Module « scipy.linalg »

Fonction pascal - module scipy.linalg

Signature de la fonction pascal

def pascal(n, kind='symmetric', exact=True) 

Description

pascal.__doc__

    Returns the n x n Pascal matrix.

    The Pascal matrix is a matrix containing the binomial coefficients as
    its elements.

    Parameters
    ----------
    n : int
        The size of the matrix to create; that is, the result is an n x n
        matrix.
    kind : str, optional
        Must be one of 'symmetric', 'lower', or 'upper'.
        Default is 'symmetric'.
    exact : bool, optional
        If `exact` is True, the result is either an array of type
        numpy.uint64 (if n < 35) or an object array of Python long integers.
        If `exact` is False, the coefficients in the matrix are computed using
        `scipy.special.comb` with `exact=False`. The result will be a floating
        point array, and the values in the array will not be the exact
        coefficients, but this version is much faster than `exact=True`.

    Returns
    -------
    p : (n, n) ndarray
        The Pascal matrix.

    See Also
    --------
    invpascal

    Notes
    -----
    See https://en.wikipedia.org/wiki/Pascal_matrix for more information
    about Pascal matrices.

    .. versionadded:: 0.11.0

    Examples
    --------
    >>> from scipy.linalg import pascal
    >>> pascal(4)
    array([[ 1,  1,  1,  1],
           [ 1,  2,  3,  4],
           [ 1,  3,  6, 10],
           [ 1,  4, 10, 20]], dtype=uint64)
    >>> pascal(4, kind='lower')
    array([[1, 0, 0, 0],
           [1, 1, 0, 0],
           [1, 2, 1, 0],
           [1, 3, 3, 1]], dtype=uint64)
    >>> pascal(50)[-1, -1]
    25477612258980856902730428600
    >>> from scipy.special import comb
    >>> comb(98, 49, exact=True)
    25477612258980856902730428600