spyrit.misc.walsh_hadamard.fwalsh_G

spyrit.misc.walsh_hadamard.fwalsh_G(x, ind=True)[source]

Fast Walsh G-transform of the signal x

Args:

x (np.ndarray): signals of shape (*,n), where n+1 must 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: G-transformed signal of shape (*,n).

Example:

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)
[ -8  -2  -2 -16   8   6  -2]

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)
[ 16 -16  -2   8  -8   6  -2]

Example 3: Repeating the Walsh-ordered G-transform using input indices is faster

>>> import timeit
>>> x = np.random.rand(100,2**12-1)
>>> t = timeit.timeit(lambda: wh.fwalsh_G(x), number=100)
>>> print(f"No indices as inputs (10x): {t:.3f} seconds")
No indices as inputs (10x): ... seconds
>>> ind = wh.sequency_perm_ind(x.shape[-1]+1)
>>> t = timeit.timeit(lambda: wh.fwalsh_G(x,ind), number=100)
>>> print(f"With indices as inputs (10x): {t:.3f} seconds")
With indices as inputs (10x): ... 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)}")
Diff = 0.0