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| import numpy as np | |
| import torch | |
| import torch.nn as nn | |
| from torch.nn import functional as F | |
| def dct1(x): | |
| """ | |
| Discrete Cosine Transform, Type I | |
| :param x: the input signal | |
| :return: the DCT-I of the signal over the last dimension | |
| """ | |
| x_shape = x.shape | |
| x = x.view(-1, x_shape[-1]) | |
| #return torch.rfft(torch.cat([x, x.flip([1])[:, 1:-1]], dim=1), 1)[:, :, 0].view(*x_shape) | |
| return torch.fft.fft(torch.cat([x, x.flip([1])[:, 1:-1]], dim=1), 1)[:, :, 0].view(*x_shape) | |
| def idct1(X): | |
| """ | |
| The inverse of DCT-I, which is just a scaled DCT-I | |
| Our definition if idct1 is such that idct1(dct1(x)) == x | |
| :param X: the input signal | |
| :return: the inverse DCT-I of the signal over the last dimension | |
| """ | |
| n = X.shape[-1] | |
| return dct1(X) / (2 * (n - 1)) | |
| def dct(x, norm=None): | |
| """ | |
| Discrete Cosine Transform, Type II (a.k.a. the DCT) | |
| For the meaning of the parameter `norm`, see: | |
| https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html | |
| :param x: the input signal | |
| :param norm: the normalization, None or 'ortho' | |
| :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.fft.rfft(v, 1, onesided=False) | |
| Vc = torch.view_as_real(torch.fft.fft(v, dim=1)) | |
| 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 | |
| if norm == 'ortho': | |
| V[:, 0] /= np.sqrt(N) * 2 | |
| V[:, 1:] /= np.sqrt(N / 2) * 2 | |
| V = 2 * V.view(*x_shape) | |
| return V | |
| def idct(X, norm=None): | |
| """ | |
| The inverse to DCT-II, which is a scaled Discrete Cosine Transform, Type III | |
| Our definition of idct is that idct(dct(x)) == x | |
| For the meaning of the parameter `norm`, see: | |
| https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html | |
| :param X: the input signal | |
| :param norm: the normalization, None or 'ortho' | |
| :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 | |
| if norm == 'ortho': | |
| X_v[:, 0] *= np.sqrt(N) * 2 | |
| X_v[:, 1:] *= np.sqrt(N / 2) * 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) | |
| v = torch.fft.irfft(torch.view_as_complex(V), n=V.shape[1], dim=1) | |
| 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) | |
| def dct_2d(x, norm=None): | |
| """ | |
| 2-dimentional Discrete Cosine Transform, Type II (a.k.a. the DCT) | |
| For the meaning of the parameter `norm`, see: | |
| https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html | |
| :param x: the input signal | |
| :param norm: the normalization, None or 'ortho' | |
| :return: the DCT-II of the signal over the last 2 dimensions | |
| """ | |
| X1 = dct(x, norm=norm) | |
| X2 = dct(X1.transpose(-1, -2), norm=norm) | |
| return X2.transpose(-1, -2) | |
| def idct_2d(X, norm=None): | |
| """ | |
| The inverse to 2D DCT-II, which is a scaled Discrete Cosine Transform, Type III | |
| Our definition of idct is that idct_2d(dct_2d(x)) == x | |
| For the meaning of the parameter `norm`, see: | |
| https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html | |
| :param X: the input signal | |
| :param norm: the normalization, None or 'ortho' | |
| :return: the DCT-II of the signal over the last 2 dimensions | |
| """ | |
| x1 = idct(X, norm=norm) | |
| x2 = idct(x1.transpose(-1, -2), norm=norm) | |
| return x2.transpose(-1, -2) | |
| def dct_3d(x, norm=None): | |
| """ | |
| 3-dimentional Discrete Cosine Transform, Type II (a.k.a. the DCT) | |
| For the meaning of the parameter `norm`, see: | |
| https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html | |
| :param x: the input signal | |
| :param norm: the normalization, None or 'ortho' | |
| :return: the DCT-II of the signal over the last 3 dimensions | |
| """ | |
| X1 = dct(x, norm=norm) | |
| X2 = dct(X1.transpose(-1, -2), norm=norm) | |
| X3 = dct(X2.transpose(-1, -3), norm=norm) | |
| return X3.transpose(-1, -3).transpose(-1, -2) | |
| def idct_3d(X, norm=None): | |
| """ | |
| The inverse to 3D DCT-II, which is a scaled Discrete Cosine Transform, Type III | |
| Our definition of idct is that idct_3d(dct_3d(x)) == x | |
| For the meaning of the parameter `norm`, see: | |
| https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html | |
| :param X: the input signal | |
| :param norm: the normalization, None or 'ortho' | |
| :return: the DCT-II of the signal over the last 3 dimensions | |
| """ | |
| x1 = idct(X, norm=norm) | |
| x2 = idct(x1.transpose(-1, -2), norm=norm) | |
| x3 = idct(x2.transpose(-1, -3), norm=norm) | |
| return x3.transpose(-1, -3).transpose(-1, -2) | |
| # class LinearDCT(nn.Linear): | |
| # """Implement any DCT as a linear layer; in practice this executes around | |
| # 50x faster on GPU. Unfortunately, the DCT matrix is stored, which will | |
| # increase memory usage. | |
| # :param in_features: size of expected input | |
| # :param type: which dct function in this file to use""" | |
| # | |
| # def __init__(self, in_features, type, norm=None, bias=False): | |
| # self.type = type | |
| # self.N = in_features | |
| # self.norm = norm | |
| # super(LinearDCT, self).__init__(in_features, in_features, bias=bias) | |
| # | |
| # def reset_parameters(self): | |
| # # initialise using dct function | |
| # I = torch.eye(self.N) | |
| # if self.type == 'dct1': | |
| # self.weight.data = dct1(I).data.t() | |
| # elif self.type == 'idct1': | |
| # self.weight.data = idct1(I).data.t() | |
| # elif self.type == 'dct': | |
| # self.weight.data = dct(I, norm=self.norm).data.t() | |
| # elif self.type == 'idct': | |
| # self.weight.data = idct(I, norm=self.norm).data.t() | |
| # self.weight.require_grad = False # don't learn this! | |
| class LinearDCT(nn.Module): | |
| """Implement any DCT as a linear layer; in practice this executes around | |
| 50x faster on GPU. Unfortunately, the DCT matrix is stored, which will | |
| increase memory usage. | |
| :param in_features: size of expected input | |
| :param type: which dct function in this file to use""" | |
| def __init__(self, in_features, type, norm=None): | |
| super(LinearDCT, self).__init__() | |
| self.type = type | |
| self.N = in_features | |
| self.norm = norm | |
| I = torch.eye(self.N) | |
| if self.type == 'dct1': | |
| self.weight = dct1(I).data.t() | |
| elif self.type == 'idct1': | |
| self.weight = idct1(I).data.t() | |
| elif self.type == 'dct': | |
| self.weight = dct(I, norm=self.norm).data.t() | |
| elif self.type == 'idct': | |
| self.weight = idct(I, norm=self.norm).data.t() | |
| # self.register_buffer('weight', kernel) | |
| # self.weight = kernel | |
| def forward(self, x): | |
| return F.linear(x, weight=self.weight.cuda(x.get_device())) | |
| def apply_linear_2d(x, linear_layer): | |
| """Can be used with a LinearDCT layer to do a 2D DCT. | |
| :param x: the input signal | |
| :param linear_layer: any PyTorch Linear layer | |
| :return: result of linear layer applied to last 2 dimensions | |
| """ | |
| X1 = linear_layer(x) | |
| X2 = linear_layer(X1.transpose(-1, -2)) | |
| return X2.transpose(-1, -2) | |
| def apply_linear_3d(x, linear_layer): | |
| """Can be used with a LinearDCT layer to do a 3D DCT. | |
| :param x: the input signal | |
| :param linear_layer: any PyTorch Linear layer | |
| :return: result of linear layer applied to last 3 dimensions | |
| """ | |
| X1 = linear_layer(x) | |
| X2 = linear_layer(X1.transpose(-1, -2)) | |
| X3 = linear_layer(X2.transpose(-1, -3)) | |
| return X3.transpose(-1, -3).transpose(-1, -2) | |
| if __name__ == '__main__': | |
| x = torch.Tensor(1000, 4096) | |
| x.normal_(0, 1) | |
| linear_dct = LinearDCT(4096, 'dct') | |
| error = torch.abs(dct(x) - linear_dct(x)) | |
| assert error.max() < 1e-3, (error, error.max()) | |
| linear_idct = LinearDCT(4096, 'idct') | |
| error = torch.abs(idct(x) - linear_idct(x)) | |
| assert error.max() < 1e-3, (error, error.max()) | |