def generate_sinc_filterbank(f0, f1, J, N):
# get the center frequencies
freqs = get_scaled_freqs(f0, f1, J + 1)
# make it with difference and make it a variable
freqs = np.stack([freqs[:-1], freqs[1:]], 1)
freqs[:, 1] -= freqs[:, 0]
freqs = T.Variable(freqs, name='c_freq')
# parametrize the frequencies
f0 = T.abs(freqs[:, 0])
f1 = f0 + T.abs(freqs[:, 1])
# sampled the bandpass filters
time = T.linspace(-N // 2, N // 2 - 1, N)
time_matrix = time.reshape((-1, 1))
sincs = T.signal.sinc_bandpass(time_matrix, f0, f1)
# apodize
apod_filters = sincs * T.signal.hanning(N).reshape((-1, 1))
# normalize
normed_filters = apod_filters / T.linalg.norm(
apod_filters, 2, 0, keepdims=True)
filters = T.transpose(T.expand_dims(normed_filters, 1), [2, 1, 0])
return filters, freqs
def generate_gaussian_filterbank(N, M, J, f0, f1, modes=1):
# gaussian parameters
freqs = get_scaled_freqs(f0, f1, J)
freqs *= (J - 1) * 10
if modes > 1:
other_modes = np.random.randint(0, J, J * (modes - 1))
freqs = np.concatenate([freqs, freqs[other_modes]])
# crate the average vectors
mu_init = np.stack([freqs, 0.1 * np.random.randn(J * modes)], 1)
mu = T.Variable(mu_init.astype('float32'), name='mu')
# create the covariance matrix
cor = T.Variable(0.01 * np.random.randn(J * modes).astype('float32'),
name='cor')
sigma_init = np.stack([freqs / 6, 1. + 0.01 * np.random.randn(J * modes)],
1)
sigma = T.Variable(sigma_init.astype('float32'), name='sigma')
# create the mixing coefficients
mixing = T.Variable(np.ones((modes, 1, 1)).astype('float32'))
# now apply our parametrization
coeff = T.stop_gradient(T.sqrt((T.abs(sigma) + 0.1).prod(1))) * 0.95
Id = T.eye(2)
cov = Id * T.expand_dims((T.abs(sigma)+0.1),1) +\
T.flip(Id, 0) * (T.tanh(cor) * coeff).reshape((-1, 1, 1))
cov_inv = T.linalg.inv(cov)
# get the gaussian filters
time = T.linspace(-5, 5, M)
freq = T.linspace(0, J * 10, N)
x, y = T.meshgrid(time, freq)
grid = T.stack([y.flatten(), x.flatten()], 1)
centered = grid - T.expand_dims(mu, 1)
# asdf
gaussian = T.exp(-(T.matmul(centered, cov_inv)**2).sum(-1))
norm = T.linalg.norm(gaussian, 2, 1, keepdims=True)
gaussian_2d = T.abs(mixing) * T.reshape(gaussian / norm, (J, modes, N, M))
return gaussian_2d.sum(1, keepdims=True), mu, cor, sigma, mixing
import sys
sys.path.insert(0, "../")
import symjax as sj
import symjax.tensor as T
import matplotlib.pyplot as plt
import matplotlib
matplotlib.use('Agg')
###### 2D GAUSSIAN EXAMPLE
t = T.linspace(-5, 5, 5)
x, y = T.meshgrid(t, t)
X = T.stack([x.flatten(), y.flatten()], 1)
p = T.pdfs.multivariate_normal.pdf(X, T.zeros(2), T.eye(2))
p = p.reshape((5, 5)).round(2)
print(p)
# Tensor(Op=round_, shape=(5, 5), dtype=float32)
# lazy evaluation (not compiled nor optimized)
print(p.get())
# [[0. 0. 0. 0. 0. ]
# [0. 0. 0.01 0. 0. ]
# [0. 0.01 0.16 0.01 0. ]
# [0. 0. 0.01 0. 0. ]
# [0. 0. 0. 0. 0. ]]
# create the function which internall compiles and optimizes
randn = T.random.randn(SHAPE)
rand = T.random.rand(SHAPE)
out = randn
out2 = out.clone({randn: rand})
out3 = out2.clone({rand: 3})
get_vars = symjax.function(outputs=[out, out2])
for i in range(10):
print(get_vars())
asdf
# test shuffle
matrix = T.linspace(0, 1, 16).reshape((4, 4))
smatrix = matrix[T.random.permutation(T.range(4))]
get_shuffle = symjax.function(outputs=smatrix)
for i in range(10):
print(get_shuffle())
asdfsadf
# test the random uniform
SHAPE = (2, 2)
z = T.Variable(np.random.randn(*SHAPE).astype("float32"), name="z")
get_z = symjax.function(outputs=z)
for i in range(10):
import symjax
import symjax.tensor as T
import matplotlib.pyplot as plt
import numpy as np
J = 5
Q = 4
scales = T.power(2, T.linspace(0.1, J - 1, J * Q))
scales = scales[:, None]
print(scales.get())
wavelet = symjax.tensor.signal.complex_morlet(5 * scales, np.pi / scales)
waveletw = symjax.tensor.signal.fourier_complex_morlet(5 * scales,
np.pi / scales,
wavelet.shape[-1])
waveletlp = symjax.tensor.signal.littewood_paley_normalization(waveletw,
down=np.pi /
scales[-1, 0])
wavelet = wavelet.get()
waveletw = waveletw.get()
waveletlp = waveletlp.get()
plt.subplot(321)
for i in range(J * Q):
fr = np.real(np.fft.fft(np.fft.ifftshift(wavelet[i])))
fi = np.imag(np.fft.fft(np.fft.ifftshift(wavelet[i])))
plt.plot(i + fr, '--b')
plt.plot(i + fi, '--r')