spyrit.misc.walsh_hadamard.iwalsh_S_matrix

spyrit.misc.walsh_hadamard.iwalsh_S_matrix(n, H=None)

Return the inverse Walsh S-matrix of order n.

Args:

x (np.ndarray): signals of shape (*,n), where n+1 must be a power of two.

H (np.ndarray, optional): Hadamard matrix of order n+1.

Returns:

np.ndarray: Inverse S-matrix of shape (n,n).

Examples:

Example 1: Inverse Walsh S-matrix of order 7

>>> import spyrit.misc.walsh_hadamard as wh
>>> print(wh.iwalsh_S_matrix(7))
[[-0.25 -0.25 -0.25  0.25  0.25  0.25  0.25]
 [-0.25  0.25  0.25  0.25  0.25 -0.25 -0.25]
 [-0.25  0.25  0.25 -0.25 -0.25  0.25  0.25]
 [ 0.25  0.25 -0.25 -0.25  0.25  0.25 -0.25]
 [ 0.25  0.25 -0.25  0.25 -0.25 -0.25  0.25]
 [ 0.25 -0.25  0.25  0.25 -0.25  0.25 -0.25]
 [ 0.25 -0.25  0.25 -0.25  0.25 -0.25  0.25]]

Example 2: Check the inverse of the Walsh S-matrix of order 7

>>> import spyrit.misc.walsh_hadamard as wh
>>> print(wh.iwalsh_S_matrix(7) @ wh.walsh_S_matrix(7))
[[1. 0. 0. 0. 0. 0. 0.]
 [0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 1. 0. 0. 0. 0.]
 [0. 0. 0. 1. 0. 0. 0.]
 [0. 0. 0. 0. 1. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0.]
 [0. 0. 0. 0. 0. 0. 1.]]