From 320aedd827b0070f0699fe8bc0c20a790a267b69 Mon Sep 17 00:00:00 2001
From: marcellus <msimon_fr@hotmail.com>
Date: Wed, 11 Jun 2025 12:44:10 +0200
Subject: update

---
 ... pour r\303\251soudre Ax = b -- Exercice.ipynb" | 161 +++++++++++++++------
 1 file changed, 114 insertions(+), 47 deletions(-)

(limited to 'PVCM')

diff --git "a/PVCM/cama/fr/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb" "b/PVCM/cama/fr/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb"
index 2a7cf27..46ec5a8 100644
--- "a/PVCM/cama/fr/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb"	
+++ "b/PVCM/cama/fr/ma54 Gradient pour r\303\251soudre Ax = b -- Exercice.ipynb"	
@@ -1,25 +1,4 @@
 {
- "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": "3.10.12"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 4,
  "cells": [
   {
    "cell_type": "markdown",
@@ -41,27 +20,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def solve_with_gradiant(A, b):\n",
-    "    mu = 0.01\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([[49, 13],\n",
-       "       [13, 13]])"
+       "array([[0.15, 0.15],\n",
+       "       [0.15, 0.55]])"
       ]
      },
-     "execution_count": 34,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -71,21 +40,22 @@
     "A = np.random.randint(10, size=(2,2))\n",
     "A = A + A.T\n",
     "A += np.diag(A.sum(axis=1))\n",
+    "A = A / np.sum(np.abs(A))\n",
     "A"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 26,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([62, 26])"
+       "array([0.3, 0.7])"
       ]
      },
-     "execution_count": 35,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -97,9 +67,37 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 36,
    "metadata": {},
    "outputs": [],
+   "source": [
+    "def solve_with_gradiant(A, b):\n",
+    "    mu = 0.01\n",
+    "    xi = np.array(np.zeros(b.shape))\n",
+    "    while True:\n",
+    "        xn = xi - mu * (A @ xi - b)\n",
+    "        if np.square(xn - xi).sum() < 1e-6 ** 2:\n",
+    "            break\n",
+    "        xi = xn\n",
+    "    return xi"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0.9990519 , 1.00031603])"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "solve_with_gradiant(A,b)"
    ]
@@ -117,10 +115,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 39,
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0.9990519 , 1.00031603])"
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def solve_with_gradiant_inertie(A, b):\n",
+    "    mu = 0.01\n",
+    "    i = 0.5\n",
+    "    xi = np.array(np.zeros(b.shape))\n",
+    "    while True:\n",
+    "        xn = xi - mu * (A @ xi - b)\n",
+    "        if np.square(xn - xi).sum() < 1e-6 ** 2:\n",
+    "            break\n",
+    "        xi = xn\n",
+    "    return xi\n",
+    "solve_with_gradiant_inertie(A, b)"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -173,10 +194,56 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 40,
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0.99999941, 0.99999941])"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def solve_with_gradiant_inertie_opti(A, b):\n",
+    "    mu = 0.01\n",
+    "    i = 0.5\n",
+    "    xi = np.array(np.zeros(b.shape))\n",
+    "    while True:\n",
+    "        J = A @ xi - b\n",
+    "        mu = np.dot(J, J) / np.dot(A @ J, J)\n",
+    "        xn = xi - mu * (A @ xi - b)\n",
+    "        if np.square(xn - xi).sum() < 1e-6 ** 2:\n",
+    "            break\n",
+    "        xi = xn\n",
+    "    return xi\n",
+    "solve_with_gradiant_inertie_opti(A,b)"
+   ]
   }
- ]
-}
\ No newline at end of file
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "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": "3.13.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
-- 
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