spyrit.misc.walsh_hadamard.fwalsh_G

spyrit.misc.walsh_hadamard.fwalsh_G(x, ind=True)

Fast Walsh G-transform of x

Args:

x (np.ndarray): n-by-1 signal. n+1 should be a power of two.

ind (bool, optional): True for sequency (default)

ind (list, optional): permutation indices. This is faster than True

when repeating the sequency-ordered transform multilple times.

Returns:

np.ndarray: n-by-1 S-transformed signal

Example 1:

Walsh-ordered G-transform of a signal of length 7

>>> import spyrit.misc.walsh_hadamard as wh
>>> import numpy as np
>>> x = np.array([1, 3, 0, -1, 7, 5, 1])
>>> s = wh.fwalsh_G(x)
>>> print(s)

Example 2:

Permuted fast G-transform

>>> import numpy as np
>>> import spyrit.misc.walsh_hadamard as wh
>>> x = np.array([1, 3, 0, -1, 7, 5, 1])
>>> ind = [1, 0, 3, 2, 7, 4, 5, 6]
>>> y = wh.fwalsh_G(x, ind)
>>> print(y)

Example 3:

Repeating the Walsh-ordered G-transform using input indices is faster

>>> import timeit
>>> x = np.random.rand(2**12-1,1)
>>> t = timeit.timeit(lambda: wh.fwalsh_G(x), number=10)
>>> print(f"No indices as inputs (10x): {t:.3f} seconds")
>>> ind = wh.sequency_perm_ind(len(x)+1)
>>> t = timeit.timeit(lambda: wh.fwalsh_G(x,ind), number=10)
>>> print(f"With indices as inputs (10x): {t:.3f} seconds")

Example 4:

Comparison with G-transform via matrix-vector product

>>> import numpy as np
>>> import spyrit.misc.walsh_hadamard as wh
>>> x = np.array([3, 0, -1, 7, 5, 1, -2])
>>> y1 = wh.fwalsh_G(x)
>>> y2 = wh.walsh_G(x)
>>> print(f"Diff = {np.linalg.norm(y1-y2)}")