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