scipy.linalg.cho_factor

scipy.linalg.cho_factor(a, lower=False, overwrite_a=False, check_finite=True)

Compute the Cholesky decomposition of a matrix, to use in cho_solve

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.

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

>>> 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]])
>>> 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