scipy.linalg.toeplitz¶
- 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: 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
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:]]. Whatever the actual shape of r, it will be converted to a 1-D array.
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]])