Skip to main content
`Ctrl`+`K`
scipy.linalg.

# toeplitz

scipy.linalg.toeplitz(c, r=None)

  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.

    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:]]`.

      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]])