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 1D array.
r : array_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:]]
. Whatever the actual shape of r, it will be converted to a 1D array.Returns: A : (len(c), len(r)) ndarray
The Toeplitz matrix. Dtype is the same as
(c[0] + r[0]).dtype
.See also
circulant
 circulant matrix
hankel
 Hankel matrix
solve_toeplitz
 Solve a Toeplitz system.
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, 41j]) 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]])