SciPy

scipy.linalg.hankel

scipy.linalg.hankel(c, r=None)[source]

Construct a Hankel matrix.

The Hankel matrix has constant anti-diagonals, with c as its first column and r as its last row. If r is not given, then r = zeros_like(c) is assumed.

Parameters:

c : array_like

First column of the matrix. Whatever the actual shape of c, it will be converted to a 1-D array.

r : array_like

Last row of the matrix. If None, r = zeros_like(c) is assumed. r[0] is ignored; the last row of the returned matrix is [c[-1], r[1:]]. Whatever the actual shape of r, it will be converted to a 1-D array.

Returns:

A : (len(c), len(r)) ndarray

The Hankel matrix. Dtype is the same as (c[0] + r[0]).dtype.

See also

toeplitz
Toeplitz matrix
circulant
circulant matrix

Examples

>>> from scipy.linalg import hankel
>>> hankel([1, 17, 99])
array([[ 1, 17, 99],
       [17, 99,  0],
       [99,  0,  0]])
>>> hankel([1,2,3,4], [4,7,7,8,9])
array([[1, 2, 3, 4, 7],
       [2, 3, 4, 7, 7],
       [3, 4, 7, 7, 8],
       [4, 7, 7, 8, 9]])

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