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March 8, 2022 08:29
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SPL_gauss_jordan.ipynb
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| { | |
| "nbformat": 4, | |
| "nbformat_minor": 0, | |
| "metadata": { | |
| "colab": { | |
| "name": "SPL_gauss_jordan.ipynb", | |
| "provenance": [], | |
| "authorship_tag": "ABX9TyOWlUir9FlEhypKGF32I3yi", | |
| "include_colab_link": true | |
| }, | |
| "kernelspec": { | |
| "name": "python3", | |
| "display_name": "Python 3" | |
| }, | |
| "language_info": { | |
| "name": "python" | |
| } | |
| }, | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "view-in-github", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "<a href=\"https://colab.research.google.com/gist/DianSano/43d5dc0697bb82c1481875d1a5ce2165/spl_gauss_jordan.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "whqaL78NotM0", | |
| "outputId": "5f36791c-9806-488b-c747-8705f7078fef" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[[1. 1. 1. ]\n", | |
| " [0. 2. 2. ]\n", | |
| " [0. 0. 2.33333333]]\n", | |
| "[4. 6. 2.33333333]\n", | |
| "[[1. 0. 0.]\n", | |
| " [0. 1. 0.]\n", | |
| " [0. 0. 1.]]\n", | |
| "Gauss-Jordan \n", | |
| "The solution of the system is:\n", | |
| "[1. 2. 1.]\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "from numpy import array, zeros, fabs, linalg\n", | |
| "\n", | |
| "a = array([[1, 1, 1],\n", | |
| " [1, -1, -1],\n", | |
| " [2, 8, 1]], float)\n", | |
| "#the b matrix constant terms of the equations \n", | |
| "b = array([4, -2, 19], float)\n", | |
| "\n", | |
| "n = len(b)\n", | |
| "x = zeros(n, float)\n", | |
| "\n", | |
| "# Forward Elimination\n", | |
| "for k in range(n-1):\n", | |
| " if fabs(a[k,k]) < 1.0e-12:\n", | |
| " # if statements checks if the pivot element is zero\n", | |
| " # and swap it with the appropriate row\n", | |
| " for i in range(k+1, n): \n", | |
| " if fabs(a[i,k]) > fabs(a[k,k]):\n", | |
| " a[[k,i]] = a[[i,k]] # Note a[[0,1]] is not the same to a[0,1]\n", | |
| " b[[k,i]] = b[[i,k]]\n", | |
| " break\n", | |
| "\n", | |
| " for i in range(k+1,n):\n", | |
| " if a[i,k] == 0:continue\n", | |
| "\n", | |
| " factor = a[k,k]/a[i,k]\n", | |
| " for j in range(k,n):\n", | |
| " a[i,j] = a[k,j] - a[i,j]*factor\n", | |
| " #we also calculate the b vector of each row\n", | |
| " b[i] = b[k] - b[i]*factor\n", | |
| "print(a)\n", | |
| "print(b)\n", | |
| "\n", | |
| "# Backward Elimination\n", | |
| "for k in range(n-1,0-1,-1):\n", | |
| " c = a[k,k]\n", | |
| " for i in range(0,k):\n", | |
| " b[i] = b[i] - b[k]*a[i,k]/c\n", | |
| " for j in range(n-1,k-1, -1):\n", | |
| " a[i,j] = a[i,j] - a[k,j]* a[i, k]/c\n", | |
| "\n", | |
| " b[k] = b[k]/c\n", | |
| " a[k,k] /= c\n", | |
| " \n", | |
| "\n", | |
| "print(a)\n", | |
| "print(\"Gauss-Jordan \")\n", | |
| "print(\"The solution of the system is:\")\n", | |
| "print(b)\n" | |
| ] | |
| } | |
| ] | |
| } |
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