Skip to content

Instantly share code, notes, and snippets.

@kylemcdonald
Created November 2, 2015 01:15
Show Gist options
  • Save kylemcdonald/662f93a4bcaf0c046b6a to your computer and use it in GitHub Desktop.
Save kylemcdonald/662f93a4bcaf0c046b6a to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
Loading
Sorry, something went wrong. Reload?
Sorry, we cannot display this file.
Sorry, this file is invalid so it cannot be displayed.
import theano
import theano.tensor as T
from lasagne import init
from lasagne import nonlinearities
from lasagne.utils import as_tuple
from lasagne.layers.base import Layer, MergeLayer
import numpy as np
# from scipy.linalg.dft, this method prepares a matrix of complex numbers that computes the dft
def dft(n, scale=None):
if scale not in [None, 'sqrtn', 'n']:
raise ValueError("scale must be None, 'sqrtn', or 'n'; "
"%r is not valid." % (scale,))
omegas = np.exp(-2j * np.pi * np.arange(n) / n).reshape(-1, 1)
m = omegas ** np.arange(n)
if scale == 'sqrtn':
m /= math.sqrt(n)
elif scale == 'n':
m /= n
return m
# this computes the real half of the dft using only real numbers
def hdft(n, scale=None):
half = dft(n, scale)[:n//2+1]
return np.vstack([np.real(half), np.imag(half)]).astype(np.float32)
class DFTLayer(Layer):
def __init__(self, incoming, **kwargs):
super(DFTLayer, self).__init__(incoming, **kwargs)
n = incoming.output_shape[-1]
dft_matrix = hdft(n).transpose()
self.num_units = dft_matrix.shape[1]
self.W = self.add_param(dft_matrix, dft_matrix.shape, name="W")
self.params[self.W].remove("trainable")
def get_output_shape_for(self, input_shape):
return (input_shape[0], self.num_units)
def get_output_for(self, input, **kwargs):
activation = T.dot(input, self.W)
return activation.reshape((-1, self.num_units))
def real(x):
mid = x.shape[1]//2
return x[:,:mid]
def imag(x):
mid = x.shape[1]//2
return x[:,mid:]
# input a and b are in format [r0, r1, r2.. rn, i0, i1, i2... in]
def dft_error(a, b):
ra = real(a)
rb = real(b)
ia = imag(a)
ib = imag(b)
realdiff = ra - rb
imagdiff = ia - ib
rmsdiff = realdiff**2 + imagdiff**2
amag = T.sqrt(ra**2 + ia**2)
bmag = T.sqrt(rb**2 + ib**2)
magdiff = (amag - bmag)**2
n = rmsdiff.shape[1]
weights = (T.cast(1., 'float32') + theano.tensor.arange(n)) / T.cast(1. + n, 'float32') # linspace (0, 1)
return T.stack([rmsdiff * (1. - weights), magdiff * weights]).dimshuffle(2,1,3,).flatten(2)
from lasagne.layers import get_output, InputLayer
def dft_batch(x):
input_layer = InputLayer((None, 1, x.shape[1]))
dft_layer = DFTLayer(input_layer)
return get_output(dft_layer, x).eval()
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment