scipy.linalg.

cho_solve_banded#

scipy.linalg.cho_solve_banded(cb_and_lower, b, overwrite_b=False, check_finite=True)[source]#

Solve the linear equations A x = b, given the Cholesky factorization of the banded Hermitian A.

The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details.

Parameters:

(cb, lower)tuple, (ndarray, bool): cb is the Cholesky factorization of A, as given by cholesky_banded. lower must be the same value that was given to cholesky_banded.
barray_like: Right-hand side
overwrite_bbool, optional: If True, the function will overwrite the values in b.
check_finitebool, optional: Whether to check that the input matrices contain 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:

xarray: The solution to the system A x = b

See also

cholesky_banded: Cholesky factorization of a banded matrix

Notes

Added in version 0.8.0.

Examples

>>> import numpy as np
>>> from scipy.linalg import cholesky_banded, cho_solve_banded
>>> Ab = np.array([[0, 0, 1j, 2, 3j], [0, -1, -2, 3, 4], [9, 8, 7, 6, 9]])
>>> A = np.diag(Ab[0,2:], k=2) + np.diag(Ab[1,1:], k=1)
>>> A = A + A.conj().T + np.diag(Ab[2, :])
>>> c = cholesky_banded(Ab)
>>> x = cho_solve_banded((c, False), np.ones(5))
>>> np.allclose(A @ x - np.ones(5), np.zeros(5))
True