papyri
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bundles / scipy 1.18.0 / scipy / linalg / _special_matrices / invpascal

function

scipy.linalg._special_matrices:invpascal

source: /scipy/linalg/_special_matrices.py:769

Signature

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

Summary

Returns the inverse of the n x n Pascal matrix.

Extended Summary

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.int64 (if n <= 35) or an object array of Python 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 for large n, the values in the array will not be the exact coefficients.

Returns

invp : (n, n) ndarray

The inverse of the Pascal matrix.

Notes

Examples

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 `kind` and `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 also

pascal

Aliases

  • scipy.linalg.invpascal

Referenced by

This package