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Module « scipy.linalg »

Fonction toeplitz - module scipy.linalg

Signature de la fonction toeplitz

def toeplitz(c, r=None) 

Description

help(scipy.linalg.toeplitz)

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.
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:]]``.

    .. warning::

        Beginning in SciPy 1.17, multidimensional input will be treated as a batch,
        not ``ravel``\ ed. 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``.

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]])

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