Module « scipy.linalg »

Fonction lu_factor - module scipy.linalg

Signature de la fonction lu_factor

def lu_factor(a, overwrite_a=False, check_finite=True) 

Description

lu_factor.__doc__

    Compute pivoted LU decomposition of a matrix.

    The decomposition is::

        A = P L U

    where P is a permutation matrix, L lower triangular with unit
    diagonal elements, and U upper triangular.

    Parameters
    ----------
    a : (M, M) array_like
        Matrix to decompose
    overwrite_a : bool, optional
        Whether to overwrite data in A (may increase 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
    -------
    lu : (N, N) ndarray
        Matrix containing U in its upper triangle, and L in its lower triangle.
        The unit diagonal elements of L are not stored.
    piv : (N,) ndarray
        Pivot indices representing the permutation matrix P:
        row i of matrix was interchanged with row piv[i].

    See also
    --------
    lu_solve : solve an equation system using the LU factorization of a matrix

    Notes
    -----
    This is a wrapper to the ``*GETRF`` routines from LAPACK.

    Examples
    --------
    >>> from scipy.linalg import lu_factor
    >>> A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])
    >>> lu, piv = lu_factor(A)
    >>> piv
    array([2, 2, 3, 3], dtype=int32)

    Convert LAPACK's ``piv`` array to NumPy index and test the permutation

    >>> piv_py = [2, 0, 3, 1]
    >>> L, U = np.tril(lu, k=-1) + np.eye(4), np.triu(lu)
    >>> np.allclose(A[piv_py] - L @ U, np.zeros((4, 4)))
    True