Gauss Elimination Method Python Program (With Output)


This python program solves systems of linear equation with n unknowns using Gauss Elimination Method.

In Gauss Elimination method, given system is first transformed to Upper Triangular Matrix by row operations then solution is obtained by Backward Substitution.

Gauss Elimination Python Program


# Importing NumPy Library
import numpy as np
import sys

# Reading number of unknowns
n = int(input('Enter number of unknowns: '))

# Making numpy array of n x n+1 size and initializing 
# to zero for storing augmented matrix
a = np.zeros((n,n+1))

# Making numpy array of n size and initializing 
# to zero for storing solution vector
x = np.zeros(n)

# Reading augmented matrix coefficients
print('Enter Augmented Matrix Coefficients:')
for i in range(n):
    for j in range(n+1):
        a[i][j] = float(input( 'a['+str(i)+']['+ str(j)+']='))

# Applying Gauss Elimination
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]

# Back Substitution
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]

# Displaying solution
print('\nRequired solution is: ')
for i in range(n):
    print('X%d = %0.2f' %(i,x[i]), end = '\t')

Output

Enter number of unknowns: 3
Enter Augmented Matrix Coefficients:
a[0][0]=1
a[0][1]=1
a[0][2]=1
a[0][3]=9
a[1][0]=2
a[1][1]=-3
a[1][2]=4
a[1][3]=13
a[2][0]=3
a[2][1]=4
a[2][2]=5
a[2][3]=40

Required solution is: 
X0 = 1.00	X1 = 3.00	X2 = 5.00

Recommended Readings

  1. Gauss Elimination Method Algorithm
  2. Gauss Elimination Method Pseudocode
  3. Gauss Elimination Method Using C
  4. Gauss Elimination Method Using C++
  5. Gauss Elimination Method Python Program