cholesky_banded(ab, overwrite_ab=False, lower=False, check_finite=True)

The matrix a is stored in ab either in lower-diagonal or upper- diagonal ordered form:

ab[u + i - j, j] == a[i,j]        (if upper form; i <= j)
ab[    i - j, j] == a[i,j]        (if lower form; i >= j)

Example of ab (shape of a is (6,6), u=2):

upper form:
*   *   a02 a13 a24 a35
*   a01 a12 a23 a34 a45
a00 a11 a22 a33 a44 a55

lower form:
a00 a11 a22 a33 a44 a55
a10 a21 a32 a43 a54 *
a20 a31 a42 a53 *   *

Parameters

ab : (u + 1, M) array_like

Banded matrix

overwrite_ab : bool, optional

Discard data in ab (may enhance performance)

lower : bool, optional

Is the matrix in the lower form. (Default is upper form)

check_finite : bool, 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 : (u + 1, M) ndarray

Cholesky factorization of a, in the same banded format as ab

Cholesky decompose a banded Hermitian positive-definite matrix

See Also

cho_solve_banded

Solve a linear set equations, given the Cholesky factorization of a banded Hermitian.

Examples

>>> from scipy.linalg import cholesky_banded
... from numpy import allclose, zeros, diag
... 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)
... C = np.diag(c[0, 2:], k=2) + np.diag(c[1, 1:], k=1) + np.diag(c[2, :])
... np.allclose(C.conj().T @ C - A, np.zeros((5, 5)))
True

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.linalg._decomp_cholesky.cholesky_banded scipy.linalg._decomp_cholesky.cho_solve_banded scipy.interpolate._bspl._norm_eq_lsq

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