Python numpy 模块，sqrt() 实例源码
我们从Python开源项目中，提取了以下50个代码示例，用于说明如何使用numpy.sqrt()。
def gelu(x):
return 0.5 * x * (1 + T.tanh(T.sqrt(2 / np.pi) * (x + 0.044715 * T.pow(x, 3))))
def normvectorfield(xs,ys,fs,**kw):
"""
plot normalized vector field
kwargs
======
- length is a desired length of the lines (default: 1)
- the rest of kwards are passed to plot
"""
length = kw.pop('length') if 'length' in kw else 1
x, y = np.meshgrid(xs, ys)
# calculate vector field
vx,vy = fs(x,y)
# plot vecor field
norm = length /np.sqrt(vx**2+vy**2)
plt.quiver(x, y, vx * norm, vy * norm, angles='xy',**kw)
def adam_updates(params, cost, lr=0.001, mom1=0.9, mom2=0.999):
updates = []
grads = T.grad(cost, params)
t = th.shared(np.cast[th.config.floatX](1.))
for p, g in zip(params, grads):
v = th.shared(np.cast[th.config.floatX](p.get_value() * 0.))
mg = th.shared(np.cast[th.config.floatX](p.get_value() * 0.))
v_t = mom1*v + (1. - mom1)*g
mg_t = mom2*mg + (1. - mom2)*T.square(g)
v_hat = v_t / (1. - mom1 ** t)
mg_hat = mg_t / (1. - mom2 ** t)
g_t = v_hat / T.sqrt(mg_hat + 1e-8)
p_t = p - lr * g_t
updates.append((v, v_t))
updates.append((mg, mg_t))
updates.append((p, p_t))
updates.append((t, t+1))
return updates
def fit(self, graphs, y=None):
rnd = check_random_state(self.random_state)
n_samples = len(graphs)
# get basis vectors
if self.n_components > n_samples:
n_components = n_samples
else:
n_components = self.n_components
n_components = min(n_samples, n_components)
inds = rnd.permutation(n_samples)
basis_inds = inds[:n_components]
basis = []
for ind in basis_inds:
basis.append(graphs[ind])
basis_kernel = self.kernel(basis, basis, **self._get_kernel_params())
# sqrt of kernel matrix on basis vectors
U, S, V = svd(basis_kernel)
S = np.maximum(S, 1e-12)
self.normalization_ = np.dot(U * 1. / np.sqrt(S), V)
self.components_ = basis
self.component_indices_ = inds
return self
def alpha(self):
# Cronbach Alpha
alpha = pd.DataFrame(0, index=np.arange(1), columns=self.latent)
for i in range(self.lenlatent):
block = self.data_[self.Variables['measurement']
[self.Variables['latent'] == self.latent[i]]]
p = len(block.columns)
if(p != 1):
p_ = len(block)
correction = np.sqrt((p_ - 1) / p_)
soma = np.var(np.sum(block, axis=1))
cor_ = pd.DataFrame.corr(block)
denominador = soma * correction**2
numerador = 2 * np.sum(np.tril(cor_) - np.diag(np.diag(cor_)))
alpha_ = (numerador / denominador) * (p / (p - 1))
alpha[self.latent[i]] = alpha_
else:
alpha[self.latent[i]] = 1
return alpha.T
def xavier_initializer(shape):
dim_sum = np.sum(shape)
if len(shape) == 1:
dim_sum += 1
bound = np.sqrt(2.0 / dim_sum)
return tf.random_uniform(shape, minval=-bound, maxval=bound)
# # Assigning network variables to target network variables
# def assign_network_to_target():
# update_wfc = tf.assign(w_fc_target, w_fc)
# update_bfc = tf.assign(b_fc_target, b_fc)
# sess.run(update_wfc)
# sess.run(update_bfc)
# cell_target = cell
# Input
def _ikf_iteration(self, x, n, ranges, h, H, z, estimate, R):
"""Update tracker based on a multi-range message.
Args:
multi_range_msg (uwb.msg.UWBMultiRangeWithOffsets): ROS multi-range message.
Returns:
new_estimate (StateEstimate): Updated position estimate.
"""
new_position = n[0:3]
self._compute_measurements_and_jacobians(ranges, new_position, h, H, z)
res = z - h
S = np.dot(np.dot(H, estimate.covariance), H.T) + R
K = np.dot(estimate.covariance, self._solve_equation_least_squares(S.T, H).T)
mahalanobis = np.sqrt(np.dot(self._solve_equation_least_squares(S.T, res).T, res))
if res.size not in self.outlier_thresholds:
self.outlier_thresholds[res.size] = scipy.stats.chi2.isf(self.outlier_threshold_quantile, res.size)
outlier_threshold = self.outlier_thresholds[res.size]
if mahalanobis < outlier_threshold:
n = x + np.dot(K, (res - np.dot(H, x - n)))
outlier_flag = False
else:
outlier_flag = True
return n, K, outlier_flag
def dist_to_opt(self):
global_state = self._global_state
beta = self._beta
if self._iter == 0:
global_state["grad_norm_avg"] = 0.0
global_state["dist_to_opt_avg"] = 0.0
global_state["grad_norm_avg"] = \
global_state["grad_norm_avg"] * beta + (1 - beta) * math.sqrt(global_state["grad_norm_squared"] )
global_state["dist_to_opt_avg"] = \
global_state["dist_to_opt_avg"] * beta \
+ (1 - beta) * global_state["grad_norm_avg"] / (global_state['grad_norm_squared_avg'] + eps)
if self._zero_debias:
debias_factor = self.zero_debias_factor()
self._dist_to_opt = global_state["dist_to_opt_avg"] / debias_factor
else:
self._dist_to_opt = global_state["dist_to_opt_avg"]
if self._sparsity_debias:
self._dist_to_opt /= (np.sqrt(self._sparsity_avg) + eps)
return
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() ) )
def dist_to_opt(self):
global_state = self._global_state
beta = self._beta
if self._iter == 0:
global_state["grad_norm_avg"] = 0.0
global_state["dist_to_opt_avg"] = 0.0
global_state["grad_norm_avg"] = \
global_state["grad_norm_avg"] * beta + (1 - beta) * math.sqrt(global_state["grad_norm_squared"] )
global_state["dist_to_opt_avg"] = \
global_state["dist_to_opt_avg"] * beta \
+ (1 - beta) * global_state["grad_norm_avg"] / (global_state['grad_norm_squared_avg'] + eps)
if self._zero_debias:
debias_factor = self.zero_debias_factor()
self._dist_to_opt = global_state["dist_to_opt_avg"] / debias_factor
else:
self._dist_to_opt = global_state["dist_to_opt_avg"]
if self._sparsity_debias:
self._dist_to_opt /= (np.sqrt(self._sparsity_avg) + eps)
return
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() ) )
def get_cubic_root(self):
# We have the equation x^2 D^2 + (1-x)^4 * C / h_min^2
# where x = sqrt(mu).
# We substitute x, which is sqrt(mu), with x = y + 1.
# It gives y^3 + py = q
# where p = (D^2 h_min^2)/(2*C) and q = -p.
# We use the Vieta's substution to compute the root.
# There is only one real solution y (which is in [0, 1] ).
# http://mathworld.wolfram.com/VietasSubstitution.html
# eps in the numerator is to prevent momentum = 1 in case of zero gradient
p = (self._dist_to_opt + eps)**2 * (self._h_min + eps)**2 / 2 / (self._grad_var + eps)
w3 = (-math.sqrt(p**2 + 4.0 / 27.0 * p**3) - p) / 2.0
w = math.copysign(1.0, w3) * math.pow(math.fabs(w3), 1.0/3.0)
y = w - p / 3.0 / (w + eps)
x = y + 1
if DEBUG:
logging.debug("p %f, den %f", p, self._grad_var + eps)
logging.debug("w3 %f ", w3)
logging.debug("y %f, den %f", y, w + eps)
return x
def update_hyper_param(self):
for group in self._optimizer.param_groups:
group['momentum'] = self._mu
if self._force_non_inc_step == False:
group['lr'] = min(self._lr * self._lr_factor,
self._lr_grad_norm_thresh / (math.sqrt(self._global_state["grad_norm_squared"] ) + eps) )
elif self._iter > self._curv_win_width:
# force to guarantee lr * grad_norm not increasing dramatically.
# Not necessary for basic use. Please refer to the comments
# in YFOptimizer.__init__ for more details
self.lr_grad_norm_avg()
debias_factor = self.zero_debias_factor()
group['lr'] = min(self._lr * self._lr_factor,
2.0 * self._global_state["lr_grad_norm_avg_min"] \
/ (np.sqrt(np.exp(self._global_state['grad_norm_squared_avg_log'] / debias_factor) ) + eps) )
return
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
def fit_transform(self, X, y=None):
"""Fit the model with X and apply the dimensionality reduction on X.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Training data, where n_samples is the number of samples
and n_features is the number of features.
Returns
-------
X_new : array-like, shape (n_samples, n_components)
"""
U, S, V = self._fit(X)
U = U[:, :int(self.n_components_)]
if self.whiten:
# X_new = X * V / S * sqrt(n_samples) = U * sqrt(n_samples)
U *= sqrt(X.shape[0])
else:
# X_new = X * V = U * S * V^T * V = U * S
U *= S[:int(self.n_components_)]
return U
def get_covariance(self):
"""Compute data covariance with the generative model.
``cov = components_.T * S**2 * components_ + sigma2 * eye(n_features)``
where S**2 contains the explained variances.
Returns
-------
cov : array, shape=(n_features, n_features)
Estimated covariance of data.
"""
components_ = self.components_
exp_var = self.explained_variance_
if self.whiten:
components_ = components_ * np.sqrt(exp_var[:, np.newaxis])
exp_var_diff = np.maximum(exp_var - self.noise_variance_, 0.)
cov = np.dot(components_.T * exp_var_diff, components_)
cov.flat[::len(cov) + 1] += self.noise_variance_ # modify diag inplace
return cov
def inverse_transform(self, X):
"""Transform data back to its original space, i.e.,
return an input X_original whose transform would be X
Parameters
----------
X : array-like, shape (n_samples, n_components)
New data, where n_samples is the number of samples
and n_components is the number of components.
Returns
-------
X_original array-like, shape (n_samples, n_features)
"""
check_is_fitted(self, 'mean_')
if self.whiten:
return fast_dot(
X,
np.sqrt(self.explained_variance_[:, np.newaxis]) *
self.components_) + self.mean_
else:
return fast_dot(X, self.components_) + self.mean_
def infExact_scipy_post(self, K, covars, y, sig2e, fixedEffects):
n = y.shape[0]
#mean vector
m = covars.dot(fixedEffects)
if (K.shape[1] < K.shape[0]): K_true = K.dot(K.T)
else: K_true = K
if sig2e<1e-6:
L = la.cholesky(K_true + sig2e*np.eye(n), overwrite_a=True, check_finite=False) #Cholesky factor of covariance with noise
sl = 1
pL = -self.solveChol(L, np.eye(n)) #L = -inv(K+inv(sW^2))
else:
L = la.cholesky(K_true/sig2e + np.eye(n), overwrite_a=True, check_finite=False) #Cholesky factor of B
sl = sig2e
pL = L #L = chol(eye(n)+sW*sW'.*K)
alpha = self.solveChol(L, y-m, overwrite_b=False) / sl
post = dict([])
post['alpha'] = alpha #return the posterior parameters
post['sW'] = np.ones(n) / np.sqrt(sig2e) #sqrt of noise precision vector
post['L'] = pL
return post
def removeTopPCs(X, numRemovePCs):
t0 = time.time()
X_mean = X.mean(axis=0)
X -= X_mean
XXT = symmetrize(blas.dsyrk(1.0, X, lower=0))
s,U = la.eigh(XXT)
if (np.min(s) < -1e-4): raise Exception('Negative eigenvalues found')
s[s<0]=0
ind = np.argsort(s)[::-1]
U = U[:, ind]
s = s[ind]
s = np.sqrt(s)
#remove null PCs
ind = (s>1e-6)
U = U[:, ind]
s = s[ind]
V = X.T.dot(U/s)
#print 'max diff:', np.max(((U*s).dot(V.T) - X)**2)
X = (U[:, numRemovePCs:]*s[numRemovePCs:]).dot((V.T)[numRemovePCs:, :])
X += X_mean
return X
def normalizeSNPs(normMethod, X, y, prev=None, frqFile=None):
if (normMethod == 'frq'):
print 'flipping SNPs for standardization...'
empMean = X.mean(axis=0) / 2.0
X[:, empMean>0.5] = 2 - X[:, empMean>0.5]
mafs = np.loadtxt(frqFile, usecols=[1,2]).mean(axis=1)
snpsMean = 2*mafs
snpsStd = np.sqrt(2*mafs*(1-mafs))
elif (normMethod == 'controls'):
controls = (y<y.mean())
cases = ~controls
snpsMeanControls, snpsStdControls = X[controls, :].mean(axis=0), X[controls, :].std(axis=0)
snpsMeanCases, snpsStdCases = X[cases, :].mean(axis=0), X[cases, :].std(axis=0)
snpsMean = (1-prev)*snpsMeanControls + prev*snpsMeanCases
snpsStd = (1-prev)*snpsStdControls + prev*snpsStdCases
elif (normMethod is None): snpsMean, snpsStd = X.mean(axis=0), X.std(axis=0)
else: raise Exception('Unrecognized normalization method: ' + normMethod)
return snpsMean, snpsStd
def conv2d(x, num_filters, name, filter_size=(3, 3), stride=(1, 1), pad="SAME", dtype=tf.float32, collections=None):
with tf.variable_scope(name):
stride_shape = [1, stride[0], stride[1], 1]
filter_shape = [filter_size[0], filter_size[1], int(x.get_shape()[3]), num_filters]
# there are "num input feature maps * filter height * filter width"
# inputs to each hidden unit
fan_in = np.prod(filter_shape[:3])
# each unit in the lower layer receives a gradient from:
# "num output feature maps * filter height * filter width" /
# pooling size
fan_out = np.prod(filter_shape[:2]) * num_filters
# initialize weights with random weights
w_bound = np.sqrt(6. / (fan_in + fan_out))
w = tf.get_variable("W", filter_shape, dtype, tf.random_uniform_initializer(-w_bound, w_bound),
collections=collections)
b = tf.get_variable("b", [1, 1, 1, num_filters], initializer=tf.constant_initializer(0.0),
collections=collections)
return tf.nn.conv2d(x, w, stride_shape, pad) + b
def conv2d(x, num_filters, name, filter_size=(3, 3), stride=(1, 1), pad="SAME", dtype=tf.float32, collections=None):
with tf.variable_scope(name):
stride_shape = [1, stride[0], stride[1], 1]
filter_shape = [filter_size[0], filter_size[1], int(x.get_shape()[3]), num_filters]
# there are "num input feature maps * filter height * filter width"
# inputs to each hidden unit
fan_in = np.prod(filter_shape[:3])
# each unit in the lower layer receives a gradient from:
# "num output feature maps * filter height * filter width" /
# pooling size
fan_out = np.prod(filter_shape[:2]) * num_filters
# initialize weights with random weights
w_bound = np.sqrt(6. / (fan_in + fan_out))
w = tf.get_variable("W", filter_shape, dtype, tf.random_uniform_initializer(-w_bound, w_bound),
collections=collections)
b = tf.get_variable("b", [1, 1, 1, num_filters], initializer=tf.constant_initializer(0.0),
collections=collections)
return tf.nn.conv2d(x, w, stride_shape, pad) + b
def batchnorm(x, name, phase, updates, gamma=0.96):
k = x.get_shape()[1]
runningmean = tf.get_variable(name+"/mean", shape=[1, k], initializer=tf.constant_initializer(0.0), trainable=False)
runningvar = tf.get_variable(name+"/var", shape=[1, k], initializer=tf.constant_initializer(1e-4), trainable=False)
testy = (x - runningmean) / tf.sqrt(runningvar)
mean_ = mean(x, axis=0, keepdims=True)
var_ = mean(tf.square(x), axis=0, keepdims=True)
std = tf.sqrt(var_)
trainy = (x - mean_) / std
updates.extend([
tf.assign(runningmean, runningmean * gamma + mean_ * (1 - gamma)),
tf.assign(runningvar, runningvar * gamma + var_ * (1 - gamma))
])
y = switch(phase, trainy, testy)
out = y * tf.get_variable(name+"/scaling", shape=[1, k], initializer=tf.constant_initializer(1.0), trainable=True)\
+ tf.get_variable(name+"/translation", shape=[1,k], initializer=tf.constant_initializer(0.0), trainable=True)
return out
# ================================================================
# Mathematical utils
# ================================================================
def normalize_and_transpose(matrix):
matrix.tocsc()
m = normalize_by_umi(matrix)
# Use log counts
m.data = np.log2(1 + m.data)
# Transpose
m = m.T
# compute centering (mean) and scaling (stdev)
(c,v) = summarize_columns(m)
s = np.sqrt(v)
return (m, c, s)
def merge_filtered_metrics(filtered_metrics):
result = {
'filtered_bcs': 0,
'filtered_bcs_lb': 0,
'filtered_bcs_ub': 0,
'max_filtered_bcs': 0,
'filtered_bcs_var': 0,
'filtered_bcs_cv': 0,
}
for i, fm in enumerate(filtered_metrics):
# Add per-gem group metrics
result.update({'gem_group_%d_%s' % (i + 1, key): value for key, value in fm.iteritems()})
# Compute metrics over all gem groups
result['filtered_bcs'] += fm['filtered_bcs']
result['filtered_bcs_lb'] += fm['filtered_bcs_lb']
result['filtered_bcs_ub'] += fm['filtered_bcs_ub']
result['max_filtered_bcs'] += fm['max_filtered_bcs']
result['filtered_bcs_var'] += fm['filtered_bcs_var']
# Estimate CV based on sum of variances and means
result['filtered_bcs_cv'] = tk_stats.robust_divide(
np.sqrt(result['filtered_bcs_var']), fm['filtered_bcs'])
return result
def reshapeWeights(self, weights, normalize=True, modifier=None):
# reshape the weights matrix to a grid for visualization
n_rows = int(np.sqrt(weights.shape[1]))
n_cols = int(np.sqrt(weights.shape[1]))
kernel_size = int(np.sqrt(weights.shape[0]/3))
weights_grid = np.zeros((int((np.sqrt(weights.shape[0]/3)+1)*n_rows), int((np.sqrt(weights.shape[0]/3)+1)*n_cols), 3), dtype=np.float32)
for i in range(weights_grid.shape[0]/(kernel_size+1)):
for j in range(weights_grid.shape[1]/(kernel_size+1)):
index = i * (weights_grid.shape[0]/(kernel_size+1))+j
if not np.isclose(np.sum(weights[:, index]), 0):
if normalize:
weights_grid[i * (kernel_size + 1):i * (kernel_size + 1) + kernel_size, j * (kernel_size + 1):j * (kernel_size + 1) + kernel_size]=\
(weights[:, index].reshape(kernel_size, kernel_size, 3) - np.min(weights[:, index])) / ((np.max(weights[:, index]) - np.min(weights[:, index])) + 1.e-6)
else:
weights_grid[i * (kernel_size + 1):i * (kernel_size + 1) + kernel_size, j * (kernel_size + 1):j * (kernel_size + 1) + kernel_size] =\
(weights[:, index].reshape(kernel_size, kernel_size, 3))
if modifier is not None:
weights_grid[i * (kernel_size + 1):i * (kernel_size + 1) + kernel_size, j * (kernel_size + 1):j * (kernel_size + 1) + kernel_size] *= modifier[index]
return weights_grid
def __init__(self, input_shape, output_shape):
self.input_shape = input_shape
self.input = np.zeros((output_shape[0], self.input_shape[0] * self.input_shape[1] *
self.input_shape[2]),dtype=np.float32)
self.output = np.zeros(output_shape, dtype=np.float32)
self.output_raw = np.zeros_like(self.output)
self.output_error = np.zeros_like(self.output)
self.output_average = np.zeros(self.output.shape[1], dtype=np.float32)
self.weights = np.random.normal(0, np.sqrt(2.0 / (self.output.shape[1] + self.input.shape[1])),
size=(self.input.shape[1], self.output.shape[1])).astype(np.float32)
self.gradient = np.zeros_like(self.weights)
self.reconstruction = np.zeros_like(self.weights)
self.errors = np.zeros_like(self.weights)
self.output_ranks = np.zeros(self.output.shape[1], dtype=np.int32)
self.learning_rate = 1
self.norm_limit = 0.1
def Verify(**kwargs):
'''
Verification for the signature
i/p:
msg: the string sent by the sender
(z,c): vectors in Zq, the signature
A : numpy array, Verification Key dimension nxm
T : the matrix AS mod q ,it is used in the Verification of the signature
'''
msg, z, c, A, T, sd, eta, m, k, q = kwargs['msg'], kwargs['z'], kwargs['c'], kwargs['A'], kwargs['T'], kwargs['sd'], kwargs['eta'], kwargs['m'], kwargs['k'], kwargs['q']
norm_bound = eta * sd * np.sqrt(m)
# checks for norm of z being small and that H(Az-Tc mod q,msg) hashes to c
vec = util.vector_to_Zq(np.array(np.matmul(A,z) - np.matmul(T,c)), q)
hashedList = util.hash_to_baseb(vec, msg, 3, k)
print hashedList, c
if np.sqrt(z.dot(z)) <= norm_bound and np.array_equal(c, hashedList):
return True
else:
return False
def compute_similarity(self, doc1, doc2):
"""
Calculates the similarity between two spaCy documents. Extracts the
nBOW from them and evaluates the WMD.
:return: The calculated similarity.
:rtype: float.
"""
doc1 = self._convert_document(doc1)
doc2 = self._convert_document(doc2)
vocabulary = {
w: i for i, w in enumerate(sorted(set(doc1).union(doc2)))}
w1 = self._generate_weights(doc1, vocabulary)
w2 = self._generate_weights(doc2, vocabulary)
evec = numpy.zeros((len(vocabulary), self.nlp.vocab.vectors_length),
dtype=numpy.float32)
for w, i in vocabulary.items():
evec[i] = self.nlp.vocab[w].vector
evec_sqr = (evec * evec).sum(axis=1)
dists = evec_sqr - 2 * evec.dot(evec.T) + evec_sqr[:, numpy.newaxis]
dists[dists < 0] = 0
dists = numpy.sqrt(dists)
return libwmdrelax.emd(w1, w2, dists)
def quaternion_matrix(quaternion):
"""Return homogeneous rotation matrix from quaternion.
>>> R = quaternion_matrix([0.06146124, 0, 0, 0.99810947])
>>> numpy.allclose(R, rotation_matrix(0.123, (1, 0, 0)))
True
"""
q = numpy.array(quaternion[:4], dtype=numpy.float64, copy=True)
nq = numpy.dot(q, q)
if nq < _EPS:
return numpy.identity(4)
q *= math.sqrt(2.0 / nq)
q = numpy.outer(q, q)
return numpy.array((
(1.0-q[1, 1]-q[2, 2], q[0, 1]-q[2, 3], q[0, 2]+q[1, 3], 0.0),
( q[0, 1]+q[2, 3], 1.0-q[0, 0]-q[2, 2], q[1, 2]-q[0, 3], 0.0),
( q[0, 2]-q[1, 3], q[1, 2]+q[0, 3], 1.0-q[0, 0]-q[1, 1], 0.0),
( 0.0, 0.0, 0.0, 1.0)
), dtype=numpy.float64)
def im_detect_and_describe(img, mask=None, detector='dense', descriptor='SIFT', colorspace='gray',
step=4, levels=7, scale=np.sqrt(2)):
"""
Describe image using dense sampling / specific detector-descriptor combination.
"""
detector = get_detector(detector=detector, step=step, levels=levels, scale=scale)
extractor = cv2.DescriptorExtractor_create(descriptor)
try:
kpts = detector.detect(img, mask=mask)
kpts, desc = extractor.compute(img, kpts)
if descriptor == 'SIFT':
kpts, desc = root_sift(kpts, desc)
pts = np.vstack([kp.pt for kp in kpts]).astype(np.int32)
return pts, desc
except Exception as e:
print 'im_detect_and_describe', e
return None, None
def compHistDistance(h1, h2):
def normalize(h):
if np.sum(h) == 0:
return h
else:
return h / np.sum(h)
def smoothstep(x, x_min=0., x_max=1., k=2.):
m = 1. / (x_max - x_min)
b = - m * x_min
x = m * x + b
return betainc(k, k, np.clip(x, 0., 1.))
def fn(X, Y, k):
return 4. * (1. - smoothstep(Y, 0, (1 - Y) * X + Y + .1)) \
* np.sqrt(2 * X) * smoothstep(X, 0., 1. / k, 2) \
+ 2. * smoothstep(Y, 0, (1 - Y) * X + Y + .1) \
* (1. - 2. * np.sqrt(2 * X) * smoothstep(X, 0., 1. / k, 2) - 0.5)
h1 = normalize(h1)
h2 = normalize(h2)
return max(0, np.sum(fn(h2, h1, len(h1))))
# return np.sum(np.where(h2 != 0, h2 * np.log10(h2 / (h1 + 1e-10)), 0)) # KL divergence
def __call__(self, z):
z1 = tf.reshape(tf.slice(z, [0, 0], [-1, 1]), [-1])
z2 = tf.reshape(tf.slice(z, [0, 1], [-1, 1]), [-1])
v1 = tf.sqrt((z1 - 5) * (z1 - 5) + z2 * z2) * 2
v2 = tf.sqrt((z1 + 5) * (z1 + 5) + z2 * z2) * 2
v3 = tf.sqrt((z1 - 2.5) * (z1 - 2.5) + (z2 - 2.5 * np.sqrt(3)) * (z2 - 2.5 * np.sqrt(3))) * 2
v4 = tf.sqrt((z1 + 2.5) * (z1 + 2.5) + (z2 + 2.5 * np.sqrt(3)) * (z2 + 2.5 * np.sqrt(3))) * 2
v5 = tf.sqrt((z1 - 2.5) * (z1 - 2.5) + (z2 + 2.5 * np.sqrt(3)) * (z2 + 2.5 * np.sqrt(3))) * 2
v6 = tf.sqrt((z1 + 2.5) * (z1 + 2.5) + (z2 - 2.5 * np.sqrt(3)) * (z2 - 2.5 * np.sqrt(3))) * 2
pdf1 = tf.exp(-0.5 * v1 * v1) / tf.sqrt(2 * np.pi * 0.25)
pdf2 = tf.exp(-0.5 * v2 * v2) / tf.sqrt(2 * np.pi * 0.25)
pdf3 = tf.exp(-0.5 * v3 * v3) / tf.sqrt(2 * np.pi * 0.25)
pdf4 = tf.exp(-0.5 * v4 * v4) / tf.sqrt(2 * np.pi * 0.25)
pdf5 = tf.exp(-0.5 * v5 * v5) / tf.sqrt(2 * np.pi * 0.25)
pdf6 = tf.exp(-0.5 * v6 * v6) / tf.sqrt(2 * np.pi * 0.25)
return -tf.log((pdf1 + pdf2 + pdf3 + pdf4 + pdf5 + pdf6) / 6)
def _compute_score(self, context):
'''
Args:
context (list)
Returns:
(dict):
K (str): action
V (float): score
'''
a_inv = self.model['act_inv']
theta = self.model['theta']
estimated_reward = {}
uncertainty = {}
score_dict = {}
max_score = 0
for action_id in xrange(len(self.actions)):
action_context = np.reshape(context[action_id], (-1, 1))
estimated_reward[action_id] = float(theta[action_id].T.dot(action_context))
uncertainty[action_id] = float(self.alpha * np.sqrt(action_context.T.dot(a_inv[action_id]).dot(action_context)))
score_dict[action_id] = estimated_reward[action_id] + uncertainty[action_id]
return score_dict
def getMedianDistanceBetweenSamples(self, sampleSet=None) :
"""
Jaakkola's heuristic method for setting the width parameter of the Gaussian
radial basis function kernel is to pick a quantile (usually the median) of
the distribution of Euclidean distances between points having different
labels.
Reference:
Jaakkola, M. Diekhaus, and D. Haussler. Using the Fisher kernel method to detect
remote protein homologies. In T. Lengauer, R. Schneider, P. Bork, D. Brutlad, J.
Glasgow, H.- W. Mewes, and R. Zimmer, editors, Proceedings of the Seventh
International Conference on Intelligent Systems for Molecular Biology.
"""
numrows = sampleSet.shape[0]
samples = sampleSet
G = sum((samples * samples), 1)
Q = numpy.tile(G[:, None], (1, numrows))
R = numpy.tile(G, (numrows, 1))
distances = Q + R - 2 * numpy.dot(samples, samples.T)
distances = distances - numpy.tril(distances)
distances = distances.reshape(numrows**2, 1, order="F").copy()
return numpy.sqrt(0.5 * numpy.median(distances[distances > 0]))
def per_image_whiten(X):
""" Subtracts the mean of each image in X and renormalizes them to unit norm.
"""
num_examples, height, width, depth = X.shape
X_flat = X.reshape((num_examples, -1))
X_mean = X_flat.mean(axis=1)
X_cent = X_flat - X_mean[:, None]
X_norm = np.sqrt( np.sum( X_cent * X_cent, axis=1) )
X_out = X_cent / X_norm[:, None]
X_out = X_out.reshape(X.shape)
return X_out
# Assumes the following ordering for X: (num_images, height, width, num_channels)
def compile(self, in_x, train_feed, eval_feed):
n = np.product(self.in_d)
m, param_init_fn = [dom[i] for (dom, i) in zip(self.domains, self.chosen)]
#sc = np.sqrt(6.0) / np.sqrt(m + n)
#W = tf.Variable(tf.random_uniform([n, m], -sc, sc))
W = tf.Variable( param_init_fn( [n, m] ) )
b = tf.Variable(tf.zeros([m]))
# if the number of input dimensions is larger than one, flatten the
# input and apply the affine transformation.
if len(self.in_d) > 1:
in_x_flat = tf.reshape(in_x, shape=[-1, n])
out_y = tf.add(tf.matmul(in_x_flat, W), b)
else:
out_y = tf.add(tf.matmul(in_x, W), b)
return out_y
# computes the output dimension based on the padding scheme used.
# this comes from the tensorflow documentation
def _update_ps(self, es):
if not self.is_initialized:
self.initialize(es)
if self._ps_updated_iteration == es.countiter:
return
z = es.sm.transform_inverse((es.mean - es.mean_old) / es.sigma_vec.scaling)
# works unless a re-parametrisation has been done
# assert Mh.vequals_approximately(z, np.dot(es.B, (1. / es.D) *
# np.dot(es.B.T, (es.mean - es.mean_old) / es.sigma_vec)))
z *= es.sp.weights.mueff**0.5 / es.sigma / es.sp.cmean
# zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
if es.opts['CSA_clip_length_value'] is not None:
vals = es.opts['CSA_clip_length_value']
min_len = es.N**0.5 + vals[0] * es.N / (es.N + 2)
max_len = es.N**0.5 + vals[1] * es.N / (es.N + 2)
act_len = sum(z**2)**0.5
new_len = Mh.minmax(act_len, min_len, max_len)
if new_len != act_len:
z *= new_len / act_len
# z *= (es.N / sum(z**2))**0.5 # ==> sum(z**2) == es.N
# z *= es.const.chiN / sum(z**2)**0.5
self.ps = (1 - self.cs) * self.ps + np.sqrt(self.cs * (2 - self.cs)) * z
self._ps_updated_iteration = es.countiter
def result_pretty(self, number_of_runs=0, time_str=None,
fbestever=None):
"""pretty print result.
Returns `result` of ``self``.
"""
if fbestever is None:
fbestever = self.best.f
s = (' after %i restart' + ('s' if number_of_runs > 1 else '')) \
% number_of_runs if number_of_runs else ''
for k, v in self.stop().items():
print('termination on %s=%s%s' % (k, str(v), s +
(' (%s)' % time_str if time_str else '')))
print('final/bestever f-value = %e %e' % (self.best.last.f,
fbestever))
if self.N < 9:
print('incumbent solution: ' + str(list(self.gp.pheno(self.mean, into_bounds=self.boundary_handler.repair))))
print('std deviation: ' + str(list(self.sigma * self.sigma_vec.scaling * np.sqrt(self.dC) * self.gp.scales)))
else:
print('incumbent solution: %s ...]' % (str(self.gp.pheno(self.mean, into_bounds=self.boundary_handler.repair)[:8])[:-1]))
print('std deviations: %s ...]' % (str((self.sigma * self.sigma_vec.scaling * np.sqrt(self.dC) * self.gp.scales)[:8])[:-1]))
return self.result
def isotropic_mean_shift(self):
"""normalized last mean shift, under random selection N(0,I)
distributed.
Caveat: while it is finite and close to sqrt(n) under random
selection, the length of the normalized mean shift under
*systematic* selection (e.g. on a linear function) tends to
infinity for mueff -> infty. Hence it must be used with great
care for large mueff.
"""
z = self.sm.transform_inverse((self.mean - self.mean_old) /
self.sigma_vec.scaling)
# works unless a re-parametrisation has been done
# assert Mh.vequals_approximately(z, np.dot(es.B, (1. / es.D) *
# np.dot(es.B.T, (es.mean - es.mean_old) / es.sigma_vec)))
z /= self.sigma * self.sp.cmean
z *= self.sp.weights.mueff**0.5
return z
def __init__(self, dimension, randn=np.random.randn, debug=False):
"""pass dimension of the underlying sample space
"""
try:
self.N = len(dimension)
std_vec = np.array(dimension, copy=True)
except TypeError:
self.N = dimension
std_vec = np.ones(self.N)
if self.N < 10:
print('Warning: Not advised to use VD-CMA for dimension < 10.')
self.randn = randn
self.dvec = std_vec
self.vvec = self.randn(self.N) / math.sqrt(self.N)
self.norm_v2 = np.dot(self.vvec, self.vvec)
self.norm_v = np.sqrt(self.norm_v2)
self.vn = self.vvec / self.norm_v
self.vnn = self.vn**2
self.pc = np.zeros(self.N)
self._debug = debug # plot covariance matrix
def _evalfull(self, x):
fadd = self.fopt
curshape, dim = self.shape_(x)
# it is assumed x are row vectors
if self.lastshape != curshape:
self.initwithsize(curshape, dim)
# BOUNDARY HANDLING
# TRANSFORMATION IN SEARCH SPACE
x = x - self.arrxopt
x = monotoneTFosc(x)
idx = (x > 0)
x[idx] = x[idx] ** (1 + self.arrexpo[idx] * np.sqrt(x[idx]))
x = self.arrscales * x
# COMPUTATION core
ftrue = 10 * (self.dim - np.sum(np.cos(2 * np.pi * x), -1)) + np.sum(x ** 2, -1)
fval = self.noise(ftrue) # without noise
# FINALIZE
ftrue += fadd
fval += fadd
return fval, ftrue
def normalize_2D_cov_matrix(covmatrix,verbose=True):
"""
Calculate the normalization foctor for a multivariate gaussian from it's covariance matrix
However, not that gaussian returned by tu.gen_2Dgauss() is normalized for scale=1
--- INPUT ---
covmatrix covariance matrix to normaliz
verbose Toggle verbosity
"""
detcov = np.linalg.det(covmatrix)
normfac = 1.0 / (2.0 * np.pi * np.sqrt(detcov) )
return normfac
# = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
def get_dXdr(self,X):
"Derivative of compactified coordinate with respect to radial"
L = self.L
r_h = self.r_h
num = ((X-1)**2)*np.sqrt((r_h*(X-1))**2 + (L*(X+1))**2)
denom = 2*L*L*(1+X)
dXdr = num/denom
return dXdr
def get_x_from_r(self,r):
"x = 0 when r = rh"
r_h = self.r_h
x = np.sqrt(r**2 - r_h**2)
return x
def get_r_from_x(self,x):
"x = 0 when r = rh"
r_h = self.r_h
r = np.sqrt(x**2 + r_h**2)
return r
def get_norm2_difference(foo,bar,xmin,xmax):
"""
Returns sqrt(integral((foo-bar)**2)) on the interval [xmin,xmax]
"""
out = integrator(lambda x: (foo(x)-bar(x))**2,xmin,xmax)[0]
out /= float(xmax-xmin)
out = np.sqrt(out)
return out
# ======================================================================
# ======================================================================
# Nodal and Modal Details
# ======================================================================
def norm2(self,grid_func):
"""Calculates the 2norm of grid_func"""
factor = np.prod([(s.xmax-s.xmin) for s in self.stencils])
integral = self.inner_product(grid_func,grid_func) / factor
norm2 = np.sqrt(integral)
return norm2
def fit(self, x):
s = x.shape
x = x.copy().reshape((s[0],np.prod(s[1:])))
m = np.mean(x, axis=0)
x -= m
sigma = np.dot(x.T,x) / x.shape[0]
U, S, V = linalg.svd(sigma)
tmp = np.dot(U, np.diag(1./np.sqrt(S+self.regularization)))
tmp2 = np.dot(U, np.diag(np.sqrt(S+self.regularization)))
self.ZCA_mat = th.shared(np.dot(tmp, U.T).astype(th.config.floatX))
self.inv_ZCA_mat = th.shared(np.dot(tmp2, U.T).astype(th.config.floatX))
self.mean = th.shared(m.astype(th.config.floatX))