Classe « SuperLU »

Informations générales

Héritage

builtins.object
    builtins.SuperLU

Définition

class SuperLU(builtins.object):

help(SuperLU)

LU factorization of a sparse matrix.

    Factorization is represented as::

        Pr @ A @ Pc = L @ U

    To construct these `SuperLU` objects, call the `splu` and `spilu`
    functions.

    Attributes
    ----------
    shape
    nnz
    perm_c
    perm_r
    L
    U

    Methods
    -------
    solve

    Notes
    -----

    .. versionadded:: 0.14.0

    Examples
    --------
    The LU decomposition can be used to solve matrix equations. Consider:

    >>> import numpy as np
    >>> from scipy.sparse import csc_array
    >>> from scipy.sparse.linalg import splu
    >>> A = csc_array([[1,2,0,4], [1,0,0,1], [1,0,2,1], [2,2,1,0.]])

    This can be solved for a given right-hand side:

    >>> lu = splu(A)
    >>> b = np.array([1, 2, 3, 4])
    >>> x = lu.solve(b)
    >>> A.dot(x)
    array([ 1.,  2.,  3.,  4.])

    The ``lu`` object also contains an explicit representation of the
    decomposition. The permutations are represented as mappings of
    indices:

    >>> lu.perm_r
    array([2, 1, 3, 0], dtype=int32)  # may vary
    >>> lu.perm_c
    array([0, 1, 3, 2], dtype=int32)  # may vary

    The L and U factors are sparse matrices in CSC format:

    >>> lu.L.toarray()
    array([[ 1. ,  0. ,  0. ,  0. ],  # may vary
           [ 0.5,  1. ,  0. ,  0. ],
           [ 0.5, -1. ,  1. ,  0. ],
           [ 0.5,  1. ,  0. ,  1. ]])
    >>> lu.U.toarray()
    array([[ 2. ,  2. ,  0. ,  1. ],  # may vary
           [ 0. , -1. ,  1. , -0.5],
           [ 0. ,  0. ,  5. , -1. ],
           [ 0. ,  0. ,  0. ,  2. ]])

    The permutation matrices can be constructed:

    >>> Pr = csc_array((np.ones(4), (lu.perm_r, np.arange(4))))
    >>> Pc = csc_array((np.ones(4), (np.arange(4), lu.perm_c)))

    We can reassemble the original matrix:

    >>> (Pr.T @ (lu.L @ lu.U) @ Pc.T).toarray()
    array([[ 1.,  2.,  0.,  4.],
           [ 1.,  0.,  0.,  1.],
           [ 1.,  0.,  2.,  1.],
           [ 2.,  2.,  1.,  0.]])