scipy.linalg.cho_solve_banded

scipy.linalg.cho_solve_banded(cb_and_lower, b, overwrite_b=False, check_finite=True)

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

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.

b : array_like

Right-hand side

overwrite_b : bool, optional

If True, the function will overwrite the values in b.

check_finite : bool, 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:

x : array

The solution to the system A x = b

See also

cholesky_banded

Cholesky factorization of a banded matrix

Notes

New in version 0.8.0.

Examples

>>> 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