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complexnn/fft.py
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#!/usr/bin/env python # -*- coding: utf-8 -*- # # Authors: Olexa Bilaniuk # import keras.backend as KB import keras.engine as KE import keras.layers as KL import keras.optimizers as KO import theano as T import theano.ifelse as TI import theano.tensor as TT import theano.tensor.fft as TTF import numpy as np # # FFT functions: # # fft(): Batched 1-D FFT (Input: (Batch, TimeSamples)) # ifft(): Batched 1-D IFFT (Input: (Batch, FreqSamples)) # fft2(): Batched 2-D FFT (Input: (Batch, TimeSamplesH, TimeSamplesW)) # ifft2(): Batched 2-D IFFT (Input: (Batch, FreqSamplesH, FreqSamplesW)) # def fft(z): B = z.shape[0]//2 L = z.shape[1] C = TT.as_tensor_variable(np.asarray([[[1,-1]]], dtype=T.config.floatX)) Zr, Zi = TTF.rfft(z[:B], norm="ortho"), TTF.rfft(z[B:], norm="ortho") isOdd = TT.eq(L%2, 1) Zr = TI.ifelse(isOdd, TT.concatenate([Zr, C*Zr[:,1: ][:,::-1]], axis=1), TT.concatenate([Zr, C*Zr[:,1:-1][:,::-1]], axis=1)) Zi = TI.ifelse(isOdd, TT.concatenate([Zi, C*Zi[:,1: ][:,::-1]], axis=1), TT.concatenate([Zi, C*Zi[:,1:-1][:,::-1]], axis=1)) Zi = (C*Zi)[:,:,::-1] # Zi * i Z = Zr+Zi return TT.concatenate([Z[:,:,0], Z[:,:,1]], axis=0) def ifft(z): B = z.shape[0]//2 L = z.shape[1] C = TT.as_tensor_variable(np.asarray([[[1,-1]]], dtype=T.config.floatX)) Zr, Zi = TTF.rfft(z[:B], norm="ortho"), TTF.rfft(z[B:]*-1, norm="ortho") isOdd = TT.eq(L%2, 1) Zr = TI.ifelse(isOdd, TT.concatenate([Zr, C*Zr[:,1: ][:,::-1]], axis=1), TT.concatenate([Zr, C*Zr[:,1:-1][:,::-1]], axis=1)) Zi = TI.ifelse(isOdd, TT.concatenate([Zi, C*Zi[:,1: ][:,::-1]], axis=1), TT.concatenate([Zi, C*Zi[:,1:-1][:,::-1]], axis=1)) Zi = (C*Zi)[:,:,::-1] # Zi * i Z = Zr+Zi return TT.concatenate([Z[:,:,0], Z[:,:,1]*-1], axis=0) def fft2(x): tt = x tt = KB.reshape(tt, (x.shape[0] *x.shape[1], x.shape[2])) tf = fft(tt) tf = KB.reshape(tf, (x.shape[0], x.shape[1], x.shape[2])) tf = KB.permute_dimensions(tf, (0, 2, 1)) tf = KB.reshape(tf, (x.shape[0] *x.shape[2], x.shape[1])) ff = fft(tf) ff = KB.reshape(ff, (x.shape[0], x.shape[2], x.shape[1])) ff = KB.permute_dimensions(ff, (0, 2, 1)) return ff def ifft2(x): ff = x ff = KB.permute_dimensions(ff, (0, 2, 1)) ff = KB.reshape(ff, (x.shape[0] *x.shape[2], x.shape[1])) tf = ifft(ff) tf = KB.reshape(tf, (x.shape[0], x.shape[2], x.shape[1])) tf = KB.permute_dimensions(tf, (0, 2, 1)) tf = KB.reshape(tf, (x.shape[0] *x.shape[1], x.shape[2])) tt = ifft(tf) tt = KB.reshape(tt, (x.shape[0], x.shape[1], x.shape[2])) return tt # # FFT Layers: # # FFT: Batched 1-D FFT (Input: (Batch, FeatureMaps, TimeSamples)) # IFFT: Batched 1-D IFFT (Input: (Batch, FeatureMaps, FreqSamples)) # FFT2: Batched 2-D FFT (Input: (Batch, FeatureMaps, TimeSamplesH, TimeSamplesW)) # IFFT2: Batched 2-D IFFT (Input: (Batch, FeatureMaps, FreqSamplesH, FreqSamplesW)) # class FFT(KL.Layer): def call(self, x, mask=None): a = KB.permute_dimensions(x, (1,0,2)) a = KB.reshape(a, (x.shape[1] *x.shape[0], x.shape[2])) a = fft(a) a = KB.reshape(a, (x.shape[1], x.shape[0], x.shape[2])) return KB.permute_dimensions(a, (1,0,2)) class IFFT(KL.Layer): def call(self, x, mask=None): a = KB.permute_dimensions(x, (1,0,2)) a = KB.reshape(a, (x.shape[1] *x.shape[0], x.shape[2])) a = ifft(a) a = KB.reshape(a, (x.shape[1], x.shape[0], x.shape[2])) return KB.permute_dimensions(a, (1,0,2)) class FFT2(KL.Layer): def call(self, x, mask=None): a = KB.permute_dimensions(x, (1,0,2,3)) a = KB.reshape(a, (x.shape[1] *x.shape[0], x.shape[2], x.shape[3])) a = fft2(a) a = KB.reshape(a, (x.shape[1], x.shape[0], x.shape[2], x.shape[3])) return KB.permute_dimensions(a, (1,0,2,3)) class IFFT2(KL.Layer): def call(self, x, mask=None): a = KB.permute_dimensions(x, (1,0,2,3)) a = KB.reshape(a, (x.shape[1] *x.shape[0], x.shape[2], x.shape[3])) a = ifft2(a) a = KB.reshape(a, (x.shape[1], x.shape[0], x.shape[2], x.shape[3])) return KB.permute_dimensions(a, (1,0,2,3)) # # Tests # # Note: The IFFT is the conjugate of the FFT of the conjugate. # # np.fft.ifft(x) == np.conj(np.fft.fft(np.conj(x))) # if __name__ == "__main__": # Numpy np.random.seed(1) L = 19 r = np.random.normal(0.8, size=(L,)) i = np.random.normal(0.8, size=(L,)) x = r+i*1j R = np.fft.rfft(r, norm="ortho") I = np.fft.rfft(i, norm="ortho") X = np.fft.fft (x, norm="ortho") if L&1: R = np.concatenate([R, np.conj(R[1: ][::-1])]) I = np.concatenate([I, np.conj(I[1: ][::-1])]) else: R = np.concatenate([R, np.conj(R[1:-1][::-1])]) I = np.concatenate([I, np.conj(I[1:-1][::-1])]) Y = R+I*1j print np.allclose(X, Y) # Theano z = TT.dmatrix() f = T.function([z], ifft(fft(z))) v = np.concatenate([np.real(x)[np.newaxis,:], np.imag(x)[np.newaxis,:]], axis=0) print v print f(v) print np.allclose(v, f(v)) # Keras x = i = KL.Input(shape=(128, 32,32)) x = IFFT2()(x) model = KE.Model([i],[x]) loss = "mse" opt = KO.Adam() model.compile(opt, loss) model._make_train_function() model._make_predict_function() model._make_test_function() v = np.random.normal(size=(13,128,32,32)) #print v V = model.predict(v) #print V print V.shape |