Module « scipy.linalg »

Fonction cholesky - module scipy.linalg

Signature de la fonction cholesky

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

Description

cholesky.__doc__

    Compute the Cholesky decomposition of a matrix.

    Returns the Cholesky decomposition, :math:`A = L L^*` or
    :math:`A = U^* U` of a Hermitian positive-definite matrix A.

    Parameters
    ----------
    a : (M, M) array_like
        Matrix to be decomposed
    lower : bool, optional
        Whether to compute the upper- or lower-triangular Cholesky
        factorization.  Default is upper-triangular.
    overwrite_a : bool, optional
        Whether to overwrite data in `a` (may improve performance).
    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 : (M, M) ndarray
        Upper- or lower-triangular Cholesky factor of `a`.

    Raises
    ------
    LinAlgError : if decomposition fails.

    Examples
    --------
    >>> from scipy.linalg import cholesky
    >>> a = np.array([[1,-2j],[2j,5]])
    >>> L = cholesky(a, lower=True)
    >>> L
    array([[ 1.+0.j,  0.+0.j],
           [ 0.+2.j,  1.+0.j]])
    >>> L @ L.T.conj()
    array([[ 1.+0.j,  0.-2.j],
           [ 0.+2.j,  5.+0.j]])