cholesky#
- scipy.linalg.cholesky(a, lower=False, overwrite_a=False, check_finite=True)[source]#
- Compute the Cholesky decomposition of a matrix. - Returns the Cholesky decomposition, \(A = L L^*\) or \(A = U^* U\) of a Hermitian positive-definite matrix A. - Parameters:
- a(M, M) array_like
- Matrix to be decomposed 
- lowerbool, optional
- Whether to compute the upper- or lower-triangular Cholesky factorization. During decomposition, only the selected half of the matrix is referenced. Default is upper-triangular. 
- overwrite_abool, optional
- Whether to overwrite data in a (may improve performance). 
- check_finitebool, optional
- Whether to check that the entire input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs. 
 
- Returns:
- c(M, M) ndarray
- Upper- or lower-triangular Cholesky factor of a. 
 
- Raises:
- LinAlgErrorif decomposition fails.
 
 - Notes - During the finiteness check (if selected), the entire matrix a is checked. During decomposition, a is assumed to be symmetric or Hermitian (as applicable), and only the half selected by option lower is referenced. Consequently, if a is asymmetric/non-Hermitian, - choleskymay still succeed if the symmetric/Hermitian matrix represented by the selected half is positive definite, yet it may fail if an element in the other half is non-finite.- Examples - >>> import numpy as np >>> from scipy.linalg import cholesky >>> a = np.array([[1,-2j],[2j,5]]) >>> L = cholesky(a, lower=True) >>> L array([[ 1.+0.j, 0.+0.j], [ 0.+2.j, 1.+0.j]]) >>> L @ L.T.conj() array([[ 1.+0.j, 0.-2.j], [ 0.+2.j, 5.+0.j]])