bundles / scipy 2.0.0.dev0+git20260907.41eeb59 / scipy / linalg / _decomp_cholesky / cho_factor
function
scipy.linalg._decomp_cholesky:cho_factor
source: build-install/usr/lib/python3.14/site-packages/scipy/linalg/_decomp_cholesky.py:125
Signature
def cho_factor(a, lower = False, overwrite_a = False, check_finite = True)Summary
Compute the Cholesky decomposition of a matrix, to use in cho_solve.
Extended Summary
Returns a matrix containing the Cholesky decomposition, A = L L* or A = U* U of a Hermitian positive-definite matrix a. The return value can be directly used as the first parameter to cho_solve.
Parameters
a: (..., M, M) array_likeMatrix to be decomposed
lower: bool, optionalWhether to compute the upper or lower triangular Cholesky factorization. During decomposition, only the selected half of the matrix is referenced. (Default: upper-triangular)
overwrite_a: bool, optionalWhether to overwrite data in
a(may improve performance). Default is False. See tutorial_linalg_overwrite for details.check_finite: bool, optionalWhether 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) ndarrayMatrix whose upper or lower triangle contains the Cholesky factor of
a. Other parts of the matrix contain random data.lower: ndarray, boolFlag indicating whether the factor is in the lower or upper triangle
Raises
: LinAlgErrorRaised if 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, cholesky may 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 cho_factor A = np.array([[9, 3, 1, 5], [3, 7, 5, 1], [1, 5, 9, 2], [5, 1, 2, 6]], dtype=float, order="F") A_ref = np.copy(A) c, low = cho_factor(A)✓
c
✗array([[ 3. , 1. , 0.33, 1.67],
[ 0. , 2.45, 1.91, -0.27],
[ 0. , 0. , 2.29, 0.86],
[ 0. , 0. , 0. , 1.55]])
np.allclose(c.T @ c - A, np.zeros((4, 4))) c, low = cho_factor(A, overwrite_a=True)✓
c
✗array([[ 3. , 1. , 0.33, 1.67],
[ 3. , 2.45, 1.91, -0.27],
[ 1. , 5. , 2.29, 0.86],
[ 5. , 1. , 2. , 1.55]])
np.allclose(np.triu(c).T @ np.triu(c) - A_ref, np.zeros((4, 4)))
✓True
See also
Aliases
scipy.linalg.cho_factor