mohammedfaizal05 / lu-decomposition

LU Decomposition

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

1. TO FIND L AND U MATRICES WITH LU DEOMPOSITION

STEP 1:

get the matrix from the user.

STEP 2:

using "from scipy.linalg import lu"to import scipy (LU) module.

STEP 3:

using "L,U=LU(a)" we can get the matrix of L and U.

STEP 4:

print the result matrices (L and U) matrices.

2. to find X matrix with LU decomposition

STEP 1:

get the matrix from the user.

step 2:

using "from scipy.linalg import lu_actor,lu_solve" to import scipy module for factorisation and solving X.

step 3:

using "lu,piv=lu_factor(a)"

step 4:

print the ouput(x matrix)

step %:

ed the program.

Program:

(i) To find the L and U matrix

/*
Program to find the L and U matrix.
Developed by: mohammed faizal
RegisterNumber: 22003412
*/

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

(ii) To find the LU Decomposition of a matrix

/*
Program to find the LU Decomposition of a matrix.
Developed by: mohammed faizal
RegisterNumber: 22003412
*/

import numpy as mp
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)

Output:

Result:

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