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Module « scipy.linalg »

Fonction cholesky_banded - module scipy.linalg

Signature de la fonction cholesky_banded

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

Description

help(scipy.linalg.cholesky_banded)

Cholesky decompose a banded Hermitian positive-definite matrix

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

See Also
--------
cho_solve_banded :
    Solve a linear set equations, given the Cholesky factorization
    of a banded Hermitian.

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)))
True

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