linalg.cholesky

Description

Return the Cholesky decomposition, L * L.H, of the square matrix a, where L is lower-triangular, and .H is the conjugate-transpose operator (which is a regular transposed operator if a is real-valued). a must be Hermitian (symmetric if real-valued) and positive-definite. No checking is performed to verify whether a is Hermitian or not. In addition, only the lower-triangular and diagonal elements of a are used. Only L is actually returned.

Mandatory Input Parameters

Parameter	Type	Description
a	(…,M,M) array_like	Hermitian (symmetric if all elements are real), positive-definite input matrix

Optional Input Parameters

None

Return Value

Type	Description
(…, M, M) array_like	Lower-triangular Cholesky factor of a. A matrix object is returned if a is a matrix object.

Examples

>>> import numpy as np
>>> A = np.array([[1,-2j], [2j,5]])
>>> A
array([[ 1.+0.j, -0.-2.j],
       [ 0.+2.j,  5.+0.j]])
>>> L = np.linalg.cholesky(A)
>>> L
array([[1.+0.j, 0.+0.j],
       [0.+2.j, 1.+0.j]])
>>> 
>>> np.allclose(A, np.dot(L, L.T.conj()))
True
>>> 
>>> A = [[1,-2j], [2j,5]]
>>> L = np.linalg.cholesky(A)
>>> L
array([[1.+0.j, 0.+0.j],
       [0.+2.j, 1.+0.j]])
>>> 
>>> np.linalg.cholesky(np.matrix(A))
matrix([[1.+0.j, 0.+0.j],
        [0.+2.j, 1.+0.j]])
>>>

Parent topic: Linear Algebra Functions