lu-decomposition's Introduction

LU Decomposition without zero on the diagonal

5A

AIM:

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

Equipments Required:

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

Algorithm

Step 1:

Import numpy library using import statement.

Step 2:

From scipy package import lu().

Step 3:

Get input from user and pass it as an array.

Step 4:

Get P, L, U matrix using lu()

Step 5:

Print L and U matrix

Program:

'''Program to find L and U matrix using LU decomposition.
Developed by: Keerthika N
RegisterNumber: 21000385
'''

# To print L and U matrix
import numpy as np
from scipy.linalg import lu
A = np.array(eval(input()))
P, L, U = lu(A)
print(L)
print(U)

Output:

Result:

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

5B

AIM:

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

Equipments Required:

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

Algorithm

Step 1:

Import numpy library using import statement.

Step 2:

From scipy package import lu_factor() and lu_solve().

Step 3:

Get two inputs from user and pass it as matrix array.

Step 4:

Find lu and pivot value of first matrix using lu_factor().

Step 5:

Find solution of the matrix by using lu_solve() by passing lu, pivot values as first argument and second matrix as second argument.

Step 6:

Print the solution.

Program:

'''Program to solve a matrix using LU decomposition.
Developed by: Keerthika N
RegisterNumber: 21000385
'''

# To print X matrix (solution to the equations)
import numpy as np
from scipy.linalg import lu_factor, lu_solve
A = np.array(eval(input()))
B = np.array(eval(input()))
lu, pivot = lu_factor(A)
x = lu_solve((lu,pivot),B)
print(x)