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utils.py
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utils.py
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import torch
import numpy as np
from scipy import sparse
@torch.no_grad()
def scipy_to_torch_sparse(A):
A = sparse.coo_matrix(A)
row = torch.tensor(A.row)
col = torch.tensor(A.col)
index = torch.stack((row, col), dim=0)
value = torch.Tensor(A.data)
return torch.sparse_coo_tensor(index, value, A.shape)
def ChebyshevApprox(f, n): # assuming f : [0, pi] -> R
quad_points = 500
c = np.zeros(n)
a = np.pi / 2
for k in range(1, n + 1):
Integrand = lambda x: np.cos((k - 1) * x) * f(a * (np.cos(x) + 1))
x = np.linspace(0, np.pi, quad_points)
y = Integrand(x)
c[k - 1] = 2 / np.pi * np.trapz(y, x)
return c
def get_operator(L, DFilters, n, s, J, Lev):
r = len(DFilters)
c = [None] * r
for j in range(r):
c[j] = ChebyshevApprox(DFilters[j], n)
a = np.pi / 2 # consider the domain of masks as [0, pi]
# Fast Tight Frame Decomposition (FTFD)
FD1 = sparse.identity(L.shape[0])
d = dict()
for l in range(1, Lev + 1):
for j in range(r):
T0F = FD1
T1F = ((s ** (-J + l - 1) / a) * L) @ T0F - T0F
d[j, l - 1] = (1 / 2) * c[j][0] * T0F + c[j][1] * T1F
for k in range(2, n):
TkF = ((2 / a * s ** (-J + l - 1)) * L) @ T1F - 2 * T1F - T0F
T0F = T1F
T1F = TkF
d[j, l - 1] += c[j][k] * TkF
FD1 = d[0, l - 1]
return d