def objective(pars,Z,ycovar):
"""The objective function"""
bcost= pars[0]
t= pars[1]
Pb= pars[2]
Xb= pars[3]
Yb= pars[4]
Zb= sc.array([Xb,Yb])
Vb1= sc.exp(pars[5])
Vb2= sc.exp(pars[6])
corr= pars[7]
V= sc.array([[Vb1,sc.sqrt(Vb1*Vb2)*corr],[sc.sqrt(Vb1*Vb2)*corr,Vb2]])
v= sc.array([-sc.sin(t),sc.cos(t)])
if Pb < 0. or Pb > 1.:
return -sc.finfo(sc.dtype(sc.float64)).max
if corr < -1. or corr > 1.:
return -sc.finfo(sc.dtype(sc.float64)).max
delta= sc.dot(v,Z.T)-bcost
sigma2= sc.dot(v,sc.dot(ycovar,v))
ndata= Z.shape[0]
detVycovar= sc.zeros(ndata)
deltaOUT= sc.zeros(ndata)
for ii in range(ndata):
detVycovar[ii]= m.sqrt(linalg.det(V+ycovar[:,ii,:]))
deltaOUT[ii]= sc.dot(Z[ii,:]-Zb,sc.dot(linalg.inv(V+ycovar[:,ii,:]),Z[ii,:]-Zb))
return sc.sum(sc.log((1.-Pb)/sc.sqrt(2.*m.pi*sigma2)*
sc.exp(-0.5*delta**2./sigma2)
+Pb/2./m.pi/detVycovar
*sc.exp(-0.5*deltaOUT)))
def __init__(self, renderer=True, realtime=True, ip="127.0.0.1", port="21560"):
# initialize base class
GraphicalEnvironment.__init__(self)
self.actLen=12
self.mySensors=sensors.Sensors(["EdgesReal"])
self.dists=array([20.0, sqrt(2.0)*20, sqrt(3.0)*20])
self.gravVect=array([0.0,-100.0,0.0])
self.centerOfGrav=zeros((1,3),float)
self.pos=ones((8,3),float)
self.vel=zeros((8,3),float)
self.SpringM = ones((8,8),float)
self.d=60.0
self.dt=0.02
self.startHight=10.0
self.dumping=0.4
self.fraktMin=0.7
self.fraktMax=1.3
self.minAkt=self.dists[0]*self.fraktMin
self.maxAkt=self.dists[0]*self.fraktMax
self.reset()
self.count=0
self.setEdges()
self.act(array([20.0]*12))
self.euler()
self.realtime=realtime
self.step=0
if renderer:
self.setRenderInterface(FlexCubeRenderInterface(ip, port))
self.getRenderInterface().updateData(self.pos, self.centerOfGrav)
def _initParams_fast(self): """ initialize the gp parameters 1) project Y on the known factor X0 -> Y0 average variance of Y0 is used to initialize the variance explained by X0 2) considers the residual Y1 = Y-Y0 (this equivals to regress out X0) 3) perform PCA on cov(Y1) and considers the first k PC for initializing X 4) the variance of all other PCs is used to initialize the noise 5) the variance explained by interaction is set to a small random number """ Xd = LA.pinv(self.X0) Y0 = self.X0.dot(Xd.dot(self.Y)) Y1 = self.Y-Y0 YY = SP.cov(Y1) S,U = LA.eigh(YY) X = U[:,-self.k:]*SP.sqrt(S[-self.k:]) a = SP.array([SP.sqrt(Y0.var(0).mean())]) b = 1e-3*SP.randn(1) c = SP.array([SP.sqrt((YY-SP.dot(X,X.T)).diagonal().mean())]) # gp hyper params params = limix.CGPHyperParams() if self.interaction: params['covar'] = SP.concatenate([a,X.reshape(self.N*self.k,order='F'),SP.ones(1),b]) else: params['covar'] = SP.concatenate([a,X.reshape(self.N*self.k,order='F')]) params['lik'] = c return params
def V_Multi(m, n):
x,y,z=(m[0],m[1],m[2])
a,b,c=(n[0],n[1],n[2])
p,q,r = (a-x,b-y,c-z)
return 90-degrees(acos( (x*p+y*q+z*r)/ (sqrt(x**2+y**2+z**2)*sqrt(p**2+q**2+r**2))))
def Rz_to_coshucosv(R,z,delta=1.):
"""
NAME:
Rz_to_coshucosv
PURPOSE:
calculate prolate confocal cosh(u) and cos(v) coordinates from R,z, and delta
INPUT:
R - radius
z - height
delta= focus
OUTPUT:
(cosh(u),cos(v))
HISTORY:
2012-11-27 - Written - Bovy (IAS)
"""
d12= (z+delta)**2.+R**2.
d22= (z-delta)**2.+R**2.
coshu= 0.5/delta*(sc.sqrt(d12)+sc.sqrt(d22))
cosv= 0.5/delta*(sc.sqrt(d12)-sc.sqrt(d22))
return (coshu,cosv)
def r_t_mat_anallo(an1, an2):
""" Returns R12, T12, R21, T21 at an interface between thin films.
R12 is the reflection matrix from Anallo 1 off Anallo 2
The sign of elements in T12 and T21 is fixed to be positive,
in the eyes of `numpy.sign`
"""
if len(an1.k_z) != len(an2.k_z):
raise ValueError, "Need the same number of plane waves in \
Anallos %(an1)s and %(an2)s" % {'an1' : an1, 'an2' : an2}
Z1 = an1.Z()
Z2 = an2.Z()
R12 = np.mat(np.diag((Z2 - Z1)/(Z2 + Z1)))
# N.B. there is potentially a branch choice problem here, stemming
# from the normalisation to unit flux.
# We normalise each field amplitude by
# $chi^{\pm 1/2} = sqrt(k_z/k)^{\pm 1} = sqrt(Z/Zc)^{\pm 1}$
# The choice of branch in those square roots must be the same as the
# choice in the related square roots that we are about to take:
T12 = np.mat(np.diag(2.*sqrt(Z2)*sqrt(Z1)/(Z2+Z1)))
R21 = -R12
T21 = T12
return R12, T12, R21, T21
def get_stderr_fit(f,Xdata,popt,pcov):
Y= f(Xdata, popt)
listdY=[]
for i in xrange(len(popt)):
p=popt[i]
dp= abs(p)/1e6+1e-20
popt[i]+=dp
Yi= f(Xdata, popt)
dY= (Yi-Y)/dp
listdY.append(dY)
popt[i]-=dp
listdY= scipy.array(listdY)
#list dy is the d in the derivation. it has N X M
#pcov is N X N
left= scipy.dot(listdY.T,pcov)
right=scipy.dot(left,listdY)
sigma2y= right.diagonal()
#sigma2y is a standard function of fit
mean_sigma2y= scipy.mean(right.diagonal())
M= Xdata.shape[0]
N= len(popt)
avg_stddev_data=scipy.sqrt(M*mean_sigma2y/N)
sigmay= scipy.sqrt(sigma2y)
return sigmay,avg_stddev_data
def test_covariate_shift(self):
n_sample = 100
# Biased training
var_bias = .5**2
mean_bias = .7
x_train = SP.random.randn(n_sample)*SP.sqrt(var_bias) + mean_bias
y_train = self.complete_sample(x_train)
# Unbiased test set
var = .3**2
mean = 0
x_test = SP.random.randn(n_sample)*SP.sqrt(var) + mean
x_complete = SP.hstack((x_train, x_test))
kernel = utils.getQuadraticKernel(x_complete, d=1) +\
10 * SP.dot(x_complete.reshape(-1, 1), x_complete.reshape(1, -1))
kernel = utils.scale_K(kernel)
kernel_train = kernel[SP.ix_(SP.arange(x_train.size),
SP.arange(x_train.size))]
kernel_test = kernel[SP.ix_(SP.arange(x_train.size, x_complete.size),
SP.arange(x_train.size))]
mf = MF(n_estimators=100, kernel=kernel_train, min_depth=0,
subsampling=False)
mf.fit(x_train.reshape(-1, 1), y_train.reshape(-1, 1))
response_gp = mf.predict(x_test.reshape(-1, 1), kernel_test, depth=0)
self.assertTrue(((response_gp - self.polynom(x_test))**2).sum() < 2.4)
def specular_incidence(self, pol = 'TE'):
""" Return a vector of plane wave amplitudes corresponding
to specular incidence in the specified polarisation.
i.e. all elements are 0 except the zeroth order.
"""
# Element corresponding to 0th order, TE
spec_TE = self.specular_order
# Element corresponding to 0th order, TM
spec_TM = self.specular_order + self.structure.num_pw_per_pol
tot_num_pw = self.structure.num_pw_per_pol * 2
inc_amp = np.mat(np.zeros(tot_num_pw, dtype='complex128')).T
if 'TE' == pol:
inc_amp[spec_TE] = 1
elif 'TM' == pol:
inc_amp[spec_TM] = 1
elif 'R Circ' == pol:
inc_amp[spec_TE] = 1/sqrt(2.)
inc_amp[spec_TM] = +1j/sqrt(2.)
elif 'L Circ' == pol:
inc_amp[spec_TE] = 1/sqrt(2.)
inc_amp[spec_TM] = -1j/sqrt(2.)
else:
raise NotImplementedError, \
"Must select from the currently implemented polarisations; \
TE, TM, R Circ, L Circ."
return inc_amp
def MakePulseDataRepLPC(pulse,spec,N,rep1,numtype = sp.complex128):
""" This will make data by assuming the data is an autoregressive process.
Inputs
spec - The properly weighted spectrum.
N - The size of the ar process used to model the filter.
pulse - The pulse shape.
rep1 - The number of repeats of the process.
Outputs
outdata - A numpy Array with the shape of the """
lp = len(pulse)
lenspec = len(spec)
r1 = scfft.ifft(scfft.ifftshift(spec))
rp1 = r1[:N]
rp2 = r1[1:N+1]
# Use Levinson recursion to find the coefs for the data
xr1 = sp.linalg.solve_toeplitz(rp1, rp2)
lpc = sp.r_[sp.ones(1), -xr1]
# The Gain term.
G = sp.sqrt(sp.sum(sp.conjugate(r1[:N+1])*lpc))
Gvec = sp.r_[G, sp.zeros(N)]
Npnt = (N+1)*3+lp
# Create the noise vector and normalize
xin = sp.random.randn(rep1, Npnt)+1j*sp.random.randn(rep1, Npnt)
xinsum = sp.tile(sp.sqrt(sp.mean(xin.real**2+xin.imag**2, axis=1))[:, sp.newaxis],(1, Npnt))
xin = xin/xinsum
outdata = sp.signal.lfilter(Gvec, lpc, xin, axis=1)
outpulse = sp.tile(pulse[sp.newaxis], (rep1, 1))
outdata = outpulse*outdata[:, 2*N:2*N+lp]
return outdata
def survival_function(loss_ratio, **kwargs):
"""
Static method that prepares the calculation parameters
to be passed to stats.lognorm.sf
:param loss_ratio: current loss ratio
:type loss_ratio: float
:param kwargs: convenience dictionary
:type kwargs: :py:class:`dict` with the following
keys:
**vf** - vulnerability function as provided by
:py:class:`openquake.shapes.VulnerabilityFunction`
**col** - matrix column number
"""
vuln_function = kwargs.get('vf')
position = kwargs.get('col')
vf_loss_ratio = vuln_function.loss_ratios[position]
stddev = vuln_function.covs[position] * vf_loss_ratio
variance = stddev ** 2.0
sigma = sqrt(log((variance / vf_loss_ratio ** 2.0) + 1.0))
mu = exp(log(vf_loss_ratio ** 2.0 /
sqrt(variance + vf_loss_ratio ** 2.0)))
return stats.lognorm.sf(loss_ratio, sigma, scale=mu)
def compute_continuous_prob_value(parameters, distribution, rvs):
mean = float(parameters[0])
stddev = float(parameters[1]) / 100 * mean
A = float(parameters[2])
B = float(parameters[3])
result = float("-inf")
if rvs is None:
while result <= A or result > B:
if distribution == "normal":
rvs = stats.norm.rvs
result = rvs(mean, stddev)
elif distribution == "lognormal":
variance = stddev ** 2.0
mu = log(mean ** 2.0 / sqrt(variance + mean ** 2.0))
sigma = sqrt(log((variance / mean ** 2.0) + 1.0))
rvs = stats.lognorm.rvs
result = rvs(sigma, scale=scipy.exp(mu))
elif distribution == "gamma":
betha = (stddev) ** 2 / mean
alpha = mean / betha
rvs = stats.gamma.rvs
result = rvs(alpha, scale=betha)
else:
result = 1
return result
def test_periodogram_csd():
"""Test corner cases of periodogram_csd"""
arsig1, _, _ = utils.ar_generator(N=1024)
arsig2, _, _ = utils.ar_generator(N=1024)
tseries = np.vstack([arsig1, arsig2])
Sk = np.fft.fft(tseries)
f1, c1 = tsa.periodogram_csd(tseries)
f2, c2 = tsa.periodogram_csd(tseries, Sk=Sk)
npt.assert_equal(c1, c2)
# Check that providing a complex signal does the right thing
# (i.e. two-sided spectrum):
N = 1024
r, _, _ = utils.ar_generator(N=N)
c, _, _ = utils.ar_generator(N=N)
arsig1 = r + c * scipy.sqrt(-1)
r, _, _ = utils.ar_generator(N=N)
c, _, _ = utils.ar_generator(N=N)
arsig2 = r + c * scipy.sqrt(-1)
tseries = np.vstack([arsig1, arsig2])
f, c = tsa.periodogram_csd(tseries)
npt.assert_equal(f.shape[0], N) # Should be N, not the one-sided N/2 + 1
def simulate_genotypes_w_ld(n, m, n_samples, m_ld_chunk_size=100, r2=0.9, validation = False): val_set_gen = [] val_set_D = [] for i in xrange(n_samples): snps = sp.zeros((m, n), dtype='float32') num_chunks = m / m_ld_chunk_size for chunk in xrange(num_chunks): X = sp.zeros((m_ld_chunk_size, n), dtype='float32') X[0] = stats.norm.rvs(size=n) for j in xrange(1, m_ld_chunk_size): X[j] = sp.sqrt(r2) * X[j - 1] + sp.sqrt(1 - r2) * stats.norm.rvs(size=n) start_i = chunk * m_ld_chunk_size stop_i = start_i + m_ld_chunk_size snps[start_i:stop_i] = X snps_means = sp.mean(snps, axis=1) snps_stds = sp.std(snps, axis=1) snps_means.shape = (m, 1) snps_stds.shape = (m, 1) snps = (snps - snps_means) / snps_stds val_set_gen.append(snps) if validation: val_set_D = 0 else: val_set_D.append(get_sample_D(n=n, m=m, num_sim=100, r2=r2)) if sp.isnan(val_set_gen).any(): return simulate_genotypes_w_ld(n, m, n_samples, m_ld_chunk_size=100, r2=0.9) return val_set_gen, val_set_D
def _getScalesDiag(self,termx=0):
"""
Internal function for parameter initialization
Uses 2 term single trait model to get covar params for initialization
Args:
termx: non-noise term terms that is used for initialization
"""
assert self.P>1, 'VarianceDecomposition:: diagonal init_method allowed only for multi trait models'
assert self.noisPos!=None, 'VarianceDecomposition:: noise term has to be set'
assert termx<self.n_randEffs-1, 'VarianceDecomposition:: termx>=n_randEffs-1'
assert self.trait_covar_type[self.noisPos] not in ['lowrank','block','fixed'], 'VarianceDecomposition:: diagonal initializaiton not posible for such a parametrization'
assert self.trait_covar_type[termx] not in ['lowrank','block','fixed'], 'VarianceDecimposition:: diagonal initializaiton not posible for such a parametrization'
scales = []
res = self._getH2singleTrait(self.vd.getTerm(termx).getK())
scaleg = sp.sqrt(res['varg'].mean())
scalen = sp.sqrt(res['varn'].mean())
for term_i in range(self.n_randEffs):
if term_i==termx:
_scales = scaleg*self.diag[term_i]
elif term_i==self.noisPos:
_scales = scalen*self.diag[term_i]
else:
_scales = 0.*self.diag[term_i]
if self.jitter[term_i]>0:
_scales = sp.concatenate((_scales,sp.array([sp.sqrt(self.jitter[term_i])])))
scales.append(_scales)
return sp.concatenate(scales)
def _Efficiency(self):
Gas = self.kwargs["entradaGas"]
Liquido = self.kwargs["entradaLiquido"]
rhoS = Gas.solido.rho
muG = Gas.Gas.mu
rhoL = Liquido.Liquido.rho
rendimiento_fraccional = []
if self.kwargs["modelo_rendimiento"] == 0:
# Modelo de Johnstone (1954)
l = sqrt(pi/8)*Gas.Gas.mu/0.4987445/sqrt(Gas.Gas.rho*Gas.P)
for dp in Gas.solido.diametros:
Kn = l/dp*2
C = Cunningham(l, Kn)
kp = C*rhoS*dp**2*self.Vg/9/Gas.Gas.mu/self.dd
penetration = exp(-self.k*self.R*kp**0.5)
rendimiento_fraccional.append(1-penetration)
elif self.kwargs["modelo_rendimiento"] == 1:
# Modelo de Calvert (1972)
l = sqrt(pi/8)*muG/0.4987445/sqrt(Gas.Gas.rho*Gas.P)
for dp in Gas.solido.diametros:
Kn = l/dp*2
C = Cunningham(l, Kn)
kp = C*rhoS*dp**2*self.Vg/9/muG/self.dd
b = (-0.7-kp*self.f+1.4*log((kp*self.f+0.7)/0.7)+0.49 /
(0.7+kp*self.f))
penetration = exp(self.R*self.Vg*rhoL*self.dd/55/muG*b/kp)
if penetration > 1:
penetration = 1
elif penetration < 0:
penetration = 0
rendimiento_fraccional.append(1-penetration)
return rendimiento_fraccional
def get_stderr_fit(f,Xdata,popt,pcov): Y=f(Xdata,popt) listdY=[] for i in xrange(len(popt)): p=popt[i] dp=abs(p)/1e6+1e-20 popt[i]+=dp Yi=f(Xdata,popt) dY=(Yi-Y)/dp listdY.append(dY) popt[i]-=dp listdY=scipy.array(listdY) #listdY is an array with N rows and M columns, N=len(popt), M=len(xdata[0]) #pcov is an array with N rows and N columns left=scipy.dot(listdY.T,pcov) #left is an array of M rows and N columns right=scipy.dot(left,listdY) #right is an array of M rows and M columns sigma2y=right.diagonal() #sigma2y is standard error of fit and function of X mean_sigma2y=scipy.mean(right.diagonal()) M=Xdata.shape[1];print M N=len(popt);print N avg_stddev_data=scipy.sqrt(M*mean_sigma2y/N) #this is because if exp error is constant at sig_dat,then mean_sigma2y=N/M*sig_dat**2 sigmay=scipy.sqrt(sigma2y) return sigmay,avg_stddev_data
def __init__(self, render=True, realtime=True, ip="127.0.0.1", port="21560"):
# initialize base class
self.render = render
if self.render:
self.updateDone = True
self.updateLock = threading.Lock()
self.server = UDPServer(ip, port)
self.actLen = 12
self.mySensors = sensors.Sensors(["EdgesReal"])
self.dists = array([20.0, sqrt(2.0) * 20, sqrt(3.0) * 20])
self.gravVect = array([0.0, -100.0, 0.0])
self.centerOfGrav = zeros((1, 3), float)
self.pos = ones((8, 3), float)
self.vel = zeros((8, 3), float)
self.SpringM = ones((8, 8), float)
self.d = 60.0
self.dt = 0.02
self.startHight = 10.0
self.dumping = 0.4
self.fraktMin = 0.7
self.fraktMax = 1.3
self.minAkt = self.dists[0] * self.fraktMin
self.maxAkt = self.dists[0] * self.fraktMax
self.reset()
self.count = 0
self.setEdges()
self.act(array([20.0] * 12))
self.euler()
self.realtime = realtime
self.step = 0
def f(self,x,t):
N = len(x)/2
xdot = pl.array([])
# modulus the x for periodicity.
x[N:2*N]= x[N:2*N]%self.d
# HERE ---->> 1Dify
for i in range(N):
temp = 0.0
for j in range(N):
if i == j:
continue
#repulsive x interparticle force of j on i
temp += self.qq*(x[N+i]-x[N+j])/(pl.sqrt((x[N+i]-x[N+j])**2)**3)
# Add the forces from the two ancored charges
# First one at x=0
temp += self.qq*(x[N+i]-0.0)/(pl.sqrt((x[N+i]-0.0)**2)**3)
# Second one at the other boundary i.e. self.d
temp += self.qq*(x[N+i]-self.d)/(pl.sqrt((x[N+i]-self.d)**2)**3)
# periodic force on particle i
temp += self.As[i]*pl.sin(x[N+i])*pl.cos(t)
temp -= self.beta*x[i]
xdot = pl.append(xdot,temp)
for i in range(N):
xdot = pl.append(xdot,x[i])
return xdot
def relative_bin_deviation(h1, h2): # 79 us @array, 104 us @list \w 100 bins
r"""
Calculate the bin-wise deviation between two histograms.
The relative bin deviation between two histograms :math:`H` and :math:`H'` of size
:math:`m` is defined as:
.. math::
d_{rbd}(H, H') = \sum_{m=1}^M
\frac{
\sqrt{(H_m - H'_m)^2}
}{
\frac{1}{2}
\left(
\sqrt{H_m^2} +
\sqrt{{H'}_m^2}
\right)
}
*Attributes:*
- semimetric (triangle equation satisfied?)
*Attributes for normalized histograms:*
- :math:`d(H, H')\in[0, \infty)`
- :math:`d(H, H) = 0`
- :math:`d(H, H') = d(H', H)`
*Attributes for not-normalized histograms:*
- :math:`d(H, H')\in[0, \infty)`
- :math:`d(H, H) = 0`
- :math:`d(H, H') = d(H', H)`
*Attributes for not-equal histograms:*
- not applicable
Parameters
----------
h1 : sequence
The first histogram.
h2 : sequence
The second histogram, same bins as ``h1``.
Returns
-------
relative_bin_deviation : float
Relative bin deviation between the two histograms.
"""
h1, h2 = __prepare_histogram(h1, h2)
numerator = scipy.sqrt(scipy.square(h1 - h2))
denominator = (scipy.sqrt(scipy.square(h1)) + scipy.sqrt(scipy.square(h2))) / 2.
old_err_state = scipy.seterr(invalid='ignore') # divide through zero only occurs when the bin is zero in both histograms, in which case the division is 0/0 and leads to (and should lead to) 0
result = numerator / denominator
scipy.seterr(**old_err_state)
result[scipy.isnan(result)] = 0 # faster than scipy.nan_to_num, which checks for +inf and -inf also
return scipy.sum(result)
def xyz2longlat(x,y,z):
""" converts cartesian x,y,z coordinates into spherical longitude and latitude """
r = sc.sqrt(x*x + y*y + z*z)
long = sc.arctan2(y,x)
d = sc.sqrt(x*x + y*y)
lat = sc.arcsin(z/r)
return long*deg, lat*deg, r
def generate_test_data_w_sum_stats(h2=0.5, n=100000, n_sample=100, m=50000, model='gaussian',
p=1.0, conseq_r2=0, m_ld_chunk_size=100):
"""
Generate
"""
#Get LD sample matrix
D_sample = genotypes.get_sample_D(200,conseq_r2=conseq_r2,m=m_ld_chunk_size)
#Simulate beta_hats
ret_dict = simulate_beta_hats(h2=h2, n=n, n_sample=n_sample, m=m, model=model, p=p,
conseq_r2=conseq_r2, m_ld_chunk_size=m_ld_chunk_size, D_sample=D_sample)
#Simulate test genotypes
test_snps = genotypes.simulate_genotypes_w_ld(n_sample=n_sample, m=m, conseq_r2=conseq_r2,
m_ld_chunk_size=m_ld_chunk_size)
ret_dict['test_snps'] = test_snps
#Simulate test phenotypes
phen_noise = stats.norm.rvs(0, sp.sqrt(1.0 - h2), size=n_sample)
phen_noise = sp.sqrt((1.0 - h2) / sp.var(phen_noise)) * phen_noise
genetic_part = sp.dot(test_snps.T, ret_dict['betas'])
genetic_part = sp.sqrt(h2 / sp.var(genetic_part)) * genetic_part
test_phen = genetic_part + phen_noise
ret_dict['test_phen'] = test_phen
return ret_dict
def drazin(A, tol):
CB = A.copy()
Bs = []
Cs = []
k = 1
while not (sp.absolute(CB) < tol).all() and sp.absolute(la.det(CB)) < tol:
U, s, Vh = la.svd(CB)
S = sp.diag(s)
S = S * (S > tol)
r = sp.count_nonzero(S)
B = sp.dot(U, sp.sqrt(S))
C = sp.dot(sp.sqrt(S), Vh)
B = B[:, 0:r]
Bs.append(B)
C = C[0:r, :]
Cs.append(C)
CB = sp.dot(C, B)
k += 1
D = sp.eye(A.shape[0])
for B in Bs:
D = sp.dot(D, B)
if (sp.absolute(CB) < tol).all():
D = sp.dot(D, CB)
else:
D = sp.dot(D, np.linalg.matrix_power(CB, -(k + 1)))
for C in reversed(Cs):
D = sp.dot(D, C)
return D
def _genBgTerm_fromXX(self,vTot,vCommon,XX,a=None,c=None):
"""
generate background term from SNPs
Args:
vTot: variance of Yc+Yi
vCommon: variance of Yc
XX: kinship matrix
a: common scales, it can be set for debugging purposes
c: indipendent scales, it can be set for debugging purposes
"""
vSpecific = vTot-vCommon
SP.random.seed(0)
if c==None: c = SP.randn(self.P)
XX += 1e-3 * SP.eye(XX.shape[0])
L = LA.cholesky(XX,lower=True)
# common effect
R = self.genWeights(self.N,self.P)
A = self.genTraitEffect()
if a is not None: A[0,:] = a
Yc = SP.dot(L,SP.dot(R,A))
Yc*= SP.sqrt(vCommon)/SP.sqrt(Yc.var(0).mean())
# specific effect
R = SP.randn(self.N,self.P)
Yi = SP.dot(L,SP.dot(R,SP.diag(c)))
Yi*= SP.sqrt(vSpecific)/SP.sqrt(Yi.var(0).mean())
return Yc, Yi
def _sampling_matrix(hessian, cutoff=0, temperature=1, step_scale=1):
# basically need SVD of hessian - singular values and eigenvectors
# hessian = u * diag(singVals) * vh
u, sing_vals, vh = scipy.linalg.svd(0.5 * hessian)
# scroll through the singular values and find the ones whose inverses will
# be huge and set them to zero also, load up the array of singular values
# that we store
# cutoff = (1.0/_.singVals[0])*1.0e03
# double cutoff = _.singVals[0]*1.0e-02
cutoff_sing_val = cutoff * max(sing_vals)
D = 1.0/scipy.maximum(sing_vals, cutoff_sing_val)
## now fill in the sampling matrix ("square root" of the Hessian)
## note that sqrt(D[i]) is taken here whereas Kevin took sqrt(D[j])
## this is because vh is the transpose of his PT -JJW
samp_mat = scipy.transpose(vh) * scipy.sqrt(D)
# Divide the sampling matrix by an additional factor such
# that the expected quadratic increase in cost will be about 1.
cutoff_vals = scipy.compress(sing_vals < cutoff_sing_val, sing_vals)
if len(cutoff_vals):
scale = scipy.sqrt(len(sing_vals) - len(cutoff_vals)
+ sum(cutoff_vals)/cutoff_sing_val)
else:
scale = scipy.sqrt(len(sing_vals))
samp_mat /= scale
samp_mat *= step_scale
samp_mat *= scipy.sqrt(temperature)
return samp_mat
def ZYFF(Te, EIJ):
"""Computes `ZY` and `FF`, used in other functions.
If `EIJ` is a scalar, the output has the same shape as `Te`. If `EIJ` is an
array, the output has shape `EIJ.shape` + `Te.shape`. This should keep the
output broadcastable with `Te`.
Parameters
----------
Te : array of float
Electron temperature. Shape is arbitrary.
EIJ : scalar float or array of float
Energy difference.
"""
# Expand the dimensions of EIJ to produce the desired output shape:
Te = scipy.asarray(Te, dtype=float)
EIJ = scipy.asarray(EIJ, dtype=float)
for n in xrange(Te.ndim):
EIJ = scipy.expand_dims(EIJ, axis=-1)
ZY = EIJ / (1e3 * Te)
FF = scipy.zeros_like(ZY)
mask = (ZY >= 1.5)
FF[mask] = scipy.log((ZY[mask] + 1) / ZY[mask]) - (0.36 + 0.03 * scipy.sqrt(ZY[mask] + 0.01)) / (ZY[mask] + 1)**2
mask = ~mask
FF[mask] = scipy.log((ZY[mask] + 1) / ZY[mask]) - (0.36 + 0.03 / scipy.sqrt(ZY[mask] + 0.01)) / (ZY[mask] + 1)**2
return ZY, FF
def test_gets_thermal_with_correlated(self):
"""Checks that the part of the freq_modes code that compensates the
thermal for mode subtraction works."""
self.data *= sp.sqrt(self.bw * 2) # Makes thermal unity.
# Need to add something correlated so the modes arn't just the
# channels.
correlated_overf = noise_power.generate_overf_noise(1,
-2, 0.5, self.dt, self.data.shape[0])
correlated_overf += (rand.normal(size=(self.data.shape[0],))
* sp.sqrt((self.bw * 2) * 0.3))
self.data += correlated_overf[:,None,None,None] / sp.sqrt(self.nf)
Blocks = self.make_blocks()
# Mask a channel out completly.
for Data in Blocks:
Data.data[:,:,:,3] = ma.masked
model = 'freq_modes_over_f_4' # Take out 20% of the thermal power.
parameters = mn.measure_noise_parameters(Blocks,
[model])
right_ans = sp.ones(self.nf)
right_ans[3] = T_infinity**2
for p in parameters.itervalues():
pars = p[model]
thermal = pars['thermal']
self.assertTrue(sp.allclose(thermal,
right_ans, rtol=0.3))
mean_thermal = sp.mean(thermal[right_ans==1])
self.assertTrue(sp.allclose(mean_thermal, 1, rtol=0.05))
self.assertTrue(sp.allclose(pars['over_f_mode_0']['thermal'],
0.3, atol=0.1))
def ndot_product(features1,
features2 = None):
"""
generates kernel based on normalized dot product
input :
features1 : vectors representing the rows in the matrix
features2 : vectors representing the columns in the matrix
output :
out : similarity matrix
"""
features1.shape = features1.shape[0], -1
features1 = features1/sp.sqrt((features1**2.).sum(1))[:, None]
if features2 is None:
features2 = features1
else:
features2.shape = features2.shape[0], -1
features2 = features2/sp.sqrt((features2**2.).sum(1))[:, None]
out = sp.dot(features1, features2.T)
return out
def heart(scale,ndim,time):
percent = 1.05 + 0.5*np.random.rand()
real_heart = int(time*percent)
ratio = 0.5*np.random.rand() #xy ratio
x = scipy.linspace(-2,2,real_heart/2)
y1 = scipy.sqrt(1-(abs(x)-1)**2)
y2 = -3*scipy.sqrt(1-(abs(x[::-1])/2)**0.5)
Y = np.concatenate([y1,y2])
X = ratio*np.concatenate([x,x[::-1]])
shift = np.random.randint(0,real_heart)
Y = np.roll(Y,shift)[:time]
X = np.roll(X,shift)[:time]
traj = np.array([X,Y,np.zeros_like(Y)]).T
alpha = 2*3.14 * np.random.rand()
if ndim == 2:
traj = traj[::,:2]
noise = diffusive(scale/800.,ndim,time+1,epsilon=1e-7)
return scale*random_rot(traj,alpha,ndim) + noise[:-1]-noise[1:]
def pix2sky(header,x,y): hdr_info = parse_header(header) x0 = x-hdr_info[1][0]+1. # Plus 1 python->image y0 = y-hdr_info[1][1]+1. x0 = x0.astype(scipy.float64) y0 = y0.astype(scipy.float64) x = hdr_info[2][0,0]*x0 + hdr_info[2][0,1]*y0 y = hdr_info[2][1,0]*x0 + hdr_info[2][1,1]*y0 if hdr_info[3]=="DEC": a = x.copy() x = y.copy() y = a.copy() ra0 = hdr_info[0][1] dec0 = hdr_info[0][0]/raddeg else: ra0 = hdr_info[0][0] dec0 = hdr_info[0][1]/raddeg if hdr_info[5]=="TAN": r_theta = scipy.sqrt(x*x+y*y)/raddeg theta = arctan(1./r_theta) phi = arctan2(x,-1.*y) elif hdr_info[5]=="SIN": r_theta = scipy.sqrt(x*x+y*y)/raddeg theta = arccos(r_theta) phi = artan2(x,-1.*y) ra = ra0 + raddeg*arctan2(-1.*cos(theta)*sin(phi-pi), sin(theta)*cos(dec0)-cos(theta)*sin(dec0)*cos(phi-pi)) dec = raddeg*arcsin(sin(theta)*sin(dec0)+cos(theta)*cos(dec0)*cos(phi-pi)) return ra,dec
def plotRatioWav(self, inputfilename, no_peak=False):
'''
Plot ratios as a function of their central wavelength.
In blue and green, the peak-to-peak ratios are plotted. Blue for normal
peak-to-peak ratios, green for ratios that involve a data point that is
in the noise. Plotting peak-to-peak ratios can be turned off with the
no_peak keyword.
In red and magenta, the integrated line strengths are plotted. Red for
isolated lines that are not tagged as a blend, magenta for lines that
are tagged as a blend due to 1) too wide lines with respect to the PACS
resolution, or 2) multiple sample transitions in the width of an
observed line.
@param inputfilename: the input filename for the grid, which will be
attached to the final plot filename
@type inputfilename: string
@keyword no_peak: Hide the peak ratios.
(default: False)
@type no_peak: bool
'''
if not self.chi2_inttot:
print "No Sphinx models calculated. Aborting statistics plot. "
return
this_grid = self.sortStarGrid()
plot_filenames = []
inst = self.instrument
for star in this_grid:
this_id = star['LAST_%s_MODEL' % inst.instrument.upper()]
lp = []
waves = []
ratios = []
ratios_err = []
#-- the ratios included in the statistics
if not no_peak:
this_wav_inc = self.getRatios(data_type='central_mwav',\
this_id=this_id)
this_ratio_inc = self.getRatios(this_id=this_id)
if list(this_wav_inc):
waves.append(this_wav_inc)
ratios.append(this_ratio_inc)
ratios_err.append(None)
lp.append('ob')
#-- ratios replaced by lower limits if data point is in the noise
# ie data point can only be smaller than or equal to used value
this_wav_lower = self.getRatios(data_type='central_mwav',\
this_id=this_id,\
return_negative=1)
this_ratio_lower = self.getRatios(return_negative=1,\
this_id=this_id)
this_ratio_lower = [abs(r) for r in this_ratio_lower]
if list(this_wav_lower):
waves.append(this_wav_lower)
ratios.append(this_ratio_lower)
ratios_err.append(None)
lp.append('dg')
if not inst.linefit is None:
#-- If integrated intensities are available for the instrument, get
# the integrated intensity ratios
this_wav_int = self.getRatios(sel_type='int_ratios',\
data_type='central_mwav',\
this_id=this_id)
this_ratio_int = self.getRatios(sel_type='int_ratios',\
data_type='int_ratios',\
this_id=this_id)
this_ratio_int_err = self.getRatios(sel_type='int_ratios',\
data_type='int_ratios_err',\
this_id=this_id)
if list(this_wav_int):
waves.append(this_wav_int)
ratios.append(this_ratio_int)
ratios_err.append(this_ratio_int_err)
lp.append('or')
#-- Get the ratios that are lower limits due to line blends.
# Line blends detected due to fitted FHWM/PACS FHWM > 120%
# ie model int can only be larger than or equal to used value
this_wav_lowerint = self.getRatios(sel_type='int_ratios',\
data_type='central_mwav',\
this_id=this_id,\
return_negative=1)
this_ratio_lowerint = self.getRatios(sel_type='int_ratios',\
data_type='int_ratios',\
this_id=this_id,\
return_negative=1)
this_ratio_lowerint_err = self.getRatios(sel_type='int_ratios',\
data_type='int_ratios_err',\
this_id=this_id,\
return_negative=1)
this_ratio_lowerint = [abs(r) for r in this_ratio_lowerint]
if list(this_wav_lowerint):
waves.append(this_wav_lowerint)
ratios.append(this_ratio_lowerint)
ratios_err.append(this_ratio_lowerint_err)
lp.append('dm')
#- prepping input for the plot command
xmin = min([min(x) for x in waves])
xmax = max([max(x) for x in waves])
waves.extend([[0.5 * xmin, 1.5 * xmax]] * 3)
ratios.extend([[1,1],\
[1-inst.absflux_err,\
1-inst.absflux_err],\
[1+inst.absflux_err,\
1+inst.absflux_err]])
ratios_err.extend([None, None, None])
lp.extend(['-k', '--k', '--k'])
plot_filename = os.path.join(getattr(cc.path,self.code.lower()),\
self.path_code,'stars',\
self.star_name,\
'%s_results_'%inst.instrument+\
'ratio_wav_%s'%str(this_id))
labels = [('Mdot = %.2e Msolar/yr'%star['MDOT_GAS'],0.05,0.05),\
('Teff = %.1f K'%star['T_STAR'],0.05,0.1),\
('$\psi$ = %0.2e'%star['DUST_TO_GAS_CHANGE_ML_SP'],0.05,\
0.15),\
('A$_{H_2O}$/A$_{H_2}$ = %0.2e'%star['F_H2O'],0.05,0.2),\
('R$_(o,H_2O)$ = %i'%int(star['R_OUTER_H2O']),0.05,0.25)]
if star.getMolecule('1H1H16O') \
and star.getMolecule('1H1H16O').set_keyword_change_abundance:
labels.append(('$H_2O$ profile = %s'\
%os.path.split(star.getMolecule('1H1H16O')\
.change_fraction_filename\
.replace('_','\_'))[1],\
0.05,0.30))
plot_title = '%s: $\chi^2_\mathrm{con}$ %.4f'\
%(str(this_id).replace('_','\_'),\
self.chi2_con[this_id])
if self.chi2_inttot[this_id]:
plot_title += ', $\chi^2_\mathrm{int}$ %.4f'\
%(self.chi2_inttot[this_id])
plot_filenames.append(Plotting2.plotCols(\
filename=plot_filename,x=waves,y=ratios,yerr=ratios_err,\
yaxis=r'$F_{\nu,p,m}/F_{\nu,p,d}$',\
plot_title=plot_title,labels=labels,extension='pdf',\
xlogscale=0,ylogscale=1,line_types=lp,xmin=xmin*0.9,\
xmax=xmax*1.03,figsize=(10.*scipy.sqrt(2.), 10.),\
linewidth=2,fontsize_title=20,fontsize_label=16))
inputf_short = os.path.splitext(os.path.split(inputfilename)[1])[0]
new_filename = os.path.join(getattr(cc.path,self.code.lower()),\
self.path_code,'stars',self.star_name,\
'%s_results_'%inst.instrument+\
'ratio_wav_%s.pdf'%inputf_short)
DataIO.joinPdf(old=plot_filenames, new=new_filename)
print '** Stat plots can be found at:'
print new_filename
print '***********************************'
def _evaluate(self, x, t=0.):
return self._K * (sc.sqrt(x**2. + self._D2) -
self._D) + self._F * x**2.
def mse(y_test, y):
return sp.sqrt(sp.mean((y_test - y)**2))
def parspar(n):
i = n/ndim
j = n%ndim
data = cubo[:,i,j]
datamax = data.max()
noise_level = 0
noise = sp.random.normal(scale=noise_level,size=len(data))
data = data+ruido
if (i-int(ndim/2.))**2 + (j-int(ndim/2.))**2 > r**2 or 0.4*cubomax>datamax:
return [None]
print i,j
m0 = sp.integrate.simps(data,nu)
m1 = sp.integrate.simps(velocities*data, nu)/m0
mom2[i,j] = sp.integrate.simps(data*(velocities-m1)**2, nu)*1000/m0
datamin = data.min()
data1 = data -data.min()
centroid = (nu*(cubo[:,i,j]-datamin)).sum()/(cubo[:,i,j]-datamin).sum()
i0 = datamin
if i0==0:
i0=1e-10
i0_lim=(0.5*i0,1.2*i0)
r_ij = sp.sqrt((i-128)**2 +(j-128)**2)
rho_ij = r_ij/sp.cos(incli)
if rho_ij<30:
temp_0 = 70
tlim = (10,200)
else:
temp_0 = 70 * (r_ij / 30.)**(-0.5)
tlim = (10,120)
vels = (nu-nu0)*3e5/nu0
velg = vels[data==data.max()][0]
noise = data[(velocities<velg-1) | (velocities>velg+1.)]
rms = np.sqrt(sp.sum(noise**2)/float(len(noise)))
## Cont=True Fit lines considering the presence of continuum.
if cont:
line_model = pm.Model()
with line_model:
var = ['Temp','nu_c','log(N_CO)','v_turb','Continuum']
# Priors for unknown model parameters
Temp = pm.TruncatedNormal('Temp', mu=temp_0, sd=5, lower=tlim[0], upper=tlim[1])
nu_c = pm.TruncatedNormal('nu_c', mu=centroid, sd=abs(dnu)/10., lower=centroid-0.5*abs(dnu), upper=centroid+0.5*abs(dnu))
NCO = pm.Uniform('log(N_CO)', lower=10, upper=24)
v_turb = pm.Uniform('v_turb', lower=sp.sqrt(k*tlim[0]/m), upper=300000) ## This is really broadening in velocity space, not turbulent vel.
i_0 = pm.TruncatedNormal('Continuum', mu=i0, sd=5, lower=i0_lim[0], upper=i0_lim[1])
# Expected value of outcome
predict = intensity_continuum(nu, Temp, nu_c, alpha, 10**NCO, v_turb, angle, i_0, head, iso)
# Likelihood (sampling distribution) of observations
Y_obs = pm.Normal('Y_obs', mu=predict, sd=rms, observed=data)
step = pm.NUTS()
st = {'Temp':temp_0,
'nu_c':centroid,
'log(N_CO)':20,
'v_turb':20000,
'Continuum':i0}
trace = pm.sample(5000,tune=1000,cores=2,step=step,start=st)
stats = pm.summary(trace)
mean_pars = [stats['mean'][x] for x in var]
hpd_2_5 = [stats['hpd_2.5'][x] for x in var]
hpd_97_5 = [stats['hpd_2.5'][x] for x in var]
var_std = [stats['sd'][x] for x in var]
medians_pars = [sp.median(trace[x]) for x in var]
Map = [float(pm.find_MAP(model=line_model)[x]) for x in var]
fit = mean_pars
model = intensity_continuum(nu, fit[0], fit[1],alpha, 10**fit[2], fit[3], angle,fit[4], head, iso)
else:
line_model = pm.Model()
with line_model:
var = ['Temp','nu_c','log(N_CO)','v_turb']
# Priors for unknown model parameters
Temp = pm.TruncatedNormal('Temp', mu=temp_0, sd=5, lower=tlim[0], upper=tlim[1])
nu_c = pm.TruncatedNormal('nu_c', mu=centroid, sd=abs(dnu)/10., lower=centroid-0.5*abs(dnu), upper=centroid+0.5*abs(dnu))
NCO = pm.Uniform('log(N_CO)', lower=10, upper=24)
v_turb = pm.Uniform('v_turb', lower=sp.sqrt(k*tlim[0]/m), upper=300000) ## This is really broadening in velocity space, not turbulent vel.
# Expected value of outcome
predict = intensity(nu, Temp, nu_c, 10**NCO, v_turb, angle, head, iso)
# Likelihood (sampling distribution) of observations
Y_obs = pm.Normal('Y_obs', mu=predict, sd=rms, observed=data)
step = pm.NUTS()
st = {'Temp':temp_0,
'nu_c':centroid,
'log(N_CO)':20,
'v_turb':20000}
trace = pm.sample(5000,tune=1000,cores=2,step=step,start=st)
stats = pm.summary(trace)
mean_pars = [stats['mean'][x] for x in var]
hpd_2_5 = [stats['hpd_2.5'][x] for x in var]
hpd_97_5 = [stats['hpd_2.5'][x] for x in var]
var_std = [stats['sd'][x] for x in var]
medians_pars = [sp.median(trace[x]) for x in var]
Map = [float(pm.find_MAP(model=line_model)[x]) for x in var]
fit = mean_pars
model = intensity(nu, fit[0], fit[1], 10**fit[2], fit[3], angle, head, iso)
Temperature[i,j,:] = sp.array([fit[0],var_std[0],medians_pars[0],Map[0],hpd_2_5[0],hpd_2_5[0]])
Denscol[i,j,:] = sp.array([10**fit[2],10**fit[2]*sp.log(10)*var_std[2],10**medians_pars[2],10**Map[2],10**hpd_2_5[2],10**hpd_2_5[2]])
Turbvel[i,j,:] = sp.sqrt(((sp.array([fit[3],var_std[3],medians_pars[3],Map[3],hpd_2_5[3],hpd_2_5[3]]))**2 - k*fit[0]/m))*1e-5
aux_nu = sp.array([fit[1],var_std[1],medians_pars[1],Map[1],hpd_2_5[1],hpd_2_5[1]])
vel_cen[i,j,:] = sp.around(((nu0-aux_nu)*c*1e-5/nu0))
return [i,j,Temperature[i,j,:], Denscol[i,j,:], Turbvel[i,j,:],vel_cen[i,j,:]]
# Isotopologue image and centroid map
cubo, head = datafits(image)
dnu = head['CDELT3']
len_nu = head['NAXIS3']
nui = head['CRVAL3']- head['CRPIX3']*dnu
nuf = nui + (len_nu-1)*dnu
nu = sp.linspace(nui, nuf, len_nu)
nu0 = sp.mean(nu)
#Gaussian Convolution
if False:
resol = abs(head['CDELT1'])*3600
stdev = Beam / (2 * sp.sqrt (2 * sp.log(2)))
stdev /= resol
x_size = int(8*stdev + 1.)
print 'convolution with gaussian'
print '\tbeam '+str(Beam)+' arcsec'
print '\tbeam '+str(stdev)+' pixels'
# circular Gaussian
beam = Gaussian2DKernel (stddev = stdev, x_size = x_size, y_size = x_size,
model ='integrate')
smooth = np.zeros((80, 256, 256))
for k in range(80):
smooth[k, :,:] += convolve_fft(cubo[k,:,:], beam)
print '\tsmoothed'
cubo = smooth
def psi_n(n, x):
psi0 = 0
for m in range(100):
psi0 += sqrt(2 / L) * psi[n][m] * sin(pi * (m + 1) * x / L)
return psi0
def main():
(sensdict,simparams) = readconfigfile(inifile)
simdtype = simparams['dtype']
sumrule = simparams['SUMRULE']
npts = simparams['numpoints']
amb_dict = simparams['amb_dict']
# for spectrum
ISS2 = ISRSpectrum(centerFrequency = 440.2*1e6, bMag = 0.4e-4, nspec=npts, sampfreq=sensdict['fs'],dFlag=True)
ti = 2e3
te = 2e3
Ne = 1e11
Ni = 1e11
datablock90 = sp.array([[Ni,ti],[Ne,te]])
species = simparams['species']
(omega,specorig,rcs) = ISS2.getspecsep(datablock90, species,rcsflag = True)
cur_filt = sp.sqrt(scfft.ifftshift(specorig*npts*npts*rcs/specorig.sum()))
#for data
Nrep = 10000
pulse = sp.ones(14)
lp_pnts = len(pulse)
N_samps = 100
minrg = -sumrule[0].min()
maxrg = N_samps+lp_pnts-sumrule[1].max()
Nrng2 = maxrg-minrg;
out_data = sp.zeros((Nrep,N_samps+lp_pnts),dtype=simdtype)
samp_num = sp.arange(lp_pnts)
for isamp in range(N_samps):
cur_pnts = samp_num+isamp
cur_pulse_data = MakePulseDataRep(pulse,cur_filt,rep=Nrep)
out_data[:,cur_pnts] = cur_pulse_data+out_data[:,cur_pnts]
lagsData = CenteredLagProduct(out_data,numtype=simdtype,pulse =pulse)
lagsData=lagsData/Nrep # divide out the number of pulses summed
Nlags = lagsData.shape[-1]
lagsDatasum = sp.zeros((Nrng2,Nlags),dtype=lagsData.dtype)
for irngnew,irng in enumerate(sp.arange(minrg,maxrg)):
for ilag in range(Nlags):
lagsDatasum[irngnew,ilag] = lagsData[irng+sumrule[0,ilag]:irng+sumrule[1,ilag]+1,ilag].mean(axis=0)
lagsDatasum=lagsDatasum/lp_pnts # divide out the pulse length
(tau,acf) = spect2acf(omega,specorig)
# apply ambiguity function
tauint = amb_dict['Delay']
acfinterp = sp.zeros(len(tauint),dtype=simdtype)
acfinterp.real =spinterp.interp1d(tau,acf.real,bounds_error=0)(tauint)
acfinterp.imag =spinterp.interp1d(tau,acf.imag,bounds_error=0)(tauint)
# Apply the lag ambiguity function to the data
guess_acf = sp.zeros(amb_dict['Wlag'].shape[0],dtype=sp.complex128)
for i in range(amb_dict['Wlag'].shape[0]):
guess_acf[i] = sp.sum(acfinterp*amb_dict['Wlag'][i])
# pdb.set_trace()
guess_acf = guess_acf*rcs/guess_acf[0].real
# fit to spectrums
spec_interm = scfft.fftshift(scfft.fft(guess_acf,n=npts))
spec_final = spec_interm.real
allspecs = scfft.fftshift(scfft.fft(lagsDatasum,n=len(spec_final),axis=-1),axes=-1)
# allspecs = scfft.fftshift(scfft.fft(lagsDatasum,n=npts,axis=-1),axes=-1)
fig = plt.figure()
plt.plot(omega,spec_final.real,label='In',linewidth=5)
plt.hold(True)
plt.plot(omega,allspecs[40].real,label='Out',linewidth=5)
plt.axis((omega.min(),omega.max(),0.0,2e11))
plt.show(False)
def main():
fm = fmtest()
tstart = time.time()
fm.run()
tend = time.time()
if 1:
fig1 = pylab.figure(1, figsize=(12, 10), facecolor="w")
fig2 = pylab.figure(2, figsize=(12, 10), facecolor="w")
fig3 = pylab.figure(3, figsize=(12, 10), facecolor="w")
Ns = 10000
Ne = 100000
fftlen = 8192
winfunc = scipy.blackman
# Plot transmitted signal
fs = fm._if_rate
d = fm.snk_tx.data()[Ns:Ns + Ne]
sp1_f = fig1.add_subplot(2, 1, 1)
X, freq = sp1_f.psd(d,
NFFT=fftlen,
noverlap=fftlen / 4,
Fs=fs,
window=lambda d: d * winfunc(fftlen),
visible=False)
X_in = 10.0 * scipy.log10(abs(fftpack.fftshift(X)))
f_in = scipy.arange(-fs / 2.0, fs / 2.0, fs / float(X_in.size))
p1_f = sp1_f.plot(f_in, X_in, "b")
sp1_f.set_xlim([min(f_in), max(f_in) + 1])
sp1_f.set_ylim([-120.0, 20.0])
sp1_f.set_title("Input Signal", weight="bold")
sp1_f.set_xlabel("Frequency (Hz)")
sp1_f.set_ylabel("Power (dBW)")
Ts = 1.0 / fs
Tmax = len(d) * Ts
t_in = scipy.arange(0, Tmax, Ts)
x_in = scipy.array(d)
sp1_t = fig1.add_subplot(2, 1, 2)
p1_t = sp1_t.plot(t_in, x_in.real, "b-o")
#p1_t = sp1_t.plot(t_in, x_in.imag, "r-o")
sp1_t.set_ylim([-5, 5])
# Set up the number of rows and columns for plotting the subfigures
Ncols = int(scipy.floor(scipy.sqrt(fm.num_rx_channels())))
Nrows = int(scipy.floor(fm.num_rx_channels() / Ncols))
if (fm.num_rx_channels() % Ncols != 0):
Nrows += 1
# Plot each of the channels outputs. Frequencies on Figure 2 and
# time signals on Figure 3
fs_o = fm._audio_rate
for i in xrange(len(fm.snks)):
# remove issues with the transients at the beginning
# also remove some corruption at the end of the stream
# this is a bug, probably due to the corner cases
d = fm.snks[i].data()[Ns:Ne]
sp2_f = fig2.add_subplot(Nrows, Ncols, 1 + i)
X, freq = sp2_f.psd(d,
NFFT=fftlen,
noverlap=fftlen / 4,
Fs=fs_o,
window=lambda d: d * winfunc(fftlen),
visible=False)
#X_o = 10.0*scipy.log10(abs(fftpack.fftshift(X)))
X_o = 10.0 * scipy.log10(abs(X))
#f_o = scipy.arange(-fs_o/2.0, fs_o/2.0, fs_o/float(X_o.size))
f_o = scipy.arange(0, fs_o / 2.0, fs_o / 2.0 / float(X_o.size))
p2_f = sp2_f.plot(f_o, X_o, "b")
sp2_f.set_xlim([min(f_o), max(f_o) + 0.1])
sp2_f.set_ylim([-120.0, 20.0])
sp2_f.grid(True)
sp2_f.set_title(("Channel %d" % i), weight="bold")
sp2_f.set_xlabel("Frequency (kHz)")
sp2_f.set_ylabel("Power (dBW)")
Ts = 1.0 / fs_o
Tmax = len(d) * Ts
t_o = scipy.arange(0, Tmax, Ts)
x_t = scipy.array(d)
sp2_t = fig3.add_subplot(Nrows, Ncols, 1 + i)
p2_t = sp2_t.plot(t_o, x_t.real, "b")
p2_t = sp2_t.plot(t_o, x_t.imag, "r")
sp2_t.set_xlim([min(t_o), max(t_o) + 1])
sp2_t.set_ylim([-1, 1])
sp2_t.set_xlabel("Time (s)")
sp2_t.set_ylabel("Amplitude")
pylab.show()
def l1qc_newton(x0,
u0,
A,
b,
epsilon,
tau,
newtontol=np.float64(1e-3),
newtonmaxiter=50,
cgtol=np.float64(1e-8),
cgmaxiter=200):
# line search params
f64one = np.float64(1.)
alpha = np.float64(0.01)
beta = np.float64(0.5)
AtA = np.float64(A.T.dot(A))
# initial point
x = np.float64(x0)
u = np.float64(u0)
r = np.float64(A.dot(x) - b)
fu1 = np.float64(x - u)
fu2 = np.float64(-x - u)
fe = np.float64(0.5) * (r.T.dot(r) - epsilon**2)
f = np.float64(
sum(u) - (f64one / tau) * (sum(log(-fu1)) + sum(log(-fu2)) + log(-fe)))
niter = 0
done = False
while not done:
atr = A.T.dot(r)
ntgz = f64one / fu1 - f64one / fu2 + f64one / fe * atr
ntgu = -tau - f64one / fu1 - f64one / fu2
gradf = -(f64one / tau) * np.hstack((ntgz, ntgu))
sig11 = f64one / fu1**2 + f64one / fu2**2
sig12 = -f64one / fu1**2 + f64one / fu2**2
sigx = sig11 - np.float64(sig12**2) / sig11
w1p = ntgz - np.float64(sig12) / sig11 * ntgu
H11p = np.diag(sigx) - (f64one / fe) * AtA + (f64one /
fe)**2 * atr.dot(atr.T)
dx = np.linalg.solve(H11p, w1p)
Adx = A.dot(dx)
du = (f64one / sig11) * ntgu - (np.float64(sig12) / sig11) * dx
# minimum step size that stays in the interior
ifu1 = [i for i in xrange(len(dx)) if dx[i] - du[i] > 0]
ifu2 = [i for i in xrange(len(dx)) if -dx[i] - du[i] > 0]
aqe = Adx.T.dot(Adx)
bqe = np.float64(2) * r.T.dot(Adx)
cqe = r.T.dot(r) - epsilon**2
temp = -fu1[ifu1] / (dx[ifu1] - du[ifu1])
smax = np.float64(1)
if len(temp) > 0:
smax = min(smax, np.min(temp))
temp = -fu2[ifu2] / (-dx[ifu2] - du[ifu2])
if len(temp) > 0:
smax = min(smax, np.min(temp))
smax = min(smax, (-bqe + sqrt(bqe**2 - 4. * aqe * cqe)) / (2. * aqe))
s = np.float64(0.99) * smax
# backtracking line search
suffdec = False
backiter = 0
while not suffdec:
xp = x + s * dx
up = u + s * du
rp = r + s * Adx
fu1p = xp - up
fu2p = -xp - up
fep = f64one / 2 * (rp.T.dot(rp) - epsilon**2)
fp = sum(up) - (f64one / tau) * (sum(log(-fu1p)) +
sum(log(-fu2p)) + log(-fep))
flin = f + alpha * s * (gradf.T.dot(np.hstack((dx, du))))
# print fep,fp,flin
suffdec = (fp <= flin)
s = beta * s
backiter = backiter + 1
if backiter > 48:
# print "Stuck on backtracking line search, returning previous iterate."
xp = x
up = u
break
# set upt for next iteration
x = xp
u = up
r = rp
fu1 = fu1p
fu2 = fu2p
fe = fep
f = fp
lambda2 = np.float64(-(gradf.T.dot(np.hstack((dx, du)))))
stepsize = np.float64(s * norm(np.hstack((dx, du))))
niter = niter + 1
done = (lambda2 / 2 < newtontol) or (niter >= newtonmaxiter)
# print "Newton iter = %d, Functional = %8.3f, Newton decrement = %8.3f, Stepsize = %8.3e"%(niter, f, lambda2/2, stepsize)
return xp, up, niter
def Mittelwert(x): #Funktionsdefinition: def Name(argumente): Blocks mit tab
mw = sp.mean(x)
N = len(x)
f_mw = sp.sqrt((sp.sum((x - mw)**2)) / (N * (N - 1)))
return mw, f_mw
def directed_laplacian_matrix(G,
nodelist=None,
weight='weight',
walk_type=None,
alpha=0.95):
r"""Return the directed Laplacian matrix of G.
The graph directed Laplacian is the matrix
.. math::
L = I - (\Phi^{1/2} P \Phi^{-1/2} + \Phi^{-1/2} P^T \Phi^{1/2} ) / 2
where `I` is the identity matrix, `P` is the transition matrix of the
graph, and `\Phi` a matrix with the Perron vector of `P` in the diagonal and
zeros elsewhere.
Depending on the value of walk_type, `P` can be the transition matrix
induced by a random walk, a lazy random walk, or a random walk with
teleportation (PageRank).
Parameters
----------
G : DiGraph
A NetworkX graph
nodelist : list, optional
The rows and columns are ordered according to the nodes in nodelist.
If nodelist is None, then the ordering is produced by G.nodes().
weight : string or None, optional (default='weight')
The edge data key used to compute each value in the matrix.
If None, then each edge has weight 1.
walk_type : string or None, optional (default=None)
If None, `P` is selected depending on the properties of the
graph. Otherwise is one of 'random', 'lazy', or 'pagerank'
alpha : real
(1 - alpha) is the teleportation probability used with pagerank
Returns
-------
L : NumPy array
Normalized Laplacian of G.
Raises
------
NetworkXError
If NumPy cannot be imported
NetworkXNotImplemnted
If G is not a DiGraph
Notes
-----
Only implemented for DiGraphs
See Also
--------
laplacian_matrix
References
----------
.. [1] Fan Chung (2005).
Laplacians and the Cheeger inequality for directed graphs.
Annals of Combinatorics, 9(1), 2005
"""
import scipy as sp
from scipy.sparse import identity, spdiags, linalg
if walk_type is None:
if nx.is_strongly_connected(G):
if nx.is_aperiodic(G):
walk_type = "random"
else:
walk_type = "lazy"
else:
walk_type = "pagerank"
M = nx.to_scipy_sparse_matrix(G,
nodelist=nodelist,
weight=weight,
dtype=float)
n, m = M.shape
if walk_type in ["random", "lazy"]:
DI = spdiags(1.0 / sp.array(M.sum(axis=1).flat), [0], n, n)
if walk_type == "random":
P = DI * M
else:
I = identity(n)
P = (I + DI * M) / 2.0
elif walk_type == "pagerank":
if not (0 < alpha < 1):
raise nx.NetworkXError('alpha must be between 0 and 1')
# this is using a dense representation
M = M.todense()
# add constant to dangling nodes' row
dangling = sp.where(M.sum(axis=1) == 0)
for d in dangling[0]:
M[d] = 1.0 / n
# normalize
M = M / M.sum(axis=1)
P = alpha * M + (1 - alpha) / n
else:
raise nx.NetworkXError("walk_type must be random, lazy, or pagerank")
evals, evecs = linalg.eigs(P.T, k=1)
v = evecs.flatten().real
p = v / v.sum()
sqrtp = sp.sqrt(p)
Q = spdiags(sqrtp, [0], n, n) * P * spdiags(1.0 / sqrtp, [0], n, n)
I = sp.identity(len(G))
return I - (Q + Q.T) / 2.0
# - t_value = (mu - x) / se # 標本平均 mu = sp.mean(junk_food) mu # 自由度 df = len(junk_food) - 1 df # 標本標準偏差 sigma = sp.std(junk_food, ddof=1) sigma # 標準誤差 se = sigma / sp.sqrt(len(junk_food)) se # t値 # --- 理論値 t_value = (mu - 50) / se t_value # 3 t検定の実装：p値の計算 -------------------------------------------------------------- # p値 alpha = stats.t.cdf(t_value, df=df) (1 - alpha) * 2 # 関数によるt検定 # --- t値とp値が直接出力される
def extract(data, varimg, width=WIDTH, nsig=NSIG, noise=NOISE):
WIDTH = width
NSIG = nsig
NOISE = noise
data = data.copy()
spectra = []
# Replace nan with zero
data[scipy.isnan(data)] = 0.
varimg[scipy.isnan(varimg)] = 0.
# Create model of real flux. We ignore the slit ends, which may have
# artifacts from the resampling.
slit = data[:, 8:-8].astype(scipy.float32)
var = varimg[:, 8:-8]
# OK...so negative-variance also isn't good; set these pixels to zero
var[var < 0] = 0
# Create noise models
sigmaimg = slit / scipy.sqrt(var)
highpix = scipy.where(sigmaimg > 1.5, sigmaimg, 0.)
source_columns = highpix.sum(axis=0)
# MASKING DISABLED (this would take only columns with lotsa flux...)
# mask = scipy.where(source_columns>4.,1.,scipy.nan)
mask = source_columns * 0.
# Condition 1, dealing with bad pixels
if (var == 0).any():
cond = var == 0
var[cond] = scipy.nan
slit[cond] = scipy.nan
mask = scipy.where(cond, 0, 1)
flux = scipy.nansum(slit / var, axis=1) / scipy.nansum(1. / var,
axis=1)
noise = scipy.sqrt(scipy.nansum(var, axis=1)) / mask.sum(axis=1)
# Condition 2, no masking
elif scipy.nansum(mask) == 0:
flux = (slit / var).sum(axis=1) / (1. / var).sum(axis=1)
noise = scipy.sqrt(var.sum(axis=1)) / mask.size
# Condition 3, masking
else:
fluxmodel = slit * mask
noisemodel = var * mask
noise = scipy.sqrt(scipy.nansum(noisemodel,
axis=1)) / scipy.nansum(mask)
flux = stats.stats.nanmean(fluxmodel, axis=1)
# A smooth S/N estimate for the slit
# sig2noise = ndimage.gaussian_filter1d(flux,1)/noise
row = scipy.arange(flux.size)
model = flux.copy()
nspec = 10 # Maximum number of attempts
while nspec:
nspec -= 1
# Fit a gaussian around the peak of the S/N model
start = model.argmax() - WIDTH
end = model.argmax() + WIDTH + 1
if start < 0:
start = 0.
if end > model.size:
end = model.size
fitarr = model[start:end]
p = scipy.zeros(4)
p[1] = fitarr.max()
p[2] = fitarr.argmax()
p[3] = 2.
fit, val = special_functions.ngaussfit(fitarr, p)
chi2 = val / (fitarr.size - 3)
fit[2] += start
# If the centroid doesn't lie on the slit, get use the edge pix
midcol = fit[2].round()
if midcol >= flux.size:
midcol = flux.size - 1
elif midcol < 0:
midcol = 0
# Require a reasonable S/N and width
if fit[3] > fitarr.size / 2. or fit[3] < 0.85:
break
elif fit[0] > 0 and fit[1] < NOISE * noise[midcol]:
break
elif fit[0] < 0 and fit[1] - fit[0] < NOISE * noise[midcol]:
break
else:
fit[1] += fit[0]
fit[0] = 0.
# Subtract away a model of the source
source = special_functions.ngauss(row, fit)
model -= scipy.where(source > noise, source, 0.)
# Skip residuals!
if fit[2] < flux.size and fit[1] < scipy.sqrt(flux[fit[2]]):
continue
fit[1] = 1.
weight = special_functions.ngauss(row, fit)
cond = (row > fit[2] - fit[3] * NSIG) & (row <
fit[2] + fit[3] * NSIG)
weight = scipy.where(cond, weight, 0)
weight /= weight.sum()
spec = weight * data.T
spec = spec.sum(axis=1)
varspec = weight * varimg.T
varspec = varspec.sum(axis=1)
spec[varspec == 0] = 0.
smooth = signal.wiener(spec, FILTSIZE, varspec)
smooth[scipy.isnan(smooth)] = 0.
spectra.append([fit, spec, smooth, varspec])
return spectra
def normalized_laplacian_matrix(G, nodelist=None, weight='weight'):
r"""Return the normalized Laplacian matrix of G.
The normalized graph Laplacian is the matrix
.. math::
N = D^{-1/2} L D^{-1/2}
where `L` is the graph Laplacian and `D` is the diagonal matrix of
node degrees.
Parameters
----------
G : graph
A NetworkX graph
nodelist : list, optional
The rows and columns are ordered according to the nodes in nodelist.
If nodelist is None, then the ordering is produced by G.nodes().
weight : string or None, optional (default='weight')
The edge data key used to compute each value in the matrix.
If None, then each edge has weight 1.
Returns
-------
N : NumPy matrix
The normalized Laplacian matrix of G.
Notes
-----
For MultiGraph/MultiDiGraph, the edges weights are summed.
See to_numpy_matrix for other options.
If the Graph contains selfloops, D is defined as diag(sum(A,1)), where A is
the adjacency matrix [2]_.
See Also
--------
laplacian_matrix
References
----------
.. [1] Fan Chung-Graham, Spectral Graph Theory,
CBMS Regional Conference Series in Mathematics, Number 92, 1997.
.. [2] Steve Butler, Interlacing For Weighted Graphs Using The Normalized
Laplacian, Electronic Journal of Linear Algebra, Volume 16, pp. 90-98,
March 2007.
"""
import scipy
import scipy.sparse
if nodelist is None:
nodelist = G.nodes()
A = nx.to_scipy_sparse_matrix(G,
nodelist=nodelist,
weight=weight,
format='csr')
n, m = A.shape
diags = A.sum(axis=1).flatten()
D = scipy.sparse.spdiags(diags, [0], m, n, format='csr')
L = D - A
with scipy.errstate(divide='ignore'):
diags_sqrt = 1.0 / scipy.sqrt(diags)
diags_sqrt[scipy.isinf(diags_sqrt)] = 0
DH = scipy.sparse.spdiags(diags_sqrt, [0], m, n, format='csr')
return DH.dot(L.dot(DH))
print count1,
nSub = sub_data.shape[2]
cat_data = sp.zeros((nSub * sub_data.shape[0], sub_data.shape[1]))
for ind in range(nSub):
sub_data[:, :, ind] = rot_sub_data(ref=sub_data[:, :, 0],
sub=sub_data[:, :, ind])
# cat_data[sub_data.shape[0]*ind:sub_data.shape[0]*(ind+1),:] = sub_data[:,:,ind]
print ind, sub_data.shape, cat_data.shape
SC = DBSCAN(
eps=.1
) #,min_samples=50,leaf_size=50)# min_cluster_size=5) #KMeans(n_clusters=nClusters,random_state=5324)
lab_sub = sp.zeros((sub_data.shape[0], nSub))
for ind in [0]: # range(nSub):
dat1 = (0.000001 + sub_data[:, :, ind]) / sp.sum(
0.000001 + sp.sqrt(sub_data[:, :, ind] * sub_data[:, :, ind]),
axis=1)[:, None]
met = sp.absolute(sp.arccos(sp.corrcoef(dat1)))
lab_sub[:, ind] = SC.fit_predict(dat1)
print ind, sp.amax(lab_sub)
#labs_all = SC.fit_predict(cat_data)
#lab_sub=labs_all.reshape((sub_data.shape[0],nSub),order='F')
sp.savez_compressed('labs_all_data1_rot_individual_nclusters_30_HDBSCAN_sub0',
lab_sub=lab_sub,
cat_data=cat_data,
lst=lst)
H_tau.set_xlabel('tau')
H_tau.set_ylabel('H')
H_tau.set_title('Imaginary time evolution: Energy')
M_tau = fig2.add_subplot(111)
M_tau.set_xlabel('tau')
M_tau.set_ylabel('M')
M_tau.set_title('Imaginary time evolution: Magnetization')
H_tau.plot(tau, H)
M_tau.plot(tau, M)
plt.figure()
ex_p = sp.array(ex_p).ravel()
ex_ev = sp.array(ex_ev).ravel()
ex_ev_nt = sp.array(ex_ev_nt).ravel()
plt.plot(ex_p, ex_ev, 'bo', label='top. trivial')
if top_non_triv:
plt.plot(ex_p, ex_ev_nt, 'ro', label='top. non-trivial')
elem_ex = lambda p: 2 * J * sp.sqrt(1 + h**2 / J**2 - 2 * h / J * sp.cos(p))
p = sp.linspace(0, sp.pi, num=100)
plt.plot(p, elem_ex(p), 'c-', label='exact elem. excitation')
plt.title('Excitation spectrum')
plt.xlabel('p')
plt.ylabel('dE')
plt.ylim(0, max(ex_ev.max(), ex_ev_nt.max()) * 1.1)
plt.legend()
plt.show()
def Spot_size(self, z):
"""Returns the spot size of the beam at axial position z."""
return self.waist * sp.sqrt(1 + (z / self.RL)**2)
def PlotHist(field, imfile=None):
""" field is a HistMaker object """
H = field.H
# Scale and flip if necessary
vmin = field.varea[0]
if field.varea[1] == None: vmax = np.ma.max(H)
else: vmax = field.varea[1]
if field.scale == 'sqrt':
field.H = sc.sqrt(H)
vmax = sc.sqrt(vmax)
elif field.scale == 'log':
field.H = sc.log10(H)
vmax = sc.log10(vmax)
if field.xflip == 1: H = H[:, ::-1]
if field.yflip == 1: H = H[::-1, :]
# Plot the image
if field.cmap == 'color': cmap = spectral_wb
elif field.cmap == 'color_c': cmap = spec_center
elif field.cmap == 'bw': cmap = 'gist_yarg'
else: cmap = field.cmap
plt.figure()
plt.imshow(H,
cmap=cmap,
norm=None,
aspect=None,
interpolation='nearest',
alpha=None,
vmin=vmin,
vmax=vmax,
origin='lower',
extent=None)
cbar = plt.colorbar() #May need to adjust these ticks...
# Add xTicks and labels
xlocs, xlabels, ylocs, ylabels = [], [], [], []
if field.ticks[0] == None:
xpos = np.arange(field.xmin, field.xmax + 0.000001,
((field.xmax - field.xmin) / 10.0))
else:
xpos = field.ticks[0]
for pos in xpos:
xlocs.append((pos - field.xmin) / field.xsize)
xlabels.append("${0:.1f}$".format(pos))
if field.xflip == 1:
plt.xticks(xlocs, xlabels[::-1], rotation=45, fontsize=14)
else:
plt.xticks(xlocs, xlabels, rotation=45, fontsize=14)
# Add yTicks and labels
if field.ticks[1] == None:
ypos = np.arange(field.ymin, field.ymax + 0.000001,
((field.ymax - field.ymin) / 10.0))
else:
ypos = field.ticks[1]
for pos in ypos:
ylocs.append((pos - field.ymin) / field.ysize)
ylabels.append("${0:.1f}$".format(pos))
if field.yflip == 1:
plt.yticks(ylocs, ylabels[::-1], rotation=0, fontsize=14)
else:
plt.yticks(ylocs, ylabels, rotation=0, fontsize=14)
# Add axes labels
if field.labels[0] != None: plt.xlabel(field.labels[0])
if field.labels[1] != None: plt.ylabel(field.labels[1])
# Save file, if outfile declared
if imfile != None: plt.savefig(imfile)
else: plt.show()
plt.close('all')
def __init__(self,
f,
mu,
amat,
eta_mu=1.0,
eta_sigma=None,
eta_bmat=None,
npop=None,
use_fshape=True,
use_adasam=False,
patience=100,
n_jobs=1):
self.f = f
self.mu = mu
self.eta_mu = eta_mu
self.use_adasam = use_adasam
self.n_jobs = n_jobs
dim = len(mu)
sigma = abs(det(amat))**(1.0 / dim)
bmat = amat * (1.0 / sigma)
self.dim = dim
self.sigma = sigma
self.bmat = bmat
# default population size and learning rates
npop = int(4 + 3 * log(dim)) if npop is None else npop
eta_sigma = 3 * (3 + log(dim)) * (
1.0 / (5 * dim * sqrt(dim))) if eta_sigma is None else eta_sigma
eta_bmat = 3 * (3 + log(dim)) * (
1.0 / (5 * dim * sqrt(dim))) if eta_bmat is None else eta_bmat
self.npop = npop
self.eta_sigma = eta_sigma
self.eta_bmat = eta_bmat
# compute utilities if using fitness shaping
if use_fshape:
a = log(1 + 0.5 * npop)
utilities = array([max(0, a - log(k)) for k in range(1, npop + 1)])
utilities /= sum(utilities)
utilities -= 1.0 / npop # broadcast
utilities = utilities[::-1] # ascending order
else:
utilities = None
self.use_fshape = use_fshape
self.utilities = utilities
# stuff for adasam
self.eta_sigma_init = eta_sigma
self.sigma_old = None
# logging
self.fitness_best = None
self.mu_best = None
self.done = False
self.counter = 0
self.patience = patience
self.history = {'eta_sigma': [], 'sigma': [], 'fitness': []}
# do not use these when hill-climbing
if npop == 1:
self.use_fshape = False
self.use_adasam = False
if r == 'petit':
rev = False
else:
rev = True
rankings = []
for i in range(n):
row = [col[i] for col in args]
row_sort = sorted(row, reverse=rev)
rankings.append([
row_sort.index(v) + 1 + (row_sort.count(v) - 1) / 2. for v in row
])
rankings_avg = [sp.mean([case[j] for case in rankings]) for j in range(k)]
rankings_cmp = [r / sp.sqrt(k * (k + 1) / (6. * n)) for r in rankings_avg]
chi2 = ((12 * n) / float(
(k * (k + 1)))) * ((sp.sum(r**2 for r in rankings_avg)) -
((k * (k + 1)**2) / float(4)))
iman_davenport = ((n - 1) * chi2) / float((n * (k - 1) - chi2))
p_value = 1 - st.f.cdf(iman_davenport, k - 1, (k - 1) * (n - 1))
return iman_davenport, p_value, rankings_avg, rankings_cmp
def wilco_approche_adapt_vs_nonadapt(df_metrics_adapt, df_metrics_nonadapt,
metric, timeParams, datasets, methods):
cols = ['method', 'timeParam', 'null_hypothesis_rejected', 'z']
print('METS : ', methods)
def correctedFWHM(self, FWHM_PSF):
return scipy.sqrt(self.FWHMnm()**2 - self.FWHM_PSF**2)
def __init__(self, limit):
self.primes = Primes.MakePrimeList(int(sp.sqrt(2*limit)))
self.memo = {}
import matplotlib.pyplot as plt
in_degrees = G.in_degree()
in_h = Counter(in_degrees.values())
in_dic = collections.OrderedDict(sorted(in_h.items()))
in_hist = list(in_dic.values())
in_values = list(in_dic.keys())
out_degrees = G.out_degree()
out_h = Counter(out_degrees.values())
out_dic = collections.OrderedDict(sorted(out_h.items()))
out_hist = list(out_dic.values())
out_values = list(out_dic.keys())
mu = 2.17
sigma = sp.sqrt(mu)
mu_plus_sigma = mu + sigma
x = range(0, 10)
prob = stats.poisson.pmf(x, mu) * 4426
plt.figure(figsize=(12, 8))
plt.grid(True)
plt.loglog(out_values, out_hist, 'ro-') # in-degree
plt.loglog(in_values, in_hist, 'bv-') # in-degree
plt.plot(x, prob, "o-", color="black")
plt.legend(['In-degree', 'Out-degree', 'Poission'])
plt.xlabel('Degree')
plt.ylabel('Number of nodes')
plt.title('Manhatten Street Network')
plt.xlim([0, 2 * 10**2])
plt.show()
def extract_pore_network(im, dt=None, voxel_size=1):
r"""
Analyzes an image that has been partitioned into pore regions and extracts
the pore and throat geometry as well as network connectivity.
Parameters
----------
im : ND-array
An image of the pore space partitioned into individual pore regions.
Note that this image must have zeros indicating the solid phase.
dt : ND-array
The distance transform of the pore space. If not given it will be
calculated, but it can save time to provide one if available.
voxel_size : scalar
The resolution of the image, expressed as the length of one side of a
voxel, so the volume of a voxel would be **voxel_size**-cubed. The
default is 1, which is useful when overlaying the PNM on the original
image since the scale of the image is alway 1 unit lenth per voxel.
Returns
-------
A dictionary containing all the pore and throat size data, as well as the
network topological information. The dictionary names use the OpenPNM
convention (i.e. 'pore.coords', 'throat.conns') so it may be converted
directly to an OpenPNM network object using the ``update`` command.
"""
print('_' * 60)
print('Extracting pore and throat information from image')
from skimage.morphology import disk, square, ball, cube
if im.ndim == 2:
cube = square
ball = disk
if ~sp.any(im == 0):
raise Exception('The received image has no solid phase (0\'s)')
if dt is None:
dt = spim.distance_transform_edt(im > 0)
dt = spim.gaussian_filter(input=dt, sigma=0.5)
# Get 'slices' into im for each pore region
slices = spim.find_objects(im)
# Initialize arrays
Ps = sp.arange(1, sp.amax(im) + 1)
Np = sp.size(Ps)
p_coords = sp.zeros((Np, im.ndim), dtype=float)
p_volume = sp.zeros((Np, ), dtype=float)
p_dia_local = sp.zeros((Np, ), dtype=float)
p_dia_global = sp.zeros((Np, ), dtype=float)
p_label = sp.zeros((Np, ), dtype=int)
p_area_surf = sp.zeros((Np, ), dtype=int)
p_area_solid = sp.zeros((Np, ), dtype=int)
t_conns = []
t_dia_inscribed = []
t_area = []
t_perimeter = []
t_coords = []
# Start extracting size information for pores and throats
for i in tqdm(Ps):
pore = i - 1
# if slices[pore] is None:
# continue
s = extend_slice(slices[pore], im.shape)
sub_im = im[s]
sub_dt = dt[s]
pore_im = sub_im == i
pore_dt = spim.distance_transform_edt(
sp.pad(pore_im, pad_width=1, mode='constant'))
s_offset = sp.array([i.start for i in s])
p_label[pore] = i
p_coords[pore, :] = spim.center_of_mass(pore_im) + s_offset
p_volume[pore] = sp.sum(pore_im)
p_dia_local[pore] = 2 * sp.amax(pore_dt)
p_dia_global[pore] = 2 * sp.amax(sub_dt)
p_area_surf[pore] = sp.sum(pore_dt == 1)
p_area_solid[pore] = sp.sum(sub_dt == 1)
im_w_throats = spim.binary_dilation(input=pore_im, structure=ball(1))
im_w_throats = im_w_throats * sub_im
Pn = sp.unique(im_w_throats)[1:] - 1
for j in Pn:
if j > pore:
t_conns.append([pore, j])
vx = sp.where(im_w_throats == (j + 1))
t_dia_inscribed.append(2 * sp.amax(sub_dt[vx]))
t_perimeter.append(sp.sum(sub_dt[vx] < 2))
t_area.append(sp.size(vx[0]))
t_inds = tuple([i + j for i, j in zip(vx, s_offset)])
temp = sp.where(dt[t_inds] == sp.amax(dt[t_inds]))[0][0]
if im.ndim == 2:
t_coords.append(tuple((t_inds[0][temp], t_inds[1][temp])))
else:
t_coords.append(
tuple((t_inds[0][temp], t_inds[1][temp],
t_inds[2][temp])))
# Clean up values
Nt = len(t_dia_inscribed) # Get number of throats
if im.ndim == 2: # If 2D, add 0's in 3rd dimension
p_coords = sp.vstack((p_coords.T, sp.zeros((Np, )))).T
t_coords = sp.vstack((sp.array(t_coords).T, sp.zeros((Nt, )))).T
# Start creating dictionary of pore network information
net = {}
net['pore.all'] = sp.ones((Np, ), dtype=bool)
net['throat.all'] = sp.ones((Nt, ), dtype=bool)
net['pore.coords'] = sp.copy(p_coords) * voxel_size
net['pore.centroid'] = sp.copy(p_coords) * voxel_size
net['throat.centroid'] = sp.array(t_coords) * voxel_size
net['throat.conns'] = sp.array(t_conns)
net['pore.label'] = sp.array(p_label)
net['pore.volume'] = sp.copy(p_volume) * (voxel_size**3)
net['throat.volume'] = sp.zeros((Nt, ), dtype=float)
net['pore.diameter'] = sp.copy(p_dia_local) * voxel_size
net['pore.inscribed_diameter'] = sp.copy(p_dia_local) * voxel_size
net['pore.equivalent_diameter'] = 2 * (
(3 / 4 * net['pore.volume'] / sp.pi)**(1 / 3))
net['pore.extended_diameter'] = sp.copy(p_dia_global) * voxel_size
net['pore.surface_area'] = sp.copy(p_area_surf) * (voxel_size)**2
net['pore.solid_area'] = sp.copy(p_area_solid) * (voxel_size)**2
net['throat.diameter'] = sp.array(t_dia_inscribed) * voxel_size
net['throat.inscribed_diameter'] = sp.array(t_dia_inscribed) * voxel_size
net['throat.area'] = sp.array(t_area) * (voxel_size**2)
net['throat.perimeter'] = sp.array(t_perimeter) * voxel_size
net['throat.equivalent_diameter'] = (sp.array(t_area) *
(voxel_size**2))**(0.5)
P12 = net['throat.conns']
PT1 = sp.sqrt(
sp.sum(((p_coords[P12[:, 0]] - t_coords) * voxel_size)**2, axis=1))
PT2 = sp.sqrt(
sp.sum(((p_coords[P12[:, 1]] - t_coords) * voxel_size)**2, axis=1))
net['throat.total_length'] = PT1 + PT2
PT1 = PT1 - p_dia_local[P12[:, 0]] / 2 * voxel_size
PT2 = PT2 - p_dia_local[P12[:, 1]] / 2 * voxel_size
net['throat.length'] = PT1 + PT2
dist = (p_coords[P12[:, 0]] - p_coords[P12[:, 1]]) * voxel_size
net['throat.direct_length'] = sp.sqrt(sp.sum(dist**2, axis=1))
return net
#plot constant
#if constant != None and subplot:
if fit:
# Sometimes the curve_fit will not be able to calculate the variance
# Instead it returns inf as the var_matrix. In this case, scaling
# the y-values can help.
scale = 1.0
while True:
try:
coeff, var_matrix = curve_fit(func, xy[:, 0],
scale * xy[:, 1])
coeff = coeff / scale
variance = sp.diagonal(var_matrix)
SE = sp.sqrt(variance)
SE = SE / scale
results = {}
for k in range(len(SE)):
results[parameters[k]] = [coeff[k], SE[k]]
print
print '{0:>5} {1:>12} {2:>12}'.format(
'Coeff', 'Value', 'Error')
for v, c in results.iteritems():
print '{0:>5} {1:>12.5f} {2:>12.5f}'.format(
v, c[0], c[1])
break
except ValueError, e:
scale *= 10
if scale == 1000000:
# zero-padding and calulate frequency axis
N = zero_padding(T)
freq = fftpack.fftfreq(N,
d=para_dict['step'] * 10**(-15)) # frequency axes in Hz
if para_dict['step'] < 0:
freq = freq[::-1] # reverse array
wn = freq / 100.0 / const.c + para_dict[
'wn_M'] # measured wavenumbers in cm^-1
cut_index = np.argmin(wn)
wn = redistribute(wn, cut_index)
# create spectrogram-matrix
S = np.zeros((np.size(T), np.size(wn)))
# calculate start position
data_window[0] /= 1000.0 # back to ps
data_window[1] /= 1000.0 # back to ps
HWFP = sp.sqrt(3.0 / sp.log(
2)) * FWHM / 2.0 # half width where gaussian has dropped to 5% i.e. 1/e^3
slide_pos = data_window[0] - HWFP
n = 0
while slide_pos <= data_window[1] + HWFP:
Z_slide = slide_window(
T, Z, slide_pos, FWHM
) # multiply gaussian onto data set which is centered at current sliding position
DFT_slide = redistribute(
abs(fftpack.fft(Z_slide, n=N)), cut_index
) # FFT of interferogram which has been truncated by mulitplying wiht gaussian
n += 1
if para_dict['step'] < 0:
DFT_slide = DFT_slide[::-1] # reverse array
# add DFT to spectrum-matrix while weighting with temporal gaussian envelope
for i in range(np.size(T)):
def sqrt(self):
return simple_diag_matrix(sp.sqrt(self.diag))
Sy = 490.0 # MPa
F_max = 15000.0 # Newtons
F_min = 5000.0 # Newtons
w = 30.0 # mm
h = 10.0 # mm
n = 1.2 # Safety Factor
#%%
# Loading Factors:
C_load = 0.7
A_95 = 0.05 * w * h # mm^2
d_rect_area = sp.sqrt(A_95 / 0.076) # mm
C_size = 1.189 * d_rect_area**(-0.097)
C_surface = 1.58 * (590**(-0.085))
C_temp = 1.0
C_reliab = 0.814
Se_prime = 0.5 * Sut # MPa
def get_Se(Se_prime, C_load, C_size, C_surface, C_reliab, C_temp):
''' Returns the value of Se '''
return Se_prime * C_load * C_size * C_surface * C_temp * C_reliab
def dij_particle(p1, p2):
return sp.sqrt((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2 +
(p1[2] - p2[2])**2)
def van_rossum_dist(trains, tau=1.0 * pq.s, sort=True):
"""
Calculates the van Rossum distance.
It is defined as Euclidean distance of the spike trains convolved with a
causal decaying exponential smoothing filter. A detailed description can
be found in *Rossum, M. C. W. (2001). A novel spike distance. Neural
Computation, 13(4), 751-763.* This implementation is normalized to yield
a distance of 1.0 for the distance between an empty spike train and a
spike train with a single spike. Divide the result by sqrt(2.0) to get
the normalization used in the cited paper.
Given :math:`N` spike trains with :math:`n` spikes on average the run-time
complexity of this function is :math:`O(N^2 n)`.
Parameters
----------
trains : Sequence of :class:`neo.core.SpikeTrain` objects of
which the van Rossum distance will be calculated pairwise.
tau : Quantity scalar
Decay rate of the exponential function as time scalar. Controls for
which time scale the metric will be sensitive. This parameter will
be ignored if `kernel` is not `None`. May also be :const:`scipy.inf`
which will lead to only measuring differences in spike count.
Default: 1.0 * pq.s
sort : bool
Spike trains with sorted spike times might be needed for the
calculation. You can set `sort` to `False` if you know that your
spike trains are already sorted to decrease calculation time.
Default: True
Returns
-------
2-D array
Matrix containing the van Rossum distances for all pairs of
spike trains.
Example
-------
import elephant.spike_train_dissimilarity_measures as stdm
tau = 10.0 * pq.ms
st_a = SpikeTrain([10, 20, 30], units='ms', t_stop= 1000.0)
st_b = SpikeTrain([12, 24, 30], units='ms', t_stop= 1000.0)
vr = stdm.van_rossum_dist([st_a, st_b], tau)[0, 1]
"""
for train in trains:
if not (isinstance(train, (pq.quantity.Quantity, SpikeTrain))
and train.dimensionality.simplified == pq.Quantity(
1, "s").dimensionality.simplified):
raise TypeError("Spike trains must have a time unit.")
if not (isinstance(tau, pq.quantity.Quantity)
and tau.dimensionality.simplified == pq.Quantity(
1, "s").dimensionality.simplified):
raise TypeError("tau must be a time quantity.")
if tau == 0:
spike_counts = [st.size for st in trains]
return np.sqrt(spike_counts + np.atleast_2d(spike_counts).T)
elif tau == np.inf:
spike_counts = [st.size for st in trains]
return np.absolute(spike_counts - np.atleast_2d(spike_counts).T)
k_dist = _summed_dist_matrix([st.view(type=pq.Quantity) for st in trains],
tau, not sort)
vr_dist = np.empty_like(k_dist)
for i, j in np.ndindex(k_dist.shape):
vr_dist[i, j] = (k_dist[i, i] + k_dist[j, j] - k_dist[i, j] -
k_dist[j, i])
return sp.sqrt(vr_dist)