imsl.linalg.lu_factor_full¶

lu_factor_full(a)¶

Compute the LU decomposition of matrix A, PA=LU.

Parameters:

Parameters:	a : (N,N) array_like Square matrix to be factorized.
Returns:	P : (N,N) ndarray A permutation matrix, matrix P in the factorization PA=LU. L : (N,N) ndarray A unit lower triangular matrix, the L factor in the factorization PA=LU. U : (N,N) ndarray An upper triangular matrix, the U factor in the factorization PA=LU.

a : (N,N) array_like

Square matrix to be factorized.

Returns:

P : (N,N) ndarray

A permutation matrix, matrix P in the factorization PA=LU.

L : (N,N) ndarray

A unit lower triangular matrix, the L factor in the factorization PA=LU.

U : (N,N) ndarray

An upper triangular matrix, the U factor in the factorization PA=LU.

Notes

Function lu_factor_full returns full matrices P, L and U that describe the LU factorization PA=LU. This is in contrast to function lu_factor which returns only a compressed form of the factorization.

Examples

>>> import numpy as np
>>> import imsl.linalg as la
>>> A = [[1.0, 3.0, 3.0], [1.0, 3.0, 4.0], [1.0, 4.0, 3.0]]
>>> P, L, U = la.lu_factor_full(A)
>>> print("P*A:\n"+str(np.dot(P,A))) 
P*A:
[[ 1.  3.  3.]
 [ 1.  4.  3.]
 [ 1.  3.  4.]]
>>> print("L*U:\n"+str(np.dot(L,U))) 
L*U:
[[ 1.  3.  3.]
 [ 1.  4.  3.]
 [ 1.  3.  4.]]