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Module « scipy.linalg »

Fonction cho_factor - module scipy.linalg

Signature de la fonction cho_factor

def cho_factor(a, lower=False, overwrite_a=False, check_finite=True) 

Description

help(scipy.linalg.cho_factor)

Compute the Cholesky decomposition of a matrix, to use in cho_solve

Returns a matrix containing the Cholesky decomposition,
``A = L L*`` or ``A = U* U`` of a Hermitian positive-definite matrix `a`.
The return value can be directly used as the first parameter to cho_solve.

.. warning::
    The returned matrix also contains random data in the entries not
    used by the Cholesky decomposition. If you need to zero these
    entries, use the function `cholesky` instead.

Parameters
----------
a : (M, M) array_like
    Matrix to be decomposed
lower : bool, optional
    Whether to compute the upper or lower triangular Cholesky factorization.
    During decomposition, only the selected half of the matrix is referenced.
    (Default: upper-triangular)
overwrite_a : bool, optional
    Whether to overwrite data in a (may improve performance)
check_finite : bool, optional
    Whether to check that the entire 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 : (M, M) ndarray
    Matrix whose upper or lower triangle contains the Cholesky factor
    of `a`. Other parts of the matrix contain random data.
lower : bool
    Flag indicating whether the factor is in the lower or upper triangle

Raises
------
LinAlgError
    Raised if decomposition fails.

See Also
--------
cho_solve : Solve a linear set equations using the Cholesky factorization
            of a matrix.

Notes
-----
During the finiteness check (if selected), the entire matrix `a` is
checked. During decomposition, `a` is assumed to be symmetric or Hermitian
(as applicable), and only the half selected by option `lower` is referenced.
Consequently, if `a` is asymmetric/non-Hermitian, `cholesky` may still
succeed if the symmetric/Hermitian matrix represented by the selected half
is positive definite, yet it may fail if an element in the other half is
non-finite.

Examples
--------
>>> import numpy as np
>>> from scipy.linalg import cho_factor
>>> A = np.array([[9, 3, 1, 5], [3, 7, 5, 1], [1, 5, 9, 2], [5, 1, 2, 6]])
>>> c, low = cho_factor(A)
>>> c
array([[3.        , 1.        , 0.33333333, 1.66666667],
       [3.        , 2.44948974, 1.90515869, -0.27216553],
       [1.        , 5.        , 2.29330749, 0.8559528 ],
       [5.        , 1.        , 2.        , 1.55418563]])
>>> np.allclose(np.triu(c).T @ np. triu(c) - A, np.zeros((4, 4)))
True

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