`scipy.linalg._special_matrices:pascal`

Signature

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

Returns the n x n Pascal matrix.

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

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.

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

from scipy.linalg import pascal
pascal(4)
pascal(4, kind='lower')
pascal(50)[-1, -1]
from scipy.special import comb
comb(98, 49, exact=True)

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