`scipy.linalg._decomp_cholesky:cho_solve_banded`

source: /scipy/linalg/_decomp_cholesky.py:381

Signature

def cho_solve_banded(cb_and_lower, b, overwrite_b = False, check_finite = True)

Summary

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

Extended Summary

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 linalg_batch for details.

Parameters

cb_and_lower : tuple, (ndarray, bool): The first element of the tuple is the matrix containing the Cholesky factor, as provided by cholesky_banded. The second element is a boolean flag indicating whether the factor is in the lower triangle, as provided to cholesky_banded.
b : array_like: Right-hand side
overwrite_b : bool, optional: If True, the function will overwrite the values in b. See tutorial_linalg_overwrite for details.
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

Notes

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

Aliases

scipy.linalg.cho_solve_banded