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
python类sqrt()的实例源码
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))
def normaliza(self, X):
correction = np.sqrt((len(X) - 1) / len(X)) # std factor corretion
mean_ = np.mean(X, 0)
scale_ = np.std(X, 0)
X = X - mean_
X = X / (scale_ * correction)
return X
