Question

Need a python code for LU factorization( for partial pivoting and complete pivoting) of a random matrix size 5x5.

Answer 1

# Python3 Program to decompose

MAX = 100;

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 triangular matrix  

    # 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)

            sum = 0;

            for j in range(i):

                sum += (lower[i][j] * upper[j][k]);

   # Evaluating U(i, k)

            upper[i][k] = mat[i][k] - sum;

    # 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)

                sum = 0;

                for j in range(i):

                    sum += (lower[k][j] * upper[j][i]);

    # Evaluating L(k, i)

                lower[k][i] = int((mat[k][i] - sum) /

                                       upper[i][i]);

   # setw is for displaying nicely

    print("Lower Triangular\t\tUpper Triangular");

    # 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 = [[2, -1, -2],

  [-4, 6, 3],

  [-4, -2, 8],

[-2 , 4 , 6],

[5, 8, -4]];

  

luDecomposition(mat, 5);