From 7dbffb1f42d822e940559e41acccfca248c0d8b1 Mon Sep 17 00:00:00 2001 From: theking90000 Date: Tue, 10 Dec 2024 13:44:37 +0100 Subject: [PATCH] Modification Q9 --- QUESTION9.ipynb | 72 ++++++++++++++++++++++++++++++++++++------------- 1 file changed, 53 insertions(+), 19 deletions(-) diff --git a/QUESTION9.ipynb b/QUESTION9.ipynb index 1803ec8..d154119 100644 --- a/QUESTION9.ipynb +++ b/QUESTION9.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 4, "id": "0ae8d8f4-2f60-4ef3-bf50-eae61169de5d", "metadata": { "tags": [] @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 5, "id": "d984aa22-593e-48ea-a27d-beeb3b6377d8", "metadata": { "tags": [] @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 6, "id": "8835175c-38bc-42cf-8af5-ec9a13c7410f", "metadata": { "tags": [] @@ -57,7 +57,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 16, "id": "94e34e9e-d397-4010-8b0a-d51d79ae52a4", "metadata": { "tags": [] @@ -75,6 +75,7 @@ " for j in range(i+1, n):\n", " if pivot == 0:\n", " pass\n", + " raise Exception('Singular Matrix')\n", " # print('pivot is 0', 'ij',i,j, A[i,:])\n", " c = A[j,i]/pivot\n", " b[j] -= c * b[i]\n", @@ -85,7 +86,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 17, "id": "6834425f-f943-4c17-906d-5409e0f90413", "metadata": { "tags": [] @@ -102,7 +103,7 @@ " pmax =A[i,i]\n", " lmax = i\n", " for j in range(i+1,n):\n", - " if A[j, i] >= pmax:\n", + " if abs(A[j, i]) >= abs(pmax):\n", " pmax = A[j,i]\n", " lmax = j\n", " \n", @@ -121,6 +122,7 @@ " for j in range(i+1, n):\n", " if pivot == 0:\n", " pass\n", + " raise Exception('Singular Matrix')\n", " # print('pivot is 0', 'ij',i,j, A[i,:])\n", " c = A[j,i]/pivot\n", " b[j] -= c * b[i]\n", @@ -131,27 +133,41 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 26, "id": "556548f6-bc0c-4f04-8cad-8f0be037e8d2", "metadata": { "tags": [] }, "outputs": [ { - "name": "stderr", + "name": "stdout", "output_type": "stream", "text": [ - "C:\\Users\\theking\\AppData\\Local\\Temp\\ipykernel_35980\\378739895.py:13: RuntimeWarning: divide by zero encountered in scalar divide\n", - " c = A[j,i]/pivot\n", - "C:\\Users\\theking\\AppData\\Local\\Temp\\ipykernel_35980\\378739895.py:15: RuntimeWarning: invalid value encountered in multiply\n", - " A[j] -= c * A[i]\n", - "C:\\Users\\theking\\AppData\\Local\\Temp\\ipykernel_35980\\378739895.py:13: RuntimeWarning: invalid value encountered in scalar divide\n", - " c = A[j,i]/pivot\n" + "1.1102230246251565e-16\n", + "1.1157603309187458e-15\n", + "3.356474311340335e-15\n", + "1.0045524680675924e-14\n", + "4.368329060208651e-14\n", + "1.952160427256209e-13\n", + "1.9973313828599363e-11\n", + "3.7077837198237614e-10\n", + "5.231805851568996e-11\n", + "3.0347215613783297e-10\n", + "6.285550799311683e-11\n", + "6.777947420435342e-11\n", + "1.3628762349179106e-11\n", + "2.8897510754239285e-12\n", + "7.201856338832219e-12\n", + "1.5802032097691353e-10\n", + "Enable to solve(gauss) for n = 19 Singular Matrix\n", + "4.3542124286715616e-12\n", + "Enable to solve(gauss) for n = 20 Singular Matrix\n", + "2.9464159842374688e-12\n" ] }, { "data": { - "image/png": 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", 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", 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" ] @@ -164,16 +180,34 @@ "en = np.arange(3, 21, 1)\n", "e = []\n", "epivot = []\n", + "\n", + "er = []\n", "for n in en:\n", " A,b = getAb(n)\n", - " x = GaussianElimination(A, b)\n", - " e.append(np.linalg.norm(A@x - b))\n", + " try:\n", + " x = GaussianElimination(A, b)\n", + " e.append(np.linalg.norm(A@x - b))\n", + " except Exception as ex:\n", + " print('Enable to solve(gauss) for n =', n, ex)\n", + " e.append(0)\n", " \n", - " x = GaussianEliminationWithPivoting(A, b)\n", - " epivot.append(np.linalg.norm(A@x - b))\n", + " try:\n", + " x = GaussianEliminationWithPivoting(A, b)\n", + " epivot.append(np.linalg.norm(A@x - b))\n", + " except Exception as e:\n", + " print('Enable to solve(Pivot) for n =', n, e)\n", + " epivot.append(0)\n", + " \n", + " try:\n", + " x = np.linalg.solve(A, b)\n", + " print(np.linalg.norm(A@x - b))\n", + " er.append(np.linalg.norm(A@x - b))\n", + " except Exception as e:\n", + " print('Enable to solve for n =', n, e)\n", "\n", "plt.plot(en, e, label='||Ax-b|| sans pivoting')\n", "plt.plot(en, epivot, label='||Ax-b|| avec pivoting')\n", + "plt.plot(en, er, label='||Ax-b|| avec numpy')\n", "plt.yscale('log')\n", "plt.legend()\n", "plt.show()"