{"metadata": {"signature": "sha256:ef423c670af97e2e4421195e937d9a6c3accb1a75e6970e4b8e190ee48e567e9", "name": ""}, "nbformat_minor": 0, "nbformat": 3, "worksheets": [{"metadata": {}, "cells": [{"metadata": {}, "cell_type": "markdown", "source": ["# Gaussian elimination"]}, {"outputs": [], "prompt_number": 3, "language": "python", "cell_type": "code", "metadata": {}, "collapsed": false, "input": ["import numpy as np"]}, {"outputs": [{"metadata": {}, "text": ["array([[  2.,  -2.,  12.,  -1.],\n", "       [  1.,   8.,  -5.,  -3.],\n", "       [  1.,  -2.,  -6.,  -1.],\n", "       [ -2.,   3.,  -8.,  -4.]])"], "prompt_number": 18, "output_type": "pyout"}], "prompt_number": 18, "language": "python", "cell_type": "code", "metadata": {}, "collapsed": false, "input": ["\n", "np.random.seed(5)\n", "n = 4\n", "A = np.round(np.random.randn(n, n) * 5)\n", "A"]}, {"metadata": {}, "cell_type": "markdown", "source": ["Now compute `A1` to eliminate `A[1,0]`:"]}, {"outputs": [{"metadata": {}, "text": ["array([[  2. ,  -2. ,  12. ,  -1. ],\n", "       [  0. ,   9. , -11. ,  -2.5],\n", "       [  1. ,  -2. ,  -6. ,  -1. ],\n", "       [ -2. ,   3. ,  -8. ,  -4. ]])"], "prompt_number": 23, "output_type": "pyout"}], "prompt_number": 23, "language": "python", "cell_type": "code", "metadata": {}, "collapsed": false, "input": ["A1 = A.copy()\n", "A1[1] -= 1/2*A1[0]\n", "A1"]}, {"metadata": {}, "cell_type": "markdown", "source": ["And `A2` with `A[2,0] == 0`:"]}, {"outputs": [{"metadata": {}, "text": ["array([[  2. ,  -2. ,  12. ,  -1. ],\n", "       [  0. ,   9. , -11. ,  -2.5],\n", "       [  0. ,  -1. , -12. ,  -0.5],\n", "       [ -2. ,   3. ,  -8. ,  -4. ]])"], "prompt_number": 25, "output_type": "pyout"}], "prompt_number": 25, "language": "python", "cell_type": "code", "metadata": {}, "collapsed": false, "input": ["A2 = A1.copy()\n", "A2[2] -= 1/2*A[0]\n", "A2"]}, {"outputs": [], "language": "python", "cell_type": "code", "metadata": {}, "collapsed": false, "input": []}]}]}