pascal(n, kind='symmetric', exact=True)
The Pascal matrix is a matrix containing the binomial coefficients as its elements.
See https://en.wikipedia.org/wiki/Pascal_matrix for more information about Pascal matrices.
The size of the matrix to create; that is, the result is an n x n matrix.
Must be one of 'symmetric', 'lower', or 'upper'. Default is 'symmetric'.
If :None:None:`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 :None:None:`exact` is False, the coefficients in the matrix are computed using scipy.special.comb
with :None:None:`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 :None:None:`exact=True`.
The Pascal matrix.
Returns the n x n Pascal matrix.
>>> 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 combSee :
... comb(98, 49, exact=True) 25477612258980856902730428600
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._special_matrices.invpascal
scipy.linalg._special_matrices.pascal
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