TP_Reseau_Notebook_3.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": "markdown",
   "metadata": {},
   "source": [
    " **Algorithm 9.2: Backtracking line search.**  \n",
    "given a descent direction $ \\Delta x$ for $f$ at $x \\in \\operatorname{dom}f$, $\\alpha \\in(0,0.5)$, $\\beta \\in (0,1)$, $t:=1$.  \n",
    "while $ f(x+t \\Delta x)>f(x)+\\alpha t \\nabla f(x)^{T} \\Delta x $:  \n",
    "  $ t:=\\beta t $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BacktrackingLineSearch(qc,critere,gradient,delta_x,\n",
    "                           alpha = 0.1, beta = 0.9):\n",
    "    step = 0.0006\n",
    "    qc_new = qc + step * delta_x\n",
    "    q = q0 + B.dot (qc_new)\n",
    "    critere_new = 1/3*q.dot(r*q*abs(q)) + pr.dot(Ar.dot(q))\n",
    "    while critere_new > critere + alpha * step * gradient.transpose()@delta_x:\n",
    "        step *= beta\n",
    "    return step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I. Résolution du problème primal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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 $\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def OraclePG(qc):\n",
    "    \n",
    "    gradient =B.transpose()@(r*(q0+B@qc)*abs(q0+B@qc))+B.transpose()@Ar.transpose()@pr\n",
    "    critere = dot(q0+B@qc, r*(q0+B@qc)*abs(q0+B@qc))/3 + dot(pr, Ar@(q0+B@qc))\n",
    "    \n",
    "    return critere, gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\nabla^{2} F\\left(q_{c}\\right)=2B^{T} \\operatorname{diag}(\\mathrm{r} \\cdot|q| ) \\mathrm{B} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT A PAS FIXE\n",
      "\n",
      "Iteration : 4251\n",
      "Temps CPU : 0.46875\n",
      "Critere optimal : -3.7340070480435035\n",
      "Norme du gradient : 9.969921205401012e-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 : 2.220446049250313e-16\n",
      "Sur les pressions : 9.96987274293204e-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 = 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": 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 : -3.7340070480435674\n",
      "Norme du gradient : 1.7102387853126185e-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 : 1.6653345369377348e-16\n",
      "Sur les pressions : 1.5422566002065707e-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 = 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": [
    "### I.b On écrit l'algorithme de recherche linéaire (conditions de Wolfe)."
   ]
  },
  {
   "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": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "cond1 = (1<3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cond1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "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": "markdown",
   "metadata": {},
   "source": [
    "### I.c On écrit l'algorithme du gradient à pas variable et on le teste"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT A PAS VARIABLE\n",
      "\n",
      "Iteration : 278\n",
      "Temps CPU : 0.140625\n",
      "Critere optimal : -3.7340070480435177\n",
      "Norme du gradient : 8.916973748167236e-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 : 8.25503188583987e-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 = 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": [
    "### I.d On écrit l'algorithme de gradient conjugué (Polak-Ribière) et on le teste"
   ]
  },
  {
   "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": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [1,2,3,4,5]\n",
    "a[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "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 = 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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DU GRADIENT CONJUGUE\n",
      "\n",
      "Iteration : 186\n",
      "Temps CPU : 0.140625\n",
      "Critere optimal : -3.734007048043555\n",
      "Norme du gradient : 6.278062157055749e-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 : 3.862137845089819e-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 = 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": "markdown",
   "metadata": {},
   "source": [
    "### I.e On écrit l'algorithme de quasi-Newton (BFGS) et on le teste"
   ]
  },
  {
   "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": 307,
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "MINIMISATION DU PROBLEME PRIMAL\n",
      "\n",
      "ALGORITHME DE QUASI-NEWTON\n",
      "\n",
      "Iteration : 25\n",
      "Temps CPU : 0.0\n",
      "Critere optimal : -3.7340070480435728\n",
      "Norme du gradient : 6.351514259831606e-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 : 4.210555033523633e-07\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 = 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": [
    "### 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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