Narendran-sec / Gaussian

Gaussian Elimination

AIM:

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

Equipments Required:

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

Algorithm

1. import numpy and sys
2. get the input as 'n'
3. solve a matrix using guassian elimination method without partial pivoting
4. produce the output

Program:

/*
Program to find the solution of a matrix using Gaussian Elimination.
Developed by: NARENDRAN . K
RegisterNumber: 23013500
*/
import numpy as np
import sys
n=int(input())
matrix=np.zeros((n,n+1))
x=np.zeros(n)
for i in range(n):
    for j in range(n+1):
        matrix[i][j]=int(input())
for i in range(n):
    if matrix[i][j]==0.0:
        sys.exit("Divide by zero error")
    for j in range(i+1,n):
        ratio=matrix[j][i]/matrix[i][i]
        for k in range(n+1):
            matrix[j][k]=matrix[j][k]-ratio*matrix[i][k]
x[n-1]=matrix[n-1][n]/matrix[n-1][n-1]
for i in range (n-2,-1,-1):
    x[i]=matrix[i][n]
    for j in range (i+1,n):
        x[i]=x[i]-matrix[i][j]*x[j]
    x[i]=x[i]/matrix[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.