gaussian's Introduction

Gaussian Elimination

AIM:

To write a program to find the solution of a matrix using Gaussian Elimination.

Equipments Required:

Hardware – PCs
Anaconda – Python 3.7 Installation / Moodle-Code Runner

Algorithm

STEP 1:

Import the numpy module to use the built-in functions for calculation

STEP 2:

Get input from the user for number of unknows as n

STEP 3:

Making numpy array of n x n+1 size and initializing to zeroes for argumented matrix

STEP 4:

Making numpy array of n size and initializig to zero for storing solution vector

STEP 5:

Reading argumented matrix coefficients

Step 6:

Applying gauss elimination i.e., interchanging the rows and columns, multiplying them with a scalar and adding the rows with multiplied scalar

STEP 7:

Applying back substitution

STEP 8:

Displaying the solution

STEP 9:

End of program

Program:

/*
Program to find the solution of a matrix using Gaussian Elimination.
Developed by: vignesh v
RegisterNumber:23002301
import numpy as np
import sys
n=int(input())
a=np.zeros((n,n+1))
x=np.zeros(n)
for i in range(n):
    for j in range(n+1):
        a[i][j] = float(input())
for i in range(n):
    if a[i][i]==0.0:
        sys.exit('Divided by zero detected')
    for j in range(i+1,n):
        ratio=a[j][i]/a[i][i]
        for k in range(n+1):
            a[j][k]=a[j][k] - ratio * a[i][k]
x[n-1]=a[n-1][n]/a[n-1][n-1]
for i in range(n-2,-1,-1):
    x[i]=a[i][n]
    for j in range (i+1,n):
        x[i]=x[i]-a[i][j]*x[j]
    x[i]=x[i]/a[i][i]
for i in range(n):
    print('X%d = %0.2f' %(i,x[i]), end = ' ')
*/