Module « scipy.linalg »

Fonction lu - module scipy.linalg

Signature de la fonction lu

def lu(a, permute_l=False, overwrite_a=False, check_finite=True) 

Description

lu.__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, N) array_like
        Array to decompose
    permute_l : bool, optional
        Perform the multiplication P*L (Default: do not permute)
    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
    -------
    **(If permute_l == False)**

    p : (M, M) ndarray
        Permutation matrix
    l : (M, K) ndarray
        Lower triangular or trapezoidal matrix with unit diagonal.
        K = min(M, N)
    u : (K, N) ndarray
        Upper triangular or trapezoidal matrix

    **(If permute_l == True)**

    pl : (M, K) ndarray
        Permuted L matrix.
        K = min(M, N)
    u : (K, N) ndarray
        Upper triangular or trapezoidal matrix

    Notes
    -----
    This is a LU factorization routine written for SciPy.

    Examples
    --------
    >>> from scipy.linalg import lu
    >>> A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])
    >>> p, l, u = lu(A)
    >>> np.allclose(A - p @ l @ u, np.zeros((4, 4)))
    True