toeplitz — SciPy v1.15.2 Manual (original) (raw)

scipy.linalg.

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

Construct a Toeplitz matrix.

The Toeplitz matrix has constant diagonals, with c as its first column and r as its first row. If r is not given, r == conjugate(c) is assumed.

Parameters:

carray_like

First column of the matrix.

rarray_like, optional

First row of the matrix. If None, r = conjugate(c) is assumed; in this case, if c[0] is real, the result is a Hermitian matrix. r[0] is ignored; the first row of the returned matrix is[c[0], r[1:]].

Warning

Beginning in SciPy 1.17, multidimensional input will be treated as a batch, not raveled. To preserve the existing behavior, ravel arguments before passing them to toeplitz.

Returns:

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

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

Notes

The behavior when c or r is a scalar, or when c is complex and_r_ is None, was changed in version 0.8.0. The behavior in previous versions was undocumented and is no longer supported.

Examples

from scipy.linalg import toeplitz toeplitz([1,2,3], [1,4,5,6]) array([[1, 4, 5, 6], [2, 1, 4, 5], [3, 2, 1, 4]]) toeplitz([1.0, 2+3j, 4-1j]) array([[ 1.+0.j, 2.-3.j, 4.+1.j], [ 2.+3.j, 1.+0.j, 2.-3.j], [ 4.-1.j, 2.+3.j, 1.+0.j]])