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bundles / scipy latest / scipy / linalg / _decomp_cholesky / cholesky_banded

function

scipy.linalg._decomp_cholesky:cholesky_banded

source: /scipy/linalg/_decomp_cholesky.py :262

Signature

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

Summary

Cholesky decompose a banded Hermitian positive-definite matrix

Extended Summary

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 *   *

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. Note that calls with zero-size batches are unsupported and will raise a ValueError.

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

Examples

import numpy as np
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)))
✓

See also

cho_solve_banded

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

Aliases

  • scipy.linalg.cholesky_banded

Referenced by

This package