{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "06e7bcdb-1ecc-4bd2-9aa9-7fb025fc63cd",
   "metadata": {},
   "source": [
    "## MT09 - TP4 - Automne 2025\n",
    "### Calcul approché de valeurs propres, puissances itérées, puissances inverses, déflation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "668fd69c-d772-469c-a611-76e49a3797d4",
   "metadata": {},
   "source": [
    "### 1. Algorithme des puissances itérées\n",
    "\n",
    "Programmer l'algorithme des puissances itérées \n",
    "\n",
    "```\n",
    "xsol, lambdasol, kout, boolcvg = puissancesIterees(A, x0, tol, kmax)\n",
    "```\n",
    "\n",
    "pour une matrice $A$ et un vecteur initial $x_0\\neq 0$, une tolérance de précision $tol$ et un nombre maximal d'itérations $k_{max}$. La sortie ```boolcvg``` retournera 1 si la tolérance est atteinte, 0 sinon. Le critère de convergence à l'itération $k$ sera\n",
    "\n",
    "$$\n",
    "\\|A x^{(k)} - \\lambda^{(k)} x^{(k)}\\|_2\\, < tol.\n",
    "$$\n",
    "L'entier $k_{out}$ est l'indice d'itération de sortie."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5adc3ca8-8334-440d-8639-ca3719def520",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.linalg as la\n",
    "\n",
    "def puissancesIterees(A, x0, tol, kmax):\n",
    "    k=0\n",
    "    xk = x0\n",
    "    while (k<kmax):\n",
    "        k = k + 1\n",
    "        xk = A@xk;\n",
    "        xk = xk / la.norm(xk)\n",
    "        lambdak = xk.T @ A @ xk\n",
    "        if ( la.norm(A@xk-lambdak*xk)<tol ):\n",
    "            boolcvg = 1\n",
    "            return xk, lambdak, k, boolcvg\n",
    "    boolcvg = 0\n",
    "    return xk, lambdak, k, boolcvg\n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7bee834-9014-4442-9ce8-feb93a346dc2",
   "metadata": {},
   "source": [
    "Codez une matrice générique $A$ de taille $n$ définie par\n",
    "$$\n",
    "A = \\text{tridiag}(-1, 2, -1).\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2de7ec55-6104-4e7f-a078-35599fce28b1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A = \n",
      " [[ 2. -1.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [-1.  2. -1.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0. -1.  2. -1.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0. -1.  2. -1.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0. -1.  2. -1.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0. -1.  2. -1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0. -1.  2. -1.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0. -1.  2. -1.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0. -1.  2. -1.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0. -1.  2.]]\n"
     ]
    }
   ],
   "source": [
    "n = 10;\n",
    "A = 2*np.diag(np.ones(n)) - np.diag(np.ones(n-1),-1) - np.diag(np.ones(n-1),1)\n",
    "print(\"A = \\n\", A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f4a0519-5a11-4948-9885-afbc8297017e",
   "metadata": {
    "tags": []
   },
   "source": [
    "Appliquer l'algorithme de puissances itérées à la matrice $A$ en choisissant $x_0=(1,0,...,0)^T=\\mathbf{e}_1$, $kmax=1000$ et $tol=10^{-8}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8f86faf0-6a32-453e-89af-e156ef7ca5b6",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "kmax = 2000\n",
    "x0 = np.zeros(n)\n",
    "x0[0] = 1\n",
    "tol = 1e-8\n",
    "xsol, lambdasol, kout, boolcvg = puissancesIterees(A, x0, tol, kmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "28a1e657-3d87-4c83-ae2d-8bfe968a724e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.12013118, -0.23053003,  0.32225272, -0.3878684 ,  0.42206129,\n",
       "        -0.42206128,  0.38786837, -0.32225268,  0.23053   , -0.12013116]),\n",
       " np.float64(3.9189859472289945),\n",
       " 284)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xsol, lambdasol, kout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1600635c-9f64-464f-9e80-8651785dbd7c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lambda =  3.9189859472289945 kout =  284\n"
     ]
    }
   ],
   "source": [
    "print(\"lambda = \", lambdasol, \"kout = \", kout)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "15eec56f-7467-43ff-8a2f-ebf483811df4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(9.55676310414599e-09)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "la.norm(A@xsol - lambdasol*xsol)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab425569-5195-4efb-afdc-052c60104a1c",
   "metadata": {
    "tags": []
   },
   "source": [
    "En fait, dans ce cas particulier, on peut calculer analytiquement les valeurs propres de $A$, elles sont données par la formule\n",
    "\n",
    "$$\n",
    "\\lambda_j = 4\\sin^2\\left(\\frac{j\\pi}{2(n+1)}\\right), \\quad 1\\leq j\\leq n.\n",
    "$$\n",
    "Vérifiez que l'algorithme de puissances itérées approche bien la plus grande valeur propre de $A$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e41ede6c-52c5-4ad6-8d35-0b121b2cafc8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.08101405 0.31749293 0.69027853 1.16916997 1.71537032 2.28462968\n",
      " 2.83083003 3.30972147 3.68250707 3.91898595]\n",
      "erreur =  0.0\n"
     ]
    }
   ],
   "source": [
    "j = np.arange(1,n+1)\n",
    "lambdaj = 4*( np.sin(0.5*j*np.pi/(n+1)) )**2\n",
    "print(lambdaj)\n",
    "print(\"erreur = \", lambdasol - lambdaj[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b07f1ff2-4633-4fec-b1ef-a70471440fb9",
   "metadata": {},
   "source": [
    "### 2. Algorithme des puissances itérées inverses\n",
    "\n",
    "Programmer l'algorithme des puissances itérées inverses\n",
    "\n",
    "```\n",
    "xsol, lambdasol, kout, boolcvg = puissancesItereesInverses(A, x0, tol, kmax)\n",
    "```\n",
    "\n",
    "pour une matrice $A$ et un vecteur initial $x_0\\neq 0$, une tolérance de précision $tol$ et un nombre maximal d'itérations $k_{max}$. La sortie ```boolcvg``` retournera 1 si la tolérance est atteinte, 0 sinon. Le critère de convergence à l'itération $k$ sera\n",
    "\n",
    "$$\n",
    "\\|A x^{(k)} - \\lambda^{(k)} x^{(k)}\\|< tol.\n",
    "$$\n",
    "\n",
    "On utilisera ```la.solve()``` pour résoudre les systèmes linéaires de l'algorithme."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0e2f392f-724e-446c-a99e-0ac9715e2ae9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def puissancesItereesInverses(A, x0, tol, kmax):\n",
    "    k=0\n",
    "    xk = x0\n",
    "    while (k<kmax):\n",
    "        k = k + 1\n",
    "        zk = la.solve(A, xk) \n",
    "        xk = zk / la.norm(zk)\n",
    "        lambdak = xk @ A @ xk # x.T A  x\n",
    "        if ( la.norm(A@xk - lambdak*xk)<tol ):\n",
    "            boolcvg = 1\n",
    "            return xk, lambdak, k, boolcvg\n",
    "    boolcvg = 0\n",
    "    return xk, lambdak, k, boolcvg"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75893490-2456-49bc-984d-ed8d11353003",
   "metadata": {},
   "source": [
    "Appliquer l'algorithme de puissances itérées à la matrice tridiagonale $A$ en choisissant $x_0=(1,0,...,0)^T$, $kmax=1000$ et $tol=10^{-5}$. Vérifiez que l'algorithme de puissances itérées inverses approche bien la plus petite valeur propre de $A$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ff1366b4-8b6f-4aeb-b9c2-a27701cf3b27",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "kmax = 200\n",
    "x0 = np.zeros(n)\n",
    "x0[0] = 1\n",
    "tol = 1e-5\n",
    "xsol, lambdasol, kout, boolcvg = puissancesItereesInverses(A, x0, tol, kmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e9134c1e-6e73-401b-9b54-7657974e5631",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.12013915, 0.23054344, 0.32226728, 0.38787949, 0.42206539,\n",
       "       0.4220571 , 0.38785726, 0.32223817, 0.23051668, 0.12012325])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xsol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "65aaa9bf-fa4c-41c2-9b79-c65f075b4b86",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lambda =  0.08101405305230241\n",
      "erreur =  2.812971938714881e-10\n"
     ]
    }
   ],
   "source": [
    "print(\"lambda = \", lambdasol)\n",
    "print(\"erreur = \", lambdasol - lambdaj[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7a34f67-4c4c-4ada-96f5-8249f749acb4",
   "metadata": {},
   "source": [
    "### 3. Méthode de déflation pour une matrice symétrique\n",
    "\n",
    "La méthode de déflation permet de calculer toutes les valeurs propres d'une matrice. Dans le cas d'une matrice symétrique, l'algorithme de déflation est particulièrement simple. Une fois calculé la plus grande valeur propre $\\lambda_n$ (en valeur absolue) avec le vecteur propre associé $\\mathbf{x}_n$, on considère la matrice \"retranchée\"\n",
    "\n",
    "$$\n",
    "A \\leftarrow A - \\lambda_n\\, \\mathbf{x}_n \\mathbf{x}_n^T,\n",
    "$$\n",
    "\n",
    "et on réapplique la méthode de puissances itérées. On itère jusqu'à obtenir la matrice nulle.\n",
    "Programmer une méthode \n",
    "\n",
    "```\n",
    "D, V = deflation(A)\n",
    "```\n",
    "\n",
    "qui calcule le tableau $D$ constitué des valeurs propres de $A$ et la matrice $V$ des vecteurs propres en faisant appel à ```puissancesIterees()```. Appliquer à la matrice tridiagonale précédente. Comparer les valeurs propres calculées aux valeurs propres exactes. Pour cette matrice $A$ symétrique, vérifiez que la matrice $V$ est une matrice orthogonale aux erreurs d'approximation près (on prendra $k_{max}=1000$ et $tol=10^{-8}$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3a75ddc1-ff0d-4b0d-be34-fa2e41b1193b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def deflation(Ainput):\n",
    "    A = np.copy(Ainput)\n",
    "    m,n = A.shape\n",
    "    kmax = 1000\n",
    "    x0 = np.zeros(n)\n",
    "    x0[0] = 1\n",
    "    tol = 1e-12\n",
    "    D = np.zeros(n)\n",
    "    V = np.zeros((n,n))\n",
    "    for k in range(0,n):\n",
    "        xsol, lambdasol, kout, boolcvg = puissancesIterees(A, x0, tol, kmax)\n",
    "        D[(n-1)-k] = lambdasol\n",
    "        V[:, (n-1)-k] = xsol\n",
    "        A = A - lambdasol * np.outer(xsol, xsol)\n",
    "    return D, V, A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "653fb0b4-72ba-4cde-820b-90f338d9e1f8",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "D, V, A = deflation(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "f78d65ed-ca96-4d5b-9332-59f194fdfde3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.15544362e-30  3.15544362e-30  3.15544362e-30  6.31088724e-30\n",
      "  6.31088724e-30  6.31088724e-30  6.31088724e-30  6.31088724e-30\n",
      "  1.26217745e-29  1.26217745e-29  1.26217745e-29  1.26217745e-29\n",
      "  1.57772181e-29  1.57772181e-29  1.57772181e-29  4.10207671e-29\n",
      "  3.47098798e-29 -3.62876016e-28 -5.30891131e-12  5.55046181e-12] \n",
      "\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (20,) (10,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[36], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[38;5;28mprint\u001b[39m(D,\u001b[38;5;124m\"\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m----> 2\u001b[0m \u001b[38;5;28mprint\u001b[39m(D \u001b[38;5;241m-\u001b[39m lambdaj)\n\u001b[0;32m      3\u001b[0m \u001b[38;5;28mprint\u001b[39m(A)\n",
      "\u001b[1;31mValueError\u001b[0m: operands could not be broadcast together with shapes (20,) (10,) "
     ]
    }
   ],
   "source": [
    "print(D,\"\\n\")\n",
    "print(D - lambdaj)\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "a40392b4-40cc-417a-91c0-c438810778f8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.28371386,  0.28371386,  0.28371386,  0.28371386,  0.28371386,\n",
       "         0.28371386,  0.28371386,  0.28371386,  0.28371386,  0.28371386,\n",
       "         0.28371386,  0.28371386,  0.28371386,  0.28371386,  0.28371386,\n",
       "         0.28371386,  0.28371386,  0.28371386, -0.28371386,  0.23471473],\n",
       "       [-0.15842894, -0.15842894, -0.15842894, -0.15842894, -0.15842894,\n",
       "        -0.15842894, -0.15842894, -0.15842894, -0.15842894, -0.15842894,\n",
       "        -0.15842894, -0.15842894, -0.15842894, -0.15842894, -0.15842894,\n",
       "        -0.15842894, -0.15842894, -0.15842894,  0.15842894, -0.32048294],\n",
       "       [ 0.21240904,  0.21240904,  0.21240904,  0.21240904,  0.21240904,\n",
       "         0.21240904,  0.21240904,  0.21240904,  0.21240904,  0.21240904,\n",
       "         0.21240904,  0.21240904,  0.21240904,  0.21240904,  0.21240904,\n",
       "         0.21240904,  0.21240904,  0.21240904, -0.21240904,  0.01420563],\n",
       "       [-0.02840721, -0.02840721, -0.02840721, -0.02840721, -0.02840721,\n",
       "        -0.02840721, -0.02840721, -0.02840721, -0.02840721, -0.02840721,\n",
       "        -0.02840721, -0.02840721, -0.02840721, -0.02840721, -0.02840721,\n",
       "        -0.02840721, -0.02840721, -0.02840721,  0.02840721, -0.31328552],\n",
       "       [ 0.2939967 ,  0.2939967 ,  0.2939967 ,  0.2939967 ,  0.2939967 ,\n",
       "         0.2939967 ,  0.2939967 ,  0.2939967 ,  0.2939967 ,  0.2939967 ,\n",
       "         0.2939967 ,  0.2939967 ,  0.2939967 ,  0.2939967 ,  0.2939967 ,\n",
       "         0.2939967 ,  0.2939967 ,  0.2939967 , -0.2939967 , -0.02024108],\n",
       "       [ 0.2644595 ,  0.2644595 ,  0.2644595 ,  0.2644595 ,  0.2644595 ,\n",
       "         0.2644595 ,  0.2644595 ,  0.2644595 ,  0.2644595 ,  0.2644595 ,\n",
       "         0.2644595 ,  0.2644595 ,  0.2644595 ,  0.2644595 ,  0.2644595 ,\n",
       "         0.2644595 ,  0.2644595 ,  0.2644595 , -0.2644595 , -0.10340615],\n",
       "       [ 0.20942243,  0.20942243,  0.20942243,  0.20942243,  0.20942243,\n",
       "         0.20942243,  0.20942243,  0.20942243,  0.20942243,  0.20942243,\n",
       "         0.20942243,  0.20942243,  0.20942243,  0.20942243,  0.20942243,\n",
       "         0.20942243,  0.20942243,  0.20942243, -0.20942243, -0.20560167],\n",
       "       [ 0.20352963,  0.20352963,  0.20352963,  0.20352963,  0.20352963,\n",
       "         0.20352963,  0.20352963,  0.20352963,  0.20352963,  0.20352963,\n",
       "         0.20352963,  0.20352963,  0.20352963,  0.20352963,  0.20352963,\n",
       "         0.20352963,  0.20352963,  0.20352963, -0.20352963, -0.24454117],\n",
       "       [ 0.09463993,  0.09463993,  0.09463993,  0.09463993,  0.09463993,\n",
       "         0.09463993,  0.09463993,  0.09463993,  0.09463993,  0.09463993,\n",
       "         0.09463993,  0.09463993,  0.09463993,  0.09463993,  0.09463993,\n",
       "         0.09463993,  0.09463993,  0.09463993, -0.09463993, -0.38536269],\n",
       "       [ 0.32137628,  0.32137628,  0.32137628,  0.32137628,  0.32137628,\n",
       "         0.32137628,  0.32137628,  0.32137628,  0.32137628,  0.32137628,\n",
       "         0.32137628,  0.32137628,  0.32137628,  0.32137628,  0.32137628,\n",
       "         0.32137628,  0.32137628,  0.32137628, -0.32137628, -0.1492625 ],\n",
       "       [ 0.21281607,  0.21281607,  0.21281607,  0.21281607,  0.21281607,\n",
       "         0.21281607,  0.21281607,  0.21281607,  0.21281607,  0.21281607,\n",
       "         0.21281607,  0.21281607,  0.21281607,  0.21281607,  0.21281607,\n",
       "         0.21281607,  0.21281607,  0.21281607, -0.21281607, -0.26765153],\n",
       "       [ 0.30166864,  0.30166864,  0.30166864,  0.30166864,  0.30166864,\n",
       "         0.30166864,  0.30166864,  0.30166864,  0.30166864,  0.30166864,\n",
       "         0.30166864,  0.30166864,  0.30166864,  0.30166864,  0.30166864,\n",
       "         0.30166864,  0.30166864,  0.30166864, -0.30166864, -0.1595687 ],\n",
       "       [ 0.3195911 ,  0.3195911 ,  0.3195911 ,  0.3195911 ,  0.3195911 ,\n",
       "         0.3195911 ,  0.3195911 ,  0.3195911 ,  0.3195911 ,  0.3195911 ,\n",
       "         0.3195911 ,  0.3195911 ,  0.3195911 ,  0.3195911 ,  0.3195911 ,\n",
       "         0.3195911 ,  0.3195911 ,  0.3195911 , -0.3195911 , -0.11795041],\n",
       "       [ 0.22457166,  0.22457166,  0.22457166,  0.22457166,  0.22457166,\n",
       "         0.22457166,  0.22457166,  0.22457166,  0.22457166,  0.22457166,\n",
       "         0.22457166,  0.22457166,  0.22457166,  0.22457166,  0.22457166,\n",
       "         0.22457166,  0.22457166,  0.22457166, -0.22457166, -0.18907022],\n",
       "       [ 0.00492879,  0.00492879,  0.00492879,  0.00492879,  0.00492879,\n",
       "         0.00492879,  0.00492879,  0.00492879,  0.00492879,  0.00492879,\n",
       "         0.00492879,  0.00492879,  0.00492879,  0.00492879,  0.00492879,\n",
       "         0.00492879,  0.00492879,  0.00492879, -0.00492879, -0.38643426],\n",
       "       [ 0.14336067,  0.14336067,  0.14336067,  0.14336067,  0.14336067,\n",
       "         0.14336067,  0.14336067,  0.14336067,  0.14336067,  0.14336067,\n",
       "         0.14336067,  0.14336067,  0.14336067,  0.14336067,  0.14336067,\n",
       "         0.14336067,  0.14336067,  0.14336067, -0.14336067, -0.18451539],\n",
       "       [ 0.26712198,  0.26712198,  0.26712198,  0.26712198,  0.26712198,\n",
       "         0.26712198,  0.26712198,  0.26712198,  0.26712198,  0.26712198,\n",
       "         0.26712198,  0.26712198,  0.26712198,  0.26712198,  0.26712198,\n",
       "         0.26712198,  0.26712198,  0.26712198, -0.26712198,  0.00901095],\n",
       "       [ 0.22602695,  0.22602695,  0.22602695,  0.22602695,  0.22602695,\n",
       "         0.22602695,  0.22602695,  0.22602695,  0.22602695,  0.22602695,\n",
       "         0.22602695,  0.22602695,  0.22602695,  0.22602695,  0.22602695,\n",
       "         0.22602695,  0.22602695,  0.22602695, -0.22602695,  0.02906181],\n",
       "       [ 0.04149066,  0.04149066,  0.04149066,  0.04149066,  0.04149066,\n",
       "         0.04149066,  0.04149066,  0.04149066,  0.04149066,  0.04149066,\n",
       "         0.04149066,  0.04149066,  0.04149066,  0.04149066,  0.04149066,\n",
       "         0.04149066,  0.04149066,  0.04149066, -0.04149066, -0.10246301],\n",
       "       [-0.24694501, -0.24694501, -0.24694501, -0.24694501, -0.24694501,\n",
       "        -0.24694501, -0.24694501, -0.24694501, -0.24694501, -0.24694501,\n",
       "        -0.24694501, -0.24694501, -0.24694501, -0.24694501, -0.24694501,\n",
       "        -0.24694501, -0.24694501, -0.24694501,  0.24694501, -0.3439916 ]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f454e604-5e2b-494d-95c8-e36f682a6955",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.6639457442208882e-07)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "la.norm(V.T@V - np.eye(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "213e0c1b-9006-4a1b-8d0e-a6d0d6e30a2f",
   "metadata": {},
   "source": [
    "### 4. \"Visualisation\" des vecteurs proppres\n",
    "\n",
    "Tracez les $n$ vecteurs propres  de $A$ comme s'il s'agissait de fonctions discrétisées sur un intervalle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b72f3e64-3dca-4824-9d01-0dbc99df08ac",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "fig, axs = plt.subplots(5, 2)\n",
    "axs[0,0].plot(V[:,0], '-k')\n",
    "axs[0,1].plot(V[:,1], '-k')\n",
    "axs[1,0].plot(V[:,2], '-k')\n",
    "axs[1,1].plot(V[:,3], '-k')\n",
    "axs[2,0].plot(V[:,4], '-k')\n",
    "axs[2,1].plot(V[:,5], '-k')\n",
    "axs[3,0].plot(V[:,6], '-k')\n",
    "axs[3,1].plot(V[:,7], '-k')\n",
    "axs[4,0].plot(V[:,8], '-k')\n",
    "axs[4,1].plot(V[:,9], '-k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ed12de2-105e-4e2b-ab84-4e3f6e2d5c42",
   "metadata": {},
   "source": [
    "### 5. Vibrations propres d'un système masses-ressorts\n",
    "\n",
    "#### 5.a Solution harmonique\n",
    "\n",
    "On considère une chaîne horizontale constituée de $N$ masses-ressorts de masse $m$ et de coefficient de raideur $k$ identiques. La chaîne est de longueur $L$ et fixée à ses deux extrémités. On néglige les frottements au sol. Le mouvement global peut être représenté par les équations de la cinématique et de la dynamique :\n",
    "\n",
    "\\begin{align*}\n",
    "& \\frac{d\\mathbf{u}}{dt} = \\mathbf{v},\\\\[1.3ex]\n",
    "& m \\frac{d\\mathbf{v}}{dt} = - k\\, A\\mathbf{u}\n",
    "\\end{align*}\n",
    "\n",
    "où $A\\in\\mathcal{M}_N(\\mathbb{R})$ est la matrice\n",
    "\n",
    "$$\n",
    "A=\\frac{1}{h^2}\\,\\text{tridiag}(-1,2,-1)\n",
    "$$\n",
    "\n",
    "avec $h=\\frac{L}{N+1}$. Les vecteur $\\mathbf{u}\\in\\mathbb{R}^N$ est le vecteur des déplacements, $\\mathbf{v}\\in\\mathbb{R}^N$ le vecteur des vitesses. \n",
    "\n",
    "En regroupant les deux systèmes d'équations, on obtient\n",
    "\n",
    "$$\n",
    "m\\,\\frac{d^2\\mathbf{u}}{dt^2} + k\\,A\\mathbf{u} = 0.\n",
    "$$\n",
    "\n",
    "Sur brouillon, cherchez une solution de la forme\n",
    "\n",
    "$$\n",
    "\\mathbf{u}(t) =  \\varphi(t) \\,\\, \\mathbf{w}\n",
    "$$\n",
    "\n",
    "pour une certaine fonction temporelle $\\varphi(t)$ et un vecteur constant $\\mathbf{w}\\in\\mathbb{R}^N$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a466a250-cd51-4ebb-a31c-932b894f6f0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A w_1 = lambda_1 w_1\n",
    "# varphi(t) = sin(sqrt(\\lambda_1 \\sqrt(k/m) t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02b3687f-485e-4d10-b9ad-1db56bf12a11",
   "metadata": {},
   "source": [
    "#### 5.b Mode basse fréquence\n",
    "\n",
    "On considère $N=20$, $L=m=k=1$. Avec l'aide de la méthode des puissances itérées inverses, calculez le mode vibratoire de plus basse fréquence : on calculera\n",
    "la valeur propre et le vecteur propre associé, ainsi que la fonction temporelle $\\varphi(t)$ associée."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "b3ecc9e1-9590-40fc-a98c-b5193a3bdfc9",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.04599544 0.09096342 0.13389943 0.17384434 0.20990586 0.24127843\n",
      " 0.26726124 0.28727388 0.30086929 0.30774377 0.30774377 0.30086929\n",
      " 0.28727388 0.26726124 0.24127843 0.20990586 0.17384434 0.13389943\n",
      " 0.09096342 0.04599544] \n",
      " 15\n",
      "lambda_1 =  9.85121126943663\n",
      "lambda_2 =  39.18478529662381\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 20;\n",
    "L = 1.0\n",
    "h = L / (N+1.0)\n",
    "A = 2*np.diag(np.ones(N)) - np.diag(np.ones(N-1),-1) - np.diag(np.ones(N-1),1)\n",
    "A = A / (h*h)\n",
    "kmax = 400\n",
    "x0 = np.ones(N)\n",
    "tol = 1e-12\n",
    "xsol, lambdasol, kout, boolcvg = puissancesItereesInverses(A, x0, tol, kmax)\n",
    "w = xsol\n",
    "print(w, '\\n', kout)\n",
    "plt.plot(w, 'o-'); plt.grid()\n",
    "lambda1 = xsol@A@xsol\n",
    "print('lambda_1 = ', lambda1)\n",
    "\n",
    "# Deuxième mode : \n",
    "\n",
    "D, V, A = deflation(A)\n",
    "lambda2 = D[1]\n",
    "print('lambda_2 = ', lambda2)\n",
    "#w = V[:,1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "a9a13170-c5a7-467b-bf8a-471860e7b18a",
   "metadata": {},
   "outputs": [],
   "source": [
    "m, k = 1.0, 1.0\n",
    "def varphi(t):\n",
    "    omega = np.sqrt(lambda1 * k/m)\n",
    "    return ( np.sin(omega*t) ) # varphi(t) = sin( sqrt(\\lambda_1 * k/m) t ) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1c7bcb9-ecdb-4a95-9fd6-5a6b226c2416",
   "metadata": {},
   "source": [
    "#### 5.c Animation d'une fonction temporelle\n",
    "\n",
    "Le snippet ```python'' suivant permet d'animer une fonction dépendant du temps.\n",
    "Exécutez-le."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "acae3414-4430-40c7-a84d-65fdf2412aa1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import display, clear_output\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "\n",
    "I=60\n",
    "x = np.linspace(0, 1, 200)\n",
    "\n",
    "fig = plt.figure(figsize = (5,4))\n",
    "ax = fig.subplots() \n",
    "\n",
    "for i in range(I):\n",
    "    ax.clear()\n",
    "    clear_output(wait=True)\n",
    "    t = 0.2*i\n",
    "    y = np.sin(t)*np.sin(4*np.pi*x)\n",
    "    ax.plot(x, y, '.-g'); ax.grid()\n",
    "    plt.ylim([-1.0,1.0])\n",
    "    display(fig)\n",
    "    time.sleep(0.001)\n",
    "\n",
    "clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5004edc-0e9b-4c7c-9337-01a64b4c421f",
   "metadata": {},
   "source": [
    "#### 5.d Animation du mode vibratoire basse fréquence de la chaîne\n",
    "\n",
    "Utilisez un code similaire pour animer le mode vibratoire basse fréquence de la chaîne de masses-ressorts. On prendra\n",
    "\n",
    "```\n",
    "t = 0.5 * np.linspace(0,40)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "f2ddd34a-1107-4097-8525-0adbc7c39db6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import display, clear_output\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "\n",
    "x = np.linspace(0.0, L, N+2)\n",
    "wext = np.concatenate( (np.array([0.0]), w, np.array([0.0])) )\n",
    "\n",
    "fig = plt.figure(figsize = (7,4))\n",
    "ax = fig.subplots() \n",
    "\n",
    "T = 20\n",
    "M = 300\n",
    "for t in np.linspace(0, T, M):\n",
    "    ax.clear()\n",
    "    clear_output(wait=True)\n",
    "    ut = wext * varphi(t)\n",
    "    \n",
    "    pos = x + 0.5*ut\n",
    "    ax.plot(pos, 0*pos,   '-g', marker='s'); \n",
    "    \n",
    "    ax.grid()\n",
    "    plt.ylim([-0.1,0.1])\n",
    "    plt.xlim([-0.1,1.1])\n",
    "    display(fig)\n",
    "\n",
    "clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f1dd0b6c-f3ff-4cae-a23c-00de88b0f825",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "c3e0918b-f551-4dad-82b1-74de0c4b8ce9",
   "metadata": {},
   "source": [
    "### 6. (Optionnel) Mesure d'incertitude sur un résultat\n",
    "\n",
    "Un système est gouverné par un système algébrique\n",
    "\n",
    "$$\n",
    "\\mathbf{F}(\\mathbf{u}) = \\mathbf{b}\n",
    "$$\n",
    "\n",
    "où $\\mathbf{b}$ est le vecteur représentant une force extérieure et $\\mathbf{u}$ est la variable d'état du système (par exemple le vecteur de déplacement). On suppose que $\\mathbf{F}$ est continûment différentiable et \n",
    "qu'il existe un unique $\\mathbf{u}^\\star$ tel que $\\mathbf{F}(\\mathbf{u}^\\star)=\\mathbf{b}$.\n",
    "\n",
    "Un système de capteurs permet de mesurer $b$ avec une certaine incertitude. La certification des\n",
    "capteurs de mesure garantit une erreur relative\n",
    "\n",
    "$$\n",
    "\\frac{\\|\\delta \\mathbf{b}\\|_2}{\\|\\mathbf{b}\\|_2}\n",
    "$$\n",
    "\n",
    "inférieure à $\\eta$. Si une erreur $\\delta \\mathbf{b}$ est commise sur $\\mathbf{b}$, on a une réponse $\\mathbf{u}$ telle que $\\mathbf{F}(\\mathbf{u}) = \\mathbf{b}+\\delta \\mathbf{b}$. Sous l'hypothèse de petites perturbations, on peut linéariser $\\mathbf{F}$ selon\n",
    "\n",
    "$$\n",
    "\\mathbf{F}(\\mathbf{u}) \\approx \\mathbf{F}(\\mathbf{u}^\\star) + DF(\\mathbf{u}^\\star)(\\mathbf{u}-\\mathbf{u}^\\star) = \\mathbf{b} + DF(\\mathbf{u}^\\star)(\\mathbf{u}-\\mathbf{u}^\\star) = \\mathbf{b}+\\delta \\mathbf{b}.\n",
    "$$\n",
    "\n",
    "En notant $\\delta \\mathbf{u} = \\mathbf{u}-\\mathbf{u}^\\star$. On peut donc raisonnablement considérer que\n",
    "\n",
    "$$\n",
    "DF(\\mathbf{u}^\\star) \\delta \\mathbf{u} = \\delta \\mathbf{b}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7200bce-7611-41e3-9056-28b25d8646cf",
   "metadata": {},
   "source": [
    "Q : Comment évaluer numériquement une majoration optimale de $\\dfrac{\\|\\delta \\mathbf{u}\\|_2}{\\|\\mathbf{u}\\|_2}$ ('optimale' au sens où la borne de majoration peut être atteinte) ?."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8f63619-1f72-4ed8-90a7-9d9876ffd91e",
   "metadata": {},
   "source": [
    "**Application** : on considérera $\\mathbf{F}$ linéaire :\n",
    "\n",
    "$$\n",
    "\\mathbf{F}(\\mathbf{u}) = A\\mathbf{u}\n",
    "$$\n",
    "\n",
    "avec\n",
    "\n",
    "$$\n",
    "A = \\frac{1}{\\sqrt{\\varepsilon}} \\begin{pmatrix} 1 & 1 \\\\ 1-\\varepsilon & 1 \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "avec $\\varepsilon = 10^{-7}$. Evaluer numériquement une majoration $M$ (optimale) de\n",
    "$\\dfrac{\\|\\delta \\mathbf{u}\\|_2}{\\|\\mathbf{u}\\|_2}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e1351c2c-ed9d-4714-ae2a-8ed06b66b405",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "c5f758f6-5002-4fe1-b93c-ffca14372a0b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lambda max =  39999998.00000007\n",
      "lambda min =  2.6350182782028436e-08\n",
      "cond_2(A) =  3.896172428862996e+07\n"
     ]
    }
   ],
   "source": [
    "epsilon = 1e-7\n",
    "\n",
    "A = np.ones((2,2))\n",
    "A[1,0] = 1.0-epsilon\n",
    "A = A / np.sqrt(epsilon)\n",
    "\n",
    "B = A.T @ A\n",
    "kmax = 2000\n",
    "x0 = np.zeros(2)\n",
    "x0[0] = 1.0\n",
    "tol = 1e-14\n",
    "xsol, lambdan, kout, boolcvg = puissancesIterees(B, x0, tol, kmax)\n",
    "print(\"lambda max = \", lambdan)\n",
    "xsol, lambda1, kout, boolcvg = puissancesItereesInverses(B, x0, tol, kmax)\n",
    "print(\"lambda min = \", lambda1)\n",
    "# \n",
    "# cond_2(A) = sqrt(lambda_n(A^T A)) / sqrt(lambda_1(A^T A)) \n",
    "print('cond_2(A) = ', np.format_float_scientific(np.sqrt(lambdan/lambda1)) )"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}