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

Import numpy package.
Get the input.
Find the gaussian elimination.
Print the result.

Program:

/*
Program to find the solution of a matrix using Gaussian Elimination.
Developed by: Hemasonica.p
RegisterNumber: 22003246
*/
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('Divide 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=' ')

Output:

Result:

Thus the program to find the solution of a matrix using Gaussian Elimination is written and verified using python programming.

Hemasonica774 / Gaussian