From 74b5c790d8f5a0da3b08c605d77dfc895e5273ef Mon Sep 17 00:00:00 2001 From: theking90000 Date: Tue, 10 Dec 2024 14:58:15 +0100 Subject: [PATCH] Final --- QUESTION12.ipynb | 51 ++++++++++++++++++++++++++++---- QUESTION13.ipynb | 75 ++++++++++++++++++++++++++---------------------- 2 files changed, 86 insertions(+), 40 deletions(-) diff --git a/QUESTION12.ipynb b/QUESTION12.ipynb index 2d56241..cc6f2f2 100644 --- a/QUESTION12.ipynb +++ b/QUESTION12.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 8, + "execution_count": 6, "id": "c5dc3dd5-c340-4aa6-a898-b467845121e6", "metadata": { "tags": [] @@ -16,7 +16,7 @@ }, { "cell_type": "code", - "execution_count": 102, + "execution_count": 34, "id": "073124ba-d6bd-4f82-9431-fe81bdc77c21", "metadata": { "tags": [] @@ -36,7 +36,7 @@ " R = np.zeros((m,n))\n", " \n", " for i in range(m):\n", - " # Vecteur ligne de A = \n", + " # Vecteur ligne de A\n", " v = A[:,i]\n", " pr = 0\n", " \n", @@ -59,7 +59,7 @@ }, { "cell_type": "code", - "execution_count": 103, + "execution_count": 16, "id": "e35d7cf5-cbbe-4948-98ed-a241643110d0", "metadata": { "tags": [] @@ -74,7 +74,7 @@ }, { "data": { - "image/png": "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", + "image/png": "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", "text/plain": [ "
" ] @@ -86,16 +86,22 @@ "source": [ "x = np.arange(2, 201)\n", "y = np.zeros(len(x))\n", + "yr = np.zeros(len(x))\n", "\n", "for i in range(len(x)):\n", " A = hilbert(x[i])\n", + " \n", " Q, R = decompoQR(A)\n", " y[i] = np.linalg.norm(Q.T@Q - np.identity(x[i]))\n", " \n", + " Q, R = np.linalg.qr(A)\n", + " yr[i] = np.linalg.norm(Q.T@Q - np.identity(x[i]))\n", + " \n", "Q, R = decompoQR(hilbert(8))\n", "print(Q[:,1]@Q[:,2])\n", "#print(y)\n", "plt.plot(x, y, color= 'b')\n", + "plt.plot(x, yr, color= 'b')\n", "plt.xlabel('dimension n')\n", "plt.ylabel('Erreur ||Q\\'Q - I||')\n", "plt.title('Perte d\\'orthogonalité')\n", @@ -106,8 +112,43 @@ { "cell_type": "code", "execution_count": null, + "id": "b5d9e208-d00f-4ef7-98ca-cd398c6fcf78", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 33, "id": "ea75b7ed-f555-46b7-af0c-6549d09ffe82", "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.7085507187094725e-15\n", + "3.4655609795412117\n" + ] + } + ], + "source": [ + "n=10\n", + "A = hilbert(n)\n", + "\n", + "Q, R = np.linalg.qr(A)\n", + "# print('A=', A)\n", + "print(np.linalg.norm(Q.T@Q - np.identity(n)))\n", + "\n", + "Q2, R2 = decompoQR(A)\n", + "print(np.linalg.norm(Q2.T@Q2 - np.identity(n)))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e36ec24e-7673-4339-babe-57c12f248ae4", + "metadata": {}, "outputs": [], "source": [] } diff --git a/QUESTION13.ipynb b/QUESTION13.ipynb index 0e71a13..a480885 100644 --- a/QUESTION13.ipynb +++ b/QUESTION13.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 9, + "execution_count": 72, "id": "349bd8d2-2bc8-45e3-9f8a-7d60f7dedd39", "metadata": { "tags": [] @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 73, "id": "885fccca-d36b-4d94-ba40-03eb06df2c57", "metadata": {}, "outputs": [], @@ -33,7 +33,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 74, "id": "69c3443f-b60c-4ebd-a640-c187eedc0e69", "metadata": { "tags": [] @@ -41,12 +41,43 @@ "outputs": [], "source": [ "def decompoQR(A):\n", - " return np.linalg.qr(A) # tkt" + " \"\"\"\n", + " A = QR\n", + " \n", + " Q = Matrice vecteurs orthogonaux (colonnes)\n", + " R = Coéfficients des projections sur les vecteurs (triangulaire sup)\n", + " \n", + " \"\"\"\n", + " m, n = A.shape\n", + " Q = np.zeros((m,m))\n", + " R = np.zeros((m,n))\n", + " \n", + " for i in range(m):\n", + " # Vecteur ligne de A\n", + " v = A[:,i]\n", + " pr = 0\n", + " \n", + " # Retirer projection sur v des autres vecteurs\n", + " # proj A sur B = A@B/(B@B) * B\n", + " for j in range(0, i):\n", + " av = Q[:,j]\n", + "\n", + " pr += (av.T@v)* av\n", + " v = v - pr\n", + "\n", + " # normalisation vecteur\n", + " Q[:,i] = v/np.linalg.norm(v)\n", + " \n", + " \n", + " R = Q.T@A\n", + " \n", + " return Q, R\n", + " #return np.linalg.qr(A) # tkt" ] }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 78, "id": "0a1a13da-c084-4a5d-945f-b9edd39b5a24", "metadata": { "tags": [] @@ -56,7 +87,7 @@ "def algoQR(A, maxiter=10**3):\n", " B = A\n", " Q = np.identity(A.shape[0])\n", - " print('init', 'B=',B,'Q=', Q)\n", + " #print('init', 'B=',B,'Q=', Q)\n", " for k in range(maxiter):\n", " Qk, Rk = decompoQR(B)\n", " B = Rk@Qk\n", @@ -67,7 +98,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 79, "id": "0662681f-fac3-4db2-b296-a6720eb41ad2", "metadata": { "tags": [] @@ -82,13 +113,6 @@ " [0. 1. 2. 1.]\n", " [0. 0. 1. 2.]]\n", "Valeur propres [3.61803399 2.61803399 0.38196601 1.38196601]\n", - "init B= [[2. 1. 0. 0.]\n", - " [1. 2. 1. 0.]\n", - " [0. 1. 2. 1.]\n", - " [0. 0. 1. 2.]] Q= [[1. 0. 0. 0.]\n", - " [0. 1. 0. 0.]\n", - " [0. 0. 1. 0.]\n", - " [0. 0. 0. 1.]]\n", "[3.61803399 2.61803399 1.38196601 0.38196601]\n" ] } @@ -106,38 +130,19 @@ }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 80, "id": "bfde5aa5-407f-400f-9347-3e1a7a9a47e4", "metadata": { "tags": [] }, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "init B= [[2. 1. 0. ... 0. 0. 0.]\n", - " [1. 2. 1. ... 0. 0. 0.]\n", - " [0. 1. 2. ... 0. 0. 0.]\n", - " ...\n", - " [0. 0. 0. ... 2. 1. 0.]\n", - " [0. 0. 0. ... 1. 2. 1.]\n", - " [0. 0. 0. ... 0. 1. 2.]] Q= [[1. 0. 0. ... 0. 0. 0.]\n", - " [0. 1. 0. ... 0. 0. 0.]\n", - " [0. 0. 1. ... 0. 0. 0.]\n", - " ...\n", - " [0. 0. 0. ... 1. 0. 0.]\n", - " [0. 0. 0. ... 0. 1. 0.]\n", - " [0. 0. 0. ... 0. 0. 1.]]\n" - ] - }, { "data": { "text/plain": [ "[]" ] }, - "execution_count": 68, + "execution_count": 80, "metadata": {}, "output_type": "execute_result" },