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)
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.sum(xin.real**2 + xin.imag**2, axis=1))[:, sp.newaxis],
(1, Npnt))
xin = xin / xinsum / sp.sqrt(2.)
outdata = sp.signal.lfilter(Gvec, lpc, xin, axis=1)
outpulse = sp.tile(pulse[sp.newaxis], (rep1, 1))
outdata = outpulse * outdata[:, N:N + lp]
return outdata
def sinc_interp1d(x, s, r):
"""Interpolates `x`, sampled at times `s`
Output `y` is sampled at times `r`
inspired from from Matlab:
http://phaseportrait.blogspot.com/2008/06/sinc-interpolation-in-matlab.html
:param ndarray x: input data time series
:param ndarray s: input sampling time series (regular sample interval)
:param ndarray r: output sampling time series
:return ndarray: output data time series (regular sample interval)
"""
# init
s = sp.asarray(s)
r = sp.asarray(r)
x = sp.asarray(x)
if x.ndim == 1:
x = sp.atleast_2d(x)
else:
if x.shape[0] == len(s):
x = x.T
else:
if x.shape[1] != s.shape[0]:
raise ValueError('x and s must be same temporal extend')
if sp.allclose(s, r):
return x.T
T = s[1] - s[0]
# resample
sincM = sp.tile(r, (len(s), 1)) - sp.tile(s[:, sp.newaxis], (1, len(r)))
return sp.vstack([sp.dot(xx, sp.sinc(sincM / T)) for xx in x]).T
def massmatrix_rowcols(complex, k):
"""
Compute the row and column arrays in the COO
format of the Whitney form mass matrix
"""
simplices = complex[-1].simplices
num_simplices = simplices.shape[0]
p = complex.complex_dimension()
if k == p:
#top dimension
rows = arange(num_simplices, dtype=simplices.dtype)
cols = arange(num_simplices, dtype=simplices.dtype)
return rows, cols
k_faces = [tuple(x) for x in combinations(range(p + 1), k + 1)]
faces_per_simplex = len(k_faces)
num_faces = num_simplices * faces_per_simplex
faces = empty((num_faces, k + 1), dtype=simplices.dtype)
for n, face in enumerate(k_faces):
for m, i in enumerate(face):
faces[n::faces_per_simplex, m] = simplices[:, i]
#faces.sort() #we can't assume that the p-simplices are sorted
indices = simplex_array_searchsorted(complex[k].simplices, faces)
rows = tile(indices.reshape((-1, 1)), (faces_per_simplex, )).flatten()
cols = tile(indices.reshape((-1, faces_per_simplex)),
(faces_per_simplex, )).flatten()
return rows, cols
def trueFeatureStats(T, R, fMap, discountFactor, stateProp=1, MAT_LIMIT=1e8):
""" Gather the statistics needed for LSTD,
assuming infinite data (true probabilities).
Option: if stateProp is < 1, then only a proportion of all
states will be seen as starting state for transitions """
dim = len(fMap)
numStates = len(T)
statMatrix = zeros((dim, dim))
statResidual = zeros(dim)
ss = range(numStates)
repVersion = False
if stateProp < 1:
ss = random.sample(ss, int(numStates * stateProp))
elif dim * numStates**2 < MAT_LIMIT:
repVersion = True
# two variants, depending on how large we can afford our matrices to become.
if repVersion:
tmp1 = tile(fMap, (numStates,1,1))
tmp2 = transpose(tmp1, (2,1,0))
tmp3 = tmp2 - discountFactor * tmp1
tmp4 = tile(T, (dim,1,1))
tmp4 *= transpose(tmp1, (1,2,0))
statMatrix = tensordot(tmp3, tmp4, axes=[[0,2], [1,2]]).T
statResidual = dot(R, dot(fMap, T).T)
else:
for sto in ss:
tmp = fMap - discountFactor * repmat(fMap[:, sto], numStates, 1).T
tmp2 = fMap * repmat(T[:, sto], dim, 1)
statMatrix += dot(tmp2, tmp.T)
statResidual += R[sto] * dot(fMap, T[:, sto])
return statMatrix, statResidual
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 phenSpecificEffects(snps,pheno1,pheno2,K=None,covs=None,test='lrt'):
"""
Univariate fixed effects interaction test for phenotype specific SNP effects
Args:
snps: [N x S] SP.array of S SNPs for N individuals (test SNPs)
pheno1: [N x 1] SP.array of 1 phenotype for N individuals
pheno2: [N x 1] SP.array of 1 phenotype for N individuals
K: [N x N] SP.array of LMM-covariance/kinship koefficients (optional)
If not provided, then linear regression analysis is performed
covs: [N x D] SP.array of D covariates for N individuals
test: 'lrt' for likelihood ratio test (default) or 'f' for F-test
Returns:
limix LMM object
"""
N=snps.shape[0]
if K is None:
K=SP.eye(N)
assert (pheno1.shape[1]==pheno2.shape[1]), "Only consider equal number of phenotype dimensions"
if covs is None:
covs = SP.ones(N,1)
assert (pheno1.shape[1]==1 and pheno2.shape[1]==1 and pheno1.shape[0]==N and pheno2.shape[0]==N and K.shape[0]==N and K.shape[1]==N and covs.shape[0]==N), "shapes missmatch"
Inter = SP.zeros((N*2,1))
Inter[0:N,0]=1
Inter0 = SP.ones((N*2,1))
Yinter=SP.concatenate((pheno1,pheno2),0)
Xinter = SP.tile(snps,(2,1))
Covitner= SP.tile(covs(2,1))
lm = simple_interaction(snps=Xinter,pheno=Yinter,covs=Covinter,Inter=Inter,Inter0=Inter0,test=test)
return lm
def MakePulseDataRep(pulse_shape, filt_freq, delay=16,rep=1,numtype = sp.complex128):
""" This function will create a repxLp numpy array, where rep is number of independent
repeats and Lp is number of pulses, of noise shaped by the filter who's frequency
response is passed as the parameter filt_freq. The pulse shape is delayed by the parameter
delay into the data. The noise vector that will be multiplied by the filter's frequency
response will be zero mean complex white Gaussian noise with a power of 1. The user
then will need to multiply the filter by its size to get the desired power from using
the function.
Inputs:
pulse_shape: A numpy array that holds the shape of the single pulse.
filt_freq - a numpy array that holds the complex frequency response of the filter
that will be used to shape the noise data.
delay - The number of samples that the pulse will be delayed into the
array of noise data to avoid any problems with filter overlap.
rep - Number of indepent samples/pulses shaped by the filter.
numtype - The type of numbers used for the output.
Output
data_out - A repxLp of data that has been shaped by the filter. Points along
The first axis are independent of each other while samples along the second
axis are colored using the filter and multiplied by the pulse shape.
"""
npts = len(filt_freq)
filt_tile = sp.tile(filt_freq[sp.newaxis,:],(rep,1))
shaperep = sp.tile(pulse_shape[sp.newaxis,:],(rep,1))
noisereal = sp.random.randn(rep,npts).astype(numtype)
noiseimag = sp.random.randn(rep,npts).astype(numtype)
noise_vec =(noisereal+1j*noiseimag)/sp.sqrt(2.0)
# noise_vec = noisereal
mult_freq = filt_tile.astype(numtype)*noise_vec
data = scfft.ifft(mult_freq,axis=-1)
data_out = shaperep*data[:,delay:(delay+len(pulse_shape))]
return data_out
def massmatrix_rowcols(complex,k):
"""
Compute the row and column arrays in the COO
format of the Whitney form mass matrix
"""
simplices = complex[-1].simplices
num_simplices = simplices.shape[0]
p = complex.complex_dimension()
if k == p:
#top dimension
rows = arange(num_simplices,dtype=simplices.dtype)
cols = arange(num_simplices,dtype=simplices.dtype)
return rows,cols
k_faces = [tuple(x) for x in combinations(range(p+1),k+1)]
faces_per_simplex = len(k_faces)
num_faces = num_simplices*faces_per_simplex
faces = empty((num_faces,k+1),dtype=simplices.dtype)
for n,face in enumerate(k_faces):
for m,i in enumerate(face):
faces[n::faces_per_simplex,m] = simplices[:,i]
#faces.sort() #we can't assume that the p-simplices are sorted
indices = simplex_array_searchsorted(complex[k].simplices,faces)
rows = tile(indices.reshape((-1,1)),(faces_per_simplex,)).flatten()
cols = tile(indices.reshape((-1,faces_per_simplex)),(faces_per_simplex,)).flatten()
return rows,cols
def rpeuc(x, m=1, t=1, e=0.1, normed=True): """Returns the recurrence matrix based on Euclidean metric. """ x = x.squeeze() if normed: x = (x - x.mean()) / x.std() # embed x with dimension 'm' and delay 't' n = x.shape[0] step = (m-1)*t count = step+1 y = sp.zeros((n-count+1,m)) for i in range(n-count+1): tt = i+step y[i,:] = x[-(n-tt):-(n-tt)-step-1:-t] # get distance matrix n = y.shape[0] dist = sp.zeros((n,n)) if m > 1: for i in range(n-1): dist[i+1:n,i] = sp.sqrt(sp.sum(sp.square(sp.tile(y[i,:], (n-i-1, 1)) - y[i+1:n,:]), axis=1 )) elif m == 1: for i in range(n-1): dist[i+1:n,i] = abs(sp.tile(y[i], (n-i-1,1)) - y[i+1:n]).squeeze() dist = dist + dist.T RP = sp.zeros((n,n), dtype=sp.int8) RP[(dist <= e) & (dist > 0)] = 1 RP = RP + sp.eye(n, dtype=sp.int8) return RP
def sinc_interp1d(x, s, r):
"""Interpolates `x`, sampled at times `s`
Output `y` is sampled at times `r`
inspired from from Matlab:
http://phaseportrait.blogspot.com/2008/06/sinc-interpolation-in-matlab.html
:param ndarray x: input data time series
:param ndarray s: input sampling time series (regular sample interval)
:param ndarray r: output sampling time series
:return ndarray: output data time series (regular sample interval)
"""
# init
s = sp.asarray(s)
r = sp.asarray(r)
x = sp.asarray(x)
if x.ndim == 1:
x = sp.atleast_2d(x)
else:
if x.shape[0] == len(s):
x = x.T
else:
if x.shape[1] != s.shape[0]:
raise ValueError('x and s must be same temporal extend')
if sp.allclose(s, r):
return x.T
T = s[1] - s[0]
# resample
sincM = sp.tile(r, (len(s), 1)) - sp.tile(s[:, sp.newaxis], (1, len(r)))
return sp.vstack([sp.dot(xx, sp.sinc(sincM / T)) for xx in x]).T
def _LMLgrad_covar(self, hyperparams):
"""
evaluates the gradient of the log marginal likelihood with respect to the
hyperparameters of the covariance function
"""
try:
KV = self.get_covariances(hyperparams)
except LA.LinAlgError:
LG.error('linalg exception in _LMLgrad_covar')
return {
'covar_r': SP.zeros(len(hyperparams['covar_r'])),
'covar_c': SP.zeros(len(hyperparams['covar_c'])),
'covar_r': SP.zeros(len(hyperparams['covar_r']))
}
except ValueError:
LG.error('value error in _LMLgrad_covar')
return {
'covar_r': SP.zeros(len(hyperparams['covar_r'])),
'covar_c': SP.zeros(len(hyperparams['covar_c'])),
'covar_r': SP.zeros(len(hyperparams['covar_r']))
}
RV = {}
Si = unravel(1. / KV['S'], self.n, self.t)
if 'covar_r' in hyperparams:
theta = SP.zeros(len(hyperparams['covar_r']))
for i in range(len(theta)):
Kgrad_r = self.covar_r.Kgrad_theta(hyperparams['covar_r'], i)
d = (KV['U_r'] * SP.dot(Kgrad_r, KV['U_r'])).sum(0)
LMLgrad_det = reduce(SP.dot, [d, Si, KV['S_c_tilde']])
UdKU = reduce(SP.dot, [KV['U_r'].T, Kgrad_r, KV['U_r']])
SYUdKU = SP.dot(
UdKU,
(KV['Ytilde'] * SP.tile(KV['S_c_tilde'][SP.newaxis, :],
(self.n, 1))))
LMLgrad_quad = -(KV['Ytilde'] * SYUdKU).sum()
LMLgrad = 0.5 * (LMLgrad_det + LMLgrad_quad)
theta[i] = LMLgrad
RV['covar_r'] = theta
if 'covar_c' in hyperparams:
theta = SP.zeros(len(hyperparams['covar_c']))
for i in range(len(theta)):
Kgrad_c = self.covar_c.Kgrad_theta(hyperparams['covar_c'], i)
S_c_tilde_grad = reduce(
SP.dot, [KV['UBinvB'], Kgrad_c, KV['UBinvB'].T])
LMLgrad_det = reduce(
SP.dot,
[KV['S_r'], Si, SP.diag(S_c_tilde_grad)])
SYUdKU = SP.dot(
(KV['Ytilde'] * SP.tile(KV['S_r'][:, SP.newaxis],
(1, self.t))), S_c_tilde_grad.T)
LMLgrad_quad = -SP.sum(KV['Ytilde'] * SYUdKU)
LMLgrad = 0.5 * (LMLgrad_det + LMLgrad_quad)
theta[i] = LMLgrad
RV['covar_c'] = theta
return RV
def plot_results_interval(twosample_interval_object, xlabel='Time/hr', ylabel='expression level', title="", legend=False, *args, **kwargs):
"""
Plot results of resampling of a (subclass of)
:py:class:`gptwosample.twosample.interval_smooth.GPTwoSampleInterval`.
This method will predict some data new, for plotting purpose.
**Parameters:**
twosample_interval_object: :py:class:`gptwosample.twosample.interval_smooth`
The GPTwosample resample object, from which to take the results.
"""
predicted_indicators = twosample_interval_object.get_predicted_indicators()
model_dist,Xp = twosample_interval_object.get_predicted_model_distribution()
IS = SP.tile(~predicted_indicators, twosample_interval_object._n_replicates_ind)
IJ = SP.tile(predicted_indicators, twosample_interval_object._n_replicates_comm)
# predict GPTwoSample object with indicators as interval_indices
if(IS.any() and IJ.any()):
twosample_interval_object._twosample_object.predict_model_likelihoods(\
interval_indices={individual_id:IS, common_id:IJ}, messages=False)
twosample_interval_object._twosample_object.predict_mean_variance(Xp,\
interval_indices={individual_id:IS, common_id:IJ})
else:
twosample_interval_object._twosample_object.predict_model_likelihoods(messages=False)
twosample_interval_object._twosample_object.predict_mean_variance(Xp)
#now plot stuff
ax1 = PL.axes([0.15, 0.1, 0.8, 0.7])
plot_results(twosample_interval_object._twosample_object,
alpha=model_dist,
legend=legend,#interval_indices={individual_id:IS, common_id:IJ},
xlabel=xlabel,
ylabel=ylabel,
title="", *args, **kwargs)
PL.suptitle(title,fontsize=20)
PL.xlim([Xp.min(), Xp.max()])
yticks = ax1.get_yticks()[0:-1]
ax1.set_yticks(yticks)
data = twosample_interval_object._twosample_object.get_data(common_id)
Ymax = data[1].max()
Ymin = data[1].min()
DY = Ymax - Ymin
PL.ylim([Ymin - 0.1 * DY, Ymax + 0.1 * DY])
#2nd. plot prob. of diff
ax2 = PL.axes([0.15, 0.8, 0.8, 0.10], sharex=ax1)
PL.plot(Xp, model_dist, 'k-', linewidth=2)
PL.ylabel('$P(z(t)=1)$')
# PL.yticks([0.0,0.5,1.0])
PL.yticks([0.5])
#horizontal bar
PL.axhline(linewidth=0.5, color='#aaaaaa', y=0.5)
PL.ylim([0, 1])
PL.setp(ax2.get_xticklabels(), visible=False)
def _LMLgrad_covar(self,hyperparams,debugging=False):
"""
evaluates the gradient of the log marginal likelihood with respect to the
hyperparameters of the covariance function
"""
try:
KV = self.get_covariances(hyperparams,debugging=debugging)
except LA.LinAlgError:
LG.error('linalg exception in _LMLgrad_covar')
return {'covar_r':SP.zeros(len(hyperparams['covar_r'])),'covar_c':SP.zeros(len(hyperparams['covar_c'])),'covar_r':SP.zeros(len(hyperparams['covar_r']))}
except ValueError:
LG.error('value error in _LMLgrad_covar')
return {'covar_r':SP.zeros(len(hyperparams['covar_r'])),'covar_c':SP.zeros(len(hyperparams['covar_c'])),'covar_r':SP.zeros(len(hyperparams['covar_r']))}
RV = {}
Si = unravel(1./KV['S'],self.n,self.t)
if 'covar_r' in hyperparams:
theta = SP.zeros(len(hyperparams['covar_r']))
for i in range(len(theta)):
Kgrad_r = self.covar_r.Kgrad_theta(hyperparams['covar_r'],i)
d=(KV['U_r']*SP.dot(Kgrad_r,KV['U_r'])).sum(0)
LMLgrad_det = SP.dot(d,SP.dot(Si,KV['S_c']))
UdKU = SP.dot(KV['U_r'].T,SP.dot(Kgrad_r,KV['U_r']))
SYUdKU = SP.dot(UdKU,(KV['Ytilde']*SP.tile(KV['S_c'][SP.newaxis,:],(self.n,1))))
LMLgrad_quad = - (KV['Ytilde']*SYUdKU).sum()
LMLgrad = 0.5*(LMLgrad_det + LMLgrad_quad)
theta[i] = LMLgrad
if debugging:
Kd = SP.kron(KV['K_c'], Kgrad_r)
_LMLgrad = 0.5 * (KV['W']*Kd).sum()
assert SP.allclose(LMLgrad,_LMLgrad), 'ouch, gradient is wrong for covar_r'
RV['covar_r'] = theta
if 'covar_c' in hyperparams:
theta = SP.zeros(len(hyperparams['covar_c']))
for i in range(len(theta)):
Kgrad_c = self.covar_c.Kgrad_theta(hyperparams['covar_c'],i)
d=(KV['U_c']*SP.dot(Kgrad_c,KV['U_c'])).sum(0)
LMLgrad_det = SP.dot(KV['S_r'],SP.dot(Si,d))
UdKU = SP.dot(KV['U_c'].T,SP.dot(Kgrad_c,KV['U_c']))
SYUdKU = SP.dot((KV['Ytilde']*SP.tile(KV['S_r'][:,SP.newaxis],(1,self.t))),UdKU.T)
LMLgrad_quad = -SP.sum(KV['Ytilde']*SYUdKU)
LMLgrad = 0.5*(LMLgrad_det + LMLgrad_quad)
theta[i] = LMLgrad
if debugging:
Kd = SP.kron(Kgrad_c, KV['K_r'])
_LMLgrad = 0.5 * (KV['W']*Kd).sum()
assert SP.allclose(LMLgrad,_LMLgrad), 'ouch, gradient is wrong for covar_c'
RV['covar_c'] = theta
return RV
def regular_cube_innerproduct(rcc, k):
"""
For a given regular_cube_complex, compute a matrix
representing the k-form innerproduct.
These elements are similar to Whitney forms,
except using standard linear (bilinear,trilinear,..)
elements for 0-forms.
"""
N = rcc.complex_dimension()
#standard cube is [0,0,..,0] [0,1,...,N]
standard_cube = atleast_2d(array([0] * N + range(N), dtype='i'))
standard_k_faces = standard_cube
for i in range(N, k, -1):
standard_k_faces = cube_array_boundary(standard_k_faces, i)[0]
k_faces_per_cube = standard_k_faces.shape[0]
K = zeros((k_faces_per_cube, k_faces_per_cube)) #local stiffness matrix
h = 1
V = h**N #cube volume
scale = V * (1 / h)**2 * (1 / 3.0)**(N - k)
for i, row_i in enumerate(standard_k_faces):
for j, row_j in enumerate(standard_k_faces):
if all(row_i[N:] == row_j[N:]):
differences = (row_i[:N] != row_j[:N])
differences[row_i[N:]] = 0
K[i, j] = scale * (1.0 / 2.0)**sum(differences)
else:
K[i, j] = 0
CA = rcc[-1].cube_array[:, :N]
num_cubes = CA.shape[0]
k_faces = tile(hstack((CA, zeros((CA.shape[0], k), dtype=CA.dtype))),
(1, k_faces_per_cube)).reshape((-1, N + k))
k_faces += tile(standard_k_faces, (num_cubes, 1))
k_face_array = rcc[k].cube_array
face_indices = cube_array_search(k_face_array, k_faces)
rows = face_indices.repeat(k_faces_per_cube)
cols = face_indices.reshape(
(-1, k_faces_per_cube)).repeat(k_faces_per_cube, axis=0).reshape(
(-1, ))
data = K.reshape((1, -1)).repeat(num_cubes, axis=0).reshape((-1, ))
# temporary memory cost solution - eliminate zeros from COO representation
nz_mask = data != 0.0
rows = rows[nz_mask]
cols = cols[nz_mask]
data = data[nz_mask]
shape = (len(k_face_array), len(k_face_array))
return coo_matrix((data, (rows, cols)), shape).tocsr()
def _LMLgrad_covar(self,hyperparams,debugging=False):
"""
evaluates the gradient of the log marginal likelihood with respect to the
hyperparameters of the covariance function
"""
try:
KV = self.get_covariances(hyperparams,debugging=debugging)
except LA.LinAlgError:
LG.error('linalg exception in _LMLgrad_covar')
return {'covar_r':SP.zeros(len(hyperparams['covar_r'])),'covar_c':SP.zeros(len(hyperparams['covar_c'])),'covar_r':SP.zeros(len(hyperparams['covar_r']))}
except ValueError:
LG.error('value error in _LMLgrad_covar')
return {'covar_r':SP.zeros(len(hyperparams['covar_r'])),'covar_c':SP.zeros(len(hyperparams['covar_c'])),'covar_r':SP.zeros(len(hyperparams['covar_r']))}
RV = {}
Si = unravel(1./KV['S'],self.n,self.t)
if 'covar_r' in hyperparams:
theta = SP.zeros(len(hyperparams['covar_r']))
for i in range(len(theta)):
Kgrad_r = self.covar_r.Kgrad_theta(hyperparams['covar_r'],i)
d=(KV['U_r']*SP.dot(Kgrad_r,KV['U_r'])).sum(0)
LMLgrad_det = SP.dot(d,SP.dot(Si,KV['S_c']))
UdKU = SP.dot(KV['U_r'].T,SP.dot(Kgrad_r,KV['U_r']))
SYUdKU = SP.dot(UdKU,(KV['Ytilde']*SP.tile(KV['S_c'][SP.newaxis,:],(self.n,1))))
LMLgrad_quad = - (KV['Ytilde']*SYUdKU).sum()
LMLgrad = 0.5*(LMLgrad_det + LMLgrad_quad)
theta[i] = LMLgrad
if debugging:
Kd = SP.kron(KV['K_c'], Kgrad_r)
_LMLgrad = 0.5 * (KV['W']*Kd).sum()
assert SP.allclose(LMLgrad,_LMLgrad), 'ouch, gradient is wrong for covar_r'
RV['covar_r'] = theta
if 'covar_c' in hyperparams:
theta = SP.zeros(len(hyperparams['covar_c']))
for i in range(len(theta)):
Kgrad_c = self.covar_c.Kgrad_theta(hyperparams['covar_c'],i)
d=(KV['U_c']*SP.dot(Kgrad_c,KV['U_c'])).sum(0)
LMLgrad_det = SP.dot(KV['S_r'],SP.dot(Si,d))
UdKU = SP.dot(KV['U_c'].T,SP.dot(Kgrad_c,KV['U_c']))
SYUdKU = SP.dot((KV['Ytilde']*SP.tile(KV['S_r'][:,SP.newaxis],(1,self.t))),UdKU.T)
LMLgrad_quad = -SP.sum(KV['Ytilde']*SYUdKU)
LMLgrad = 0.5*(LMLgrad_det + LMLgrad_quad)
theta[i] = LMLgrad
if debugging:
Kd = SP.kron(Kgrad_c, KV['K_r'])
_LMLgrad = 0.5 * (KV['W']*Kd).sum()
assert SP.allclose(LMLgrad,_LMLgrad), 'ouch, gradient is wrong for covar_c'
RV['covar_c'] = theta
return RV
def regular_cube_innerproduct(rcc,k):
"""
For a given regular_cube_complex, compute a matrix
representing the k-form innerproduct.
These elements are similar to Whitney forms,
except using standard linear (bilinear,trilinear,..)
elements for 0-forms.
"""
N = rcc.complex_dimension()
#standard cube is [0,0,..,0] [0,1,...,N]
standard_cube = atleast_2d(array([0]*N + range(N),dtype='i'))
standard_k_faces = standard_cube
for i in range(N,k,-1):
standard_k_faces = cube_array_boundary(standard_k_faces,i)[0]
k_faces_per_cube = standard_k_faces.shape[0]
K = zeros((k_faces_per_cube,k_faces_per_cube)) #local stiffness matrix
h = 1
V = h**N #cube volume
scale = V * (1/h)**2 * (1/3.0)**(N-k)
for i,row_i in enumerate(standard_k_faces):
for j,row_j in enumerate(standard_k_faces):
if all(row_i[N:] == row_j[N:]):
differences = (row_i[:N] != row_j[:N])
differences[row_i[N:]] = 0
K[i,j] = scale * (1.0/2.0)**sum(differences)
else:
K[i,j] = 0
CA = rcc[-1].cube_array[:,:N]
num_cubes = CA.shape[0]
k_faces = tile(hstack((CA,zeros((CA.shape[0],k),dtype=CA.dtype))),(1,k_faces_per_cube)).reshape((-1,N+k))
k_faces += tile(standard_k_faces,(num_cubes,1))
k_face_array = rcc[k].cube_array
face_indices = cube_array_search(k_face_array,k_faces)
rows = face_indices.repeat(k_faces_per_cube)
cols = face_indices.reshape((-1,k_faces_per_cube)).repeat(k_faces_per_cube,axis=0).reshape((-1,))
data = K.reshape((1,-1)).repeat(num_cubes,axis=0).reshape((-1,))
# temporary memory cost solution - eliminate zeros from COO representation
nz_mask = data != 0.0
rows = rows[nz_mask]
cols = cols[nz_mask]
data = data[nz_mask]
shape = (len(k_face_array),len(k_face_array))
return coo_matrix( (data,(rows,cols)), shape).tocsr()
def array_coords(shape): y = shape[0] x = shape[1] out = scipy.empty((2,y,x)) t = scipy.arange(y,dtype='f8') out[0] = scipy.tile(t,(x,1)).T t = scipy.arange(x,dtype='f8') out[1] = scipy.tile(t,(y,1)) return out
def f(self, x):
N = self.xdim / 3
coords = x.reshape((N, 3))
distances = sqrt(
scipy.sum((tile(coords,
(N, 1, 1)) - swapaxes(tile(coords,
(N, 1, 1)), 0, 1))**2,
axis=2)) + eye(N)
return 2 * sum(ravel(distances**-12 - distances**-6))
def nandot(x1, x2):
if len(x1.shape) == 1 and len(x2.shape) == 2:
x1T = SP.tile(x1, [x2.shape[1], 1]).transpose()
return SP.nansum(SP.multiply(x1T, x2), axis=0)
elif len(x2.shape) == 1 and len(x1.shape) == 2:
x2T = SP.tile(x2, [x1.shape[0], 1])
return SP.nansum(SP.multiply(x1, x2T), axis=1)
elif len(x1.shape) == 1 and len(x2.shape) == 1:
return SP.nansum(SP.multiply(x1, x2))
return None
def plot_stoch_value():
#Compute Solution==========================================================
sigma = .5
mu = 4 * sigma
K = 7
Gamma, eps = discretenorm.discretenorm(K, mu, sigma)
N = 100
W = sp.linspace(0, 1, N)
V = sp.zeros((N, K))
u = lambda c: sp.sqrt(c)
beta = 0.99
X, Y = sp.meshgrid(W, W)
Wdiff = Y - X
index = Wdiff < 0
Wdiff[index] = 0
util_grid = u(Wdiff)
util3 = sp.tile(util_grid[:, :, sp.newaxis], (1, 1, K))
eps_grid = eps[sp.newaxis, sp.newaxis, :]
eps_util = eps_grid * util3
Gamma_grid = Gamma[sp.newaxis, :]
delta = 1
Vprime = V
z = 0
while (delta > 10**-9):
z = z + 1
V = Vprime
gamV = Gamma_grid * V
Expval = sp.sum(gamV, 1)
Exp_grid = sp.tile(Expval[sp.newaxis, :, sp.newaxis], (N, 1, K))
arg = eps_util + beta * Exp_grid
arg[index] = -10 ^ 10
Vprime = sp.amax(arg, 1)
psi_ind = sp.argmax(arg, 1)
psi = W[psi_ind]
delta = sp.linalg.norm(Vprime - V)
#============================================================
#Plot 3D
x = sp.arange(0, N)
y = sp.arange(0, K)
X, Y = sp.meshgrid(x, y)
fig1 = plt.figure()
ax1 = Axes3D(fig1)
ax1.set_xlabel(r'$W$')
ax1.set_ylabel(r'$\varepsilon$')
ax1.set_zlabel(r'$V$')
ax1.plot_surface(W[X], Y, sp.transpose(Vprime), cmap=cm.coolwarm)
plt.savefig('stoch_value.pdf')
def correlation_1s_1s(self, op1, op2, n1, d, return_exvals=False):
"""Computes a correlation function of two 1 site operators.
The result is < op1_k op2_k+j > - <op1_k> * <op2_k+j>
with the operators acting on sites k and k + j, with j running from
0 to d.
Optionally returns the corresponding expectation values <op1_k+j> and
<op2_k+j>.
Parameters
----------
op1 : ndarray or callable
The first operator, acting on the first site.
op2 : ndarray or callable
The second operator, acting on the second site.
n1 : int
Site to begin from.
d : int
The distance (number of sites) between the two sites acted on non-trivially.
return_exvals : bool
Whether to return expectation values for op1 and op2 for all sites.
Returns
-------
ccf : sequence of complex128
The correlation function across d + 1 sites (including site k).
ex1 : sequence of complex128
Expectation values of op1 for each site. Only if return_exvals == True.
ex2 : sequence of complex128
See ex1.
"""
ex1 = sp.zeros((d + 1), dtype=sp.complex128)
for j in range(d + 1):
ex1[j] = self.expect_1s(op1, n1 + j)
if op1 is op2:
ex2 = ex1
else:
ex2 = sp.zeros((d + 1), dtype=sp.complex128)
for j in range(d + 1):
ex2[j] = self.expect_1s(op2, n1 + j)
cf = self.expect_1s_1s(op1, op2, n1, n1 + d, return_intermediates=True)
ccf = sp.zeros((d + 1), dtype=sp.complex128)
for j in range(d + 1):
ccf[j] = cf[j] - ex1[0] * ex2[j]
if return_exvals:
ex1_ = sp.tile(ex1, [(d + 1) // d + 1])[:d + 1]
ex2_ = sp.tile(ex1, [(d + 1) // d + 1])[:d + 1]
return ccf, ex1_, ex2_
else:
return ccf
def correlation_1s_1s(self, op1, op2, n1, d, return_exvals=False):
"""Computes a correlation function of two 1 site operators.
The result is < op1_k op2_k+j > - <op1_k> * <op2_k+j>
with the operators acting on sites k and k + j, with j running from
0 to d.
Optionally returns the corresponding expectation values <op1_k+j> and
<op2_k+j>.
Parameters
----------
op1 : ndarray or callable
The first operator, acting on the first site.
op2 : ndarray or callable
The second operator, acting on the second site.
n1 : int
Site to begin from.
d : int
The distance (number of sites) between the two sites acted on non-trivially.
return_exvals : bool
Whether to return expectation values for op1 and op2 for all sites.
Returns
-------
ccf : sequence of complex128
The correlation function across d + 1 sites (including site k).
ex1 : sequence of complex128
Expectation values of op1 for each site. Only if return_exvals == True.
ex2 : sequence of complex128
See ex1.
"""
ex1 = sp.zeros((d + 1), dtype=sp.complex128)
for j in xrange(d + 1):
ex1[j] = self.expect_1s(op1, n1 + j)
if op1 is op2:
ex2 = ex1
else:
ex2 = sp.zeros((d + 1), dtype=sp.complex128)
for j in xrange(d + 1):
ex2[j] = self.expect_1s(op2, n1 + j)
cf = self.expect_1s_1s(op1, op2, n1, n1 + d, return_intermediates=True)
ccf = sp.zeros((d + 1), dtype=sp.complex128)
for j in xrange(d + 1):
ccf[j] = cf[j] - ex1[0] * ex2[j]
if return_exvals:
ex1_ = sp.tile(ex1, [(d + 1) / d + 1])[:d + 1]
ex2_ = sp.tile(ex1, [(d + 1) / d + 1])[:d + 1]
return ccf, ex1_, ex2_
else:
return ccf
def plot_stoch_value():
#Compute Solution==========================================================
sigma = .5
mu = 4*sigma
K = 7
Gamma, eps = discretenorm.discretenorm(K,mu,sigma)
N = 100
W = sp.linspace(0,1,N)
V = sp.zeros((N,K))
u = lambda c: sp.sqrt(c)
beta = 0.99
X,Y= sp.meshgrid(W,W)
Wdiff = Y-X
index = Wdiff < 0
Wdiff[index] = 0
util_grid = u(Wdiff)
util3 = sp.tile(util_grid[:,:,sp.newaxis],(1,1,K))
eps_grid = eps[sp.newaxis,sp.newaxis,:]
eps_util = eps_grid*util3
Gamma_grid = Gamma[sp.newaxis,:]
delta = 1
Vprime = V
z = 0
while (delta > 10**-9):
z= z+1
V = Vprime
gamV = Gamma_grid*V
Expval = sp.sum(gamV,1)
Exp_grid = sp.tile(Expval[sp.newaxis,:,sp.newaxis],(N,1,K))
arg = eps_util+beta*Exp_grid
arg[index] = -10^10
Vprime = sp.amax(arg,1)
psi_ind = sp.argmax(arg,1)
psi = W[psi_ind]
delta = sp.linalg.norm(Vprime - V)
#============================================================
#Plot 3D
x=sp.arange(0,N)
y=sp.arange(0,K)
X,Y=sp.meshgrid(x,y)
fig1 = plt.figure()
ax1= Axes3D(fig1)
ax1.set_xlabel(r'$W$')
ax1.set_ylabel(r'$\varepsilon$')
ax1.set_zlabel(r'$V$')
ax1.plot_surface(W[X],Y,sp.transpose(Vprime), cmap=cm.coolwarm)
plt.savefig('stoch_value.pdf')
def krondiag(v1,v2):
"""calcualte diagonal of kronecker(diag(v1),diag(v2)))
note that this returns a non-flattened matrix
"""
M1 = SP.tile(v1[:,SP.newaxis],[1,v2.shape[0]])
M2 = SP.tile(v2[SP.newaxis,:],[v1.shape[0],1])
M1 *= M2
#RV = (M1).ravel()
#naive:
#r=SP.kron(SP.diag(v1), SP.diag(v2)).diagonal()
return M1
def makedata(testpath, tint):
""" This will make the input data for the test case. The data will have cases
where there will be enhancements in Ne, Ti and Te in one location. Each
case will have 3 integration periods. The first 3 integration periods will
be the default set of parameters Ne=Ne=1e11 and Te=Ti=2000.
Inputs
testpath - Directory that will hold the data.
tint - The integration time in seconds.
"""
testpath = Path(testpath).expanduser()
finalpath = testpath.joinpath('Origparams')
if not finalpath.is_dir():
finalpath.mkdir()
data = sp.array([[1e11, 1100.], [1e11, 2100.]])
z = (50. + sp.arange(50) * 10.)
nz = len(z)
params = sp.tile(data[sp.newaxis, sp.newaxis], (nz, 1, 1, 1))
epnt = range(20, 22)
p2 = sp.tile(params, (1, 4, 1, 1))
#enhancement in Ne
p2[epnt, 1, :, 0] = 5e11
#enhancement in Ti
p2[epnt, 2, 0, 1] = 2200.
#enhancement in Te
p2[epnt, 3, 1, 1] = 4200.
coords = sp.column_stack((sp.ones(nz), sp.ones(nz), z))
species = ['O+', 'e-']
times = sp.array([[0, 1e3]])
times2 = sp.column_stack((sp.arange(0, 4), sp.arange(1, 5))) * 3 * tint
vel = sp.zeros((nz, 1, 3))
vel2 = sp.zeros((nz, 4, 3))
Icontstart = IonoContainer(coordlist=coords,
paramlist=params,
times=times,
sensor_loc=sp.zeros(3),
ver=0,
coordvecs=['x', 'y', 'z'],
paramnames=None,
species=species,
velocity=vel)
Icont1 = IonoContainer(coordlist=coords,
paramlist=p2,
times=times2,
sensor_loc=sp.zeros(3),
ver=0,
coordvecs=['x', 'y', 'z'],
paramnames=None,
species=species,
velocity=vel2)
finalfile = finalpath.joinpath('0 stats.h5')
Icont1.saveh5(str(finalfile))
Icontstart.saveh5(str(testpath.joinpath('startfile.h5')))
def krondiag(v1, v2):
"""calcualte diagonal of kronecker(diag(v1),diag(v2)))
note that this returns a non-flattened matrix
"""
M1 = SP.tile(v1[:, SP.newaxis], [1, v2.shape[0]])
M2 = SP.tile(v2[SP.newaxis, :], [v1.shape[0], 1])
M1 *= M2
#RV = (M1).ravel()
#naive:
#r=SP.kron(SP.diag(v1), SP.diag(v2)).diagonal()
#pdb.set_trace()
return M1
def add_landmark_to_map(mu, sigma, z, mapout, Q, scale):
"""Add a landmark to the UKF.
We have to compute the uncertainty of the landmark given the current state
(and its uncertainty) of the newly observed landmark. To this end, we also
employ the unscented transform to propagate Q (sensor noise) through the
current state"""
# For computing sigma
# FIND OUT WHY THEY WERE USING A GLOBAL ---> global scale;
#add landmark to the map
mapout += [z.idx]
# TODO: Initialize its pose according to the measurement and add it to mu
# Append the measurement to the state vector
mu += [z['range'], z['bearing']]
# Initialize its uncertainty and add it to sigma
sigma = scipy.linalg.block_diag(sigma, Q)
# Transform from [range, bearing] to the x/y location of the landmark
# This operation intializes the uncertainty in the position of the landmark
# Sample sigma points
sig_pnts_new = compute_sigma_points(mu, sigma, scale)
# Normalize!
sig_pnts_new[2,:] = normalize_angle(sig_pnts_new[2,:])
# Compute the xy location of the new landmark according to each sigma point
newX = sig_pnts_new[0,:] + sig_pnts_new[-2,:]*scipy.cos(sig_pnts_new[2,:] + sig_pnts_new[-1,:])
newY = sig_pnts_new[1,:] + sig_pnts_new[-2,:]*scipy.sin(sig_pnts_new[2,:] + sig_pnts_new[-1,:])
# The last 2 components of the sigma points can now be replaced by the xy pose of the landmark
sig_pnts_new[-2,:] = newX
sig_pnts_new[-1,:] = newY
# Recover mu and sigma
#n = len(mu)
#lam = scale - n;
w0 = 1 - len(mu)/scale #lam/scale;
wm = [w0, scipy.tile(1/(2*scale), (1, 2*n))]
# Theta should be recovered by summing up the sines and cosines
cosines = scipy.sum(scipy.cos(sig_pnts_new[2,:])*wm)
sines = scipy.sum(scipy.sin(sig_pnts_new[2,:])*wm)
# recompute the angle and normalize it
mu_theta = scipy.arctan2(sines, cosines);
mu = scipy.sum(sig_pnts_new*scipy.tile(wm, (sig_pnts_new.shape[0], 1)), 1)
mu[2] = mu_theta
diff = sig_pnts_new - scipy.tile(mu, (1, sig_pnts_new.shape[1]))
# Normalize!
diff[2,:] = normalize_angle(diff[2,:])
sigma = scipy.dot(scipy.tile(wm, (diff.shape[0], 1))*diff, diff.T)
def _gradQuadrForm(self, hyperparams,dK,columns =True ):
"""derivative of the quadtratic form w.r.t. kernel derivative matrix (dK)"""
KV = self.get_covariances(hyperparams)
Si = KV['Si']
Ytilde = (KV['YSi'])
if columns:
UdKU = SP.dot(KV['Uc'].T,SP.dot(dK,KV['Uc']))
SYUdKU = SP.dot((Ytilde*SP.tile(KV['Sr'][:,SP.newaxis],(1,Ytilde.shape[1]))),UdKU.T)
else:
UdKU = SP.dot(KV['Ur'].T,SP.dot(dK,KV['Ur']))
SYUdKU = SP.dot(UdKU,(Ytilde*SP.tile(KV['Sc'][SP.newaxis,:],(Ytilde.shape[0],1))))
return -SP.dot(Ytilde.ravel(),SYUdKU.ravel())
def array_coords(shape): """ Faster version of scipy.indices() """ y = shape[0] x = shape[1] out = scipy.empty((2,y,x)) t = scipy.arange(y,dtype='f8') out[0] = scipy.tile(t,(x,1)).T t = scipy.arange(x,dtype='f8') out[1] = scipy.tile(t,(y,1)) return out
def __init__(self, gridObj, dt, nParticles=1.e11, tBunchSpacing=25.e-9):
self.gridObj = gridObj
self.nx = gridObj.getNxExt()
self.ny = gridObj.getNyExt()
self.np = gridObj.getNpExt()
self.lx = gridObj.getLxExt()
self.ly = gridObj.getLyExt()
self.dx = gridObj.getDx()
self.dy = gridObj.getDy()
self.dt = dt
self.nParticles = nParticles
self.charge = spc.elementary_charge
self.beamVelocity = spc.c
self.circumference = 6900
self.radiusSigma = 0.002
self.radiusLimitSigma = 5
self.xBeamCenter = 0.
self.yBeamCenter = 0.
self.tBunchSpacing = tBunchSpacing
self.bunchLengthSigma = 0.1
self.tBunchLengthSigma = self.bunchLengthSigma / self.beamVelocity
self.bunchLengthLimitSigma = 5
self.qTransversalProfile = sp.zeros(self.np)
xMesh = self.gridObj.getXMesh()
yMesh = self.gridObj.getYMesh()
xCoords = sp.tile(xMesh, self.ny)
yCoords = sp.reshape(sp.tile(yMesh, (self.nx, 1)).transpose(), self.np)
beamPoints = (
(self.radiusLimitSigma * self.radiusSigma +
max([self.dx, self.dy]))**2 - xCoords**2 - yCoords**2) > 0
self.qTransversalProfile[beamPoints] = ((sps.norm.cdf(
sp.clip(
(xCoords - self.xBeamCenter + self.dx / 2.) / self.radiusSigma,
-self.radiusLimitSigma, self.radiusLimitSigma)) - sps.norm.cdf(
sp.clip(
(xCoords - self.xBeamCenter - self.dx / 2.) /
self.radiusSigma, -self.radiusLimitSigma,
self.radiusLimitSigma))) * (sps.norm.cdf(
sp.clip(
(yCoords - self.yBeamCenter + self.dy / 2.) /
self.radiusSigma, -self.radiusLimitSigma,
self.radiusLimitSigma)) - sps.norm.cdf(
sp.clip(
(yCoords - self.yBeamCenter -
self.dy / 2.) / self.radiusSigma,
-self.radiusLimitSigma,
self.radiusLimitSigma))))[beamPoints]
self.qTransversalProfile /= sp.sum(self.qTransversalProfile)
def _gradQuadrFormX(self, hyperparams, dKx, columns=True):
"""derivative of the quadtratic form with.r.t. covarianceparameters for row or column covariance"""
KV = self.get_covariances(hyperparams)
Ytilde = (KV['YSi'])
if columns:
UY = SP.dot(KV['Uc'], Ytilde.T)
UYS = UY * SP.tile(KV['Sr'][SP.newaxis, :], (Ytilde.shape[1], 1))
else:
UY = SP.dot(KV['Ur'], Ytilde)
UYS = UY * SP.tile(KV['Sc'][SP.newaxis, :], (Ytilde.shape[0], 1))
UYSYU = SP.dot(UYS, UY.T)
trUYSYUdK = (UYSYU * dKx.T).sum(0)
return -2.0 * trUYSYUdK
def _gradQuadrFormX(self, hyperparams,dKx,columns =True ):
"""derivative of the quadtratic form with.r.t. covarianceparameters for row or column covariance"""
KV = self.get_covariances(hyperparams)
Ytilde = (KV['YSi'])
if columns:
UY=SP.dot(KV['Uc'],Ytilde.T)
UYS = UY*SP.tile(KV['Sr'][SP.newaxis,:],(Ytilde.shape[1],1))
else:
UY=SP.dot(KV['Ur'],Ytilde)
UYS = UY*SP.tile(KV['Sc'][SP.newaxis,:],(Ytilde.shape[0],1))
UYSYU=SP.dot(UYS,UY.T)
trUYSYUdK=(UYSYU*dKx.T).sum(0)
return -2.0*trUYSYUdK
def _gradQuadrForm(self, hyperparams, dK, columns=True):
"""derivative of the quadtratic form w.r.t. kernel derivative matrix (dK)"""
KV = self.get_covariances(hyperparams)
Si = KV['Si']
Ytilde = (KV['YSi'])
if columns:
UdKU = SP.dot(KV['Uc'].T, SP.dot(dK, KV['Uc']))
SYUdKU = SP.dot((Ytilde * SP.tile(KV['Sr'][:, SP.newaxis],
(1, Ytilde.shape[1]))), UdKU.T)
else:
UdKU = SP.dot(KV['Ur'].T, SP.dot(dK, KV['Ur']))
SYUdKU = SP.dot(UdKU, (Ytilde * SP.tile(KV['Sc'][SP.newaxis, :],
(Ytilde.shape[0], 1))))
return -SP.dot(Ytilde.ravel(), SYUdKU.ravel())
def __generate_potential_grid(self):
from scipy import linspace, tile
rowdim = self.canvas.shape[0]
coldim = self.canvas.shape[1]
pot_slice = linspace(p.potential_drop[0],p.potential_drop[1],rowdim)
potential = tile(pot_slice,(coldim,1)).T
self.potential_grid = potential
def addFitPlot(self, fit):
"""add a contour plot on top using fitted data and add additional plots to sidebars (TODO) """
logger.debug("adding fit plot with fit %s " % fit)
if not fit.fitted:
logger.error(
"cannot add a fitted plot for unfitted data. Run fit first")
return
if not self.drawFitBool:
logger.info("first fit plot so initialising contour plot")
self.initialiseFitPlot()
logger.info("attempting to set fit data")
self.contourPositions = [
scipy.tile(self.contourXS, len(self.contourYS)),
scipy.repeat(self.contourYS, len(self.contourXS))
] #for creating data necessary for gauss2D function
zsravelled = fit.fitFunc(self.contourPositions,
*fit._getCalculatedValues())
# logger.debug("zs ravelled shape %s " % zsravelled.shape)
self.contourZS = zsravelled.reshape(
(len(self.contourYS), len(self.contourXS)))
# logger.debug("zs contour shape %s " % self.contourZS.shape)
# logger.info("shape contour = %s " % self.contourZS)
self._fit_value.data = self.contourZS
self.container.invalidate_draw()
self.container.request_redraw()
self.drawFitBool = True
def initial_cond(coords, mass, dipole, temp, F):
cm_coords = coords - tile(center_of_mass(coords, mass), (coords.shape[0], 1))
print "computing inertia tensor and principal axes of inertia"
mol_I, mol_Ix = eig(inertia_tensor(cm_coords, mass))
mol_I.sort()
print "principal moments of inertia are: ", mol_I
# compute the ratio of the dipole energy to the
# rotational energy
print "x = (mu*F / kB*T_R) = ", norm(dipole) * F / kB_au / temp
# random initial angular velocity vector
# magnitude set so that 0.5 * I * w**2.0 = kT
w_mag = sqrt(2.0 * kB_au * temp / mol_I.mean())
w0 = 2.0 * rand(3) - 1.0
w0 = w0 / norm(w0) * w_mag
# random initial orientation / random unit quaternion
q0 = 2.0 * rand(4) - 1.0
q0 = q0 / norm(q0)
return q0, w0
def Problem1Real():
beta = 0.9;
T = 10;
N = 100;
u = lambda c: sp.sqrt(c);
W = sp.linspace(0,1,N);
X, Y = sp.meshgrid(W,W);
Wdiff = Y-X
index = Wdiff <0;
Wdiff[index] = 0;
util_grid = u(Wdiff);
util_grid[index] = -10**10;
V = sp.zeros((N,T+2));
psi = sp.zeros((N,T+1));
for k in xrange(T,-1,-1):
val = util_grid + beta*sp.tile(sp.transpose(V[:,k+1]),(N,1));
vt = sp.amax(val, axis = 1);
psi_ind = sp.argmax(val,axis = 1)
V[:,k] = vt;
psi[:,k] = W[psi_ind];
return V,psi
def make_batches(data, labels=None, batch_size=100):
if labels is not None:
num_labels = labels.shape[1]
cls_data = [data[find(labels[:,i] == 1)] for i in range(num_labels)]
cls_sizes = [d.shape[0] for d in cls_data]
cls_sels = [permutation(range(s)) for s in cls_sizes]
n = min(cls_sizes) * len(cls_sizes)
batch_size = min(n, batch_size)
lpb = batch_size / num_labels
new_dat = []
for i in range(n/batch_size):
for sel, cd in zip(cls_sels, cls_data):
new_dat.append(cd[sel[i*lpb:(i+1)*lpb]])
if sparse.issparse(data):
data = sparse.vstack(new_dat).tocsr()
else:
data = np.vstack(new_dat)
labels = np.tile(np.repeat(np.eye(num_labels),lpb,0), (n/batch_size,1))
n = len(labels)
perm = range(n)
else:
n = data.shape[0]
perm = permutation(range(n))
i = 0
while i < n:
batch = perm[i:i+batch_size]
i += batch_size
yield (data[batch], None) if labels is None else (data[batch], labels[batch])
def makedata(testpath):
""" This will make the input data for the test case. The data will have the
default set of parameters Ne=Ne=1e11 and Te=Ti=2000.
Inputs
testpath - Directory that will hold the data.
"""
finalpath = testpath.joinpath('Origparams')
if not finalpath.exists():
finalpath.mkdir()
data=SIMVALUES
z = sp.linspace(50.,1e3,50)
nz = len(z)
params = sp.tile(data[sp.newaxis,sp.newaxis,:,:],(nz,1,1,1))
coords = sp.column_stack((sp.ones(nz),sp.ones(nz),z))
species=['O+','e-']
times = sp.array([[0,1e3]])
vel = sp.zeros((nz,1,3))
Icont1 = IonoContainer(coordlist=coords,paramlist=params,times = times,sensor_loc = sp.zeros(3),ver =0,coordvecs =
['x','y','z'],paramnames=None,species=species,velocity=vel)
finalfile = finalpath.joinpath('0 stats.h5')
Icont1.saveh5(str(finalfile))
# set start temp to 1000 K.
Icont1.Param_List[:,:,:,1]=1e3
Icont1.saveh5(str(testpath.joinpath('startfile.h5')))
def fit(self, X, y):
self.Xtr = X
self.ytr = y
if self.K is None:
self.K = np.dot(X, X.T)
[n_s, n_f] = X.shape
if y.ndim == 1:
y = scipy.reshape(y, (n_s, 1))
S, U, ldelta0 = self.train_nullmodel(y,
self.K,
numintervals=self.numintervals,
ldeltamin=self.ldeltamin,
ldeltamax=self.ldeltamax,
scale=self.scale,
KSquare=self.KSquare,
KSearch=self.KSearch)
self.delta0 = scipy.exp(ldelta0)
Sdi = 1. / (S + self.delta0)
Sdi_sqrt = scipy.sqrt(Sdi)
SUX = scipy.dot(U.T, X)
SUX = SUX * scipy.tile(Sdi_sqrt, (n_f, 1)).T
SUy = scipy.dot(U.T, y)
SUy = SUy * scipy.reshape(Sdi_sqrt, (n_s, 1))
self.clf.fit(SUX, SUy)
def get_covariances(self, hyperparams):
if not self._is_cached(
hyperparams) or self._active_set_indices_changed:
#update covariance structure
K = self.covar.K(hyperparams['covar'], self.x)
#calc eigenvalue decomposition
[S, U] = SP.linalg.eigh(K)
#noise diagonal
#depending on noise model this may be either a vector or a matrix
Knoise = self.likelihood.Kdiag(hyperparams['lik'], self.x)
#noise version of S
Sn = Knoise + SP.tile(S[:, SP.newaxis], [1, self.d])
#inverse
Si = 1. / Sn
#rotate data
y_rot = SP.dot(U.T, self.y)
#also store version of data rotated and Si applied
y_roti = (y_rot * Si)
self._covar_cache = {
'S': S,
'U': U,
'K': K,
'Knoise': Knoise,
'Sn': Sn,
'Si': Si,
'y_rot': y_rot,
'y_roti': y_roti
}
self._covar_cache['hyperparams'] = copy.deepcopy(hyperparams)
pass
#return update covar cache
return self._covar_cache
def compute_h_and_H(self, state):
numVal = self.beaconLocations.shape[0]
tiledState = sp.tile(sp.reshape(state, [1, 4]), [numVal, 1])
#Compute the distances and the range model
distances = self.beaconLocations - tiledState[:, :2]
rangeModel = sp.linalg.norm(distances, axis=1, keepdims=True)
#Compute the range rate model
numerator = -distances[:,
0] * tiledState[:,
2] - distances[:,
1] * tiledState[:,
3]
rangeRateModel = sp.reshape(numerator, rangeModel.shape) / rangeModel
#Now to get the derivatives
dRangeModel = sp.hstack([-distances, sp.zeros_like(distances)])
dRangeModel = dRangeModel / rangeModel
dRangeRateModel = (sp.hstack([tiledState[:, 2:], -distances]) -
rangeRateModel * dRangeModel)
dRangeRateModel = dRangeRateModel / rangeModel
return sp.vstack([rangeModel, rangeRateModel
]), sp.vstack([dRangeModel, dRangeRateModel])
def set_normal_free_energy(self):
"""
Set free energy as a function of odorant; normal tuning curve.
"""
self.eps_base = self.mu_eps + self.normal_eps_tuning_prefactor* \
sp.exp(-(1.*sp.arange(self.Mm))**2.0/(2.0* \
self.normal_eps_tuning_width)**2.0)
self.eps_base += random_matrix(self.Mm,
params=[0, self.sigma_eps],
seed=self.seed_eps)
# If dual signal, use the average of the FULL signal nonzero components
if self.Kk_split == 0:
self.eps = self.WL_scaling * sp.log(self.mu_Ss0) + self.eps_base
else:
self.eps = self.WL_scaling*sp.log(sp.average(self.Ss\
[self.Ss != 0])) + self.eps_base
# Apply max and min epsilon value to each component
self.min_eps = random_matrix(
self.Mm,
params=[self.mu_min_eps, self.sigma_min_eps],
seed=self.seed_eps)
self.max_eps = random_matrix(
self.Mm,
params=[self.mu_max_eps, self.sigma_max_eps],
seed=self.seed_eps)
self.eps = sp.maximum(self.eps, self.min_eps)
self.eps = sp.minimum(self.eps, self.max_eps)
# If an array of signals, replicate for each signal.
if len(self.Ss.shape) > 1:
self.eps = sp.tile(self.eps, [self.Ss.shape[1], 1]).T
def center_on_cos(raw_quadratures, phi0=None, omega=None, snap_omega=False):
mean = scipy.average(raw_quadratures, axis=1)
no_angles, no_pulses = raw_quadratures.shape
model = Model(cos_model)
offset, amplitude, phi0, omega = guess_initial_parameters(mean, phi0, omega)
model.set_param_hint("offset", value=offset)
model.set_param_hint("amplitude", min=0., value=amplitude)
model.set_param_hint("phi0", value=phi0)
model.set_param_hint("omega", min=0., value=omega)
model.make_params(verbose=False)
steps = scipy.arange(no_angles)
res = model.fit(mean, x=steps, verbose=False)
omega_param = res.params["omega"]
if snap_omega:
appx_omega = float(omega_param)
no_pi_intervals = int(round(pi/appx_omega))
omega = pi/no_pi_intervals
omega_param.set(omega, vary=False)
res.fit(mean, x=steps, verbose=False)
d_value, p_value_ks = kstest(res.residual, 'norm')
mean_fit = res.eval(x=steps)
offset = mean-mean_fit
aligned_quadratures = raw_quadratures - scipy.tile(offset, (no_pulses, 1)).T
centered_quadratures = aligned_quadratures - float(res.params["offset"])
return (centered_quadratures,
float(omega_param), float(res.params["phi0"]), p_value_ks)
def makedata(testpath):
"""
This will make the input data for the test case. The data will have the
default set of parameters Ne=Ne=1e11 and Te=Ti=2000.
Inputs
testpath - Directory that will hold the data.
"""
finalpath = testpath.joinpath('Origparams')
if not finalpath.exists():
finalpath.mkdir()
data = SIMVALUES
z = sp.linspace(50., 1e3, 50)
nz = len(z)
params = sp.tile(data[sp.newaxis, sp.newaxis, :, :], (nz, 1, 1, 1))
coords = sp.column_stack((sp.ones(nz), sp.ones(nz), z))
species = ['O+', 'e-']
times = sp.array([[0, 1e9]])
vel = sp.zeros((nz, 1, 3))
Icont1 = IonoContainer(coordlist=coords,
paramlist=params,
times=times,
sensor_loc=sp.zeros(3),
ver=0,
coordvecs=['x', 'y', 'z'],
paramnames=None,
species=species,
velocity=vel)
finalfile = finalpath.joinpath('0 stats.h5')
Icont1.saveh5(str(finalfile))
# set start temp to 1000 K.
Icont1.Param_List[:, :, :, 1] = 1e3
Icont1.saveh5(str(testpath.joinpath('startfile.h5')))
def _sig_surface(self, siglevel):
'''
Significance surface for plotting.
'''
sig = wave_signif(self, siglevel, lag1(self.series))
sig = sp.tile(sig, (len(self.series), 1)).T
return sig
def __generate_potential_grid(self):
from scipy import linspace, tile
rowdim = self.canvas.shape[0]
coldim = self.canvas.shape[1]
pot_slice = linspace(p.potential_drop[0], p.potential_drop[1], rowdim)
potential = tile(pot_slice, (coldim, 1)).T
self.potential_grid = potential
def con2vert(A, b):
"""
Convert sets of constraints to a list of vertices (of the feasible region).
If the shape is open, con2vert returns False for the closed property.
"""
# Python implementation of con2vert.m by Michael Kleder (July 2005),
# available: http://www.mathworks.com/matlabcentral/fileexchange/7894
# -con2vert-constraints-to-vertices
# Author: Michael Kelder (Original)
# Andre Campher (Python implementation)
c = linalg.lstsq(mat(A), mat(b))[0]
btmp = mat(b)-mat(A)*c
D = mat(A)/matlib.repmat(btmp, 1, A.shape[1])
fmatv = qhull(D, "Ft") #vertices on facets
G = zeros((fmatv.shape[0], D.shape[1]))
for ix in range(0, fmatv.shape[0]):
F = D[fmatv[ix, :], :].squeeze()
G[ix, :] = linalg.lstsq(F, ones((F.shape[0], 1)))[0].transpose()
V = G + matlib.repmat(c.transpose(), G.shape[0], 1)
ux = uniqm(V)
eps = 1e-13
Av = dot(A, ux.T)
bv = tile(b, (1, ux.shape[0]))
closed = sciall(Av - bv <= eps)
return ux, closed
def _perform_fit(self):
"""Perform the fit using scipy optimise curve fit.
We must supply x and y as one argument and zs as anothger. in the form
xs: 0 1 2 0 1 2 0
ys: 0 0 0 1 1 1 2
zs: 1 5 6 1 9 8 2
Hence the use of repeat and tile in positions and unravel for zs
initially xs,ys is a linspace array and zs is a 2d image array
"""
if self.xs is None or self.ys is None or self.zs is None:
logger.warning(
"attempted to fit data but had no data inside the Fit object. set xs,ys,zs first"
)
return ([], [])
params = self._getParameters()
if self.fitSubSpace: #fit only the sub space
#create xs, ys and zs which are appropriate slices of the arrays
xs, ys, zs = self._get_subSpaceArrays()
else: #fit the whole array of data (slower)
xs, ys, zs = self.xs, self.ys, self.zs
positions = scipy.array([
scipy.tile(xs, len(ys)),
scipy.repeat(ys, len(xs))
]) #for creating data necessary for gauss2D function
if self.fitTimeLimitBool:
modelFitResult = self.lmfitModel.fit(scipy.ravel(zs),
positions=positions,
params=params,
iter_cb=self.getFitCallback(
time.time()))
else: #no iter callback
modelFitResult = self.lmfitModel.fit(scipy.ravel(zs),
positions=positions,
params=params)
return modelFitResult
def _non_dominated_front_arr(iterable, key=lambda x: x, allowequality=True):
"""Return a subset of items from iterable which are not dominated by any
other item in iterable.
Faster version, based on boolean matrix manipulations.
"""
items = list(iterable)
fits = map(key, items)
l = len(items)
x = array(fits)
a = tile(x, (l, 1, 1))
b = a.transpose((1, 0, 2))
if allowequality:
ndom = sum(a <= b, axis=2)
else:
ndom = sum(a < b, axis=2)
ndom = array(ndom, dtype=bool)
res = set()
for ii in range(l):
res.add(ii)
for ij in list(res):
if ii == ij:
continue
if not ndom[ij, ii]:
res.remove(ii)
break
elif not ndom[ii, ij]:
res.remove(ij)
return set(map(lambda i: items[i], res))
def e_step(self):
D,N = self.documents.shape
phi_sum = sp.zeros(D, dtype=sp.double)
# for d from 0 <= d < D:
# gam_sum = gam[d].sum()
# for n from 0 <= n < N:
# wn = documents[d,n]
# for k from 0 <= k < K:
# phi[d,n,k] = wn * beta[k,n] * np.exp(digamma(gam[d,k])-digamma(gam_sum))
# if phi[d,n].sum() > 0:
# phi[d,n] /= phi[d,n].sum()
# gamma[d] = alpha + phi[d].sum(0)
gam_sums = self.gam.sum(1)
for n in range(N):
wns = self.documents[:,n]
phi_sum[:] = 0.0
for k in range(self.K):
# print 'Wn:'
# print wns
# print 'Beta:'
# print beta[k,n]
# print 'Gamma:'
# print np.exp(digamma(gam[:,k]))
self.phi[:,n,k] = wns * self.beta[k,n] * sp.exp(digamma(self.gam[:,k])-digamma(gam_sums))
# phi[:,n,k] = beta[k,n] * np.exp(digamma(gam[:,k])-digamma(gam_sums))
# phi[:,n,k] = wns * beta[k,n] * np.exp(digamma(gam[:,k]))
phi_sum += self.phi[:,n,k]
phi_sum_ary = sp.tile(phi_sum, (self.K,1)).T
self.phi[:,n] /= phi_sum_ary + 0.0000001
self.gam = self.alpha + self.phi.sum(1)
def MNEfit(stim,resp,order):
# in order for dlogloss to work, we need to know -<g(yt(n),xt)>data
# == calculate the constrained averages over the data set
Nsamples = sp.size(stim,0)
Ndim = sp.size(stim,1)
psp = sp.mean(sp.mean(resp)) #spike probability (first constraint)
avg = (1.0*stim.T*resp)/(Nsamples*1.0)
avgs = sp.vstack((psp,avg))
if(order > 1):
avgsqrd = (stim.T*1.0)*(sp.array(sp.tile(resp,(1,Ndim)))*sp.array(stim))/(Nsamples*1.0)
avgsqrd = sp.reshape(avgsqrd,(Ndim**2,1))
avgs = sp.vstack((avgs,avgsqrd))
#initialize params:
pstart = sp.log(1/avgs[0,0] - 1)
pstart = sp.hstack((pstart,(.001*(2*sp.random.rand(Ndim)-1))))
if(order > 1):
temp = .0005*(2*sp.random.rand(Ndim,Ndim)-1)
pstart = sp.hstack((pstart,sp.reshape(temp+temp.T,(1,Ndim**2))[0]))
#redefine functions with fixed vals:
def logLoss(p):
return LLF.log_loss(p, stim, resp, order)
def dlogLoss(p):
return LLF.d_log_loss(p, stim, avgs, order)
#run the function:
#pfinal = opt.fmin_tnc(logLoss,pstart,fprime=dlogLoss)
# conjugate-gradient:
pfinal = opt.fmin_cg(logLoss,pstart,fprime=dlogLoss)
#pfinal = opt.fmin(logLoss,pstart,fprime=dlogLoss)
return pfinal
def analysisdump(maindir, configfile, suptitle=None):
""" This function will perform all of the plotting functions in this module
given the main directory that all of the files live.
Inputs
maindir - The directory for the simulation.
configfile - The name of the configuration file used.
suptitle - The supertitle used on the files.
"""
maindir = Path(maindir)
plotdir = maindir.joinpath("AnalysisPlots")
if not plotdir.is_dir():
plotdir.mkdir()
# plot spectrums
filetemplate1 = str(maindir.joinpath("AnalysisPlots", "Spec"))
filetemplate3 = str(maindir.joinpath("AnalysisPlots", "ACF"))
filetemplate4 = str(maindir.joinpath("AnalysisPlots", "AltvTime"))
(sensdict, simparams) = readconfigfile(configfile)
angles = simparams["angles"]
ang_data = sp.array([[iout[0], iout[1]] for iout in angles])
if not sensdict["Name"].lower() in ["risr", "pfisr"]:
ang_data_temp = ang_data.copy()
beamlistlist = sp.array(simparams["outangles"]).astype(int)
ang_data = sp.array([ang_data_temp[i].mean(axis=0) for i in beamlistlist])
zenang = ang_data[sp.argmax(ang_data[:, 1])]
rnggates = simparams["Rangegatesfinal"]
rngchoices = sp.linspace(sp.amin(rnggates), sp.amax(rnggates), 4)
angtile = sp.tile(zenang, (len(rngchoices), 1))
coords = sp.column_stack((sp.transpose(rngchoices), angtile))
times = simparams["Timevec"]
filetemplate2 = str(maindir.joinpath("AnalysisPlots", "Params"))
if simparams["Pulsetype"].lower() == "barker":
params = ["Ne"]
if suptitle is None:
plotbeamparametersv2(times, configfile, maindir, params=params, filetemplate=filetemplate2, werrors=True)
else:
plotbeamparametersv2(
times, configfile, maindir, params=params, filetemplate=filetemplate2, suptitle=suptitle, werrors=True
)
else:
params = ["Ne", "Nepow", "Te", "Ti", "Vi"]
if suptitle is None:
plotspecs(coords, times, configfile, maindir, cartcoordsys=False, filetemplate=filetemplate1)
plotacfs(coords, times, configfile, maindir, cartcoordsys=False, filetemplate=filetemplate3)
plotbeamparametersv2(times, configfile, maindir, params=params, filetemplate=filetemplate2, werrors=True)
beamvstime(configfile, maindir, params=params, filetemplate=filetemplate4)
else:
plotspecs(
coords, times, configfile, maindir, cartcoordsys=False, filetemplate=filetemplate1, suptitle=suptitle
)
plotacfs(
coords, times, configfile, maindir, cartcoordsys=False, filetemplate=filetemplate3, suptitle=suptitle
)
plotbeamparametersv2(
times, configfile, maindir, params=params, filetemplate=filetemplate2, suptitle=suptitle, werrors=True
)
beamvstime(configfile, maindir, params=params, filetemplate=filetemplate4, suptitle=suptitle)
def my_bh_fdr(p_val_vec):
index = scipy.argsort(p_val_vec)
exp_err = scipy.vstack((float(len(p_val_vec))/scipy.arange(1,len(p_val_vec) + 1)*p_val_vec[index],
scipy.tile(1, [1, len(p_val_vec)]))).min(axis = 0)
exp_err = scipy.vstack((exp_err,exp_err[scipy.r_[0,scipy.arange(len(exp_err)-1)]])).max(axis=0)
#scipy.r_[index[0], index[range(len(index)-1)]
resort_index = scipy.argsort(index)
return exp_err[resort_index]
def Problem6Real():
sigma = .5
mu = 4*sigma
rho = .5
sigmaZ = sigma/sp.sqrt(1-rho**2)
w = 0.5 + rho/4
baseSigma = w*sigma +(1-w)*sigmaZ
K = 7
eps, Gamma = tauchenhussey.tauchenhussey(K,mu,rho,sigma, baseSigma)
eps = sp.reshape(eps,K)
N = 100
W = sp.linspace(0,1,N)
V = sp.zeros((N,K))
u = lambda c: sp.sqrt(c)
beta = 0.9
X,Y= sp.meshgrid(W,W)
Wdiff = Y-X
index = Wdiff < 0
Wdiff[index] = 0
util_grid = u(Wdiff)
util3 = sp.tile(util_grid[:,:,sp.newaxis],(1,1,K))
eps_grid = eps[sp.newaxis,sp.newaxis,:]
eps_util = eps_grid*util3
delta = 1
Vprime = V
z=0
while (delta>10**-9):
z=z+1
V = Vprime
Expval = sp.dot(V,sp.transpose(Gamma))
Exp_grid = sp.tile(Expval[sp.newaxis,:,:],(N,1,1))
arg = eps_util+beta*Exp_grid
arg[index] = -10^10
Vprime = sp.amax(arg,1)
psi_ind = sp.argmax(arg,1)
psi = W[psi_ind]
delta = sp.linalg.norm(Vprime - V)
return Vprime,psi
def sq_dist(X1,X2=None):
"""
computes a matrix of all pariwise squared distances
"""
if X2==None:
X2 = X1
assert X1.shape[1]==X2.shape[1], 'dimensions do not match'
n = X1.shape[0]
m = X2.shape[0]
d = X1.shape[1]
# (X1 - X2)**2 = X1**2 + X2**2 - 2X1X2
X1sq = SP.reshape((X1**2).sum(1),n,1)
X2sq = SP.reshape((X2**2).sum(1),m,1)
K = SP.tile((X1*X1).sum(1),(m,1)).T + SP.tile((X2*X2).sum(1),(n,1)) - 2*SP.dot(X1,X2.T)
return K
def SRIparams2iono(filename):
fullfile = h5file(filename)
fullfiledict = fullfile.readWholeh5file()
#Size = Nrecords x Nbeams x Nranges x Nions+1 x 4 (fraction, temperature, collision frequency, LOS speed)
fits = fullfiledict['/FittedParams']['Fits']
(nt,nbeams,nrng,nspecs,nstuff) = fits.shape
nlocs = nbeams*nrng
fits = fits.transpose((1,2,0,3,4))
fits = fits.reshape((nlocs,nt,nspecs,nstuff))
# Nrecords x Nbeams x Nranges
Ne = fullfiledict['/FittedParams']['Ne']
Ne = Ne.transpose((1,2,0))
Ne = Ne.reshape((nlocs,nt))
param_lists =sp.zeros((nlocs,nt,nspecs,2))
param_lists[:,:,:,0] = fits[:,:,:,0]
param_lists[:,:,:,1] = fits[:,:,:,1]
param_lists[:,:,-1,0]=Ne
Velocity = fits[:,:,0,3]
if fullfiledict['/FittedParams']['IonMass']==16:
species = ['O+','e-']
pnames = sp.array([['Ni','Ti'],['Ne','Te']])
time= fullfiledict['/Time']['UnixTime']
time = time
rng = fullfiledict['/FittedParams']['Range']
bco = fullfiledict['/']['BeamCodes']
angles = bco[:,1:3]
(nang,nrg) = rng.shape
allang = sp.tile(angles[:,sp.newaxis],(1,nrg,1))
all_loc = sp.column_stack((rng.flatten(),allang.reshape(nang*nrg,2)))
lkeep = ~ sp.any(sp.isnan(all_loc),1)
all_loc = all_loc[lkeep]
Velocity = Velocity[lkeep]
param_lists = param_lists[lkeep]
all_loc[:,0]=all_loc[:,0]*1e-3
iono1 = IonoContainer(all_loc,param_lists,times=time,ver = 1,coordvecs = ['r','theta','phi'],
paramnames = pnames,species=species,velocity=Velocity)
# MSIS
tn = fullfiledict['/MSIS']['Tn']
tn = tn.transpose((1,2,0))
tn = tn.reshape((nlocs,nt))
startparams = sp.ones((nlocs,nt,2,2))
startparams[:,:,0,1] = tn
startparams[:,:,1,1] = tn
startparams = startparams[lkeep]
ionoS = IonoContainer(all_loc,startparams,times=time,ver = 1,coordvecs = ['r','theta','phi'],
paramnames = pnames,species=species)
return iono1,ionoS
def connect_pores(network, pores1, pores2, labels=[], add_conns=True):
r'''
Returns the possible connections between two group of pores, and optionally
makes the connections.
Parameters
----------
network : OpenPNM Network Object
pores1 : array_like
The first group of pores on the network
pores2 : array_like
The second group of pores on the network
labels : list of strings
The labels to apply to the new throats. This argument is only needed
if ``add_conns`` is True.
add_conns : bool
Indicates whether the connections should be added to the supplied
network (default is True). Otherwise, the connections are returned
as an Nt x 2 array that can be passed directly to ``extend``.
Notes
-----
It creates the connections in a format which is acceptable by
the default OpenPNM connection ('throat.conns') and either adds them to
the network or returns them.
Examples
--------
>>> import OpenPNM
>>> pn = OpenPNM.Network.TestNet()
>>> pn.Nt
300
>>> pn.connect_pores(pores1=[22, 32], pores2=[16, 80, 68])
>>> pn.Nt
306
>>> pn['throat.conns'][300:306]
array([[16, 22],
[22, 80],
[22, 68],
[16, 32],
[32, 80],
[32, 68]])
'''
size1 = _sp.size(pores1)
size2 = _sp.size(pores2)
array1 = _sp.repeat(pores1, size2)
array2 = _sp.tile(pores2, size1)
conns = _sp.vstack([array1, array2]).T
if add_conns:
extend(network=network, throat_conns=conns, labels=labels)
else:
return conns
