invpascal(n, kind='symmetric', exact=True)
The Pascal matrix is a matrix containing the binomial coefficients as its elements.
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.int64
(if n <= 35) or an object array of Python 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 for large n, the values in the array will not be the exact coefficients.
The inverse of the Pascal matrix.
Returns the inverse of the n x n Pascal matrix.
>>> from scipy.linalg import invpascal, pascal
... invp = invpascal(5)
... invp array([[ 5, -10, 10, -5, 1], [-10, 30, -35, 19, -4], [ 10, -35, 46, -27, 6], [ -5, 19, -27, 17, -4], [ 1, -4, 6, -4, 1]])
>>> p = pascal(5)
... p.dot(invp) array([[ 1., 0., 0., 0., 0.], [ 0., 1., 0., 0., 0.], [ 0., 0., 1., 0., 0.], [ 0., 0., 0., 1., 0.], [ 0., 0., 0., 0., 1.]])
An example of the use of :None:None:`kind` and :None:None:`exact`:
>>> invpascal(5, kind='lower', exact=False) array([[ 1., -0., 0., -0., 0.], [-1., 1., -0., 0., -0.], [ 1., -2., 1., -0., 0.], [-1., 3., -3., 1., -0.], [ 1., -4., 6., -4., 1.]])See :
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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