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 the ordinary transpose if a is real-valued). a must be Hermitian (symmetric if real-valued) and positive-definite. Only L is actually returned.
- a(..., M, M) array_like
Hermitian (symmetric if all elements are real), positive-definite input matrix.
- L(..., M, M) ndarray
Upper or lower-triangular Cholesky factor of a.
The Cholesky decomposition is often used as a fast way of solving
(when A is both Hermitian/symmetric and positive-definite).
First, we solve for y in , and then for x in .
>>> import nlcpy as vp >>> A = vp.array([[1,-2j],[2j,5]]) >>> A array([[ 1.+0.j, -0.-2.j], [ 0.+2.j, 5.+0.j]]) >>> L = vp.linalg.cholesky(A) >>> L array([[1.+0.j, 0.+0.j], [0.+2.j, 1.+0.j]]) >>> vp.dot(L, vp.conjugate(L.T)) # verify that L * L.H = A array([[1.+0.j, 0.-2.j], [0.+2.j, 5.+0.j]])