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Module « scipy.linalg »

Fonction bandwidth - module scipy.linalg

Signature de la fonction bandwidth

def bandwidth(a) 

Description

help(scipy.linalg.bandwidth)

bandwidth(a)
Return the lower and upper bandwidth of a 2D numeric array.

    Parameters
    ----------
    a : ndarray
        Input array of size (N, M)

    Returns
    -------
    lu : tuple
        2-tuple of ints indicating the lower and upper bandwidth. A zero
        denotes no sub- or super-diagonal on that side (triangular), and,
        say for N rows (N-1) means that side is full. Same example applies
        to the upper triangular part with (M-1).

    Raises
    ------
    TypeError
        If the dtype of the array is not supported, in particular, NumPy
        float16, float128 and complex256 dtypes.

    Notes
    -----
    This helper function simply runs over the array looking for the nonzero
    entries whether there exists a banded structure in the array or not. Hence,
    the performance depends on the density of nonzero entries and also
    memory-layout. Fortran- or C- contiguous arrays are handled best and
    otherwise suffers from extra random memory access cost.

    The strategy is to look for only untested band elements in the upper
    and lower triangular parts separately; depending on the memory layout
    we scan row-wise or column-wise. Moreover, say we are scanning rows
    and in the 6th row, 4th entry is nonzero then, on the succeeding rows
    the horizontal search is done only up to that band entries since we know
    that band is occupied. Therefore, a completely dense matrix scan cost is
    in the order of n.

    Examples
    --------
    >>> import numpy as np
    >>> from scipy.linalg import bandwidth
    >>> A = np.array([[3., 0., 0., 0., 0.],
    ...               [0., 4., 0., 0., 0.],
    ...               [0., 0., 5., 1., 0.],
    ...               [8., 0., 0., 6., 2.],
    ...               [0., 9., 0., 0., 7.]])
    >>> bandwidth(A)
    (3, 1)

    

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