Example 1
def __call__(self, params):
print '???', params
sd1 = params[0]
sd2 = params[1]
cor = params[2]
if sd1 < 0. or sd1 > 10. or sd2 < 0. or sd2 > 10. or cor < -1. or cor > 1.:
return np.inf
bandwidth = maths.stats.choleskysqrt2d(sd1, sd2, cor)
bandwidthdet = la.det(bandwidth)
bandwidthinv = la.inv(bandwidth)
diff = sample[self.__iidx] - sample[self.__jidx]
temp = diff.dot(bandwidthinv.T)
temp *= temp
e = np.exp(np.sum(temp, axis=1))
s = np.sum(e**(-.25) - 4 * e**(-.5))
cost = self.__n / bandwidthdet + (2. / bandwidthdet) * s
print '!!!', cost
return cost / 10000. Example 2
def svgd_kernel(self, h = -1):
sq_dist = pdist(self.theta)
pairwise_dists = squareform(sq_dist)**2
if h < 0: # if h < 0, using median trick
h = np.median(pairwise_dists)
h = np.sqrt(0.5 * h / np.log(self.theta.shape[0]+1))
# compute the rbf kernel
Kxy = np.exp( -pairwise_dists / h**2 / 2)
dxkxy = -np.matmul(Kxy, self.theta)
sumkxy = np.sum(Kxy, axis=1)
for i in range(self.theta.shape[1]):
dxkxy[:, i] = dxkxy[:,i] + np.multiply(self.theta[:,i],sumkxy)
dxkxy = dxkxy / (h**2)
return (Kxy, dxkxy) Example 3
def lr_grad_norm_avg(self):
# this is for enforcing lr * grad_norm not
# increasing dramatically in case of instability.
# Not necessary for basic use.
global_state = self._global_state
beta = self._beta
if "lr_grad_norm_avg" not in global_state:
global_state['grad_norm_squared_avg_log'] = 0.0
global_state['grad_norm_squared_avg_log'] = \
global_state['grad_norm_squared_avg_log'] * beta \
+ (1 - beta) * np.log(global_state['grad_norm_squared'] + eps)
if "lr_grad_norm_avg" not in global_state:
global_state["lr_grad_norm_avg"] = \
0.0 * beta + (1 - beta) * np.log(self._lr * np.sqrt(global_state['grad_norm_squared'] ) + eps)
# we monitor the minimal smoothed ||lr * grad||
global_state["lr_grad_norm_avg_min"] = \
np.exp(global_state["lr_grad_norm_avg"] / self.zero_debias_factor() )
else:
global_state["lr_grad_norm_avg"] = global_state["lr_grad_norm_avg"] * beta \
+ (1 - beta) * np.log(self._lr * np.sqrt(global_state['grad_norm_squared'] ) + eps)
global_state["lr_grad_norm_avg_min"] = \
min(global_state["lr_grad_norm_avg_min"],
np.exp(global_state["lr_grad_norm_avg"] / self.zero_debias_factor() ) ) Example 4
def lr_grad_norm_avg(self):
# this is for enforcing lr * grad_norm not
# increasing dramatically in case of instability.
# Not necessary for basic use.
global_state = self._global_state
beta = self._beta
if "lr_grad_norm_avg" not in global_state:
global_state['grad_norm_squared_avg_log'] = 0.0
global_state['grad_norm_squared_avg_log'] = \
global_state['grad_norm_squared_avg_log'] * beta \
+ (1 - beta) * np.log(global_state['grad_norm_squared'] + eps)
if "lr_grad_norm_avg" not in global_state:
global_state["lr_grad_norm_avg"] = \
0.0 * beta + (1 - beta) * np.log(self._lr * np.sqrt(global_state['grad_norm_squared'] ) + eps)
# we monitor the minimal smoothed ||lr * grad||
global_state["lr_grad_norm_avg_min"] = \
np.exp(global_state["lr_grad_norm_avg"] / self.zero_debias_factor() )
else:
global_state["lr_grad_norm_avg"] = global_state["lr_grad_norm_avg"] * beta \
+ (1 - beta) * np.log(self._lr * np.sqrt(global_state['grad_norm_squared'] ) + eps)
global_state["lr_grad_norm_avg_min"] = \
min(global_state["lr_grad_norm_avg_min"],
np.exp(global_state["lr_grad_norm_avg"] / self.zero_debias_factor() ) ) Example 5
def test_quantize_from_probs2(size, resolution):
set_random_seed(make_seed(size, resolution))
probs = np.exp(np.random.random(size)).astype(np.float32)
probs2 = probs.reshape((1, size))
quantized = quantize_from_probs2(probs2, resolution)
assert quantized.shape == probs2.shape
assert quantized.dtype == np.int8
assert np.all(quantized.sum(axis=1) == resolution)
# Check that quantized result is closer to target than any other value.
quantized = quantized.reshape((size, ))
target = resolution * probs / probs.sum()
distance = np.abs(quantized - target).sum()
for combo in itertools.combinations(range(size), resolution):
other = np.zeros(size, np.int8)
for i in combo:
other[i] += 1
assert other.sum() == resolution
other_distance = np.abs(other - target).sum()
assert distance <= other_distance Example 6
def observed_perplexity(self, counts):
"""Compute perplexity = exp(entropy) of observed variables.
Perplexity is an information theoretic measure of the number of
clusters or observed classes. Perplexity is a real number in the range
[1, dim[v]], where dim[v] is the number of categories in an observed
categorical variable or 2 for an ordinal variable.
Args:
counts: A [V]-shaped array of multinomial counts.
Returns:
A [V]-shaped numpy array of perplexity.
"""
result = self._ensemble[0].observed_perplexity(counts)
for server in self._ensemble[1:]:
result += server.observed_perplexity(counts)
result /= len(self._ensemble)
return result Example 7
def latent_correlation(self):
"""Compute correlation matrix among latent features.
This computes the generalization of Pearson's correlation to discrete
data. Let I(X;Y) be the mutual information. Then define correlation as
rho(X,Y) = sqrt(1 - exp(-2 I(X;Y)))
Returns:
A [V, V]-shaped numpy array of feature-feature correlations.
"""
result = self._ensemble[0].latent_correlation()
for server in self._ensemble[1:]:
result += server.latent_correlation()
result /= len(self._ensemble)
return result Example 8
def begin(self):
x = random.randint(self.x_range[0], self.x_range[1])
f = self.func(x)
T = self.T0
while T > self.T_min:
for i in range(self.K):
new_x = self.gen_new_x(x, T)
f_x = self.func(new_x)
delta_E = f_x - f
#
if delta_E < 0:
f = f_x
x = new_x
break
else:
#p_k = 1.0 / (1 + np.exp(- delta_E / self.func(T)))
p_k = np.exp(- delta_E / T)
if random.random() < p_k:
f = f_x
x = new_x
break
T *= self.delta
return x Example 9
def optSigma2(self, U, s, y, covars, logdetXX, reml, ldeltamin=-5, ldeltamax=5): #Prepare required matrices Uy = U.T.dot(y).flatten() UX = U.T.dot(covars) if (U.shape[1] < U.shape[0]): UUX = covars - U.dot(UX) UUy = y - U.dot(Uy) UUXUUX = UUX.T.dot(UUX) UUXUUy = UUX.T.dot(UUy) UUyUUy = UUy.T.dot(UUy) else: UUXUUX, UUXUUy, UUyUUy = None, None, None numIndividuals = U.shape[0] ldeltaopt_glob = optimize.minimize_scalar(self.negLLevalLong, bounds=(-5, 5), method='Bounded', args=(s, Uy, UX, logdetXX, UUXUUX, UUXUUy, UUyUUy, numIndividuals, reml)).x ll, sig2g, beta, r2 = self.negLLevalLong(ldeltaopt_glob, s, Uy, UX, logdetXX, UUXUUX, UUXUUy, UUyUUy, numIndividuals, reml, returnAllParams=True) sig2e = np.exp(ldeltaopt_glob) * sig2g return sig2g, sig2e, beta, ll
Example 10
def deriveKernel(self, params, i): self.checkParamsI(params, i) c = np.exp(params[-1]) #K = self.kernel.getTrainKernel(params[:-1]) #deriv1 = self.polyDegree * (c+K)**(self.polyDegree-1) K = self.kernel.getTrainKernel(params[:-1]) + c if (self.polyDegree==2): Kpower=K else: Kpower=K**2 for i in xrange(self.polyDegree-3): Kpower*=K #this is faster than direct power deriv1 = self.polyDegree * Kpower if (i==params.shape[0]-1): K_deriv = deriv1*c else: K_deriv = deriv1 * self.kernel.deriveKernel(params[:-1], i) return K_deriv
Example 11
def getTrainKernel(self, params): self.checkParams(params) if (self.sameParams(params)): return self.cache['getTrainKernel'] ell = np.exp(params[0]) if (self.K_sq is None): K = sq_dist(self.X_scaled.T / ell) #precompute squared distances else: K = self.K_sq / ell**2 self.cache['K_sq_scaled'] = K # # # #manual computation (just for sanity checks) # # # K1 = np.exp(-K / 2.0) # # # K2 = np.zeros((self.X_scaled.shape[0], self.X_scaled.shape[0])) # # # for i1 in xrange(self.X_scaled.shape[0]): # # # for i2 in xrange(i1, self.X_scaled.shape[0]): # # # diff = self.X_scaled[i1,:] - self.X_scaled[i2,:] # # # K2[i1, i2] = np.exp(-np.sum(diff**2) / (2*ell)) # # # K2[i2, i1] = K2[i1, i2] # # # print np.max((K1-K2)**2) # # # sys.exit(0) K_exp = np.exp(-K / 2.0) self.cache['getTrainKernel'] = K_exp self.saveParams(params) return K_exp
Example 12
def getTrainTestKernel(self, params, Xtest): self.checkParams(params) ell = np.exp(params[0]) p = np.exp(params[1]) Xtest_scaled = Xtest/np.sqrt(Xtest.shape[1]) d2 = sq_dist(self.X_scaled.T/ell, Xtest_scaled.T/ell) #precompute squared distances #compute dp dp = np.zeros(d2.shape) for d in xrange(self.X_scaled.shape[1]): dp += (np.outer(self.X_scaled[:,d], np.ones((1, Xtest_scaled.shape[0]))) - np.outer(np.ones((self.X_scaled.shape[0], 1)), Xtest_scaled[:,d])) dp /= p K = np.exp(-d2 / 2.0) return np.cos(2*np.pi*dp)*K
Example 13
def getTrainKernel(self, params):
self.checkParams(params)
if (self.sameParams(params)): return self.cache['getTrainKernel']
if ('K_sq_scaled' not in self.cache.keys()): self.cache['K_sq_scaled'] = [None for i in xrange(self.getNumParams())]
ell = np.exp(params)
K = 0
for i in xrange(self.getNumParams()):
if (self.sameParams(params, i)): K += self.cache['K_sq_scaled'][i]
else:
self.cache['K_sq_scaled'][i] = self.K_sq[i] / ell[i]**2
K += self.cache['K_sq_scaled'][i]
K_exp = np.exp(-K / 2.0)
self.cache['getTrainKernel'] = K_exp
self.saveParams(params)
return K_exp Example 14
def getTrainTestKernel(self, params, Xtest): self.checkParams(params) params_kernels = params[len(self.kernels):] #compute Kd and EE Kd = np.zeros((self.n, Xtest[0].shape[0], len(self.kernels))) params_ind = 0 kernel_paramsArr = params[len(self.kernels):] for k_i, k in enumerate(self.kernels): numHyp = k.getNumParams() kernelParams_range = np.array(xrange(params_ind, params_ind+numHyp), dtype=np.int) kernel_params = kernel_paramsArr[kernelParams_range] Kd[:,:,k_i] = k.getTrainTestKernel(kernel_params, Xtest[k_i]) params_ind += numHyp EE = elsympol(Kd, len(self.kernels)) #compute K K=0 for i in xrange(len(self.kernels)): K += np.exp(2*params[i]) * EE[:,:,i+1] return K
Example 15
def getTestKernelDiag(self, params, Xtest): self.checkParams(params) params_kernels = params[len(self.kernels):] #compute Kd and EE Kd = np.zeros((Xtest[0].shape[0], 1, len(self.kernels))) params_ind = 0 kernel_paramsArr = params[len(self.kernels):] for k_i, k in enumerate(self.kernels): numHyp = k.getNumParams() kernelParams_range = np.array(xrange(params_ind, params_ind+numHyp), dtype=np.int) kernel_params = kernel_paramsArr[kernelParams_range] Kd[:,0,k_i] = k.getTestKernelDiag(kernel_params, Xtest[k_i]) params_ind += numHyp EE = elsympol(Kd, len(self.kernels)) #compute K K=0 for i in xrange(len(self.kernels)): K += np.exp(2*params[i]) * EE[:,:,i+1] return K
Example 16
def getTrainTestKernel(self, params, Xtest): self.checkParams(params) ell2 = np.exp(2*params[0]) z = Xtest / np.sqrt(Xtest.shape[1]) S = 1 + self.X_scaled.dot(z.T) sz = 1 + np.sum(z**2, axis=1) sqrtEll2Psx = np.sqrt(ell2+self.sx) sqrtEll2Psz = np.sqrt(ell2+sz) K = S / np.outer(sqrtEll2Psx, sqrtEll2Psz) return np.arcsin(K)
Example 17
def sample_hparams():
hparams = {}
for k, sample_range in ranges.items():
if isinstance(sample_range, (LogRange, LinearRange)):
if isinstance(sample_range[0], int):
# LogRange not valid for ints
hparams[k] = random.randint(sample_range[0], sample_range[1])
elif isinstance(sample_range[0], float):
start, end = sample_range
if isinstance(sample_range, LogRange):
start, end = np.log10(start), np.log10(end)
choice = np.random.uniform(start, end)
if isinstance(sample_range, LogRange):
choice = np.exp(choice)
hparams[k] = choice
return hparams Example 18
def gaussian_kernel(size, std=1.):
size2 = 1 + 2 * size
kernel = np.zeros((size2, size2))
den = 2. * std * std
for row in range(size2):
for col in range(size2):
x = row - size
y = row - size
kernel[row, col] = np.exp(-(x*x + y*y) / den)
kernel /= kernel.sum()
return kernel
# TODO: check out of bounds Example 19
def sample_hparams():
hparams = {}
for k, sample_range in ranges.items():
if isinstance(sample_range, (LogRange, LinearRange)):
if isinstance(sample_range[0], int):
# LogRange not valid for ints
hparams[k] = random.randint(sample_range[0], sample_range[1])
elif isinstance(sample_range[0], float):
start, end = sample_range
if isinstance(sample_range, LogRange):
start, end = np.log10(start), np.log10(end)
choice = np.random.uniform(start, end)
if isinstance(sample_range, LogRange):
choice = np.exp(choice)
hparams[k] = choice
return hparams Example 20
def gaussian_kernel(size, std=1.):
size2 = 1 + 2 * size
kernel = np.zeros((size2, size2))
den = 2. * std * std
for row in range(size2):
for col in range(size2):
x = row - size
y = row - size
kernel[row, col] = np.exp(-(x*x + y*y) / den)
kernel /= kernel.sum()
return kernel
# TODO: check out of bounds Example 21
def sample_hparams():
hparams = {}
for k, sample_range in ranges.items():
if isinstance(sample_range, (LogRange, LinearRange)):
if isinstance(sample_range[0], int):
# LogRange not valid for ints
hparams[k] = random.randint(sample_range[0], sample_range[1])
elif isinstance(sample_range[0], float):
start, end = sample_range
if isinstance(sample_range, LogRange):
start, end = np.log10(start), np.log10(end)
choice = np.random.uniform(start, end)
if isinstance(sample_range, LogRange):
choice = np.exp(choice)
hparams[k] = choice
return hparams Example 22
def sample_hparams():
hparams = {}
for k, sample_range in ranges.items():
if isinstance(sample_range, (LogRange, LinearRange)):
if isinstance(sample_range[0], int):
# LogRange not valid for ints
hparams[k] = random.randint(sample_range[0], sample_range[1])
elif isinstance(sample_range[0], float):
start, end = sample_range
if isinstance(sample_range, LogRange):
start, end = np.log10(start), np.log10(end)
choice = np.random.uniform(start, end)
if isinstance(sample_range, LogRange):
choice = np.exp(choice)
hparams[k] = choice
return hparams Example 23
def gaussian_kernel(size, std=1.):
size2 = 1 + 2 * size
kernel = np.zeros((size2, size2))
den = 2. * std * std
for row in range(size2):
for col in range(size2):
x = row - size
y = row - size
kernel[row, col] = np.exp(-(x*x + y*y) / den)
kernel /= kernel.sum()
return kernel
# TODO: check out of bounds Example 24
def sample_hparams():
hparams = {}
for k, sample_range in ranges.items():
if isinstance(sample_range, (LogRange, LinearRange)):
if isinstance(sample_range[0], int):
# LogRange not valid for ints
hparams[k] = random.randint(sample_range[0], sample_range[1])
elif isinstance(sample_range[0], float):
start, end = sample_range
if isinstance(sample_range, LogRange):
start, end = np.log10(start), np.log10(end)
choice = np.random.uniform(start, end)
if isinstance(sample_range, LogRange):
choice = np.exp(choice)
hparams[k] = choice
return hparams Example 25
def gaussian_kernel(size, std=1.):
size2 = 1 + 2 * size
kernel = np.zeros((size2, size2))
den = 2. * std * std
for row in range(size2):
for col in range(size2):
x = row - size
y = row - size
kernel[row, col] = np.exp(-(x*x + y*y) / den)
kernel /= kernel.sum()
return kernel
# TODO: check out of bounds Example 26
def EStep(self):
P = np.zeros((self.M, self.N))
for i in range(0, self.M):
diff = self.X - np.tile(self.TY[i, :], (self.N, 1))
diff = np.multiply(diff, diff)
P[i, :] = P[i, :] + np.sum(diff, axis=1)
c = (2 * np.pi * self.sigma2) ** (self.D / 2)
c = c * self.w / (1 - self.w)
c = c * self.M / self.N
P = np.exp(-P / (2 * self.sigma2))
den = np.sum(P, axis=0)
den = np.tile(den, (self.M, 1))
den[den==0] = np.finfo(float).eps
self.P = np.divide(P, den)
self.Pt1 = np.sum(self.P, axis=0)
self.P1 = np.sum(self.P, axis=1)
self.Np = np.sum(self.P1) Example 27
def create_reference_image(size, x0=10., y0=-3., sigma_x=50., sigma_y=30., dtype='float64',
reverse_xaxis=False, correct_axes=True, sizey=None, **kwargs):
"""
Creates a reference image: a gaussian brightness with elliptical
"""
inc_cos = np.cos(0./180.*np.pi)
delta_x = 1.
x = (np.linspace(0., size - 1, size) - size / 2.) * delta_x
if sizey:
y = (np.linspace(0., sizey-1, sizey) - sizey/2.) * delta_x
else:
y = x.copy()
if reverse_xaxis:
xx, yy = np.meshgrid(-x, y/inc_cos)
elif correct_axes:
xx, yy = np.meshgrid(-x, -y/inc_cos)
else:
xx, yy = np.meshgrid(x, y/inc_cos)
image = np.exp(-(xx-x0)**2./sigma_x - (yy-y0)**2./sigma_y)
return image.astype(dtype) Example 28
def get_action_distr(self, state, beta=0.2):
'''
Args:
state (State)
beta (float): Softmax temperature parameter.
Returns:
(list of floats): The i-th float corresponds to the probability
mass associated with the i-th action (indexing into self.actions)
'''
all_q_vals = []
for i in xrange(len(self.actions)):
action = self.actions[i]
all_q_vals.append(self.get_q_value(state, action))
# Softmax distribution.
total = sum([numpy.exp(beta * qv) for qv in all_q_vals])
softmax = [numpy.exp(beta * qv) / total for qv in all_q_vals]
return softmax Example 29
def monotoneTFosc(f):
"""Maps [-inf,inf] to [-inf,inf] with different constants
for positive and negative part.
"""
if np.isscalar(f):
if f > 0.:
f = np.log(f) / 0.1
f = np.exp(f + 0.49 * (np.sin(f) + np.sin(0.79 * f))) ** 0.1
elif f < 0.:
f = np.log(-f) / 0.1
f = -np.exp(f + 0.49 * (np.sin(0.55 * f) + np.sin(0.31 * f))) ** 0.1
return f
else:
f = np.asarray(f)
g = f.copy()
idx = (f > 0)
g[idx] = np.log(f[idx]) / 0.1
g[idx] = np.exp(g[idx] + 0.49 * (np.sin(g[idx]) + np.sin(0.79 * g[idx])))**0.1
idx = (f < 0)
g[idx] = np.log(-f[idx]) / 0.1
g[idx] = -np.exp(g[idx] + 0.49 * (np.sin(0.55 * g[idx]) + np.sin(0.31 * g[idx])))**0.1
return g Example 30
def make_gaussian(size, fwhm=3, center=None):
""" Make a square gaussian kernel.
size is the length of a side of the square
fwhm is full-width-half-maximum, which
can be thought of as an effective radius.
"""
x = np.arange(0, size, 1, float)
y = x[:, np.newaxis]
if center is None:
x0 = y0 = size // 2
else:
x0 = center[0]
y0 = center[1]
return np.exp(-((x - x0) ** 2 + (y - y0) ** 2) / 2.0 / fwhm / fwhm) Example 31
def forward(self, input, *args, **kwargs):
"""A sigmoid function is a mathematical function having a
characteristic "S"-shaped curve or sigmoid curve. Often,
sigmoid function refers to the special case of the logistic
function and defined by the formula :math:`\\varphi(x) = \\frac{1}{1 + e^{-x}}`
(given the input :math:`x`).
Parameters
----------
input : float32
The activation (the summed, weighted input of a neuron).
Returns
-------
float32 in [0, 1]
The output of the sigmoid function applied to the activation.
"""
self.last_forward = 1.0 / (1.0 + np.exp(-input))
return self.last_forward Example 32
def forward(self, input):
""":math:`\\varphi(\\mathbf{x})_j =
\\frac{e^{\mathbf{x}_j}}{\sum_{k=1}^K e^{\mathbf{x}_k}}`
where :math:`K` is the total number of neurons in the layer. This
activation function gets applied row-wise.
Parameters
----------
x : float32
The activation (the summed, weighted input of a neuron).
Returns
-------
float32 where the sum of the row is 1 and each single value is in [0, 1]
The output of the softmax function applied to the activation.
"""
assert np.ndim(input) == 2
self.last_forward = input
x = input - np.max(input, axis=1, keepdims=True)
exp_x = np.exp(x)
s = exp_x / np.sum(exp_x, axis=1, keepdims=True)
return s Example 33
def step(self, mode):
if mode == "train" and self.mode == "test":
raise Exception("Cannot train during test mode")
if mode == "train":
theano_fn = self.train_fn
batch_gen = self.train_batch_gen
elif mode == "test":
theano_fn = self.test_fn
batch_gen = self.test_batch_gen
else:
raise Exception("Invalid mode")
data = next(batch_gen)
ys = data[-1]
data = data[:-1]
ret = theano_fn(*data)
return {"prediction": np.exp(ret[0]) - 1,
"answers": ys,
"current_loss": ret[1],
"loss_reg": ret[2],
"loss_mse": ret[1] - ret[2],
"log": ""} Example 34
def evaluation(self, X_test, y_test):
# normalization
X_test = self.normalization(X_test)
# average over the output
pred_y_test = np.zeros([self.M, len(y_test)])
prob = np.zeros([self.M, len(y_test)])
'''
Since we have M particles, we use a Bayesian view to calculate rmse and log-likelihood
'''
for i in range(self.M):
w1, b1, w2, b2, loggamma, loglambda = self.unpack_weights(self.theta[i, :])
pred_y_test[i, :] = self.nn_predict(X_test, w1, b1, w2, b2) * self.std_y_train + self.mean_y_train
prob[i, :] = np.sqrt(np.exp(loggamma)) /np.sqrt(2*np.pi) * np.exp( -1 * (np.power(pred_y_test[i, :] - y_test, 2) / 2) * np.exp(loggamma) )
pred = np.mean(pred_y_test, axis=0)
# evaluation
svgd_rmse = np.sqrt(np.mean((pred - y_test)**2))
svgd_ll = np.mean(np.log(np.mean(prob, axis = 0)))
return (svgd_rmse, svgd_ll) Example 35
def svgd_kernel(self, theta, h = -1):
sq_dist = pdist(theta)
pairwise_dists = squareform(sq_dist)**2
if h < 0: # if h < 0, using median trick
h = np.median(pairwise_dists)
h = np.sqrt(0.5 * h / np.log(theta.shape[0]+1))
# compute the rbf kernel
Kxy = np.exp( -pairwise_dists / h**2 / 2)
dxkxy = -np.matmul(Kxy, theta)
sumkxy = np.sum(Kxy, axis=1)
for i in range(theta.shape[1]):
dxkxy[:, i] = dxkxy[:,i] + np.multiply(theta[:,i],sumkxy)
dxkxy = dxkxy / (h**2)
return (Kxy, dxkxy) Example 36
def _linear_phase(self, n_shift):
"""
Private: Select the center of FOV
"""
om = self.st['om']
M = self.st['M']
final_shifts = tuple(
numpy.array(n_shift) +
numpy.array(self.st['Nd']) / 2)
phase = numpy.exp(
1.0j *
numpy.sum(
om * numpy.tile(
final_shifts,
(M,1)),
1))
# add-up all the linear phasees in all axes,
self.st['p'] = scipy.sparse.diags(phase, 0).dot(self.st['p0']) Example 37
def nufft_scale1(N, K, alpha, beta, Nmid):
'''
calculate image space scaling factor
'''
# import types
# if alpha is types.ComplexType:
alpha = numpy.real(alpha)
# print('complex alpha may not work, but I just let it as')
L = len(alpha) - 1
if L > 0:
sn = numpy.zeros((N, 1))
n = numpy.arange(0, N).reshape((N, 1), order='F')
i_gam_n_n0 = 1j * (2 * numpy.pi / K) * (n - Nmid) * beta
for l1 in range(-L, L + 1):
alf = alpha[abs(l1)]
if l1 < 0:
alf = numpy.conj(alf)
sn = sn + alf * numpy.exp(i_gam_n_n0 * l1)
else:
sn = numpy.dot(alpha, numpy.ones((N, 1), dtype=numpy.float32))
return sn Example 38
def linear_phase(self, n_shift):
'''
Select the center of FOV
'''
om = self.st['om']
M = self.st['M']
final_shifts = tuple(
numpy.array(n_shift) +
numpy.array(self.st['Nd']) / 2)
phase = numpy.exp(
1.0j *
numpy.sum(
om * numpy.tile(
final_shifts,
(M,1)),
1))
# add-up all the linear phasees in all axes,
self.st['p'] = scipy.sparse.diags(phase, 0).dot(self.st['p0'])
# multiply the diagonal, linear phase before the gridding matrix Example 39
def nufft_scale1(N, K, alpha, beta, Nmid):
'''
Calculate image space scaling factor
'''
# import types
# if alpha is types.ComplexType:
alpha = numpy.real(alpha)
# print('complex alpha may not work, but I just let it as')
L = len(alpha) - 1
if L > 0:
sn = numpy.zeros((N, 1))
n = numpy.arange(0, N).reshape((N, 1), order='F')
i_gam_n_n0 = 1j * (2 * numpy.pi / K) * (n - Nmid) * beta
for l1 in range(-L, L + 1):
alf = alpha[abs(l1)]
if l1 < 0:
alf = numpy.conj(alf)
sn = sn + alf * numpy.exp(i_gam_n_n0 * l1)
else:
sn = numpy.dot(alpha, numpy.ones((N, 1)))
return sn Example 40
def _linear_phase(self, n_shift):
"""
Private: Select the center of FOV
"""
om = self.st['om']
M = self.st['M']
final_shifts = tuple(
numpy.array(n_shift) +
numpy.array(self.st['Nd']) / 2)
phase = numpy.exp(
1.0j *
numpy.sum(
om * numpy.tile(
final_shifts,
(M,1)),
1))
# add-up all the linear phasees in all axes,
self.st['p'] = scipy.sparse.diags(phase, 0).dot(self.st['p0']) Example 41
def f(w, lamb):
"""
Eq. (2) in problem 2
Non-vectorized, slow
"""
total = 0
nrows = X.shape[0]
for i in range(nrows):
current = 1 + np.exp(-y[i] * X[i, ].dot(w))
total += np.log(current)
total += (lamb / 2) * w.dot(w)
return total Example 42
def f2(w, lamb):
"""
Eq. (2) in problem 2
Vectorized (no explicit loops), fast
"""
yxTw = y * X.dot(w)
firstpart = np.log(1 + np.exp(-yxTw))
total = firstpart.sum()
total += (lamb / 2) * w.dot(w)
return total Example 43
def pac_metric (solution, prediction, task='binary.classification'):
''' Probabilistic Accuracy based on log_loss metric.
We assume the solution is in {0, 1} and prediction in [0, 1].
Otherwise, run normalize_array.'''
debug_flag=False
[sample_num, label_num] = solution.shape
if label_num==1: task='binary.classification'
eps = 1e-15
the_log_loss = log_loss(solution, prediction, task)
# Compute the base log loss (using the prior probabilities)
pos_num = 1.* sum(solution) # float conversion!
frac_pos = pos_num / sample_num # prior proba of positive class
the_base_log_loss = prior_log_loss(frac_pos, task)
# Alternative computation of the same thing (slower)
# Should always return the same thing except in the multi-label case
# For which the analytic solution makes more sense
if debug_flag:
base_prediction = np.empty(prediction.shape)
for k in range(sample_num): base_prediction[k,:] = frac_pos
base_log_loss = log_loss(solution, base_prediction, task)
diff = np.array(abs(the_base_log_loss-base_log_loss))
if len(diff.shape)>0: diff=max(diff)
if(diff)>1e-10:
print('Arrggh {} != {}'.format(the_base_log_loss,base_log_loss))
# Exponentiate to turn into an accuracy-like score.
# In the multi-label case, we need to average AFTER taking the exp
# because it is an NL operation
pac = mvmean(np.exp(-the_log_loss))
base_pac = mvmean(np.exp(-the_base_log_loss))
# Normalize: 0 for random, 1 for perfect
score = (pac - base_pac) / sp.maximum(eps, (1 - base_pac))
return score Example 44
def softmax(x):
e_x = np.exp(x - np.max(x))
out = e_x / e_x.sum()
return out Example 45
def f(r,theta):
out = np.sin(theta)*r*np.exp(-r/2.)
out[-1] = 0
return out Example 46
def dfdr(r,theta):
out = np.sin(theta)*(np.exp(-r/2.) - (1./2.)*r*np.exp(-r/2.))
out[-1] = 0
return out Example 47
def dfdrdtheta(r,theta):
out = np.cos(theta)*(np.exp(-r/2.) - (1./2.)*r*np.exp(-r/2.))
out[-1] = 0
return out Example 48
def sample(self, probs, temperature):
if temperature == 0:
return np.argmax(probs)
probs = probs.astype(np.float64) #convert to float64 for higher precision
probs = np.log(probs) / temperature
probs = np.exp(probs) / math.fsum(np.exp(probs))
return np.argmax(np.random.multinomial(1, probs, 1))
#generate a sentence given conv_hidden Example 49
def softmax(x):
act = np.exp(x - np.max(x))
return act / act.sum() Example 50
def sigmoid(x, M):
return M / (1 + np.exp(-x)) 