Question

Gauss Jordan elimination using python for a 2d list (3x3) without using any library.

Thanks

Answer 1

gaus_jordon.py

def print_matrix(a, n):
    """
        * function to print the matrix of size n
    """
    for i in range(n):
        for j in range(n+1):
            print(a[i][j], " ", end="")
        print()

def print_result(a, n, flag):
    """
        * Function to print the desired result if unique solutions exists, otherwise
        prints no solution or infinite solutions depending upon the input given.
    """
    print("Result is : ")
    if flag == 2:
      print("Infinite Solutions Exists")
    elif flag == 3:
      print("No Solution Exists")
    else :
        for i in range(n):
            print(a[i][n] / a[i][i], " ")

def check_consistency(a, n, flag):
    """
        * To check whether infinite solutions exists or no solution exists
        * flag == 2 for infinite solution
        * flag == 3 for No solution
    """
    flag = 3
    for i in range(n):
        sum = 0
        for j in range(n):
            sum = sum + a[i][j]
        if sum == a[i][j]:
            flag = 2
    return flag

def perform_operation(a, n):
    """
        * function to reduce matrix to reduced row echelon form. 
    """
    k = 0
    flag = 0
    m = 0
    pro = 0

    for i in range(n):
        if a[i][i] == 0:
            c = 1
            while a[i + c][i] == 0 and (i + c) < n:
                c += 1
            if (i + c) == n:
                flag = 1
                break
            j = i
            for k in range(n+1):
                tmp = a[j][k]
                a[j][k] = a[j+c][k]
                a[j+c][k] = tmp

        for j in range(n):
            if i != j:
                pro = a[j][i] / a[i][i]
                for k in range(n+1):
                    a[j][k] = a[j][k] - (a[i][k]) * pro
    return flag

if __name__=="__main__":
    matrix =    [
                    [0, 2, 1, 4],
                    [1, 1, 2, 6],
                    [2, 1, 1, 7]
                ]
    size = 3
    flag = 0
    flag = perform_operation(matrix, size)

    if flag == 1:
        flag = check_consistency(matrix, size, flag)

    print_matrix(matrix, size)
    print_result(matrix, size, flag)

Note : the example is for linear equations:

2y + z = 4
x + y + 2z = 6
2x + y + z = 7