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 os
os.environ["DATASET_PATH"] = "/home/vrael/DATASETS/"
symjax.current_graph().reset()
mnist = symjax.data.mnist()
# 2d image
images = mnist["train_set/images"][mnist["train_set/labels"] == 2][:2, 0]
images /= images.max()
np.random.seed(0)
coordinates = T.meshgrid(T.range(28), T.range(28))
coordinates = T.Variable(
T.stack([coordinates[1].flatten(), coordinates[0].flatten()]).astype("float32")
)
interp = T.interpolation.map_coordinates(images[0], coordinates, order=1).reshape(
(28, 28)
)
loss = ((interp - images[1]) ** 2).mean()
lr = symjax.nn.schedules.PiecewiseConstant(0.05, {5000: 0.01, 8000: 0.005})
symjax.nn.optimizers.Adam(loss, lr)
train = symjax.function(outputs=loss, updates=symjax.get_updates())
rec = symjax.function(outputs=interp)
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
sys.path.insert(0, "../")
import symjax
import symjax.tensor as T
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
matplotlib.use("Agg")
###### DERIVATIVE OF GAUSSIAN EXAMPLE
t = T.Placeholder((1000, ), "float32")
print(t)
f = T.meshgrid(t, t)
f = T.exp(-(t**2))
u = f.sum()
g = symjax.gradients(u, [t])
g2 = symjax.gradients(g[0].sum(), [t])
g3 = symjax.gradients(g2[0].sum(), [t])
dog = symjax.function(t, outputs=[g[0], g2[0], g3[0]])
plt.plot(np.array(dog(np.linspace(-10, 10, 1000))).T)
###### GRADIENT DESCENT
z = T.Variable(3.0)
loss = z**2
g_z = symjax.gradients(loss, [z])
print(loss, z)