From 86f1ed1a4f122eb7dd2db0c312252224de0e222d Mon Sep 17 00:00:00 2001
From: marcellus <msimon_fr@hotmail.com>
Date: Sun, 22 Jun 2025 21:49:40 +0200
Subject: notes: 2025-06-22 21:49:40 from w11

---
 ...35 Syst\303\250me matriciel -- Exercices.ipynb" | 81 +++++++++++++++-------
 1 file changed, 56 insertions(+), 25 deletions(-)

(limited to 'PVCM/cama/fr/ma35 Système matriciel -- Exercices.ipynb')

diff --git "a/PVCM/cama/fr/ma35 Syst\303\250me matriciel -- Exercices.ipynb" "b/PVCM/cama/fr/ma35 Syst\303\250me matriciel -- Exercices.ipynb"
index 2107be6..7ce0cf2 100644
--- "a/PVCM/cama/fr/ma35 Syst\303\250me matriciel -- Exercices.ipynb"	
+++ "b/PVCM/cama/fr/ma35 Syst\303\250me matriciel -- Exercices.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": "3.8.10"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2,
  "cells": [
   {
    "cell_type": "markdown",
@@ -64,8 +43,39 @@
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x mieux = [1.0000019  0.99999905]\n",
+      "[1. 3.]\n"
+     ]
+    }
+   ],
+   "source": [
+    "def solve_partial_gauss(A, b):\n",
+    "    A = A.astype(np.float64)   # si A a des entiers, on va avoir des erreurs de calculs\n",
+    "    for i in range(len(A)-1):\n",
+    "        pivot = i + np.argmax(np.abs(A[i:,i]))\n",
+    "        A[[i,pivot]] = A[[pivot, i]]\n",
+    "        b[[i,pivot]] = b[[pivot, i]]\n",
+    "        coefs = - A[i+1:,i] / A[i,i]  # Normalement il faut tester que A[i,i] != 0\n",
+    "        A[i+1:, i:] += np.outer(coefs, A[i, i:]) # ou np.einsum('i,j -> ij', coefs, A[i, i:])\n",
+    "        b[i+1:] += coefs * b[i]\n",
+    "    # A est maintenant triangulaire surpérieur\n",
+    "    res = np.zeros(len(b), dtype=b.dtype)\n",
+    "    res[-1] = b[-1] / A[-1,-1]\n",
+    "    for i in range(len(A)-1)[::-1]:\n",
+    "        res[i] = (b[i] - A[i,i+1:] @ res[i+1:]) / A[i,i]\n",
+    "    return res\n",
+    "e = 1E-6\n",
+    "A = np.array([[e, 1], [1, 2]], dtype='float32')\n",
+    "b = np.array([1., 3.], dtype='float32')\n",
+    "x = solve_partial_gauss(A,b)\n",
+    "print(\"x mieux =\", x)\n",
+    "print(A @ x )"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -186,5 +196,26 @@
    "outputs": [],
    "source": []
   }
- ]
-}
\ 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": "3.13.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
-- 
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