bundles / scipy latest / scipy / linalg / _special_matrices / toeplitz
function
scipy.linalg._special_matrices:toeplitz
Signature
def toeplitz ( c , r = None ) Summary
Construct a Toeplitz matrix.
Extended Summary
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.
The documentation is written assuming array arguments are of specified "core" shapes. However, array argument(s) of this function may have additional "batch" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see linalg_batch for details.
Parameters
c: array_likeFirst column of the matrix.
r: array_like, optionalFirst 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:]].
Returns
A: (len(c), len(r)) ndarrayThe 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])✓
toeplitz([1.0, 2+3j, 4-1j])
✗See also
- circulant
circulant matrix
- hankel
Hankel matrix
- solve_toeplitz
Solve a Toeplitz system.
Aliases
-
scipy.linalg.toeplitz