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SPL_gauss_seidel.ipynb
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| { | |
| "nbformat": 4, | |
| "nbformat_minor": 0, | |
| "metadata": { | |
| "colab": { | |
| "name": "SPL_gauss_seidel.ipynb", | |
| "provenance": [], | |
| "authorship_tag": "ABX9TyMsSxEjKigU2NZA/xTl5Z0G", | |
| "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/a594e0998ed30bf8fad81c5353a3ceee/spl_gauss_seidel.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "TaFS0Ue5qEEw", | |
| "outputId": "25d3c3dc-36c1-4a30-8772-0f76b5313840" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[[ 4. -1. 1.]\n", | |
| " [-1. 4. -2.]\n", | |
| " [ 1. -2. 4.]]\n", | |
| "[12. -1. 5.]\n", | |
| "[3. 1. 1.]\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "import numpy as np\n", | |
| "\n", | |
| "a = np.array([[4, -1, 1],\n", | |
| " [-1, 4, -2],\n", | |
| " [1, -2, 4]], float)\n", | |
| "#the b matrix constant terms of the equations \n", | |
| "b = np.array([12, -1, 5], float)\n", | |
| "\n", | |
| "def gauss_seidel(A, b, tolerance=1e-10, max_iterations=10000):\n", | |
| " \n", | |
| " x = np.zeros_like(b, dtype=np.double)\n", | |
| " \n", | |
| " #Iterate\n", | |
| " for k in range(max_iterations):\n", | |
| " \n", | |
| " x_old = x.copy()\n", | |
| " \n", | |
| " #Loop over rows\n", | |
| " for i in range(A.shape[0]):\n", | |
| " x[i] = (b[i] - np.dot(A[i,:i], x[:i]) - np.dot(A[i,(i+1):], x_old[(i+1):])) / A[i ,i]\n", | |
| " \n", | |
| " #Stop condition \n", | |
| " if np.linalg.norm(x - x_old) / np.linalg.norm(x) < tolerance:\n", | |
| " break\n", | |
| " \n", | |
| " return x\n", | |
| "\n", | |
| "print(a)\n", | |
| "print(b)\n", | |
| "x = gauss_seidel(a, b)\n", | |
| "print(x)\n" | |
| ] | |
| } | |
| ] | |
| } |
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