def random(self, *phi, plates=None):
"""
Draw a random sample from the distribution.
"""
# Convert natural parameters to transition probabilities
p0 = np.exp(phi[0] - misc.logsumexp(phi[0], axis=-1, keepdims=True))
P = np.exp(phi[1] - misc.logsumexp(phi[1], axis=-1, keepdims=True))
# Explicit broadcasting
P = P * np.ones(plates)[..., None, None, None]
# Allocate memory
Z = np.zeros(plates + (self.N,), dtype=np.int)
# Draw initial state
Z[..., 0] = random.categorical(p0, size=plates)
# Create [0,1,2,...,len(plate_axis)] indices for each plate axis and
# make them broadcast properly
nplates = len(plates)
plates_ind = [np.arange(plate)[(Ellipsis,) + (nplates - i - 1) * (None,)] for (i, plate) in enumerate(plates)]
plates_ind = tuple(plates_ind)
# Draw next states iteratively
for n in range(self.N - 1):
# Select the transition probabilities for the current state but take
# into account the plates. This leads to complex NumPy
# indexing.. :)
time_ind = min(n, np.shape(P)[-3] - 1)
ind = plates_ind + (time_ind, Z[..., n], Ellipsis)
p = P[ind]
# Draw next state
z = random.categorical(P[ind])
Z[..., n + 1] = z
return Z
def f1(u, eigvals, Z10, Z11):
"""
A component of exact time pdf (Eq. 22, HJC92).
Parameters
----------
u : float
u = t - tres
eigvals : array_like, shape (k,)
Eigenvalues of -Q matrix.
Z10, Z11 (or gama10, gama11) : list of array_likes
Constants for the exact open/shut time pdf. Z10, Z11 for likelihood
calculation or gama10, gama11 for time distributions.
Returns
-------
f : ndarray
"""
# f = np.zeros(Z10[0].shape)
# for i in range(len(eigvals)):
# f += (Z10[i] + Z11[i] * u) * math.exp(-eigvals[i] * u)
if Z10.ndim > 1:
f = np.sum((Z10 + Z11 * u) *
np.exp(-eigvals * u).reshape(Z10.shape[0],1,1), axis=0)
else:
f = np.sum((Z10 + Z11 * u) * np.exp(-eigvals * u))
return f
def log_diff_exp(x, axis=0):
""" Calculates the logarithm of the diffs of e to the power of input 'x'. The method tries to avoid
overflows by using the relationship: log(diff(exp(x))) = alpha + log(diff(exp(x-alpha))).
:Parameter:
x: data.
-type: float or numpy array
axis: Sums along the given axis.
-type: int
:Return:
Logarithm of the sum of exp of x.
-type: float or numpy array.
"""
alpha = x.max(axis) - numx.log(numx.finfo(numx.float64).max)/2.0
if axis == 1:
return numx.squeeze(alpha + numx.log(
numx.diff(
numx.exp(x.T - alpha)
, n=1, axis=0)))
else:
return numx.squeeze(alpha + numx.log(
numx.diff(
numx.exp(x - alpha)
, n=1, axis=0)))
def plot_open_close(self, fig = None, savefig = True):
'''
Plot the open period versus shut periods.
'''
stretch_list = self.cluster_data.compute_open_close()
mode_num = len(stretch_list)
if fig is None:
fig = plt.figure()
ax = fig.add_subplot(111)
cmap = np.linspace(0,1,mode_num)
for index, stretch in enumerate(stretch_list):
ax.scatter(stretch['open_period'], stretch['shut_period'],
facecolors='none',
edgecolors=plt.cm.spectral(cmap[index]),
s=1, label = str(index + 1))
#ax.scatter(stretch['mean_open'], stretch['mean_shut'],
# color=plt.cm.spectral(cmap[index]),
# s=50, label = str(index + 1))
ax.legend()
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_ylim([0.3, np.exp(7)])
ax.set_xlim([0.3, np.exp(5)])
ax.set_xlabel('Open period (ms in log scale)')
ax.set_ylabel('Shut period (ms in log scale)')
ax.set_title('Open/Shut')
if savefig:
fig.savefig(os.path.join(self.filepath,self.name+'Open_Shut.png'),dpi=150)
def mean_quadratic_weighted_kappa(kappas, weights=None):
"""
Calculates the mean of the quadratic
weighted kappas after applying Fisher's r-to-z transform, which is
approximately a variance-stabilizing transformation. This
transformation is undefined if one of the kappas is 1.0, so all kappa
values are capped in the range (-0.999, 0.999). The reverse
transformation is then applied before returning the result.
mean_quadratic_weighted_kappa(kappas), where kappas is a vector of
kappa values
mean_quadratic_weighted_kappa(kappas, weights), where weights is a vector
of weights that is the same size as kappas. Weights are applied in the
z-space
"""
kappas = np.array(kappas, dtype=float)
if weights is None:
weights = np.ones(np.shape(kappas))
else:
weights = weights / np.mean(weights)
# ensure that kappas are in the range [-.999, .999]
kappas = np.array([min(x, .999) for x in kappas])
kappas = np.array([max(x, -.999) for x in kappas])
z = 0.5 * np.log((1 + kappas) / (1 - kappas)) * weights
z = np.mean(z)
return (np.exp(2 * z) - 1) / (np.exp(2 * z) + 1)
def filter(input): infilter = DoubleInPointerFilter(input) infilter.output_sampling_rate = sampling_rate attackreleasefilter = DoubleAttackReleaseFilter(1) attackreleasefilter.input_sampling_rate = sampling_rate attackreleasefilter.set_input_port(0, infilter, 0) attackreleasefilter.attack = np.exp(-1/(sampling_rate*1e-3)) attackreleasefilter.release = np.exp(-1/(sampling_rate*10e-3)) outdata = np.zeros(processsize, dtype=np.float64) outfilter = DoubleOutPointerFilter(outdata) outfilter.input_sampling_rate = sampling_rate outfilter.set_input_port(0, attackreleasefilter, 0) attackreleasefilter2 = DoubleAttackReleaseHysteresisFilter(1) attackreleasefilter2.input_sampling_rate = sampling_rate attackreleasefilter2.set_input_port(0, infilter, 0) attackreleasefilter2.attack = np.exp(-1/(sampling_rate*1e-3)) attackreleasefilter2.release = np.exp(-1/(sampling_rate*10e-3)) attackreleasefilter2.release_hysteresis = .5 attackreleasefilter2.attack_hysteresis = .9 outdata2 = np.zeros(processsize, dtype=np.float64) outfilter_hyst = DoubleOutPointerFilter(outdata2) outfilter_hyst.input_sampling_rate = sampling_rate outfilter_hyst.set_input_port(0, attackreleasefilter2, 0) pipelineend = PipelineGlobalSinkFilter() pipelineend.input_sampling_rate = sampling_rate pipelineend.add_filter(outfilter) pipelineend.add_filter(outfilter_hyst) pipelineend.process(processsize) return outdata, outdata2
def sample(scores, temperature=1.0):
"""
Sampling words (each sample is drawn from a categorical distribution).
In:
scores - array of size #samples x #classes;
every entry determines a score for sample i having class j
temperature - temperature for the predictions;
the higher the flatter probabilities and hence more random answers
Out:
set of indices chosen as output, a vector of size #samples
"""
logscores = np.log(scores) / temperature
# numerically stable version
normalized_logscores= logscores - np.max(logscores, axis=-1)[:, np.newaxis]
margin_logscores = np.sum(np.exp(normalized_logscores),axis=-1)
probs = np.exp(normalized_logscores) / margin_logscores[:,np.newaxis]
draws = np.zeros_like(probs)
num_samples = probs.shape[0]
# we use 1 trial to mimic categorical distributions using multinomial
for k in xrange(num_samples):
draws[k,:] = np.random.multinomial(1,probs[k,:],1)
return np.argmax(draws, axis=-1)
def posterior(kpl, pk, err, pkfold=None, errfold=None):
k0 = n.abs(kpl).argmin()
kpl = kpl[k0:]
if pkfold is None:
print 'Folding for posterior'
pkfold = pk[k0:].copy()
errfold = err[k0:].copy()
pkpos,errpos = pk[k0+1:].copy(), err[k0+1:].copy()
pkneg,errneg = pk[k0-1:0:-1].copy(), err[k0-1:0:-1].copy()
pkfold[1:] = (pkpos/errpos**2 + pkneg/errneg**2) / (1./errpos**2 + 1./errneg**2)
errfold[1:] = n.sqrt(1./(1./errpos**2 + 1./errneg**2))
#ind = n.logical_and(kpl>.2, kpl<.5)
ind = n.logical_and(kpl>.15, kpl<.5)
#ind = n.logical_and(kpl>.12, kpl<.5)
#print kpl,pk.real,err
kpl = kpl[ind]
pk= kpl**3 * pkfold[ind]/(2*n.pi**2)
err = kpl**3 * errfold[ind]/(2*n.pi**2)
s = n.logspace(5.,6.5,100)
data = []
for ss in s:
data.append(n.exp(-.5*n.sum((pk.real - ss)**2 / err**2)))
# print data[-1]
data = n.array(data)
#print data
#print s
#data/=n.sum(data)
data /= n.max(data)
p.figure(5)
p.plot(s, data)
p.plot(s, n.exp(-.5)*n.ones_like(s))
p.plot(s, n.exp(-.5*2**2)*n.ones_like(s))
p.show()
def __set_static_gaus_pmfs(self):
if np.logical_not(self.off_buff.is_full()):
print "The long term buffer is not yet full. This may give undesirable results"
# median RSS of off-state buffer
cal_med = self.off_buff.get_no_nan_median()
if (np.sum(cal_med == 127) > 0) | (np.sum(np.isnan(cal_med)) > 0):
sys.stderr.write('At least one link has a median of 127 or is nan\n\n')
quit()
if (np.sum(np.isnan(self.off_buff.get_nanvar())) > 0):
sys.stderr.write('the long term buffer has a nan')
quit()
cal_med_mat = np.tile(cal_med,(self.V_mat.shape[1],1)).T
# variance of RSS during calibration
cal_var = np.maximum(self.off_buff.get_nanvar(),self.omega) #3.0
cal_var_mat = np.tile(cal_var,(self.V_mat.shape[1],1)).T
# Compute the off_link emission probabilities for each link
x = np.exp(- (self.V_mat - cal_med_mat)**2/(2*cal_var_mat/1.0)) # 1.0
self.off_links = self.__normalize_pmf(x)
# Compute the on_link emission probabilities for each link
x = np.exp(- (self.V_mat - (cal_med_mat-self.Delta))**2/(self.eta*2*cal_var_mat)) # 3
self.on_links = self.__normalize_pmf(x)
def test_square_exponential_covariance_one_dim(self):
"""Test the SquareExponential covariance function against correct values for different sets of hyperparameters in 1D."""
for hyperparameters in self.one_dim_test_sets:
signal_variance = hyperparameters[0]
length = hyperparameters[1]
covariance = self.CovarianceClass(hyperparameters)
# One length away
truth = signal_variance * numpy.exp(-0.5)
self.assert_scalar_within_relative(
covariance.covariance(numpy.array([0.0]), numpy.array(length)),
truth,
self.epsilon,
)
# Sym
self.assert_scalar_within_relative(
covariance.covariance(numpy.array(length), numpy.array([0.0])),
truth,
self.epsilon,
)
# One length * sqrt 2 away
truth = signal_variance * numpy.exp(-1.0)
self.assert_scalar_within_relative(
covariance.covariance(numpy.array([0.0]), numpy.array([length * numpy.sqrt(2)])),
truth,
self.epsilon,
)
def solveParams(self):
# Given the specified values for w, z1 and z2, determine the offsets
# xc and zc required to match a catenary to our cable. This is done
# algerbraically. The deriviation of the equation was performed with
# the sympy package.
w = self.w
a = self.a
zd = self.z2 - self.z1
# calculate some repeated elements
e2wa = np.exp(2 * w / a)
ewa = np.exp(w / a)
a2 = a ** 2
# calculate the 3 components
c1 = (a2 * e2wa - 2 * a2 * ewa + a2 + zd ** 2 * ewa) * ewa
c2 = (-2 * a * e2wa + 2 * a * ewa)
c3 = zd / (a * (ewa - 1))
# Determine the x offset ...
self.xc = a * np.log(2 * np.abs(np.sqrt(c1) / c2) + c3)
# ... and from this the y offset
self.zc = self.z1 - a * np.cosh(self.xc / a)
def rbf_kernel(X, Y=None, gamma=None):
"""
Compute the rbf (gaussian) kernel between X and Y::
K(x, y) = exp(-gamma ||x-y||^2)
for each pair of rows x in X and y in Y.
Parameters
----------
X : array of shape (n_samples_X, n_features)
Y : array of shape (n_samples_Y, n_features)
gamma : float
Returns
-------
kernel_matrix : array of shape (n_samples_X, n_samples_Y)
"""
X, Y = check_pairwise_arrays(X, Y)
if gamma is None:
gamma = 1.0 / X.shape[1]
K = euclidean_distances(X, Y, squared=True)
K *= -gamma
np.exp(K, K) # exponentiate K in-place
return K
def CRRbinomial(S, K, T, rf, sigma, n):
'''
Option pricing using binomial tree, no dividend
:param S: underlying current prince
:param K: option strke price
:param T: expire date
:param rf: risk-free rate
:param sigma: volatility
:param n: number of periods to T
:return:
'''
dt = float(T)/n
u = np.exp(sigma * (dt**0.5))
d= 1./u
p = (np.exp(rf*dt)-d)/(u-d)
euroCall, euroPut = 0, 0
for idx in xrange(0, n+1):
prob = spmisc.comb(n, idx)* (p**idx) * (1-p)**(n-idx)
euroCall += prob*max(S*(u**idx)*(d**(n-idx))-K, 0)
euroPut += prob*max(K-S*(u**idx)*(d**(n-idx)), 0)
euroCall *= np.exp(-rf*T)
euroPut *= np.exp(-rf*T)
return euroCall, euroPut
def mycavvaccaleib(x,p, secondg=False):
latebump=False
if p==None:
return (x)*99e9
if p[8]>p[0]:
# print "late bump"
latebump=True
#fit the magnitudes with a vacca leibundgut (1997) analytical model
#p is the parameter list
#if secondg=1: secondgaussian added
#if secondg=0: secondgaussian not
#parameters are:
#p[0]=first gaussian normalization (negative if fitting mag)
#p[1]=first gaussian mean
#p[2]=first gaussian sigma
#p[3]=linear decay offset
#p[4]=linear decay slope
#p[5]=exponxential rise slope
#p[6]=exponential zero point
#p[7]=second gaussian normalization (negative if fitting mag)
#p[8]=second gaussian mean
#p[9]=second gaussian sigma
g=p[4]*(x)+p[3]
g+=p[0]*np.exp(-(x-p[1])**2/p[2]**2)
g*=(np.exp(-p[5]*(x-p[6]))+1)
if secondg:
g+=p[7]*np.exp(-(x-p[8])**2/p[9]**2)
if latebump and p[8]-p[1]<15 :
g+=(np.zeros(len(g),float)+1)
if p[8]-p[1]>70:
g+=(np.zeros(len(g),float)+1)
return g
def testCustomGradient(self):
dtype = dtypes.float32
@function.Defun(dtype, dtype, dtype)
def XentLossGrad(logits, labels, dloss):
dlogits = array_ops.reshape(dloss, [-1, 1]) * (
nn_ops.softmax(logits) - labels)
dlabels = array_ops.zeros_like(labels)
# Takes exp(dlogits) to differentiate it from the "correct" gradient.
return math_ops.exp(dlogits), dlabels
@function.Defun(dtype, dtype, grad_func=XentLossGrad)
def XentLoss(logits, labels):
return math_ops.reduce_sum(labels * math_ops.log(nn_ops.softmax(logits)),
1)
g = ops.Graph()
with g.as_default():
logits = array_ops.placeholder(dtype)
labels = array_ops.placeholder(dtype)
loss = XentLoss(logits, labels)
dlogits = gradients_impl.gradients([loss], [logits])
x = np.random.uniform(-10., 10., size=(4, 9)).astype(np.float32)
prob = np.exp(x) / np.sum(np.exp(x), 1, keepdims=1)
y = np.random.uniform(-10., 10., size=(4, 9)).astype(np.float32)
for cfg in _OptimizerOptions():
tf_logging.info("cfg = %s", cfg)
with session.Session(graph=g, config=cfg) as sess:
out, = sess.run(dlogits, {logits: x, labels: y})
self.assertAllClose(out, np.exp(prob - y))
def bbox_transform_inv(boxes, deltas):
if boxes.shape[0] == 0:
return np.zeros((0, deltas.shape[1]), dtype=deltas.dtype)
boxes = boxes.astype(deltas.dtype, copy=False)
widths = boxes[:, 2] - boxes[:, 0] + 1.0
heights = boxes[:, 3] - boxes[:, 1] + 1.0
ctr_x = boxes[:, 0] + 0.5 * widths
ctr_y = boxes[:, 1] + 0.5 * heights
dx = deltas[:, 0::4]
dy = deltas[:, 1::4]
dw = deltas[:, 2::4]
dh = deltas[:, 3::4]
pred_ctr_x = dx * widths[:, np.newaxis] + ctr_x[:, np.newaxis]
pred_ctr_y = dy * heights[:, np.newaxis] + ctr_y[:, np.newaxis]
pred_w = np.exp(dw) * widths[:, np.newaxis]
pred_h = np.exp(dh) * heights[:, np.newaxis]
pred_boxes = np.zeros(deltas.shape, dtype=deltas.dtype)
# x1
pred_boxes[:, 0::4] = pred_ctr_x - 0.5 * pred_w
# y1
pred_boxes[:, 1::4] = pred_ctr_y - 0.5 * pred_h
# x2
pred_boxes[:, 2::4] = pred_ctr_x + 0.5 * pred_w
# y2
pred_boxes[:, 3::4] = pred_ctr_y + 0.5 * pred_h
return pred_boxes
def convolve_template():
from plot_Profile_evolution import all_obs
import numpy as np
date_list, observations = all_obs()
x = np.arange(512 - 25 - 50, 512 + 45 + 51)
delay = []
for n in observations:
best_mu = 0
best_corr = 0
for mu in np.linspace(512 - 25, 512 + 45, 701):
template = np.exp(-(x - 512) ** 2 / (2.0 * 6.2 ** 2)) + 0.09 * np.exp(-(x - mu) ** 2 / (2.0 * 8.0 ** 2))
template /= template.max()
corr = np.correlate(n, template, mode="valid").max()
if corr > best_corr:
best_corr = corr
best_mu = mu
delay.append(best_mu - 512)
plt.plot(date_list, delay, "ko")
plt.show()
def InterpBeadError(X, y, bead1, bead2, write = False, name = "00"):
'''X = []
y = []
for i in xrange(1000):
a,b = generatecandidate3(.5,.25,.1)
X.append(a)
y.append(b)'''
X= np.array(X)
y=np.array(y)
errors = []
for tt in xrange(100):
#Should make this architecture independent at some point
t = tt/100.
layer_1 = 1/(1+np.exp(-(np.dot(X,synapse_interpolate(bead1[0],bead2[0],t)))))
layer_2 = 1/(1+np.exp(-(np.dot(layer_1,synapse_interpolate(bead1[1],bead2[1],t)))))
#layer_3 = 1/(1+np.exp(-(np.dot(layer_2,synapse_interpolate(bead1[2],bead2[2],t)))))
# how much did we miss the target value?
layer_2_error = layer_2 - y
errors.append(np.mean(np.abs(layer_2_error)))
if write == True:
with open("f" + str(name) + ".out",'w+') as f:
for e in errors:
f.write(str(e) + "\n")
return max(errors)
def mat_unitary(self):
s = [
math.sin(2 * self.at0),
math.sin(2 * self.at1),
math.sin(2 * self.aq0),
math.sin(2 * self.aq1),
math.sin(2 * self.aq2),
]
c = [
math.cos(2 * self.at0),
math.cos(2 * self.at1),
math.cos(2 * self.aq0),
math.cos(2 * self.aq1),
math.cos(2 * self.aq2),
]
phi = [
numpy.exp(complex(0, 4 * self.pt1)),
numpy.exp(complex(0, 2 * self.pt2)),
numpy.exp(complex(0, -2 * self.pt2)),
]
U = numpy.array(
[
[c[2] * c[3], -phi[0] * s[0] * s[2] * c[3] - phi[1] * c[0] * s[1] * s[3]],
[c[2] * s[3], -phi[0] * s[0] * s[2] * s[3] + phi[1] * c[0] * s[1] * c[3]],
[s[2] * c[4], phi[0] * s[0] * c[2] * c[4] + phi[2] * c[0] * c[1] * s[4]],
[s[2] * s[4], phi[0] * s[0] * c[2] * s[4] - phi[2] * c[0] * c[1] * c[4]],
]
)
theta = cmath.phase(U[0, 1])
for i in range(4):
U[i, 1] = U[i, 1] * numpy.exp(complex(0, -theta))
return U
def fwd_all(self,X,w=None):
""" Propagate values forward through the net.
Inputs:
inputs - vector of input values
w - packed array of weights
Returns:
array of outputs for all input patterns
"""
if w is not None:
self.wp = w
self.unpack()
# compute hidden unit values
z = N.zeros((len(X),self.centers.shape[0]))
for i in range(len(X)):
z[i] = N.exp((-1.0/(2*self.variance))*(N.sum((X[i]-self.centers)**2,axis=1)))
# compute net outputs
o = N.dot(z,self.w) + N.dot(N.ones((len(z),1)),self.b)
# compute final output activations
if self.outfxn == 'linear':
y = o
elif self.outfxn == 'logistic': # TODO: check for overflow here...
y = 1/(1+N.exp(-o))
elif self.outfxn == 'softmax': # TODO: and here...
tmp = N.exp(o)
y = tmp/(N.sum(temp,1)*N.ones((1,self.no)))
return N.array(y)
def gradWB(new,kern,BN,keep,points):
"""Computes the vector of gradients with respect to w_{n+1} of
B(x_{p},n+1)=\int\Sigma_{0}(x_{p},w,x_{n+1},w_{n+1})dp(w),
where x_{p} is a point in the discretization of the domain of x.
Args:
new: Point (x_{n+1},w_{n+1})
kern: Kernel
keep: Indexes of the points keeped of the discretization of the domain of x,
after using AffineBreakPoints
BN: Vector B(x_{p},n+1), where x_{p} is a point in the discretization of
the domain of x.
points: Discretization of the domain of x
"""
alpha1=0.5*((kern.alpha[0:n1])**2)/scaleAlpha[0:n1]**2
alpha2=0.5*((kern.alpha[n1:n1+n2])**2)/scaleAlpha[n1:n1+n2]**2
variance0=kern.variance
wNew=new[0,n1:n1+n2].reshape((1,n2))
gradWBarray=np.zeros([len(keep),n2])
M=len(keep)
# parameterLamb=parameterSetsPoisson
X=new[0,0:n1]
W=new[0,n1:n1+n2]
num=0
for i in range(n1):
num+=(2.0*alpha2*(i-wNew))*np.exp(-alpha2*((i-wNew)**2))
num=num/n1
for j in range(M):
gradWBarray[j,0]=num*(variance0)*np.exp(np.sum(alpha1*((points[keep[j],:]-X)**2)))
return gradWBarray
def all_GL(self, q, maxpiv=None):
"""return (piv, f_binodal_gas, f_binodal_liquid, f_spinodal_gas, f_spinodal_liquid) at insersion works piv sampled between the critical point and maxpiv (default to 2.2*critical pressure)"""
fc, pivc = self.critical_point(q)
Fc = np.log(fc)
#start sensibly above the critical point
startp = pivc*1.1
fm = fminbound(self.mu, fc, self.maxf(), args=(startp, q))
fM = fminbound(lambda f: -self.pv(f, startp, q), 0, fc)
initial_guess = np.log([0.5*fM, 0.5*(fm+self.maxf())])
#construct the top of the GL binodal
if maxpiv is None:
maxpiv = startp*2
topp = 1./np.linspace(1./startp, 1./maxpiv)
topGL = [initial_guess]
for piv in topp:
topGL.append(self.binodalGL(piv, q, topGL[-1]))
#construct the GL binodal between the starting piv and the critical point
botp = np.linspace(startp, pivc)[:-1]
botGL = [initial_guess]
for piv in botp:
botGL.append(self.binodalGL(piv, q, botGL[-1]))
#join the two results and convert back from log
binodal = np.vstack((
[[pivc, fc, fc]],
np.column_stack((botp, np.exp(botGL[1:])))[::-1],
np.column_stack((topp, np.exp(topGL[1:])))[1:]
))
#spinodal at the same pivs
spinodal = self.spinodalGL(q, binodal[:,0])
#join everything
return np.column_stack((binodal, spinodal[:,1:]))
def update(self,proposal,logp,bad,i):
logps = self.logps[i-1]
thresh = self.thresh
if logp>logps:
self.logps[i] = logp
self.trace[i] = proposal
self.dets.append([d.value for d in self.deterministics])
self.nbad = 0
self.stuck = False
self.temp = 1.
return
self.nbad += 1
if self.nbad>self.thresh and self.stuck==False:
self.stuck = True
self.logpTmp = logps
if self.stuck==True:
r = log(rand())*self.temp
print 'stuck',i,logps,self.logpTmp,logp,r,logp-self.logpTmp
if logp-self.logpTmp>r:
self.logpTmp = logp
self.temp /= numpy.exp(1./thresh)
else:
self.temp *= numpy.exp(1./thresh)
self.logps[i] = self.logps[i-1]
self.trace[i] = self.trace[i-1].copy()
self.dets.append(self.dets[-1])
def test_solve_poisson_becke_sa():
sigma = 8.0
rtf = ExpRTransform(1e-4, 1e2, 500)
r = rtf.get_radii()
rhoy = np.exp(-0.5*(r/sigma)**2)/sigma**3/(2*np.pi)**1.5
rhod = np.exp(-0.5*(r/sigma)**2)/sigma**3/(2*np.pi)**1.5*(-r/sigma)/sigma
rho = CubicSpline(rhoy, rhod, rtf)
v = solve_poisson_becke([rho])[0]
s2s = np.sqrt(2)*sigma
soly = erf(r/s2s)/r
sold = np.exp(-(r/s2s)**2)*2/np.sqrt(np.pi)/s2s/r - erf(r/s2s)/r**2
if False:
import matplotlib.pyplot as pt
n = 10
pt.clf()
pt.plot(r[:n], soly[:n], label='exact')
pt.plot(r[:n], v.y[:n], label='spline')
pt.legend(loc=0)
pt.savefig('denu.png')
assert abs(v.y - soly).max()/abs(soly).max() < 1e-6
assert abs(v.dx - sold).max()/abs(sold).max() < 1e-4
# Test the boundary condition at zero and infinity
assert v.extrapolation.l == 0
np.testing.assert_allclose(v.extrapolation.amp_left, np.sqrt(2/np.pi)/sigma)
np.testing.assert_allclose(v.extrapolation.amp_right, 1.0)
def __init__(self, ps=None, sigma_v=0.0, redshift=0.0, **kwargs):
if ps == None:
from os.path import join, dirname
#psfile = join(dirname(__file__),"data/ps_z1.5.dat")
#psfile = join(dirname(__file__),"data/wigglez_halofit_z1.5.dat")
psfile = join(dirname(__file__),"data/wigglez_halofit_z0.8.dat")
print "loading matter power file: " + psfile
redshift = 0.8
#pk_interp = cs.LogInterpolater.fromfile(psfile)
pwrspec_data = np.genfromtxt(psfile)
(log_k, log_pk) = (np.log(pwrspec_data[:,0]), \
np.log(pwrspec_data[:,1]))
logpk_interp = interpolate.interp1d(log_k, log_pk,
bounds_error=False,
fill_value=np.min(log_pk))
pk_interp = lambda k: np.exp(logpk_interp(np.log(k)))
kstar = 7.0
ps = lambda k: np.exp(-0.5 * k**2 / kstar**2) * pk_interp(k)
self._sigma_v = sigma_v
RedshiftCorrelation.__init__(self, ps_vv=ps, redshift=redshift)
def filter_annular_bp_kernel(shape, dtype, freq1, freq2):
''' Filter an image with a Gaussian low pass filter
Todo: optimize kernel
:Parameters:
shape : tuple
Tuple of ints describing the shape of the kernel
dtype : dtype
Data type of the image
freq1 : float
Cutoff frequency
freq2 : array
Cutoff frequency
:Returns:
out : array
Annular BP kernel
'''
kernel = numpy.zeros(shape, dtype=dtype)
irad = radial_image(shape)
val = (1.0/(1.0+numpy.exp(((numpy.sqrt(irad)-freq1))/(10.0))))*(1.0-(numpy.exp(-irad /(2*freq2*freq2))))
kernel[:, :].real = val
kernel[:, :].imag = val
return kernel
def _compute_influence_kernel(self, iter, dqd):
"""Compute the neighborhood kernel for some iteration.
Parameters
----------
iter : int
The iteration for which to compute the kernel.
dqd : array (nrows x ncolumns)
This is one quadrant of Euclidean distances between Kohonen unit
locations.
"""
# compute radius decay for this iteration
curr_max_radius = self.radius * np.exp(-1.0 * iter / self.iter_scale)
# same for learning rate
curr_lrate = self.lrate * np.exp(-1.0 * iter / self.iter_scale)
# compute Gaussian influence kernel
infl = np.exp((-1.0 * dqd) / (2 * curr_max_radius * iter))
infl *= curr_lrate
# hard-limit kernel to max radius
# XXX is this really necessary?
infl[dqd > curr_max_radius] = 0.
return infl
def logLikelihood(self, obs_seq, num_cluster, error_rate_dict, switch_rate_dict):
"""
:param obs_seq: state list of the same length as observation sequence
:param num_cluster: int
:param error_rate_dict: dict
:param switch_rate_dict: dict
:return: log likelihood
"""
pi = [1/num_cluster] * num_cluster
path_length = len(obs_seq)
alpha_dict = dict()
alpha_dict[0] = dict(zip(range(num_cluster), [np.log(pi[i]) + np.log(error_rate_dict[i][obs_seq[0]])
for i in range(num_cluster)]))
for t in range(path_length-1):
alpha_dict[t+1] = dict()
for j in range(num_cluster):
log_alpha_j = [(alpha_dict[t][i] + np.log(switch_rate_dict[i][j])) for i in range(num_cluster)]
max_log_alpha_j = max(log_alpha_j)
sum_residual = np.sum(np.exp(log_alpha_j - max_log_alpha_j))
final = max_log_alpha_j + np.log(sum_residual)
alpha_dict[t+1][j] = final + np.log(error_rate_dict[j][obs_seq[t + 1]])
alpha_df = pd.DataFrame.from_dict(alpha_dict)
max_final = max(alpha_df.ix[:, path_length-1])
llk = max_final + np.log(np.sum(np.exp(alpha_df.ix[:, path_length-1] - max_final)))
return llk
def firwin_complex_bandpass(num_taps, cutoffs, window='hamming'):
width, center = max(cutoffs) - min(cutoffs), (cutoffs[0] + cutoffs[1]) / 2
b = scipy.signal.firwin(num_taps, width / 2, window='rectangular', scale=False)
b = b * numpy.exp(1j * numpy.pi * center * numpy.arange(len(b)))
b = b * scipy.signal.get_window(window, num_taps, False)
b = b / numpy.sum(b * numpy.exp(-1j * numpy.pi * center * (numpy.arange(num_taps) - (num_taps - 1) / 2)))
return b.astype(numpy.complex64)
def estimate_from_weights(log_ais_w):
""" Safely computes the log-average of the ais-weights.
Inputs
------
log_ais_w: T.vector
Symbolic vector containing log_ais_w^{(m)}.
Returns
-------
dlogz: scalar
log(Z_B) - log(Z_A).
var_dlogz: scalar
Variance of our estimator.
"""
# Utility function for safely computing log-mean of the ais weights.
ais_w = T.vector()
max_ais_w = T.max(ais_w)
dlogz = T.log(T.mean(T.exp(ais_w - max_ais_w))) + max_ais_w
log_mean = theano.function([ais_w], dlogz, allow_input_downcast=False)
# estimate the log-mean of the AIS weights
dlogz = log_mean(log_ais_w)
# estimate log-variance of the AIS weights
# VAR(log(X)) \approx VAR(X) / E(X)^2 = E(X^2)/E(X)^2 - 1
m = numpy.max(log_ais_w)
var_dlogz = (log_ais_w.shape[0] *
numpy.sum(numpy.exp(2 * (log_ais_w - m))) /
numpy.sum(numpy.exp(log_ais_w - m)) ** 2 - 1.)
return dlogz, var_dlogz
def test_WeightedDataFrame_neff():
df = test_WeightedDataFrame_constructor()
neff = df.neff()
assert isinstance(neff, float)
assert neff < len(df)
assert neff > len(df) * np.exp(-0.25)
def sigmoid(Z):
return 1/(1+np.exp(-Z))
o.fallback_values['sea_surface_wave_stokes_drift_x_velocity'] = .3
o.fallback_values['sea_surface_wave_stokes_drift_y_velocity'] = 0
o.set_config('wave_entrainment:droplet_size_distribution', 'Johansen et al. (2015)')
o.set_config('processes:evaporation', False)
o.set_config('processes:dispersion', False)
o.set_config('turbulentmixing:droplet_diameter_min_wavebreaking', dmin)
o.set_config('turbulentmixing:droplet_diameter_max_wavebreaking', dmax)
o.seed_elements(lon=4, lat=60, time=datetime.now(), number=10000, radius=100,
z=0, oiltype='TROLL, STATOIL', oil_film_thickness=0.005)
o.run(duration=timedelta(hours=2), time_step=3600)
droplet_diameters = o.elements.diameter
sd = 0.4
Sd = np.log(10.)*sd
DV_50 = np.median(droplet_diameters)
DN_50 = np.exp( np.log(DV_50) - 3*Sd**2 )
print 'DV_50: %f' % DV_50
print 'DN_50: %f' % DN_50
################## Plotting ##########################
plt.figure(figsize=[14,14])
plt.subplot(3, 2, 1)
nVpdf, binsV, patches = plt.hist(droplet_diameters, 100, range=(dmin,dmax), align='mid')
plt.xlabel('Droplet diameter d [m]', fontsize=8)
plt.ylabel('V(d)', fontsize=8)
plt.title('volume spectrum\nJohansen et al. (2015) distribution in OpenOil3D', fontsize=10)
plt.subplot(3,2,2)
nVcum, binsV, patches = plt.hist(droplet_diameters, 100, range=(dmin,dmax), align='mid', cumulative=True)
plt.xlabel('Droplet diameter d [m]', fontsize=8)
print "Maximum logL is %g, (%g in \"SNR\")" % (max(logLs), numpy.sqrt(2*max(logLs)))
print "Which occurs at sample", numpy.argmax(logLs)
print "This corresponds to time %.20g" % tvals[numpy.argmax(logLs)]
print "The data event time is: %.20g" % sim_row.get_time_geocent()
print "Difference from geocenter t_ref is %.20g" %\
(tvals[numpy.argmax(logLs)] - sim_row.get_time_geocent())
print "This difference in discrete samples: %.20g" %\
((tvals[numpy.argmax(logLs)]-sim_row.get_time_geocent())/P.deltaT)
pyplot.plot(tvals-tref, logLs)
pyplot.ylabel("log Likelihood")
pyplot.xlabel("time (relative to %10.5f)" % tref)
pyplot.axvline(0, color="k")
pyplot.title("lnL(t),\n value at event time: %f" % logL)
pyplot.grid()
pyplot.savefig("logL.png")
integral = numpy.sum( numpy.exp(logLs) * P.deltaT )
print "Integral over t of likelihood is:", integral
print "The log of the integral is:", numpy.log(integral)
exit()
#
# Parameter integral sampling strategy
#
params = {}
sampler = mcsampler.MCSampler()
#
# Psi -- polarization angle
# sampler: uniform in [0, pi)
#
psi_sampler = functools.partial(mcsampler.uniform_samp_vector, param_limits["psi"][0], param_limits["psi"][1])
'2017-05-16', '2017-10-05', '2018-04-09', '2018-08-29', '2019-01-24', '2019-05-16']
cp_train_std = np.std(df_close.to_numpy(), axis=0)
choice = np.argsort(cp_train_std)
for phs in range(0, len(end_dates)):
print(phs)
ntrain = 250
nval = 50
ntest = 100
win = 5
nstock = len(all_stock)
cp = df_close[:end_dates[phs]].tail(ntrain+nval+ntest)
cp_train = cp.iloc[:ntrain, :]
cov_train = np.cov(np.exp(cp_train.to_numpy().T))
cp_val = cp.iloc[ntrain-win:ntrain+nval, :]
cp_test = cp.iloc[ntrain+nval-win:, :]
cp_trainx = np.zeros((ntrain - win, win * nstock))
cp_trainy = np.zeros((ntrain - win, nstock))
for i in range(win, ntrain):
cp_trainy[i - win] = cp_train.to_numpy()[i]
for s in range(nstock):
cp_trainx[i - win, s * win:(s + 1) * win] = cp_train.to_numpy()[i - win:i, s]
cp_valx = np.zeros((nval, win * nstock))
cp_valy = np.zeros((nval, nstock))
simVals = np.array(simVals)
polLeakdbs = np.array(polLeakdbs)
snrs = (np.array(snrs) / normSNR)**2.
fig = p.figure()
ax = fig.add_subplot(1, 1, 1)
fig.set_size_inches(9., 5.)
polLeakVals = np.unique(polLeakdbs)
cNorm = np.min(polLeakVals)
for pVal in polLeakVals:
idx = np.argwhere(polLeakdbs == pVal)
subSnrs = snrs[idx]
subSimVals = simVals[idx]
sIdx = np.argsort(subSnrs[:, 0])
rgb = (np.exp(pVal / 10.), 0., 1. - np.exp(pVal / 10.))
#slightly hardcoded plots and labels
#if pVal > -0.0001: labelStr='%0.f dB'%(-1.*pVal) #-0 to 0
if pVal > -0.1: continue
elif (pVal > -5.) or (pVal < -16. and pVal > -30) or pVal < -31.:
continue #skip these lines
else:
labelStr = '%0.f dB' % (pVal)
midPoint = int(subSnrs.shape[0] * .33)
p.plot(subSnrs[sIdx, 0], subSimVals[sIdx, 0], color=rgb)
p.text(subSnrs[sIdx, 0][midPoint],
0.8 * subSimVals[sIdx, 0][midPoint],
labelStr,
fontsize=18)
#lines of constant time (5, 1, .5 us)
def test_WeightedSeries_neff():
series = test_WeightedSeries_constructor()
neff = series.neff()
assert isinstance(neff, float)
assert neff < len(series)
assert neff > len(series) * np.exp(-0.25)
def forward(self, x): return np.exp(x)
def __sigmoid(self, x):
return 1 / (1 + numpy.exp(-x))
def effective_rank(X):
U,S,VT = np.linalg.svd(X)
S = S / np.linalg.norm(S,1)
assert (np.all(S >= 0) and abs(S.sum()-1) < 1e-5), 'S not a probability distribution'
H = entropy(S)
return np.exp(H)
corr = np.abs(np.fft.ifft2(conj))
alpha_p, logr_p = np.unravel_index(np.argmax(corr), corr.shape)
logr_size = im_p_logpolar.shape[0]
alpha_size = im_p_logpolar.shape[1]
if logr_p > logr_size // 2:
w = logr_size - logr_p # powiekszenie
else:
w = -logr_p # pomniejszenie
A = (alpha_p * 360.0) / alpha_size
a1 = -A
a2 = 180 - A
scale = np.exp(w / M) # M to parametr funkcji cv2.logPolar
print(scale)
im = np.zeros(im_p.shape)
x_1 = int((im_p.shape[0] - im_w.shape[0]) / 2)
x_2 = int((im_p.shape[0] + im_w.shape[0]) / 2)
y_1 = int((im_p.shape[1] - im_w.shape[1]) / 2)
y_2 = int((im_p.shape[1] + im_w.shape[1]) / 2)
im[x_1:x_2, y_1:y_2] = im_w_in
centerT = (im.shape[0] / 2 - 0.5, im.shape[1] / 2 - 0.5)
# im to obraz wzorca uzupelniony zerami, ale ze wzorcem umieszczonym na srodku, a nie w lewym, gornym rogu!
transM1 = cv.getRotationMatrix2D(centerT, a1, scale)
im_r_s1 = cv.warpAffine(im, transM1, im.shape)
transM2 = cv.getRotationMatrix2D(centerT, a2, scale)
def poly5_to_Z(z_OLS, T):
## This function takes maturity and a fitted ploynomial interest rate model and return Z(0,T)
## z_OLS must be a OLS class and T must be a list
return np.exp(np.dot(power_5(T), z_OLS.beta))
def f_o(x, pi4):
f_O= 3.106934*np.exp(-19.868080*(x/pi4)**2) + 3.235142*np.exp(-6.960252*(x/pi4)**2) + \
1.148886*np.exp(-0.170043*(x/pi4)**2) + 0.783981*np.exp(-65.693509*(x/pi4)**2) + \
0.676953*np.exp(-0.630757*(x/pi4)**2) + 0.046136
return (f_O)
def sigmoid(z):
return 1. / (1 + np.exp(- z))
def _logistic(self, x):
return np.where(x > 0, 1 / (1 + np.exp(-x)), np.exp(x) / (1 + np.exp(x)))
def f_li(x, pi4):
f_Li= 0.432724*np.exp(-0.260367*(x/pi4)**2)+0.549257*np.exp(-1.042836*(x/pi4)**2)+ \
0.376575*np.exp(-7.885294*(x/pi4)**2)- 0.336481*np.exp(-0.260368*(x/pi4)**2) + \
0.976060*np.exp(-3.042539*(x/pi4)**2) + 0.001764
return (f_Li)
A=0.004;
P=1000;
eff=0.25;
h=6.626e-34;
freq=1e15;
nphotons=P*A/h/freq;
Is=nphotons*1.6e-19*eff;
print(Is)
V1=4.7;
Vt=0.025;
n=10;
Vs=4;
I0=1e-12;
I02=1e-12;
I=I02*(np.exp((V1-Vs)/Vt)-1);
print(I)
I=Is-I0*(np.exp(V1/n/Vt)-1);
print(I)
def curr(x):
y=I02*(np.exp((x-Vs)/Vt)-1)-Is+I0*(np.exp(x/n/Vt)-1);
return y
soln=fsolve(curr,4.7)
print(soln)
P=np.linspace(0,1000,100);
I2=np.linspace(0,1000,100);
def __calculate_weights__(self, z, xichma):
weight = 1
temp = sum(z ** 2)
if temp != 0:
weight = (1.0 / sqrt(temp)) * exp(-temp / (2 * self.problem_size * xichma ** 2))
return weight
return x, y, z
if True:
x, y, z = import_h5_array('/tmp/pyrs_test_ss/test.hdf5')
print x.min(), x.max()
print y.min(), y.max()
print z.min(), z.max(), z.mean()
else:
np.random.seed(19680801)
npts = 200
x = np.random.uniform(-2, 2, npts)
y = np.random.uniform(-2, 2, npts)
z = x * np.exp(-x**2 - y**2)
fig, (ax1, ax2) = plt.subplots(nrows=2)
# -----------------------
# Interpolation on a grid
# -----------------------
# A contour plot of irregularly spaced data coordinates
# via interpolation on a grid.
# Create grid values first.
ngridx = 1000
ngridy = 2000
xi = np.linspace(-200, 200, ngridx)
yi = np.linspace(0, 70, ngridy)
def curr(x):
y=I02*(np.exp((x-Vs2[j])/Vt)-1)-Is+I0*(np.exp(x/n/Vt)-1);
return y
def weib(x, n, a):
return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)
def RECTE(
cRates,
tExp,
exptime=180,
trap_pop_s=0,
trap_pop_f=0,
dTrap_s=0,
dTrap_f=0,
dt0=0,
lost=0,
mode='scanning'
):
"""This function calculates HST/WFC3/IR ramp effect profile based on
the charge trapping explanation developed in Zhou et al. (2017).
:param cRates: intrinsic count rate of each exposures, unit: e/s
:type cRates: numpy.array
:param tExp: time stamps for the exposures, unit: seconds
:type tExp: numpy.array
:param exptime: (default 180 seconds) exposure time
:type exptime: numpy.array or float
:param trap_pop_s: (default 0) number of occupied slow population
charge traps before the very beginning of the observation
:type trap_pop_s: float or numpy.array
:param trap_pop_f: (default 0) number of occupied fast population
charge traps before the very beginning of the observation
:type trap_pop_f: float or numpy.array
:param dTrap_s: (default [0]) number of additional charges trapped
by slow population traps during earth occultation
:type dTrap_s: float or numpy.array
:param dTrap_f: (default [0]) number of additional charges trapped
by fast population traps during earth occultation
:type dTrap_f: float or numpy.array
:param dt0: (default 0) exposure time before the very beginning
of the observation. It could be due to guidence adjustment
:type dt0: float
:param lost: (default 0, no lost) fraction of trapped electrons that are
not eventually detected
:type lost: float
:param mode: (default scanning, scanning or staring, or others),
for scanning mode observation , the pixel no longer receive
photons during the overhead time, in staring mode,
the pixel keps receiving elctrons
:type mode: string
:returns: observed counts
:rtype: numpy.array
:Example:
see Examples and Cookbook
"""
nTrap_s = 1525.38
eta_trap_s = 0.013318
tau_trap_s = 1.63e4
nTrap_f = 162.38
eta_trap_f = 0.008407
tau_trap_f = 281.463
try:
dTrap_f = itertools.cycle(dTrap_f)
dTrap_s = itertools.cycle(dTrap_s)
dt0 = itertools.cycle(dt0)
except TypeError:
dTrap_f = itertools.cycle([dTrap_f])
dTrap_s = itertools.cycle([dTrap_s])
dt0 = itertools.cycle([dt0])
obsCounts = np.zeros(len(tExp))
trap_pop_s = min(trap_pop_s, nTrap_s)
trap_pop_f = min(trap_pop_f, nTrap_f)
for i in range(len(tExp)):
try:
dt = tExp[i+1] - tExp[i]
except IndexError:
dt = exptime
f_i = cRates[i]
c1_s = eta_trap_s * f_i / nTrap_s + 1 / tau_trap_s # a key factor
c1_f = eta_trap_f * f_i / nTrap_f + 1 / tau_trap_f
# number of trapped electron during one exposure
dE1_s = (eta_trap_s * f_i / c1_s - trap_pop_s) * \
(1 - np.exp(-c1_s * exptime))
dE1_f = (eta_trap_f * f_i / c1_f - trap_pop_f) * \
(1 - np.exp(-c1_f * exptime))
dE1_s = min(trap_pop_s + dE1_s, nTrap_s) - trap_pop_s
dE1_f = min(trap_pop_f + dE1_f, nTrap_f) - trap_pop_f
trap_pop_s = min(trap_pop_s + dE1_s, nTrap_s)
trap_pop_f = min(trap_pop_f + dE1_f, nTrap_f)
obsCounts[i] = f_i * exptime - dE1_s - dE1_f
if dt < 5 * exptime: # whether next exposure is in next batch of exposures
# same orbits
if mode == 'scanning':
# scanning mode, no incoming flux between exposures
dE2_s = - trap_pop_s * (1 - np.exp(-(dt - exptime)/tau_trap_s))
dE2_f = - trap_pop_f * (1 - np.exp(-(dt - exptime)/tau_trap_f))
elif mode == 'staring':
# for staring mode, there is flux between exposures
dE2_s = (eta_trap_s * f_i / c1_s - trap_pop_s) * \
(1 - np.exp(-c1_s * (dt - exptime)))
dE2_f = (eta_trap_f * f_i / c1_f - trap_pop_f) * \
(1 - np.exp(-c1_f * (dt - exptime)))
else:
# others, same as scanning
dE2_s = - trap_pop_s * (1 - np.exp(-(dt - exptime)/tau_trap_s))
dE2_f = - trap_pop_f * (1 - np.exp(-(dt - exptime)/tau_trap_f))
trap_pop_s = min(trap_pop_s + dE2_s, nTrap_s)
trap_pop_f = min(trap_pop_f + dE2_f, nTrap_f)
elif dt < 1200:
# considering in orbit download scenario
trap_pop_s = min(
trap_pop_s * np.exp(-(dt-exptime)/tau_trap_s), nTrap_s)
trap_pop_f = min(
trap_pop_f * np.exp(-(dt-exptime)/tau_trap_f), nTrap_f)
else:
# switch orbit
dt0_i = next(dt0)
trap_pop_s = min(trap_pop_s * np.exp(-(dt-exptime-dt0_i)/tau_trap_s) +
next(dTrap_s), nTrap_s)
trap_pop_f = min(trap_pop_f * np.exp(-(dt-exptime-dt0_i)/tau_trap_f) +
next(dTrap_f), nTrap_f)
f_i = cRates[i + 1]
c1_s = eta_trap_s * f_i / nTrap_s + 1 / tau_trap_s # a key factor
c1_f = eta_trap_f * f_i / nTrap_f + 1 / tau_trap_f
dE3_s = (eta_trap_s * f_i / c1_s - trap_pop_s) * \
(1 - np.exp(-c1_s * dt0_i))
dE3_f = (eta_trap_f * f_i / c1_f - trap_pop_f) * \
(1 - np.exp(-c1_f * dt0_i))
dE3_s = min(trap_pop_s + dE3_s, nTrap_s) - trap_pop_s
dE3_f = min(trap_pop_f + dE3_f, nTrap_f) - trap_pop_f
trap_pop_s = min(trap_pop_s + dE3_s, nTrap_s)
trap_pop_f = min(trap_pop_f + dE3_f, nTrap_f)
trap_pop_s = max(trap_pop_s, 0)
trap_pop_f = max(trap_pop_f, 0)
return obsCounts
# -*- coding: utf-8 -*- """ Created on Sun Apr 14 19:22:01 2019 @author: natur """ import numpy as np import matplotlib.pylab as plt import math import matplotlib t = np.linspace(0,10.0) x1 = 4*np.exp(-0.5*t)*np.sin(math.pi*t + math.pi/2) plt.title(u'4exp(-0.5t)cos(Πt)') plt.plot(t,x1)
times.append(t)
use_this_time = ((len(times) - 1) % opts.decimate) == 0
use_this_time &= time_sel(t, (len(times)-1) / opts.decimate)
if use_this_time:
plot_t['lst'].append(uv['lst'])
plot_t['jd'].append(t)
plot_t['cnt'].append((len(times)-1) / opts.decimate)
if not use_this_time: continue
#apply cal phases
if not opts.cal is None:
aa.set_jultime(t)
if not opts.src is None:
src.compute(aa)
d = aa.phs2src(d, src, i, j)
else:
d *= n.exp(-1j*n.pi*aa.get_phs_offset(i,j))
# Do delay transform if required
if opts.delay:
if opts.unmask:
d = d.data
ker = n.zeros_like(d)
ker[0] = 1.
gain = 1.
else:
flags = n.logical_not(d.mask).astype(n.float)
gain = n.sqrt(n.average(flags**2))
ker = n.fft.ifft(flags)
d = d.filled(0)
d = n.fft.ifft(d)
if not opts.clean is None and not n.all(d == 0):
d, info = a.deconv.clean(d, ker, tol=opts.clean)
def exponential_sine(t, amp, freq, growth, phase):
return amp * np.sin(2*np.pi*freq*t + phase) * np.exp(growth*t)
ub = scalar, upper bound of cake grid
size_w = integer, number of grid points in cake state space
w_grid = vector, size_w x 1 vector of cake grid points
------------------------------------------------------------------------
'''
lb = 10
ub = 15
size_c = 50
size_z = 50
c_grid = np.linspace(lb, ub, size_c)
z_grid, pi = ar1.addacooper(size_z, mu, rho, sigma_z)
z_grid = np.exp(z_grid)
prob_m = np.transpose(pi)
'''
------------------------------------------------------------------------
Create grid of current utility values
------------------------------------------------------------------------
C = matrix, current consumption (c=w-w')
U = matrix, current period utility value for all possible
choices of w and w' (rows are w, columns w')
------------------------------------------------------------------------
'''
C = np.zeros((size_c, size_c, size_c))
for i in range(size_c):
for j in range(size_c):
for k in range(size_c):
C[i, j, k] = z_grid[k] * c_grid[i]**alpha + (
def forward(self, x, t):
self.t = t
self.y = 1 / (1 + np.exp(-x))
loss = cross_entropy_error(np.c_[1 - self.y, self.y], t)
return loss
def sigmoid(in_x):
return 1.0 / (1 + np.exp(-in_x))
totalAll = 0.0
for a in range(2):
for b in range(2):
for c in range(2):
for d in range(2):
for e in range(2):
for f in range(2):
for g in range(2):
AllJointProb[a,b,c,d,e,f,g] = np.log(A[tuple([a])])
AllJointProb[a,b,c,d,e,f,g] += np.log(B[tuple([b, a])])
AllJointProb[a,b,c,d,e,f,g] += np.log(C[tuple([c, a, b, d])])
AllJointProb[a,b,c,d,e,f,g] += np.log(D[tuple([d, a])])
AllJointProb[a,b,c,d,e,f,g] += np.log(E[tuple([e, b, c, d])])
AllJointProb[a,b,c,d,e,f,g] += np.log(F[tuple([f, a, d, e])])
AllJointProb[a,b,c,d,e,f,g] += np.log(G[tuple([g, b, e])])
AllJointProb[a,b,c,d,e,f,g] = np.exp(AllJointProb[a,b,c,d,e,f,g])
totalAll += AllJointProb[a,b,c,d,e,f,g]
print totalAll
CEABF = np.zeros((2,2,2,2,2))
ABF = np.zeros((2,2,2))
CEGFABD = np.zeros((2,2,2,2,2,2,2))
ABD = np.zeros((2,2,2))
ABCDEFG = np.zeros((2,2,2,2,2,2,2))
EFG = np.zeros((2,2,2))
ACEFBG = np.zeros((2,2,2,2,2,2))
BG = np.zeros((2,2))
GBC = np.zeros((2,2,2))
BC = np.zeros((2,2))
BCDAE = np.zeros((2,2,2,2,2))
Fourier_array.append(f / (np.sqrt(N)))
return Fourier_array
x_min = -1.0
x_max = 1.0
sampling_rate_1 = 256
delta = (x_max - x_min) / (sampling_rate_1 - 1)
function_array = np.zeros(sampling_rate_1)
x_arr = np.zeros(sampling_rate_1)
for i in range(sampling_rate_1):
function_array[i] = 1
x_arr[i] = x_min + i * delta
nft = DFT(function_array)
karr = 2 * np.pi * np.fft.fftfreq(sampling_rate_1, d=delta)
fact = np.exp(-1j * karr * x_min)
aft = delta * np.sqrt(sampling_rate_1 / (2.0 * np.pi)) * fact * nft
fig1 = plt.subplots()
plt.plot(x_arr, function_array, 'r', label='The constant function')
plt.xlabel('x', fontsize=16)
plt.ylabel('f(x)', fontsize=16)
plt.grid(True)
fig2 = plt.subplots()
plt.plot(
karr,
aft,
'g',
label='The fourier transform of the constant function for sampling rate 1')
plt.xlabel('k', fontsize=16)
