Module « scipy.linalg »

Fonction funm - module scipy.linalg

Signature de la fonction funm

def funm(A, func, disp=True) 

Description

funm.__doc__

    Evaluate a matrix function specified by a callable.

    Returns the value of matrix-valued function ``f`` at `A`. The
    function ``f`` is an extension of the scalar-valued function `func`
    to matrices.

    Parameters
    ----------
    A : (N, N) array_like
        Matrix at which to evaluate the function
    func : callable
        Callable object that evaluates a scalar function f.
        Must be vectorized (eg. using vectorize).
    disp : bool, optional
        Print warning if error in the result is estimated large
        instead of returning estimated error. (Default: True)

    Returns
    -------
    funm : (N, N) ndarray
        Value of the matrix function specified by func evaluated at `A`
    errest : float
        (if disp == False)

        1-norm of the estimated error, ||err||_1 / ||A||_1

    Examples
    --------
    >>> from scipy.linalg import funm
    >>> a = np.array([[1.0, 3.0], [1.0, 4.0]])
    >>> funm(a, lambda x: x*x)
    array([[  4.,  15.],
           [  5.,  19.]])
    >>> a.dot(a)
    array([[  4.,  15.],
           [  5.,  19.]])

    Notes
    -----
    This function implements the general algorithm based on Schur decomposition
    (Algorithm 9.1.1. in [1]_).

    If the input matrix is known to be diagonalizable, then relying on the
    eigendecomposition is likely to be faster. For example, if your matrix is
    Hermitian, you can do

    >>> from scipy.linalg import eigh
    >>> def funm_herm(a, func, check_finite=False):
    ...     w, v = eigh(a, check_finite=check_finite)
    ...     ## if you further know that your matrix is positive semidefinite,
    ...     ## you can optionally guard against precision errors by doing
    ...     # w = np.maximum(w, 0)
    ...     w = func(w)
    ...     return (v * w).dot(v.conj().T)

    References
    ----------
    .. [1] Gene H. Golub, Charles F. van Loan, Matrix Computations 4th ed.