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dct_transform.py
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dct_transform.py
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import numpy as np
import torch
import torch.nn as nn
'''adapted from https://github.com/zh217/torch-dct'''
def dct_1d(x):
"""
Discrete Cosine Transform, Type II (a.k.a. the DCT)
:param x: the input signal
:return: the DCT-II of the signal over the last dimension
"""
x_shape = x.shape
N = x_shape[-1]
x = x.contiguous().view(-1, N)
v = torch.cat([x[:, ::2], x[:, 1::2].flip([1])], dim=1)
Vc = torch.rfft(v, 1, onesided=False)
k = - torch.arange(N, dtype=x.dtype, device=x.device)[None, :] * np.pi / (2 * N)
W_r = torch.cos(k)
W_i = torch.sin(k)
V = Vc[:, :, 0] * W_r - Vc[:, :, 1] * W_i
V = 2 * V.view(*x_shape)
return V
def idct_1d(X):
"""
The inverse to DCT-II, which is a scaled Discrete Cosine Transform, Type III
Our definition of idct is that idct(dct(x)) == x
:param X: the input signal
:return: the inverse DCT-II of the signal over the last dimension
"""
x_shape = X.shape
N = x_shape[-1]
X_v = X.contiguous().view(-1, x_shape[-1]) / 2
k = torch.arange(x_shape[-1], dtype=X.dtype, device=X.device)[None, :] * np.pi / (2 * N)
W_r = torch.cos(k)
W_i = torch.sin(k)
V_t_r = X_v
V_t_i = torch.cat([X_v[:, :1] * 0, -X_v.flip([1])[:, :-1]], dim=1)
V_r = V_t_r * W_r - V_t_i * W_i
V_i = V_t_r * W_i + V_t_i * W_r
V = torch.cat([V_r.unsqueeze(2), V_i.unsqueeze(2)], dim=2)
v = torch.irfft(V, 1, onesided=False)
x = v.new_zeros(v.shape)
x[:, ::2] += v[:, :N - (N // 2)]
x[:, 1::2] += v.flip([1])[:, :N // 2]
return x.view(*x_shape)
class DCTPooling2d(nn.Module):
def __init__(self, dims_in, rebalance=1.):
super().__init__()
self.ch = dims_in[0][0]
self.N = dims_in[0][1]
self.rebalance = 2 * (self.N +1) / rebalance
self.jac = (self.N**2 * self.ch) * np.log(rebalance)
assert torch.cuda.is_available(), "please father, give 1 cuda"
I = torch.eye(self.N).cuda()
# I = torch.eye(self.N)
self.weight = dct_1d(I).t()
self.inv_weight = idct_1d(I).t()
self.weight = nn.Parameter(self.weight, requires_grad=False)
self.inv_weight = nn.Parameter(self.inv_weight, requires_grad=False)
def forward(self, x, rev=False):
x = x[0]
if rev:
weight = self.inv_weight
rebal = self.rebalance
x = x.view(x.shape[0], self.N, self.N, self.ch)
x = x.transpose(1, -1).contiguous()
else:
weight = self.weight
rebal = 1/self.rebalance
out = nn.functional.linear(x, weight)
out = nn.functional.linear(out.transpose(-1, -2), weight)
out = out.transpose(-1, -2)
if not rev:
out = out.transpose(1, -1).contiguous()
out = out.view(out.shape[0], -1)
return [out * rebal]
def jacobian(self, x, rev=False):
return self.jac
def output_dims(self, input_dims):
assert len(input_dims) == 1, "Can only use 1 input"
c, w, h = input_dims[0]
comp = c*w*h
return [(comp,)]
if __name__ == '__main__':
for N in [16, 32, 64]:
x = torch.cuda.FloatTensor(1000, 3, N, N)
x.normal_(0,1)
dct_layer = DCTPooling2d([(3, N, N)])
transf = dct_layer(x)
x_inv = dct_layer(transf, rev=True)
transf = transf.contiguous()
means = transf[:, 3:6]
true_means = torch.mean(x, dim=(2,3))
err = torch.abs(x - x_inv).max()
print(N, err.item(), flush=True)