4cawBfBD5MMoDi1yTvQa5rgd+mZZxbY5t3Au8FzkrL+iXw8Yh4tRGxd0nLW0dyfK4BrmvE66wOiqi3tcPsgJD0A+DgiPhE1rGYWeFyTcsyIekwSUemv2MZRTIQ4L6s4zKzwuZfiltWOpM0CfYBVpI0qf0504jMrOC5edDMzIqGmwfNzKxoFE3zYFlZWQwaNCjrMMzMrIlNmzZtdUTU/G0hUERJa9CgQUydOjXrMMzMrIlJqvOKNm4eNDOzouGkZWZmRcNJy8zMioaTlpmZFQ0nLTMzKxpOWmZmVjQySVqSDpd0o6S7JdW8RYCZmVmt8pa0JN0iaaWk6TWmj5M0W9K83XcqjYhZEXExyQ39RuYrBjMza97y+ePiiSS3lb5t94T0jqk3AGNJ7ufznKT7I2KmpPcCV6evKVi3PrmAG//1n6zDMDMrCh8/YRCXvnNok60/b0krIqZIGlRj8ihgXkTMB5B0J3AOMDMi7gful/QgcEe+4si3qQvXsXVnFe9+6yFZh2JmVvAO7dmxSdff1Jdx6sued5etAEant6t+P8ktwB+q68WSJgATAAYMGNB0UdYjCA7u0o7vf+DITMo3M7M3NHXSUi3TIr3F9uSGXhwRNwE3AYwcOTKTe6hUV4Nq2wozMzvgmnr0YAXQP+d5P2BZE5eZV9URlDhrmZkVhKZOWs8BwyQNltQGOB+4f29WIOlsSTdt2LChSQJsSCQxZFK2mZntKZ9D3icBTwHlkiokjY+ISuAy4GFgFnBXRMzYm/VGxF8iYkLXrl3zFepeiYha2zjNzOzAy+fowQvqmP4Q9Qy2KHTVASW+boiZWUHw6bgB4T4tM7OCUfBJK+s+reqofQikmZkdeAWftDLv08IDMczMCkXBJ62sJc2DWUdhZmbgpNWg6gjXtMzMCkTBJ62s+7QicE3LzKxAFHzSyrpPqzoCeSiGmVlBKPiklbXq8LUHzcwKhZNWQwL/TsvMrEA4aTUgGYiRdRRmZgZFkLSyHojhq7ybmRWOgk9aWQ/ESH5cnEnRZmZWQ8EnrawlAzGctczMCoGTVkN8RQwzs4LhpNWAao8eNDMrGAWftAphIIZTlplZYSj4pJX5QAz3aZmZFYyCT1pZq3aflplZwXDSakD4Mk5mZgXDSasBgX9cbGZWKJy0GuAL5pqZFQ4nrQb4JpBmZoWj4JNW1kPefZV3M7PCUfBJK+sh7/6dlplZ4Sj4pJW1AA95NzMrEE5aDfCtSczMCoeTVgOqq8Htg2ZmhcFJqxFc0zIzKwxOWg3wZZzMzAqHk1YDktGDzlpmZoXASasBEVDivWRmVhAK/nSc9Y+Lq31rEjOzglHwSSvrHxeHf1xsZlYwCj5pZS35cbHTlplZIXDSakBywdysozAzM3DSalD4grlmZgXDSasBrmmZmRUOJ60GRODfaZmZFQgnrQaEr4hhZlYwnLQaUB1Q4qxlZlYQnLQa4JtAmpkVDietBgS+IoaZWaFw0mqA+7TMzAqHk1YDkmsPZh2FmZlBESStrC+Ym9S0nLXMzApBwSetrC+YWx14IIaZWYEo+KSVpYgAPBDDzKxQOGnVI81Zbh40MysQTlr1qH69ppVxIGZmBjhp1SutaHnIu5lZgXDSqke1+7TMzAqKk1Y9dvdpOWeZmRUGJ616eCCGmVlhcdKqx+7mQfdpmZkVBieterzep+WfF5uZFQQnrXrsHj3o1kEzs8LgpFWPqE7+u0/LzOz/t3d/IXJedRjHn8fEtFLLYm1aSv7YVEIgV21Z4kWh9EJrqtRUsZhcSJXQtdCIXniRimAvraAXpVXZ0tAKNSG01iYQjV4oRSiaWKJNDNE1rWZNaaKFVbwwpPPzYmZ2l92d0415Z85vMt8PhN09OzvvyY+XeTjvOe95cyC0CkLcXAwAmRBaBS1WDwJAKoRWAds4AUAuhFbB3M3FpBYAZEBoFQT3aQFAKlVCy/Z9tp+y/ZLtu2v0YTm6c1rcpwUAOTQWWrb32D5n+/iC9q22T9mesr1bkiLiJxHxoKQvSPpcU31oWnf1ICMtAMihyZHWM5K2zm+wvULSk5LukbRZ0g7bm+e95Bud36fE6kEAyKWx0IqIlyW9vaB5i6SpiDgdERck7ZO0zW2PSfppRLzaVB+a1pq7PggASKDfc1prJJ2Z9/N0p+3Lkj4q6bO2H+r1x7YnbB+1ffT8+fP97WkBIy0AyGFln99/qU/7iIjHJT3+bn8cEZOSJiVpfHw83uXljWOXdwDIpd8jrWlJ6+b9vFbS2T4fszE8BBIAcul3+PWRwgAAC5tJREFUaB2RtNH2BturJG2XdOBS3sD2vbYnZ2Zm+tLBkrmRFqkFABk0ueR9r6RXJG2yPW17Z0RclLRL0mFJJyXtj4gTl/K+EXEwIibGxsaa6uqytQZ+QRIAUNLYnFZE7OjRfkjSoaaOM1iMtAAgE7ZxKuA+LQDIJX1oZZjTIrMAIIf0oVVzTitmR1oDPzQAYAnpQ6umuZEWqQUAGRBaBcEuTgCQSvrQqjmnFSzEAIBU0odW3fu0Okve01cJAEYDH8cF3XuLeQgkAORAaBWw5B0AciG0CoK9BwEglfShlWEhBpkFADmkD60MG+Yy0gKAHNKHVk2zc1qV+wEAaCO0CuYuDxJbAJABoVUwtxCjckcAAJKGILTq7vI+24eBHxsAsFj60Kq6y7sYaQFAJulDqyZGWgCQC6FVEOyIAQCpEFoF7PIOALkQWgUtVg8CQCqEVsHcQyBJLQDIIH1o1V3yzpwWAGSSPrTYexAA0JU+tOpipAUAmRBaBYy0ACAXQquAOS0AyIXQKpi7T6tuPwAAbYRWwdxIi9QCgAwIrWUgsgAgB0KrYG5HDGILADJIH1pVby5utb8SWgCQQ/rQqvs8rTYyCwBySB9aNbHkHQByIbQKgjktAEiF0CqY3eWdzAKAFAitArZxAoBcCK2C2Tmtyv0AALQRWgVzqweJLQDIgNAqmFuIUbkjAABJhFbR3EIMUgsAMiC0ClqMtAAgFUKroMVICwBSIbQKgh0xACCV9KFVc8Pc4D4tAEglfWjV3DCXOS0AyCV9aNU0e58WtxcDQAqEVgG7vANALoRWAXNaAJALoVXA6kEAyIXQKmCXdwDIhdAqmN3GqW43AAAdhFYBCzEAIBdCqyAiZLONEwBkQWgVhLg0CACZEFoFrQgWYQBAIoRWQStYOQgAmRBaBcH1QQBIhdAqiAg2ywWARAitAua0ACAXQqsggquDAJAJoVXAQgwAyIXQKggFu2EAQCJVQsv2Lbaftv18jeMvVwS7YQBAJo2Flu09ts/ZPr6gfavtU7anbO+WpIg4HRE7mzp2v7RYPQgAqTQ50npG0tb5DbZXSHpS0j2SNkvaYXtzg8fsK0ZaAJBLY6EVES9LentB8xZJU52R1QVJ+yRtW+572p6wfdT20fPnzzfV1WVjpAUAufR7TmuNpDPzfp6WtMb2B23/QNJtth/p9ccRMRkR4xExvnr16j53dbEWIy0ASGVln99/qU/8iIh/Snqoz8duQHCfFgAk0u+R1rSkdfN+Xivp7KW8ge17bU/OzMw02rHlaLW4TwsAMul3aB2RtNH2BturJG2XdOBS3iAiDkbExNjYWF86WMKcFgDk0uSS972SXpG0yfa07Z0RcVHSLkmHJZ2UtD8iTjR1zH4LMacFAJk0NqcVETt6tB+SdKip4wxSK9gRAwAySb+NU805LbH3IACkkj60as9pkVkAkEf60KqJXd4BIBdCqyDE87QAIJP0oVX1Pi0uDwJAKulDq+acVkRweRAAEkkfWjW1d3mv3QsAQBehVdBipAUAqRBaBezyDgC5pA+tmgsxIlg9CACZpA+t6gsx0lcIAEYHH8kFIW4uBoBMCK2CVvAQSADIhNAqYCEGAORCaBUED4EEgFTSh1b11YOMtAAgjfShVfvRJIy0ACCP9KFVU/s+LVILALIgtArY5R0AciG0CoKHQAJAKoRWQYiRFgBkQmgVtBhpAUAq6UOr7pJ3RloAkEn60Kq75J37tAAgk/ShVRM7YgBALoRWAbu8A0AuhFYBu7wDQC6EVkGrxZwWAGRCaBW0Lw/W7gUAoIvQKmDJOwDkQmgVtHd5J7UAIIv0oVX/eVoDPywAoIf0oVX7eVosxACAPNKHVk3cpwUAuRBaBe2HQAIAsiC0Clps4wQAqRBaBTwEEgByIbQKWlwfBIBUCK0CRloAkAuhVcCjSQAgF0KroBWSuT4IAGkQWgWtCL2HCgFAGnwkF4QkVmIAQB7pQ6vu3oPMaQFAJulDq+beg6weBIBc0odWTS2epwUAqRBaBS1GWgCQCqFVwJOLASAXQqsguE8LAFIhtArY5R0AciG0CkLSe0gtAEiD0CpoRXBxEAASIbQKWiGZlRgAkAahVRJiTgsAEiG0Cri5GAByIbQKQtxcDACZEFoFLMQAgFwIrYJgIQYApEJo9RDRfpoWlwcBIA9Cq4dWO7NYiAEAiRBaPbRmR1qVOwIAmEVo9RCzIy1SCwCyWFnjoLavkfQ9SRck/SoinqvRj5LuSIvMAoA8Ghtp2d5j+5zt4wvat9o+ZXvK9u5O82ckPR8RD0r6VFN9aFJ3pMVCDADIo8mR1jOSnpD0w26D7RWSnpT0MUnTko7YPiBpraTXOi97p8E+9LTn16/rhVenl/362YUYfeoPAODSNRZaEfGy7ZsXNG+RNBURpyXJ9j5J29QOsLWSjqkw2rM9IWlCktavX39Z/bv26pW6aezqS/qb9de9T3dtuuGyjgsAaE6/57TWSDoz7+dpSR+R9LikJ2x/UtLBXn8cEZOSJiVpfHw8Lqcj94+v0/3j6y7nLQAAlfU7tJa6uhYR8R9JX+zzsQEAV5h+L3mfljR/eLNW0tlLeQPb99qenJmZabRjAIDh0+/QOiJpo+0NtldJ2i7pwKW8QUQcjIiJsbGxvnQQADA8mlzyvlfSK5I22Z62vTMiLkraJemwpJOS9kfEiaaOCQAYLU2uHtzRo/2QpENNHQcAMLrSb+PEnBYAoCt9aDGnBQDoSh9aAAB0EVoAgKHh7hN6s7N9XtJfL/Ntrpf0jwa6c6WhLotRk8WoydKoy2KXW5MPRcTqpX4xNKHVBNtHI2K8dj+yoS6LUZPFqMnSqMti/awJlwcBAEOD0AIADI1RC63J2h1IirosRk0WoyZLoy6L9a0mIzWnBQAYbqM20gIADDFCCwAwNEYmtGxvtX3K9pTt3bX7U4vtN2y/ZvuY7aOdtuts/8L2nztfP1C7n/1me4/tc7aPz2vrWQfbj3TOnVO2P16n1/3VoyaP2v5753w5ZvsT8343CjVZZ/uXtk/aPmH7K532kT1XCjUZzLkSEVf8P0krJP1F0i2SVkn6vaTNtftVqRZvSLp+Qdu3Je3ufL9b0mO1+zmAOtwp6XZJx9+tDpI2d86ZqyRt6JxLK2r/HwZUk0clfW2J145KTW6SdHvn+2sl/anzfx/Zc6VQk4GcK6My0toiaSoiTkfEBUn7JG2r3KdMtkl6tvP9s5Luq9iXgYiIlyW9vaC5Vx22SdoXEf+NiNclTal9Tl1RetSkl1GpyZsR8Wrn+3+r/VzANRrhc6VQk14arcmohNYaSWfm/TytcpGvZCHp57Z/Z3ui03ZjRLwptU9ISTdU611dveow6ufPLtt/6Fw+7F4GG7ma2L5Z0m2SfiPOFUmLaiIN4FwZldDyEm2jutb/joi4XdI9kh62fWftDg2BUT5/vi/pw5JulfSmpO902keqJrbfL+kFSV+NiH+VXrpE2xVZlyVqMpBzZVRCa1rSunk/r5V0tlJfqoqIs52v5yS9qPYw/S3bN0lS5+u5ej2sqlcdRvb8iYi3IuKdiGhJekpzl3VGpia236v2h/NzEfHjTvNInytL1WRQ58qohNYRSRttb7C9StJ2SQcq92ngbF9j+9ru95LulnRc7Vo80HnZA5JeqtPD6nrV4YCk7bavsr1B0kZJv63Qv4HrfjB3fFrt80UakZrYtqSnJZ2MiO/O+9XIniu9ajKoc2Xl//uHwyQiLtreJemw2isJ90TEicrdquFGSS+2zzmtlPSjiPiZ7SOS9tveKelvku6v2MeBsL1X0l2Srrc9Lembkr6lJeoQESds75f0R0kXJT0cEe9U6Xgf9ajJXbZvVftyzhuSviSNTk0k3SHp85Jes32s0/Z1jfa50qsmOwZxrrCNEwBgaIzK5UEAwBWA0AIADA1CCwAwNAgtAMDQILQAAEOD0AIADA1CCwAwNP4HbWBbvYZPxmoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : nan\n",
      "Sur les pressions : nan\n"
     ]
    }
   ],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE QUASI-NEWTON\")\n",
    "copt, gopt, xopt,gnl_QN, gsl_QN, cl_QN = BFGS_L(OraclePG, x0, 1)\n",
    "#copt, gopt, xopt = Newton_N(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### experiment of comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n"
     ]
    }
   ],
   "source": [
    "# experiment of comparison\n",
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ALGORITHME DU GRADIENT A PAS FIXE\n",
      "\n",
      "Iteration : 3957\n",
      "Temps CPU : 0.453125\n",
      "Critere optimal : -3.7340070480435\n",
      "Norme du gradient : 9.984468154399097e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 2.220446049250313e-16\n",
      "Sur les pressions : 9.984420770159375e-07\n"
     ]
    }
   ],
   "source": [
    "print(\"ALGORITHME DU GRADIENT A PAS FIXE\")\n",
    "copt, gopt, xopt,gnl_GF, gsl_GF, cl_GF = Gradient_F(OraclePG, x0, 0.0005)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ALGORITHME DE NEWTON A PAS FIXE\n",
      "\n",
      "Iteration : 5\n",
      "Temps CPU : 0.046875\n",
      "Critere optimal : -3.7340070480435763\n",
      "Norme du gradient : 2.3324847955473776e-11\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 9.71445146547012e-17\n",
      "Sur les pressions : 1.999262908003452e-11\n"
     ]
    }
   ],
   "source": [
    "print(\"ALGORITHME DE NEWTON A PAS FIXE\")\n",
    "copt, gopt, xopt,gnl_NF, gsl_NF, cl_NF  = Newton_F(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ALGORITHME DU GRADIENT A PAS VARIABLE\n",
      "\n",
      "Iteration : 259\n",
      "Temps CPU : 0.484375\n",
      "Critere optimal : -3.7340070480435035\n",
      "Norme du gradient : 9.980616892539242e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 1.1102230246251565e-16\n",
      "Sur les pressions : 9.598970013291463e-07\n"
     ]
    }
   ],
   "source": [
    "print(\"ALGORITHME DU GRADIENT A PAS VARIABLE\")\n",
    "copt, gopt, xopt,gnl_GV, gsl_GV, cl_GV = Gradient_V(OraclePG, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ALGORITHME DU GRADIENT CONJUGUE\n",
      "\n",
      "Iteration : 189\n",
      "Temps CPU : 0.296875\n",
      "Critere optimal : -3.7340070480435656\n",
      "Norme du gradient : 9.772456840615705e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 2.220446049250313e-16\n",
      "Sur les pressions : 5.908401026211152e-07\n"
     ]
    }
   ],
   "source": [
    "print(\"ALGORITHME DU GRADIENT CONJUGUE\")\n",
    "copt, gopt, xopt,gnl_GC, gsl_GC, cl_GC = PolakRibiere(OraclePG, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ALGORITHME DE QUASI-NEWTON\n",
      "\n",
      "Iteration : 20\n",
      "Temps CPU : 0.03125\n",
      "Critere optimal : -3.7340070480435728\n",
      "Norme du gradient : 8.550875761754614e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Verification des equations d'equilibre du reseau\n",
      "Sur les debits : 1.3877787807814457e-16\n",
      "Sur les pressions : 6.840609456659763e-07\n"
     ]
    }
   ],
   "source": [
    "print(\"ALGORITHME DE QUASI-NEWTON\")\n",
    "copt, gopt, xopt,gnl_QN, gsl_QN, cl_QN = BFGS(OraclePG, x0, 1)\n",
    "#copt, gopt, xopt = Newton_N(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Visualg2(gradient_lists, step_lists, criterere_lists): \n",
    "\n",
    "    import matplotlib.pyplot as plt \n",
    "    \n",
    "    plt.subplot (2, 1, 1) \n",
    "    plt.gca().set_title (\"Gradient norm during iterations\") \n",
    "    plt.gca().set_yscale ('log') \n",
    "    plt.plot(gradient_lists[0], label = \"Gradient norm_Algorithm1\")\n",
    "    plt.plot(gradient_lists[1], label = \"Gradient norm_Algorithm2\") \n",
    "    plt.plot(gradient_lists[2], label = \"Gradient norm_Algorithm3\") \n",
    "    \n",
    "    plt.subplot (2, 1, 2) \n",
    "    \n",
    "    plt.gca().set_title(\"Stepsize during iterations\") \n",
    "    plt.gca().set_yscale('log')\n",
    "    plt.plot(step_lists[0], label = \"Step length_Algorithm1\") \n",
    "    plt.plot(step_lists[1], label = \"Step length_Algorithm2\") \n",
    "    plt.plot(step_lists[2], label = \"Step length_Algorithm3\") \n",
    "    \n",
    "    plt.tight_layout (rect = (0, 0, 1, 2)) \n",
    "    plt.show ()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "gradient_lists = [gnl_GF,gnl_GV,gnl_GC]\n",
    "step_lists = [gsl_GF, gsl_GV, gsl_GC]\n",
    "criterere_lists = [cl_GF, cl_GV, cl_GC]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Visualg2(gradient_lists, step_lists, criterere_lists)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.f On écrit l'algorithme de Newton à pas variable et on le teste"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Newton_V(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy.linalg import norm\n",
    "    from numpy.linalg import solve\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables  \n",
    "    \n",
    "    iter_max = 100\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    critere_list = []\n",
    "\n",
    "    time_start = process_time()\n",
    "    \n",
    "    x = x0\n",
    "\n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        # ---> A COMPLETER\n",
    "        # ---> A COMPLETER\n",
    "           \n",
    "    ##### Resultats de l'optimisation\n",
    "    \n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "    \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE NEWTON A PAS VARIABLE\")\n",
    "copt, gopt, xopt = Newton_V(OraclePH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## II. Résolution du problème dual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from HydrauliqueD import HydrauliqueD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.a On écrit les oracles pour le problème dual d'optimisation :\n",
    "\n",
    "* **OracleDG** : calcul de la fonction et du gradient,\n",
    "* **OracleDH** : calcul de la fonction du gradient et du Hessien."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OracleDG(pd):\n",
    "    \n",
    "    # ---> A COMPLETER\n",
    "    # ---> A COMPLETER\n",
    "    \n",
    "    return critere, gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OracleDH(pd):\n",
    "    \n",
    "    # ---> A COMPLETER\n",
    "    # ---> A COMPLETER\n",
    "    \n",
    "    return critere, gradient, hessien"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.b On exécute tous les algorithmes d'optimisation déjà écrits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 100 + random.normal(size=md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME DUAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT A PAS VARIABLE\")\n",
    "copt, gopt, xopt = Gradient_V(OracleDG, x0, 5)\n",
    "qopt, zopt, fopt, popt = HydrauliqueD(xopt, m, mr, r, pr, fd, A, Ar)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 100 + random.normal(size=md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME DUAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DU GRADIENT CONJUGUE\")\n",
    "copt, gopt, xopt = PolakRibiere(OracleDG, x0, 5)\n",
    "qopt, zopt, fopt, popt = HydrauliqueD(xopt, m, mr, r, pr, fd, A, Ar)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 100 + random.normal(size=md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME DUAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE QUASI-NEWTON\")\n",
    "copt, gopt, xopt = BFGS(OracleDG, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueD(xopt, m, mr, r, pr, fd, A, Ar)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 100 + random.normal(size=md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME DUAL\")\n",
    "print()\n",
    "print(\"ALGORITHME DE NEWTON A PAS VARIABLE\")\n",
    "copt, gopt, xopt = Newton_V(OracleDH, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueD(xopt, m, mr, r, pr, fd, A, Ar)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## III. Résolution de grands réseaux (facultatif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On charge dans l'environnement les données du problème\n",
    "\n",
    "Ces données correspondent à un réseau de taille paramétrable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Probleme_P import *\n",
    "from Structures_S import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### III.a On écrit des oracles primal et dual avec Hessien creux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OraclePHS(qc):\n",
    "    \n",
    "    # ---> A COMPLETER\n",
    "    # ---> A COMPLETER\n",
    "    \n",
    "    return critere, gradient, hessien"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OracleDHS(pd):\n",
    "    \n",
    "    # ---> A COMPLETER\n",
    "    # ---> A COMPLETER\n",
    "    \n",
    "    return critere, gradient, hessien"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### III.b On écrit un algorithme de Newton exploitant le creux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Newton_S(Oracle, x0, alpha0):\n",
    "    \n",
    "    from numpy.linalg import norm\n",
    "    from scipy.sparse.linalg import spsolve\n",
    "    from time import process_time\n",
    "    \n",
    "    ##### Initialisation des variables  \n",
    "    \n",
    "    iter_max = 100\n",
    "    default_gradient_step = alpha0\n",
    "    threshold = 0.000001\n",
    "    \n",
    "    gradient_norm_list = []\n",
    "    gradient_step_list = []\n",
    "    critere_list = []\n",
    "\n",
    "    time_start = process_time()\n",
    "    \n",
    "    x = x0\n",
    "\n",
    "    ##### Boucle sur les iterations\n",
    "    \n",
    "    for k in range(iter_max):\n",
    "        \n",
    "        # ---> A COMPLETER\n",
    "        # ---> A COMPLETER\n",
    "           \n",
    "    ##### Resultats de l'optimisation\n",
    "    \n",
    "    critere_opt = critere\n",
    "    gradient_opt = gradient\n",
    "    x_opt = x\n",
    "    time_cpu = process_time() - time_start\n",
    "\n",
    "    print()\n",
    "    print('Iteration :', k)\n",
    "    print('Temps CPU :', time_cpu)\n",
    "    print('Critere optimal :', critere_opt)\n",
    "    print('Norme du gradient :', norm(gradient_opt))\n",
    "    \n",
    "    # Visualisation de la convergence\n",
    "    Visualg(gradient_norm_list, gradient_step_list, critere_list)\n",
    "    \n",
    "    return critere_opt, gradient_opt, x_opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### III.c On résoud le problème dans le primal et dans le dual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 0.1 * random.normal(size=n-md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME PRIMAL DE GRANDE TAILLE\")\n",
    "print()\n",
    "print(\"ALGORITHME DE NEWTON A PAS VARIABLE\")\n",
    "copt, gopt, xopt = Newton_S(OraclePHS, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueP(xopt, m, mr, md, r, pr, fd, Ar, AdI, B, q0)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = 100 + random.normal(size=md)\n",
    "print()\n",
    "print(\"MINIMISATION DU PROBLEME DUAL DE GRANDE TAILLE\")\n",
    "print()\n",
    "print(\"ALGORITHME DE NEWTON A PAS VARIABLE\")\n",
    "copt, gopt, xopt = Newton_S(OracleDHS, x0, 1)\n",
    "qopt, zopt, fopt, popt = HydrauliqueD(xopt, m, mr, r, pr, fd, A, Ar)\n",
    "Verification(A, qopt, zopt, fopt, popt)"
   ]
  }
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