Doolittle's LU decomposition for matrices

Question

I'm trying to implement, using python, a primitive (without import a library, such scipy or numpy) Doolittle LU decomposition for square matrices. Until now, here's my code.

def luDecomposition(mat, n):
 
    lower = [[0 for x in range(n)]
             for y in range(n)]
    upper = [[0 for x in range(n)]
             for y in range(n)]
 
    # Decomposing matrix into Upper
    # and Lower triangular matrix
    for i in range(n):
 
        # Upper Triangular
        for k in range(i, n):
 
            # Summation of L(i, j) * U(j, k)
            soma = 0
            for j in range(i):
                soma += (lower[i][j] * upper[j][k])
 
            # Evaluating U(i, k)
            upper[i][k] = mat[i][k] - soma
 
        # Lower Triangular
        for k in range(i, n):
            if (i == k):
                lower[i][i] = 1  # Diagonal as 1
            else:
 
                # Summation of L(k, j) * U(j, i)
                soma = 0
                for j in range(i):
                    soma += (lower[k][j] * upper[j][i])
 
                # Evaluating L(k, i)
                lower[k][i] = int((mat[k][i] - soma) /
                                  upper[i][i])
 
    # setw is for displaying nicely
    print("     L    \t\t          U    ")
 
    # Displaying the result :
    for i in range(n):
 
        # Lower
        for j in range(n):
            print(lower[i][j], end="\t")
        print("", end="\t")
 
        # Upper
        for j in range(n):
            print(upper[i][j], end="\t")
        print("")
 
 
# Driver code
mat = [[4, 2, -1, 1],
       [8, 4, 2, -2],
       [1, 4, 2, -2],
       [2, 1, -2, 6]]
 
luDecomposition(mat, 4)

However, I'm getting the following error:

lower[k][i] = int((mat[k][i] - soma) / ZeroDivisionError : division by zero.

I couldn't solve this problem until now. There is any theoretical error on my code?

Answer 1

if (upper[i][i]!=0): lower[k][i] = (mat[k][i] - soma) \/(upper[i][i])

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