matrices.cyclic_permutation

Generate a cyclic permutation matrix.

Module Contents

Functions

cyclic_permutation_matrix(n[, k])

Create the cyclic permutation matrix for a given dimension n [1].

matrices.cyclic_permutation.cyclic_permutation_matrix(n, k=1)

Create the cyclic permutation matrix for a given dimension n [1].

This function creates a cyclic permutation matrix of 0’s and 1’s which is a special type of square matrix that represents a cyclic permutation of its rows. The function allows fixed points and successive applications.

Examples

Generate fixed point.

>>> from toqito.matrices import cyclic_permutation_matrix
>>> n = 4
>>> cyclic_permutation_matrix(n)
array([[0, 0, 0, 1],
       [1, 0, 0, 0],
       [0, 1, 0, 0],
       [0, 0, 1, 0]])

Generate successive application.

>>> from toqito.matrices import cyclic_permutation_matrix
>>> n = 4
>>> k = 3
>>> cyclic_permutation_matrix(n, k)
array([[0, 1, 0, 0],
       [0, 0, 1, 0],
       [0, 0, 0, 1],
       [1, 0, 0, 0]])

References

[1] (1,2)

Wikipedia. Cyclic permutation. https://en.wikipedia.org/wiki/Cyclic_permutation.

Parameters:

• n (int) – int The number of rows and columns in the cyclic permutation matrix.

• k (int) – int The power to which the elements are raised, representing successive applications.

Returns:

A NumPy array representing a cyclic permutation matrix of dimension n x n. Each row of the matrix is shifted one position to the right in a cyclic manner, creating a circular permutation pattern. If k is specified, the function raises the matrix to the power of k, representing successive applications of the cyclic permutation.

Return type:

numpy.ndarray