scipy.linalg.cho_factor¶
-
scipy.linalg.
cho_factor
(a, lower=False, overwrite_a=False, check_finite=True)[source]¶ Compute the Cholesky decomposition of a matrix, to use in cho_solve
Returns a matrix containing the Cholesky decomposition,
A = L L*
orA = U* U
of a Hermitian positive-definite matrix a. The return value can be directly used as the first parameter to cho_solve.Warning
The returned matrix also contains random data in the entries not used by the Cholesky decomposition. If you need to zero these entries, use the function
cholesky
instead.- Parameters
- a(M, M) array_like
Matrix to be decomposed
- lowerbool, optional
Whether to compute the upper or lower triangular Cholesky factorization (Default: upper-triangular)
- overwrite_abool, optional
Whether to overwrite data in a (may improve performance)
- check_finitebool, optional
Whether to check that the 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
Matrix whose upper or lower triangle contains the Cholesky factor of a. Other parts of the matrix contain random data.
- lowerbool
Flag indicating whether the factor is in the lower or upper triangle
- Raises
- LinAlgError
Raised if decomposition fails.
See also
cho_solve
Solve a linear set equations using the Cholesky factorization of a matrix.
Examples
>>> 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]]) >>> c, low = cho_factor(A) >>> c array([[3. , 1. , 0.33333333, 1.66666667], [3. , 2.44948974, 1.90515869, -0.27216553], [1. , 5. , 2.29330749, 0.8559528 ], [5. , 1. , 2. , 1.55418563]]) >>> np.allclose(np.triu(c).T @ np. triu(c) - A, np.zeros((4, 4))) True