manojvenaram / lu-decomposition

LU Decomposition without zero on the diagonal

AIM:

To write a program to find the LU Decomposition of a matrix.

Equipments Required:

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

Algorithm

Step 1:

Read the elements of augmented matrix into arrays a and b.

Step 2:

Calculate elements of L and U.

Step 3:

Print elements of L and U.

Step 4:

Find V by solving LV = B by forward substitution.

Step 5:

Find X by solving UX = V by backward substitution.

Step 6:

Print Array X as the solution.

Step 7:

End of the program.

Program

Program 1:

import scipy from 
scipy.linalg import lu 
a=eval(input()) 
p,l,u=lu(a) 
print(l) 
print(u) 

Program 2:

import numpy as np 
from scipy.linalg import lu_factor,lu_solve 
a=eval(input()) 
b=eval(input()) 
lu,piv=lu_factor(a) 
x=lu_solve((lu,piv),b) 
print(x)

Output:

Output 1:

Output 2

Result:

Thus the program to find the LU Decomposition of a matrix is written and verified using python programming.