Module « scipy.sparse.linalg »

Fonction expm - module scipy.sparse.linalg

Signature de la fonction expm

def expm(A) 

Description

expm.__doc__

    Compute the matrix exponential using Pade approximation.

    Parameters
    ----------
    A : (M,M) array_like or sparse matrix
        2D Array or Matrix (sparse or dense) to be exponentiated

    Returns
    -------
    expA : (M,M) ndarray
        Matrix exponential of `A`

    Notes
    -----
    This is algorithm (6.1) which is a simplification of algorithm (5.1).

    .. versionadded:: 0.12.0

    References
    ----------
    .. [1] Awad H. Al-Mohy and Nicholas J. Higham (2009)
           "A New Scaling and Squaring Algorithm for the Matrix Exponential."
           SIAM Journal on Matrix Analysis and Applications.
           31 (3). pp. 970-989. ISSN 1095-7162

    Examples
    --------
    >>> from scipy.sparse import csc_matrix
    >>> from scipy.sparse.linalg import expm
    >>> A = csc_matrix([[1, 0, 0], [0, 2, 0], [0, 0, 3]])
    >>> A.todense()
    matrix([[1, 0, 0],
            [0, 2, 0],
            [0, 0, 3]], dtype=int64)
    >>> Aexp = expm(A)
    >>> Aexp
    <3x3 sparse matrix of type '<class 'numpy.float64'>'
        with 3 stored elements in Compressed Sparse Column format>
    >>> Aexp.todense()
    matrix([[  2.71828183,   0.        ,   0.        ],
            [  0.        ,   7.3890561 ,   0.        ],
            [  0.        ,   0.        ,  20.08553692]])