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