scipy.linalg.

circulant#

scipy.linalg.circulant(c)[source]#

Construct a circulant matrix.

Parameters:

c(…, N,) array_like: The first column(s) of the matrix. Multidimensional arrays are treated as a batch: each slice along the last axis is the first column of an output matrix.

Returns:

A(…, N, N) ndarray: A circulant matrix whose first column is given by c. For batch input, each slice of shape (N, N) along the last two dimensions of the output corresponds with a slice of shape (N,) along the last dimension of the input.

See also

toeplitz: Toeplitz matrix
hankel: Hankel matrix
solve_circulant: Solve a circulant system.

Notes

Added in version 0.8.0.

Examples

>>> from scipy.linalg import circulant
>>> circulant([1, 2, 3])
array([[1, 3, 2],
       [2, 1, 3],
       [3, 2, 1]])

>>> circulant([[1, 2, 3], [4, 5, 6]])
array([[[1, 3, 2],
        [2, 1, 3],
        [3, 2, 1]],
       [[4, 6, 5],
        [5, 4, 6],
        [6, 5, 4]]])