def advect(f, vx, vy):
"""Move field f according to x and y velocities (u and v)
using an implicit Euler integrator."""
rows, cols = f.shape
cell_xs, cell_ys = np.meshgrid(np.arange(cols), np.arange(rows))
center_xs = (cell_xs - vx).ravel()
center_ys = (cell_ys - vy).ravel()
# Compute indices of source cells.
left_ix = np.floor(center_ys).astype(np.int)
top_ix = np.floor(center_xs).astype(np.int)
rw = center_ys - left_ix # Relative weight of right-hand cells.
bw = center_xs - top_ix # Relative weight of bottom cells.
left_ix = np.mod(left_ix, rows) # Wrap around edges of simulation.
right_ix = np.mod(left_ix + 1, rows)
top_ix = np.mod(top_ix, cols)
bot_ix = np.mod(top_ix + 1, cols)
# A linearly-weighted sum of the 4 surrounding cells.
flat_f = (1 - rw) * ((1 - bw)*f[left_ix, top_ix] + bw*f[left_ix, bot_ix]) \
+ rw * ((1 - bw)*f[right_ix, top_ix] + bw*f[right_ix, bot_ix])
return np.reshape(flat_f, (rows, cols))
def load_mnist():
print("Loading training data...")
import imp, urllib
partial_flatten = lambda x : np.reshape(x, (x.shape[0], np.prod(x.shape[1:])))
one_hot = lambda x, K: np.array(x[:,None] == np.arange(K)[None, :], dtype=int)
source, _ = urllib.urlretrieve(
'https://raw.githubusercontent.com/HIPS/Kayak/master/examples/data.py')
data = imp.load_source('data', source).mnist()
train_images, train_labels, test_images, test_labels = data
train_images = partial_flatten(train_images) / 255.0
test_images = partial_flatten(test_images) / 255.0
train_labels = one_hot(train_labels, 10)
test_labels = one_hot(test_labels, 10)
N_data = train_images.shape[0]
return N_data, train_images, train_labels, test_images, test_labels
return r, p(r)
if __name__ == "__main__":
# generate data
npr.seed(0)
data = negbin_sample(r=5, p=0.5, size=1000)
# fit likelihood-extremizing parameters
r, p = fit_maxlike(data, r_guess=1)
# report fit
print('Fit parameters:')
print('r={r}, p={p}'.format(r=r, p=p))
print('Check that we are at a local stationary point:')
loglike = lambda r, p: np.sum(negbin_loglike(r, p, data))
grad_both = multigrad(loglike, argnums=[0,1])
print(grad_both(r, p))
import matplotlib.pyplot as plt
xm = data.max()
plt.figure()
plt.hist(data, bins=np.arange(xm+1)-0.5, normed=True, label='normed data counts')
plt.xlim(0,xm)
plt.plot(np.arange(xm), np.exp(negbin_loglike(r, p, np.arange(xm))), label='maxlike fit')
plt.xlabel('k')
plt.ylabel('p(k)')
plt.legend(loc='best')
plt.show()
tanh_layer(120),
tanh_layer(84),
softmax_layer(10)]
# Training parameters
param_scale = 0.1
learning_rate = 1e-3
momentum = 0.9
batch_size = 256
num_epochs = 50
# Load and process MNIST data (borrowing from Kayak)
print("Loading training data...")
import imp, urllib
add_color_channel = lambda x : x.reshape((x.shape[0], 1, x.shape[1], x.shape[2]))
one_hot = lambda x, K : np.array(x[:,None] == np.arange(K)[None, :], dtype=int)
source, _ = urllib.urlretrieve(
'https://raw.githubusercontent.com/HIPS/Kayak/master/examples/data.py')
data = imp.load_source('data', source).mnist()
train_images, train_labels, test_images, test_labels = data
train_images = add_color_channel(train_images) / 255.0
test_images = add_color_channel(test_images) / 255.0
train_labels = one_hot(train_labels, 10)
test_labels = one_hot(test_labels, 10)
N_data = train_images.shape[0]
# Make neural net functions
N_weights, pred_fun, loss_fun, frac_err = make_nn_funs(input_shape, layer_specs, L2_reg)
loss_grad = grad(loss_fun)
# Initialize weights
def string_to_one_hot(string, maxchar):
"""Converts an ASCII string to a one-of-k encoding."""
ascii = np.array([ord(c) for c in string]).T
return np.array(ascii[:,None] == np.arange(maxchar)[None, :], dtype=int)
gamma = primitive(scipy.special.gamma)
gammaln = primitive(scipy.special.gammaln)
gammasgn = primitive(scipy.special.gammasgn)
rgamma = primitive(scipy.special.rgamma)
multigammaln = primitive(scipy.special.multigammaln)
gammasgn.defgrad_is_zero()
polygamma.defgrad_is_zero(argnums=(0,))
polygamma.defgrad(lambda ans, n, x: lambda g: g * polygamma(n + 1, x), argnum=1)
psi.defgrad( lambda ans, x: lambda g: g * polygamma(1, x))
digamma.defgrad( lambda ans, x: lambda g: g * polygamma(1, x))
gamma.defgrad( lambda ans, x: lambda g: g * ans * psi(x))
gammaln.defgrad( lambda ans, x: lambda g: g * psi(x))
rgamma.defgrad( lambda ans, x: lambda g: g * psi(x) / -gamma(x))
multigammaln.defgrad(lambda ans, a, d:
lambda g: g * np.sum(digamma(np.expand_dims(a, -1) - np.arange(d)/2.), -1))
multigammaln.defgrad_is_zero(argnums=(1,))
### Bessel functions ###
j0 = primitive(scipy.special.j0)
y0 = primitive(scipy.special.y0)
j1 = primitive(scipy.special.j1)
y1 = primitive(scipy.special.y1)
jn = primitive(scipy.special.jn)
yn = primitive(scipy.special.yn)
j0.defgrad(lambda ans, x: lambda g: -g * j1(x))
y0.defgrad(lambda ans, x: lambda g: -g * y1(x))
j1.defgrad(lambda ans, x: lambda g: g * (j0(x) - jn(2, x)) / 2.0)
