def get_laplacian(A, normalization_mode = None):
"""
Compute the different laplacian of a graphs given a
Code inspired by networkx python library
"""
A = scipy.sparse.csr_matrix(A)
diags = A.sum(axis=1).flatten()#Degree
n,m = A.shape
D = scipy.sparse.spdiags(diags, [0], m, n, format='csr')
L = D - A
if normalization_mode not in ['sym', 'rw', None]:
raise Exception('Normalisation mode {} unknown'.format(normalization_mode))
elif normalization_mode == None:
return L
elif normalization_mode == 'sym':
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))
elif normalization_mode == 'rw':
with scipy.errstate(divide='ignore'):
diags_inverse = 1.0/diags
diags_inverse[scipy.isinf(diags_inverse)] = 0
DH = scipy.sparse.spdiags(diags_inverse, [0], m, n, format='csr')
return DH.dot(L)
def binarize_feature_uniform_p(name, value, min_val, max_val, num_units):
"""
Now reimplemented in c, so don't use this. Keeping around in case
of problems. But I tested that the c and python versions were identical
for many values. -- stefie10
"""
if (isnan(value) or isnan(min_val) or isnan(max_val)):
return name + "_nan"
if (isinf(min_val)):
discrete = linspace(-100 - 0.1, max_val + 0.1, num_units)
#print discrete
elif (isinf(max_val)):
discrete = linspace(min_val - 0.1, 100 + 0.1, num_units)
#print discrete
else:
discrete = linspace(min_val - 0.1, max_val + 0.1, num_units)
#print "discrete = ",
#print repr(discrete)
#print len(discrete)
i = bisect(discrete, value)
#print "i", i
if (i <= len(discrete) - 1 and i > 0):
ret_name = name + "_{0:0.2f}".format(
discrete[i - 1]) + "_{0:0.2f}".format(discrete[i])
elif (i == 0):
ret_name = name + "_lt_{0:0.2f}".format(discrete[0])
elif (i == len(discrete)):
ret_name = name + "_gt_{0:0.2f}".format(discrete[-1])
return ret_name
def lapnormadj(A):
"""
Function to perform Laplacian Normalization on m x n matrix
:param A: Adjacency Matrix
:return: Laplace normalised matrix
"""
import scipy
import numpy as np
from scipy.sparse import csgraph
n,m = A.shape
d1 = A.sum(axis=1).flatten()
d2 = A.sum(axis=0).flatten()
d1_sqrt = 1.0/scipy.sqrt(d1)
d2_sqrt = 1.0/scipy.sqrt(d2)
d1_sqrt[scipy.isinf(d1_sqrt)] = 10000
d2_sqrt[scipy.isinf(d2_sqrt)] = 10000
la = np.zeros(shape=(n,m))
for i in range(0,n):
for j in range(0,m):
la[i,j] = A[i,j]/(d1_sqrt[i]*d2_sqrt[j])
#D1 = scipy.sparse.spdiags(d1_sqrt, [0], n,m, format='coo')
#D2 = scipy.sparse.spdiags(d2_sqrt, [0], n,m, format='coo')
la[la < 1e-5] = 0
return scipy.sparse.coo_matrix(la)
def LDA_batch_normalization(dataset, sample_table, batch_col, output_folder, ncomps): # this is actually the batch normalization method
tmp_output_folder = os.path.join(output_folder, 'tmp')
if not os.path.isdir(tmp_output_folder):
os.makedirs(tmp_output_folder)
barcodes, filtered_conditions, filtered_matrix, conditions, matrix = dataset
# Remove any remaining NaNs and Infs from the filtered matrix - they would screw
# up the LDA.
filtered_matrix[scipy.isnan(filtered_matrix)] = 0
filtered_matrix[scipy.isinf(filtered_matrix)] = 0
# For full matrix, also eliminate NaNs and Infs, BUT preserve the indices and values
# so they can be added back into the matrix later (not implemented yet, and may never
# be - there should no longer be NaNs and Infs in the dataset)
# The NaNs and Infs will mess up the final step of the MATLAB LDA script, which uses
# matrix multiplication to remove the specified number of components!
matrix_nan_inds = scipy.isnan(matrix)
matrix_nan_vals = matrix[matrix_nan_inds]
matrix_inf_inds = scipy.isinf(matrix)
matrix_inf_vals = matrix[matrix_inf_inds]
matrix[matrix_nan_inds] = 0
matrix[matrix_inf_inds] = 0
# Save both the small matrix (for determining the components to remove) and the
# full matrix for the matlab script
filtered_matrix_tmp_filename = os.path.join(tmp_output_folder, 'nonreplicating_matrix.txt')
full_matrix_tmp_filename = os.path.join(tmp_output_folder, 'full_matrix.txt')
np.savetxt(filtered_matrix_tmp_filename, filtered_matrix)
np.savetxt(full_matrix_tmp_filename, matrix)
# Map the batch to integers for matlab, and write out to a file so matlab can read
# Note that yes, the batch_classes should match up with the filtered matrix, not
# the full matrix
batch_classes = get_batch_classes(dataset = [barcodes, filtered_conditions, filtered_matrix], sample_table = sample_table, batch_col = batch_col)
class_tmp_filename = os.path.join(tmp_output_folder, 'classes.txt')
writeList(batch_classes, class_tmp_filename)
output_tmp_filename = os.path.join(tmp_output_folder, 'full_matrix_lda_normalized.txt')
runLDAMatlabFunc(filtered_matrix_filename = filtered_matrix_tmp_filename, \
matrix_filename = full_matrix_tmp_filename, \
class_filename = class_tmp_filename, \
ncomps = ncomps, \
output_filename = output_tmp_filename)
# The X norm that is returned is the full matrix. In the future, we could add in
# returning the components to remove so they can be visualized or applied to other
# one-off datasets
Xnorm = scipy.genfromtxt(output_tmp_filename)
## Dump the dataset out!
#output_filename = os.path.join(mtag_effect_folder, 'scaleddeviation_full_mtag_lda_{}.dump.gz'.format(ncomps))
#of = gzip.open(output_filename, 'wb')
#cPickle.dump([barcodes, conditions, Xnorm], of)
#of.close()
return [barcodes, conditions, Xnorm]
def LDA_batch_normalization(dataset, sample_table, batch_col, output_folder, n_comps): # this is actually the batch normalization method
tmp_output_folder = os.path.join(output_folder, 'tmp')
if not os.path.isdir(tmp_output_folder):
os.makedirs(tmp_output_folder)
barcodes, filtered_conditions, filtered_matrix, conditions, matrix = dataset
# Remove any remaining NaNs and Infs from the filtered matrix - they would screw
# up the LDA.
filtered_matrix[scipy.isnan(filtered_matrix)] = 0
filtered_matrix[scipy.isinf(filtered_matrix)] = 0
# For full matrix, also eliminate NaNs and Infs, BUT preserve the indices and values
# so they can be added back into the matrix later (not implemented yet, and may never
# be - there should no longer be NaNs and Infs in the dataset)
# The NaNs and Infs will mess up the final step of the MATLAB LDA script, which uses
# matrix multiplication to remove the specified number of components!
matrix_nan_inds = scipy.isnan(matrix)
matrix_nan_vals = matrix[matrix_nan_inds]
matrix_inf_inds = scipy.isinf(matrix)
matrix_inf_vals = matrix[matrix_inf_inds]
matrix[matrix_nan_inds] = 0
matrix[matrix_inf_inds] = 0
# Save both the small matrix (for determining the components to remove) and the
# full matrix for the matlab script
filtered_matrix_tmp_filename = os.path.join(tmp_output_folder, 'nonreplicating_matrix.txt')
full_matrix_tmp_filename = os.path.join(tmp_output_folder, 'full_matrix.txt')
np.savetxt(filtered_matrix_tmp_filename, filtered_matrix)
np.savetxt(full_matrix_tmp_filename, matrix)
# Map batch classes to integers
batch_classes = get_batch_classes(dataset = [barcodes, filtered_conditions, filtered_matrix], sample_table = sample_table, batch_col = batch_col)
# Checks number of classes and limits ncomps
a = [x > 0 for x in np.sum(np.absolute(filtered_matrix), axis=0)]
classes = np.asarray([batch_classes[i] for i in range(len(batch_classes)) if a[i]])
n_samples = filtered_matrix.shape[0]
n_classes = len(np.unique(classes))
if n_samples == n_classes:
print "ERROR: The number of samples is equal to the number of classes. Exiting"
if n_classes <= n_comps:
print "Fewer classes, " + str(n_classes) + ", than components. Setting components to " + str(n_classes-1)
n_comps = n_classes-1
# Runs LDA
#Xnorm = scikit_lda(filtered_matrix, matrix, batch_classes, n_comps)
Xnorm = outer_python_lda(filtered_matrix, matrix, batch_classes, n_comps)
return [barcodes, conditions, Xnorm, n_comps]
def _normalize(spectra):
stars = spectra.index
wavelengths = spectra.flux.columns.values.copy()
flux = spectra.flux.values.copy()
error = spectra.error.reindex(columns=wavelengths).values.copy()
#TODO: Should negative fluxes be zero'd too?
bad_flux = sp.isnan(flux) | sp.isinf(flux)
bad_error = sp.isnan(error) | sp.isinf(error) | (error < 0)
bad = bad_flux | bad_error
flux[bad] = 1
error[bad] = ERROR_LIM
#TODO: Where does pixlist come from?
pixlist = sp.loadtxt('pixlist.txt', dtype=int)
var = sp.full_like(error, ERROR_LIM**2)
var[:, pixlist] = 0
inv_var = 1 / (var**2 + error**2)
norm_flux = sp.full_like(flux, 1)
norm_error = sp.full_like(error, ERROR_LIM)
for star in range(len(stars)):
for _, (left, right) in CHIPS.items():
mask = (left < wavelengths) & (wavelengths < right)
#TODO: Why are we using Chebyshev polynomials rather than smoothing splines?
#TODO: Why are we using three polynomials rather than one? Are spectra discontinuous between chips?
#TODO: Is the denominator being zero/negative ever an issue?
fit = Chebyshev.fit(x=wavelengths[mask],
y=flux[star][mask],
w=inv_var[star][mask],
deg=2)
norm_flux[star][mask] = flux[star][mask] / fit(wavelengths[mask])
norm_error[star][mask] = error[star][mask] / fit(wavelengths[mask])
#TODO: Why is the unreliability threshold different from the limit value?
unreliable = (norm_error > .3)
norm_flux[unreliable] = 1
norm_error[unreliable] = ERROR_LIM
# In the original, the masking is done in the parallax fitting code.
# Gonna do it earlier here to save a bit of memory.
mask = sp.any(
sp.vstack([(l < wavelengths) & (wavelengths < u)
for l, u in CHIPS.values()]), 0)
norm_flux = pd.DataFrame(norm_flux[:, mask], stars, wavelengths[mask])
norm_error = pd.DataFrame(norm_error[:, mask], stars, wavelengths[mask])
return pd.concat({'flux': norm_flux, 'error': norm_error}, 1)
def setRunParams(self, ic=[], params=[], t0=[], tend=[], gt0=[], refine=0,
specTimes=[], bounds=[]):
if not self.initBasic:
raise InitError, 'You must initialize the integrator before setting params. (initBasic)'
#if self.initParams == True:
# raise InitError, 'You must clear params before setting them. Use clearParams()'
if self.checkRunParams(ic, params, t0, tend, gt0, refine, specTimes,
bounds):
self.ic = ic
self.params = params
self.t0 = float(t0)
self.tend = float(tend)
self.gt0 = float(gt0)
self.refine = int(refine)
self.specTimes = specTimes
if self.t0 < self.tend:
self.direction = 1
else:
self.direction = -1
# Set bounds
if bounds != []:
self.upperBounds = bounds[1]
self.lowerBounds = bounds[0]
for i in range(self.phaseDim + self.paramDim):
if isinf(self.upperBounds[i]) and self.upperBounds[i] > 0:
self.upperBounds[i] = abs(float(self.defaultBound))
elif isinf(self.upperBounds[i]) and self.upperBounds[i] < 0:
self.upperBounds[i] = -abs(float(self.defaultBound))
if isinf(self.lowerBounds[i]) and self.lowerBounds[i] > 0:
self.lowerBounds[i] = abs(float(self.defaultBound))
elif isinf(self.lowerBounds[i]) and self.lowerBounds[i] < 0:
self.lowerBounds[i] = -abs(float(self.defaultBound))
else:
self.upperBounds = [abs(float(self.defaultBound)) for x in range(self.phaseDim + self.paramDim)]
self.lowerBounds = [-abs(float(self.defaultBound)) for x in range(self.phaseDim + self.paramDim)]
retval = self._integMod.SetRunParameters(self.ic, self.params,
self.gt0, self.t0, self.tend, self.refine,
len(self.specTimes), self.specTimes,
self.upperBounds, self.lowerBounds)
if retval[0] != 1:
raise InitError, 'SetRunParameters call failed!'
self.canContinue = False
self.setParams = True
def run(self, phase=None, throats=None):
logger.warning('This algorithm can take some time...')
conduit_lengths = sp.sum(misc.conduit_lengths(network=self._net,
mode='centroid'), axis=1)
graph = self._net.create_adjacency_matrix(data=conduit_lengths,
sprsfmt='csr')
if phase is not None:
self._phase = phase
if 'throat.occupancy' in self._phase.props():
temp = conduit_lengths*(self._phase['throat.occupancy'] == 1)
graph = self._net.create_adjacency_matrix(data=temp,
sprsfmt='csr',
prop='temp')
path = spgr.shortest_path(csgraph=graph, method='D', directed=False)
Px = sp.array(self._net['pore.coords'][:, 0], ndmin=2)
Py = sp.array(self._net['pore.coords'][:, 1], ndmin=2)
Pz = sp.array(self._net['pore.coords'][:, 2], ndmin=2)
Cx = sp.square(Px.T - Px)
Cy = sp.square(Py.T - Py)
Cz = sp.square(Pz.T - Pz)
Ds = sp.sqrt(Cx + Cy + Cz)
temp = path / Ds
temp[sp.isnan(temp)] = 0
temp[sp.isinf(temp)] = 0
return temp
def run(self,phase=None):
r'''
'''
logger.warning('This algorithm can take some time...')
graph = self._net.create_adjacency_matrix(data=self._net['throat.length'],sprsfmt='csr')
if phase is not None:
self._phase = phase
if 'throat.occupancy' in self._phase.props():
temp = self._net['throat.length']*(self._phase['throat.occupancy']==1)
graph = self._net.create_adjacency_matrix(data=temp,sprsfmt='csr',prop='temp')
#self._net.tic()
path = spgr.shortest_path(csgraph = graph, method='D', directed = False)
#self._net.toc()
Px = sp.array(self._net['pore.coords'][:,0],ndmin=2)
Py = sp.array(self._net['pore.coords'][:,1],ndmin=2)
Pz = sp.array(self._net['pore.coords'][:,2],ndmin=2)
Cx = sp.square(Px.T - Px)
Cy = sp.square(Py.T - Py)
Cz = sp.square(Pz.T - Pz)
Ds = sp.sqrt(Cx + Cy + Cz)
temp = path/Ds
#temp = path
temp[sp.isnan(temp)] = 0
temp[sp.isinf(temp)] = 0
return temp
def evaluer(self):
""" Renvoie une valeur numérique de l'expression
"""
# On crée un dictionnaire de variables : {'nom' : valeur}
# (nécessaire pour "eval")
dict = {}
for n, v in self.vari.items():
print " ", n, v
dict[n] = v.v[0]
global safe_dict
dict.update(safe_dict)
# On fait l'évaluation
try:
v = eval(self.py_expr, {"__builtins__": None}, dict)
except:
return False
# print type (v)
# On analyse le résultat
if not type(v) == float and not type(v) == scipy.float64 and not type(v) == int:
return False
elif scipy.isinf(v) or scipy.isnan(v):
return None
else:
return v
def sample(self, model, evidence):
z = evidence['z']
T = evidence['T']
g = evidence['g']
h = evidence['h']
transition_var_g = evidence['transition_var_g']
shot_id = evidence['shot_id']
observation_var_g = model.known_params['observation_var_g']
observation_var_h = model.known_params['observation_var_h']
prior_mu_g = model.hyper_params['g']['mu']
prior_cov_g = model.hyper_params['g']['cov']
N = len(z)
n = len(g)
# Make g, h, and z vector valued to avoid ambiguity
g = g.copy().reshape((n, 1))
h = h.copy().reshape((n, 1))
z_g = ma.asarray(nan + zeros((n, 1)))
obs_cov = ma.asarray(inf + zeros((n, 1, 1)))
for i in xrange(n):
z_i = z[shot_id == i]
T_i = T[shot_id == i]
if 1 in T_i and 2 in T_i:
# Sample mean and variance for multiple observations
n_obs_g, n_obs_h = sum(T_i == 1), sum(T_i == 2)
obs_cov_g, obs_cov_h = observation_var_g / n_obs_g, observation_var_h / n_obs_h
z_g[i] = (mean(z_i[T_i == 1]) / obs_cov_g +
mean(z_i[T_i == 2] - h[i]) / obs_cov_h) / (
1 / obs_cov_g + 1 / obs_cov_h)
obs_cov[i] = 1 / (1 / obs_cov_g + 1 / obs_cov_h)
elif 1 in T_i:
n_obs_g = sum(T_i == 1)
z_g[i] = mean(z_i[T_i == 1])
obs_cov[i] = observation_var_g / n_obs_g
elif 2 in T_i:
n_obs_h = sum(T_i == 2)
z_g[i] = mean(z_i[T_i == 2] - h[i])
obs_cov[i] = observation_var_h / n_obs_h
z_g[isnan(z_g)] = ma.masked
obs_cov[isinf(obs_cov)] = ma.masked
kalman = self._kalman
kalman.initial_state_mean = array([
prior_mu_g[0],
])
kalman.initial_state_covariance = array([
prior_cov_g[0],
])
kalman.transition_matrices = eye(1)
kalman.transition_covariance = array([
transition_var_g,
])
kalman.observation_matrices = eye(1)
kalman.observation_covariance = obs_cov
sampled_g = forward_filter_backward_sample(kalman, z_g, prior_mu_g,
prior_cov_g)
return sampled_g.reshape((n, ))
def mmse_stsa(infile, outfile, noise_sum):
signal, params = read_signal(infile, WINSIZE)
nf = len(signal)/(WINSIZE/2) - 1
sig_out=sp.zeros(len(signal),sp.float32)
G = sp.ones(WINSIZE)
prevGamma = G
alpha = 0.98
window = sp.hanning(WINSIZE)
gamma15=spc.gamma(1.5)
lambdaD = noise_sum / 5.0
percentage = 0
for no in xrange(nf):
p = int(math.floor(1. * no / nf * 100))
if (p > percentage):
percentage = p
print "{}%".format(p),
y = get_frame(signal, WINSIZE, no)
Y = sp.fft(y*window)
Yr = sp.absolute(Y)
Yp = sp.angle(Y)
gamma = Yr**2/lambdaD
xi = alpha * G**2 * prevGamma + (1-alpha)*sp.maximum(gamma-1, 0)
prevGamma = gamma
nu = gamma * xi / (1+xi)
G = (gamma15 * sp.sqrt(nu) / gamma ) * sp.exp(-nu/2) * ((1+nu)*spc.i0(nu/2)+nu*spc.i1(nu/2))
idx = sp.isnan(G) + sp.isinf(G)
G[idx] = xi[idx] / (xi[idx] + 1)
Yr = G * Yr
Y = Yr * sp.exp(Yp*1j)
y_o = sp.real(sp.ifft(Y))
add_signal(sig_out, y_o, WINSIZE, no)
write_signal(outfile, params, sig_out)
def makehist(testpath, npulses):
"""
This functions are will create histogram from data made in the testpath.
Inputs
testpath - The path that the data is located.
npulses - The number of pulses in the sim.
"""
sns.set_style("whitegrid")
sns.set_context("notebook")
params = ['Ne', 'Te', 'Ti', 'Vi']
pvals = [1e11, 2.1e3, 1.1e3, 0.]
histlims = [[4e10, 2e11], [1200., 3000.], [300., 1900.], [-250., 250.]]
erlims = [[-2e11, 2e11], [-1000., 1000.], [-800., -800], [-250., 250.]]
erperlims = [[-100., 100.]] * 4
lims_list = [histlims, erlims, erperlims]
errdict = makehistdata(params, testpath)[:4]
ernames = ['Data', 'Error', 'Error Percent']
sig1 = sp.sqrt(1. / npulses)
# Two dimensiontal histograms
pcombos = [i for i in itertools.combinations(params, 2)]
c_rows = int(math.ceil(float(len(pcombos)) / 2.))
(figmplf, axmat) = plt.subplots(c_rows,
2,
figsize=(12, c_rows * 6),
facecolor='w')
axvec = axmat.flatten()
for icomn, icom in enumerate(pcombos):
curax = axvec[icomn]
str1, str2 = icom
_, _, _ = make2dhist(testpath, PARAMDICT[str1], PARAMDICT[str2],
figmplf, curax)
filetemplate = str(Path(testpath).joinpath('AnalysisPlots', 'TwoDDist'))
plt.tight_layout()
plt.subplots_adjust(top=0.95)
figmplf.suptitle('Pulses: {0}'.format(npulses), fontsize=20)
fname = filetemplate + '_{0:0>5}Pulses.png'.format(npulses)
plt.savefig(fname)
plt.close(figmplf)
# One dimensiontal histograms
for ierr, iername in enumerate(ernames):
filetemplate = str(Path(testpath).joinpath('AnalysisPlots', iername))
(figmplf, axmat) = plt.subplots(2, 2, figsize=(20, 15), facecolor='w')
axvec = axmat.flatten()
for ipn, iparam in enumerate(params):
plt.sca(axvec[ipn])
if sp.any(sp.isinf(errdict[ierr][iparam])):
continue
binlims = lims_list[ierr][ipn]
bins = sp.linspace(binlims[0], binlims[1], 100)
histhand = sns.distplot(errdict[ierr][iparam],
bins=bins,
kde=True,
rug=False)
axvec[ipn].set_title(iparam)
figmplf.suptitle(iername + ' Pulses: {0}'.format(npulses), fontsize=20)
fname = filetemplate + '_{0:0>5}Pulses.png'.format(npulses)
plt.savefig(fname)
plt.close(figmplf)
def matfile_featfunc(fname,
suffix,
kernel_type = DEFAULT_KERNEL_TYPE,
variable_name = DEFAULT_VARIABLE_NAME):
fname += suffix
error = False
try:
if kernel_type == "exp_mu_da":
# hack for GB with 204 dims
fdata = io.loadmat(fname)[variable_name].reshape(-1, 204)
else:
fdata = io.loadmat(fname)[variable_name].ravel()
except TypeError:
fname_error = fname+'.error'
print "[ERROR] couldn't open", fname, "moving it to", fname_error
shutil.move(fname, fname_error)
error = True
except:
print "[ERROR] (unknown) with", fname
raise
if error:
raise RuntimeError("An error occured while loading '%s'"
% fname)
assert(not sp.isnan(fdata).any())
assert(not sp.isinf(fdata).any())
return fdata
def run(self, phase=None, throats=None):
logger.warning('This algorithm can take some time...')
conduit_lengths = sp.sum(misc.conduit_lengths(network=self._net,
mode='centroid'), axis=1)
graph = self._net.create_adjacency_matrix(data=conduit_lengths,
sprsfmt='csr')
if phase is not None:
self._phase = phase
if 'throat.occupancy' in self._phase.props():
temp = conduit_lengths*(self._phase['throat.occupancy'] == 1)
graph = self._net.create_adjacency_matrix(data=temp,
sprsfmt='csr',
prop='temp')
path = spgr.shortest_path(csgraph=graph, method='D', directed=False)
Px = sp.array(self._net['pore.coords'][:, 0], ndmin=2)
Py = sp.array(self._net['pore.coords'][:, 1], ndmin=2)
Pz = sp.array(self._net['pore.coords'][:, 2], ndmin=2)
Cx = sp.square(Px.T - Px)
Cy = sp.square(Py.T - Py)
Cz = sp.square(Pz.T - Pz)
Ds = sp.sqrt(Cx + Cy + Cz)
temp = path / Ds
temp[sp.isnan(temp)] = 0
temp[sp.isinf(temp)] = 0
return temp
def _process_image(self, fname):
kernel_type = self.kernel_type
variable_name = self.variable_name
fname += self.input_suffix
error = False
try:
if kernel_type == "exp_mu_da":
# hack for GB with 204 dims
# fdata = io.loadmat(fname)[variable_name].reshape(-1, 204)
fdata = self._load_image(fname).reshape(-1, 204)
else:
fdata = self._load_image(fname).ravel()
# fdata = io.loadmat(fname)[variable_name].ravel()
except TypeError:
fname_error = fname + ".error"
print "[ERROR] couldn't open", fname, "moving it to", fname_error
# os.unlink(fname)
shutil.move(fname, fname_error)
error = True
except:
print "[ERROR] (unknown) with", fname
raise
if error:
raise RuntimeError("An error occured while loading '%s'" % fname)
assert not sp.isnan(fdata).any()
assert not sp.isinf(fdata).any()
return fdata
def __regularized_laplacian_matrix(adj_matrix, tau):
"""
Using ARPACK solver, compute the first K eigen vector.
The laplacian is computed using the regularised formula from [2]
[2]Kamalika Chaudhuri, Fan Chung, and Alexander Tsiatas 2018.
Spectral clustering of graphs with general degrees in the extended planted partition model.
L = I - D^-1/2 * A * D ^-1/2
:param adj_matrix: adjacency matrix representation of graph where [m][n] >0 if there is edge and [m][n] = weight
:param tau: the regularisation constant
:return: the first K eigenvector
"""
import scipy.sparse
# Code inspired from nx.normalized_laplacian_matrix, with changes to allow regularisation
n, m = adj_matrix.shape
I = np.eye(n, m)
diags = adj_matrix.sum(axis=1).flatten()
# add tau to the diags to produce a regularised diags
if tau != 0:
diags = np.add(diags, tau)
# diags will be zero at points where there is no edge and/or the node you are at
# ignore the error and make it zero later
with scipy.errstate(divide="ignore"):
diags_sqrt = 1.0 / scipy.sqrt(diags)
diags_sqrt[scipy.isinf(diags_sqrt)] = 0
D = scipy.sparse.spdiags(diags_sqrt, [0], m, n, format="csr")
L = I - (D.dot(adj_matrix.dot(D)))
return L
def sigmoid(X):
## e = sp.exp(-X)
## e = 0.0000001 if e ==
v = 1. / (1. + sp.exp(-X))
if sp.isnan(v).sum() or sp.isinf(v).sum():
i=0
return v
def check_ExpCM_attributes(self):
"""Make sure has the expected attribute values."""
self.assertEqual(self.nsites, self.expcm_divpressure.nsites)
# make sure Prxy has rows summing to zero
self.assertFalse(scipy.isnan(self.expcm_divpressure.Prxy).any())
self.assertFalse(scipy.isinf(self.expcm_divpressure.Prxy).any())
diag = scipy.eye(N_CODON, dtype='bool')
for r in range(self.nsites):
self.assertTrue(scipy.allclose(0, scipy.sum(self.expcm_divpressure.Prxy[r],
axis=1)))
self.assertTrue(scipy.allclose(0, self.expcm_divpressure.Prxy[r].sum()))
self.assertTrue((self.expcm_divpressure.Prxy[r][diag] <= 0).all())
self.assertTrue((self.expcm_divpressure.Prxy[r][~diag] >= 0).all())
# make sure prx sums to 1 for each r
self.assertTrue((self.expcm_divpressure.prx >= 0).all())
for r in range(self.nsites):
self.assertTrue(scipy.allclose(1, self.expcm_divpressure.prx[r].sum()))
# prx is eigenvector or Prxy for the same r, but not different r
for r in range(self.nsites):
self.assertTrue(scipy.allclose(0, scipy.dot(self.expcm_divpressure.prx[r],
self.expcm_divpressure.Prxy[r])))
if r > 0:
self.assertFalse(scipy.allclose(0, scipy.dot(self.expcm_divpressure.prx[r],
self.expcm_divpressure.Prxy[r - 1])))
# phi sums to one
self.assertTrue(scipy.allclose(1, self.expcm_divpressure.phi.sum()))
def evaluer(self):
""" Renvoie une valeur numérique de l'expression
"""
# On crée un dictionnaire de variables : {'nom' : valeur}
# (nécessaire pour "eval")
dict = {}
for n, v in self.vari.items():
print " ", n, v
dict[n] = v.v[0]
global safe_dict
dict.update(safe_dict)
# On fait l'évaluation
try:
v = eval(self.py_expr, {"__builtins__": None}, dict)
except:
return False
# print type (v)
# On analyse le résultat
if not type(v) == float and not type(v) == scipy.float64 and not type(
v) == int:
return False
elif scipy.isinf(v) or scipy.isnan(v):
return None
else:
return v
def laplacian_layout(G, norm=False, dim=2, bad=False):
A = nx.to_scipy_sparse_matrix(G, format='csr')
A = np.array(A.todense())
n, m = A.shape
diags = A.sum(axis=1).flatten()
D = np.diag(diags)
L = D - A
B = np.eye(n)
if norm == False:
layout = eig_layout(G, L, B)
else:
if bad:
with scipy.errstate(divide='ignore'):
#diags_sqrt = 1.0 / scipy.power(diags, 1)
diags_sqrt = 1.0 / scipy.sqrt(diags)
diags_sqrt[scipy.isinf(diags_sqrt)] = 0
DH = np.diag(diags_sqrt)
L = np.dot(DH, np.dot(L, DH))
eigenvalues, eigenvectors = scipy.linalg.eigh(L)
index = np.argsort(eigenvalues)[1:dim + 1]
pos = np.real(eigenvectors[:, index])
pos = np.dot(DH, pos)
pos = dict(zip(G, pos))
layout = pos
else:
B = D
layout = eig_layout(G, L, B)
#print(L)
#print(B)
return layout
def _oneEvaluation(self, evaluable):
""" This method should be called by all optimizers for producing an evaluation. """
if self._wasUnwrapped:
self.wrappingEvaluable._setParameters(evaluable)
res = self.__evaluator(self.wrappingEvaluable)
elif self._wasWrapped:
res = self.__evaluator(evaluable.params)
else:
res = self.__evaluator(evaluable)
''' added by JPQ '''
if self.constrained:
self.feasible = self.__evaluator.outfeasible
self.violation = self.__evaluator.outviolation
# ---
if isscalar(res):
# detect numerical instability
if isnan(res) or isinf(res):
raise DivergenceError
# always keep track of the best
if (self.numEvaluations == 0 or self.bestEvaluation is None
or (self.minimize and res <= self.bestEvaluation)
or (not self.minimize and res >= self.bestEvaluation)):
self.bestEvaluation = res
self.bestEvaluable = evaluable.copy()
self.numEvaluations += 1
# if desired, also keep track of all evaluables and/or their fitness.
if self.storeAllEvaluated:
if self._wasUnwrapped:
self._allEvaluated.append(self.wrappingEvaluable.copy())
elif self._wasWrapped:
self._allEvaluated.append(evaluable.params.copy())
else:
self._allEvaluated.append(evaluable.copy())
if self.storeAllEvaluations:
if self._wasOpposed and isscalar(res):
''' added by JPQ '''
if self.constrained:
self._allEvaluations.append(
[-res, self.feasible, self.violation])
# ---
else:
self._allEvaluations.append(-res)
else:
''' added by JPQ '''
if self.constrained:
self._allEvaluations.append(
[res, self.feasible, self.violation])
# ---
else:
self._allEvaluations.append(res)
''' added by JPQ '''
if self.constrained:
return [res, self.feasible, self.violation]
else:
# ---
return res
def sample(self, model, evidence):
z = evidence['z']
T = evidence['T']
g = evidence['g']
h = evidence['h']
transition_var_g = evidence['transition_var_g']
shot_id = evidence['shot_id']
observation_var_g = model.known_params['observation_var_g']
observation_var_h = model.known_params['observation_var_h']
prior_mu_g = model.hyper_params['g']['mu']
prior_cov_g = model.hyper_params['g']['cov']
N = len(z)
n = len(g)
## Make g, h, and z vector valued to avoid ambiguity
#g = g.copy().reshape((n, 1))
#h = h.copy().reshape((n, 1))
#
pdb.set_trace()
z_g = ma.asarray(nan + zeros(n))
obs_cov = ma.asarray(inf + zeros(n))
if 1 in T:
z_g[T==1] = z[T==1]
obs_cov[T==1] = observation_var_g
if 2 in T:
z_g[T==2] = z[T==2] - h[T==2]
obs_cov[T==2] = observation_var_h
#for i in xrange(n):
# z_i = z[shot_id == i]
# T_i = T[shot_id == i]
# if 1 in T_i and 2 in T_i:
# # Sample mean and variance for multiple observations
# n_obs_g, n_obs_h = sum(T_i == 1), sum(T_i == 2)
# obs_cov_g, obs_cov_h = observation_var_g/n_obs_g, observation_var_h/n_obs_h
# z_g[i] = (mean(z_i[T_i == 1])/obs_cov_g + mean(z_i[T_i == 2] - h[i])/obs_cov_h)/(1/obs_cov_g + 1/obs_cov_h)
# obs_cov[i] = 1/(1/obs_cov_g + 1/obs_cov_h)
# elif 1 in T_i:
# n_obs_g = sum(T_i == 1)
# z_g[i] = mean(z_i[T_i == 1])
# obs_cov[i] = observation_var_g/n_obs_g
# elif 2 in T_i:
# n_obs_h = sum(T_i == 2)
# z_g[i] = mean(z_i[T_i == 2] - h[i])
# obs_cov[i] = observation_var_h/n_obs_h
z_g[isnan(z_g)] = ma.masked
obs_cov[isinf(obs_cov)] = ma.masked
kalman = self._kalman
kalman.initial_state_mean = array([prior_mu_g[0],])
kalman.initial_state_covariance = array([prior_cov_g[0],])
kalman.transition_matrices = eye(1)
kalman.transition_covariance = array([transition_var_g,])
kalman.observation_matrices = eye(1)
kalman.observation_covariance = obs_cov
sampled_g = forward_filter_backward_sample(kalman, z_g, prior_mu_g, prior_cov_g)
return sampled_g.reshape((n,))
def updateExpectations(self):
a, b = self.params['a'], self.params['b']
E = s.divide(a, a + b)
lnE = special.digamma(a) - special.digamma(a + b)
lnEInv = special.digamma(b) - special.digamma(
a + b) # expectation of ln(1-X)
lnEInv[s.isinf(
lnEInv)] = -s.inf # there is a numerical error in lnEInv if E=1
self.expectations = {'E': E, 'lnE': lnE, 'lnEInv': lnEInv}
def get_DH(A):
# D^{-1/2}
diags = A.sum(axis=1).flatten()
C, R = A.shape
with scipy.errstate(divide='ignore'):
diag_s = 1.0 / scipy.sqrt(diags)
diag_s[scipy.isinf(diag_s)] = 0
DH = scipy.sparse.spdiags(diag_s, [0], C, R, format='csr')
return DH
def _oneEvaluation(self, evaluable):
""" This method should be called by all optimizers for producing an evaluation. """
if self._wasUnwrapped:
self.wrappingEvaluable._setParameters(evaluable)
res = self.__evaluator(self.wrappingEvaluable)
elif self._wasWrapped:
res = self.__evaluator(evaluable.params)
else:
res = self.__evaluator(evaluable)
''' added by JPQ '''
if self.constrained :
self.feasible = self.__evaluator.outfeasible
self.violation = self.__evaluator.outviolation
# ---
if isscalar(res):
# detect numerical instability
if isnan(res) or isinf(res):
raise DivergenceError
# always keep track of the best
if (self.numEvaluations == 0
or self.bestEvaluation is None
or (self.minimize and res <= self.bestEvaluation)
or (not self.minimize and res >= self.bestEvaluation)):
self.bestEvaluation = res
self.bestEvaluable = evaluable.copy()
self.numEvaluations += 1
# if desired, also keep track of all evaluables and/or their fitness.
if self.storeAllEvaluated:
if self._wasUnwrapped:
self._allEvaluated.append(self.wrappingEvaluable.copy())
elif self._wasWrapped:
self._allEvaluated.append(evaluable.params.copy())
else:
self._allEvaluated.append(evaluable.copy())
if self.storeAllEvaluations:
if self._wasOpposed and isscalar(res):
''' added by JPQ '''
if self.constrained :
self._allEvaluations.append([-res,self.feasible,self.violation])
# ---
else:
self._allEvaluations.append(-res)
else:
''' added by JPQ '''
if self.constrained :
self._allEvaluations.append([res,self.feasible,self.violation])
# ---
else:
self._allEvaluations.append(res)
''' added by JPQ '''
if self.constrained :
return [res,self.feasible,self.violation]
else:
# ---
return res
def plot_update(syst,
const,
U_r=None,
U_erf=None,
G_r=None,
c_r=None,
g_r=None,
c_f=None):
# update the plotted data
# check for the minimum/maximum and update axes?
# with U_r we can have a problem (it can contain Inf and NaN)
# that doesn't work with pylab
# replace it with some other value
if (U_r != None):
U_plot = copy(U_r)
U_plot[isinf(U_plot)] = const.inf_value
U_plot[isnan(U_plot)] = const.nan_value
# it's necessary to create deep copies of objects that are subject to change
# i.e., G_r, c_r, c_f - they are all multiplied/divided by some factors. this can
# lead to problems with display, since pylab.draw() is redrawing all objects
# if
# set_ydata(c_r_ij)
# draw()
# is used, then pylab obtains reference to c_r_ij. when in the program c_r_ij is multiplied by r
# then a later invocation of
# set_ydata(G_r_ij)
# draw()
# will display updated G_r, but also updated c_r - and we don't want that!
subplot_number = 0
for i in range(syst['ncomponents']):
for j in range(i, syst['ncomponents']):
if (U_r != None):
p_U_ij[subplot_number].set_ydata(U_plot[i, j])
if (G_r != None):
p_G_ij[subplot_number].set_ydata(copy(G_r[i, j]))
if (c_r != None):
p_c_ij[subplot_number].set_ydata(copy(c_r[i, j]))
if (g_r != None):
p_g_ij[subplot_number].set_ydata(g_r[i, j])
subplot_number += 1
# end for j in range(ncomponents)
# end for i in range(ncomponents)
for i in range(syst['ncomponents']):
for j in range(i, syst['ncomponents']):
if (c_f != None):
p_c_ij[subplot_number].set_ydata(copy(c_f[i, j]))
if (U_erf != None):
p_U_ij[subplot_number].set_ydata(U_erf[i, j])
subplot_number += 1
# end for j in range(ncomponents)
# end for i in range(ncomponents)
pylab.draw()
def sample(self, model, evidence):
z = evidence['z']
g = evidence['g']
h = evidence['h']
T = evidence['T']
phi = evidence['phi']
transition_var_h = evidence['transition_var_h']
shot_id = evidence['shot_id']
observation_var_h = model.known_params['observation_var_h']
mu_h = model.known_params['mu_h']
prior_mu_h = model.hyper_params['h']['mu']
prior_cov_h = model.hyper_params['h']['cov']
n = len(h)
N = len(z)
# Making g, h, and z vector valued to avoid ambiguity
g = g.copy().reshape((n, 1))
h = h.copy().reshape((n, 1))
z_h = ma.asarray(nan + zeros((n, 1)))
obs_cov = ma.asarray(inf + zeros((n, 1, 1)))
for i in xrange(n):
z_i = z[shot_id == i]
T_i = T[shot_id == i]
if 2 in T_i:
# Sample mean and variance for multiple observations
n_obs = sum(T_i == 2)
z_h[i] = mean(z_i[T_i == 2])
obs_cov[i] = observation_var_h / n_obs
z_h[isnan(z_h)] = ma.masked
obs_cov[isinf(obs_cov)] = ma.masked
kalman = self._kalman
kalman.initial_state_mean = array([
prior_mu_h[0],
])
kalman.initial_state_covariance = array([
prior_cov_h[0],
])
kalman.transition_matrices = array([
phi,
])
kalman.transition_covariance = array([
transition_var_h,
])
kalman.transition_offsets = mu_h * (1 - phi) * ones((n, 1))
kalman.observation_matrices = eye(1)
kalman.observation_offsets = g
kalman.observation_covariance = obs_cov
sampled_h = forward_filter_backward_sample(kalman, z_h, prior_mu_h,
prior_cov_h)
return sampled_h.reshape((n, ))
def makehist(testpath,npulses):
"""
This functions are will create histogram from data made in the testpath.
Inputs
testpath - The path that the data is located.
npulses - The number of pulses in the sim.
"""
sns.set_style("whitegrid")
sns.set_context("notebook")
params = ['Ne', 'Te', 'Ti', 'Vi']
histlims = [[1e10, 3e11], [1000., 3000.], [100., 2500.], [-400., 400.]]
erlims = [[-2e11, 2e11], [-1000., 1000.], [-800., 800], [-400., 400.]]
erperlims = [[-100., 100.]]*4
lims_list = [histlims, erlims, erperlims]
errdict = makehistdata(params, testpath)[:4]
ernames = ['Data', 'Error', 'Error Percent']
# Two dimensiontal histograms
pcombos = [i for i in itertools.combinations(params, 2)]
c_rows = int(math.ceil(float(len(pcombos))/2.))
(figmplf, axmat) = plt.subplots(c_rows, 2, figsize=(12, c_rows*6), facecolor='w')
axvec = axmat.flatten()
for icomn, icom in enumerate(pcombos):
curax = axvec[icomn]
str1, str2 = icom
_, _, _ = make2dhist(testpath, PARAMDICT[str1], PARAMDICT[str2], figmplf, curax)
filetemplate = str(Path(testpath).joinpath('AnalysisPlots', 'TwoDDist'))
plt.tight_layout()
plt.subplots_adjust(top=0.95)
figmplf.suptitle('Pulses: {0}'.format(npulses), fontsize=20)
fname = filetemplate+'_{0:0>5}Pulses.png'.format(npulses)
plt.savefig(fname)
plt.close(figmplf)
# One dimensiontal histograms
for ierr, iername in enumerate(ernames):
filetemplate = str(Path(testpath).joinpath('AnalysisPlots', iername))
(figmplf, axmat) = plt.subplots(2, 2, figsize=(20, 15), facecolor='w')
axvec = axmat.flatten()
for ipn, iparam in enumerate(params):
plt.sca(axvec[ipn])
if sp.any(sp.isinf(errdict[ierr][iparam])):
continue
binlims = lims_list[ierr][ipn]
bins = sp.linspace(binlims[0], binlims[1], 100)
xdata = errdict[ierr][iparam]
xlog = sp.logical_and(xdata >= binlims[0], xdata < binlims[1])
histhand = sns.distplot(xdata[xlog], bins=bins, kde=True, rug=False)
axvec[ipn].set_title(iparam)
figmplf.suptitle(iername +' Pulses: {0}'.format(npulses), fontsize=20)
fname = filetemplate+'_{0:0>5}Pulses.png'.format(npulses)
plt.savefig(fname)
plt.close(figmplf)
def score_image(self, image):
"""
This finds whether the image is cloudy or not.
:param image:
:return:
"""
pickle_file = os.path.join(os.path.dirname(os.path.realpath(__file__)), 'cache/ck_cloud.p')
# Load the cloud thresholds
[cloudy_model, partly_cloudy_model, clear_model] = pickle.load(open(pickle_file, "rb"))
mean, std, window_size = self.process_image(image)
p = self.fit_model(window_size, std)
#p = self.fit_model(window_size, mean)
# rebuild the functions of the window range,
# find the residual vector and then the euclidean norm.
# the one with the smallest should be the model.
fitfunc = lambda p, x: p[0] * x ** p[1]
clear_residual = scipy.absolute(fitfunc(p, window_size) - fitfunc(clear_model, window_size))
pc_residual = scipy.absolute(fitfunc(p, window_size) - fitfunc(partly_cloudy_model, window_size))
cloudy_residual = scipy.absolute(fitfunc(p, window_size) - fitfunc(cloudy_model, window_size))
clear_residual[scipy.isinf(clear_residual)] = 0.0
clear_residual[scipy.isnan(clear_residual)] = 0.0
pc_residual[scipy.isinf(pc_residual)] = 0.0
pc_residual[scipy.isnan(pc_residual)] = 0.0
cloudy_residual[scipy.isinf(cloudy_residual)] = 0.0
cloudy_residual[scipy.isnan(cloudy_residual)] = 0.0
clear_norm = scipy.linalg.norm(clear_residual)
pc_norm = scipy.linalg.norm(pc_residual)
cloudy_norm = scipy.linalg.norm(cloudy_residual)
smallest_val = [clear_norm, pc_norm, cloudy_norm].index(min([clear_norm, pc_norm, cloudy_norm]))
lg.debug('score :: ' + str(smallest_val))
return smallest_val
def normalized_laplacian(W):
n, m = W.shape
diag = np.diag(W.sum(axis=0))
with sc.errstate(divide='ignore'):
diags_sqrt = 1.0 / sc.sqrt(diag)
diags_sqrt[sc.isinf(diags_sqrt)] = 0
DH = sp.spdiags(diags_sqrt, [0], m, n, format='csr')
DH=DH.toarray()
L=DH.dot(L.dot(DH))
return L
def _normalize_diffusion_matrix(A):
n, m = A.shape
A_with_selfloop = A
diags = A_with_selfloop.sum(axis=1).flatten()
with scipy.errstate(divide='ignore'):
diags_sqrt = 1.0 / scipy.sqrt(diags)
diags_sqrt[scipy.isinf(diags_sqrt)] = 0
DH = sp.spdiags(diags_sqrt, [0], m, n, format='csc')
d = DH.dot(A_with_selfloop.dot(DH))
return d
def update(i):
global t, arrow_magn, shrink_factor, full_size
for k in range(capture_interval):
wind_field.update(dt)
plume_model.update(dt)
# raw_input()
t += dt
print(t)
velocity_field = wind_field.velocity_field
u, v = velocity_field[:, :, 0], velocity_field[:, :, 1]
u,v = u[0:full_size-1:shrink_factor,0:full_size-1:shrink_factor],\
v[0:full_size-1:shrink_factor,0:full_size-1:shrink_factor]
vector_field.set_UVC(u, v)
x_wind, y_wind = scipy.cos(constant_wind_angle), scipy.sin(
constant_wind_angle)
wind_arrow.set_positions(
(xmin + (xmax - xmin) / 2, ymax - 0.2 * (ymax - ymin)),
(xmin + (xmax - xmin) / 2 + arrow_magn * x_wind, ymax - 0.2 *
(ymax - ymin) + arrow_magn * y_wind))
text = '{0} min {1} sec'.format(int(scipy.floor(abs(t / 60.))),
int(scipy.floor(abs(t) % 60.)))
timer.set_text(text)
conc_array = array_gen.generate_single_array(plume_model.puffs)
log_im = scipy.log(conc_array.T[::-1])
cutoff_l = scipy.percentile(log_im[~scipy.isinf(log_im)], 10)
cutoff_u = scipy.percentile(log_im[~scipy.isinf(log_im)], 99)
conc_im.set_data(log_im)
n = matplotlib.colors.Normalize(vmin=cutoff_l, vmax=cutoff_u)
conc_im.set_norm(n)
concStorer.store(conc_array.T[::-1])
last = time.time()
windStorer.store(velocity_field)
plumeStorer.store(plume_model.puffs)
return [conc_im]
def cocitation_modularity(partition, adjacency_matrix, resolution=1.0):
"""
Compute the modularity of a node partition of a cocitation graph.
Parameters
----------
partition: dict
The partition of the nodes.
The keys of the dictionary correspond to the nodes and the values to the communities.
adjacency_matrix: scipy.csr_matrix or np.ndarray
The adjacency matrix of the graph (sparse or dense).
resolution: double, optional
The resolution parameter in the modularity function (default=1.).
Returns
-------
modularity : float
The modularity.
"""
if type(adjacency_matrix) == sparse.csr_matrix:
adj_matrix = adjacency_matrix
elif type(adjacency_matrix) == np.ndarray:
adj_matrix = sparse.csr_matrix(adjacency_matrix)
else:
raise TypeError(
"The argument should be a NumPy array or a SciPy Compressed Sparse Row matrix."
)
n_nodes = adj_matrix.shape[0]
out_degree = np.array(adj_matrix.sum(axis=1).flatten())
in_degree = adj_matrix.sum(axis=0).flatten()
total_weight = out_degree.sum()
with errstate(divide='ignore'):
in_degree_sqrt = 1.0 / sqrt(in_degree)
in_degree_sqrt[isinf(in_degree_sqrt)] = 0
in_degree_sqrt = sparse.spdiags(in_degree_sqrt, [0],
adj_matrix.shape[1],
adj_matrix.shape[1],
format='csr')
normalized_adjacency = (adj_matrix.dot(in_degree_sqrt)).T
communities = lab2com(partition)
mod = 0.
for community in communities:
indicator_vector = np.zeros(n_nodes)
indicator_vector[list(community)] = 1
mod += np.linalg.norm(normalized_adjacency.dot(indicator_vector))**2
mod -= (resolution / total_weight) * (np.dot(out_degree,
indicator_vector))**2
return float(mod / total_weight)
def binning_distance(trains, tau, exponent=2):
if sp.isinf(tau) or any(tau > st.t_stop - st.t_start for st in trains):
num_spikes = sp.atleast_2d([st.size for st in trains])
return sp.absolute(num_spikes.T - num_spikes) ** exponent
sampling_rate = 1.0 / tau
binned, dummy = stools.bin_spike_trains({0: trains}, sampling_rate)
d = sp.empty((len(trains), len(trains)))
for i in xrange(len(trains)):
for j in xrange(i, len(trains)):
d[i, j] = d[j, i] = sp.sum(
sp.absolute(binned[0][i] - binned[0][j]) ** exponent)
return d
def sphere_features(features, sphere_vectors):
features.shape = features.shape[0], -1
fmean, fstd = sphere_vectors
features -= fmean
assert((fstd!=0).all())
features /= fstd
assert(not sp.isnan(sp.ravel(features)).any())
assert(not sp.isinf(sp.ravel(features)).any())
return features
def compute_by_noise_pow(self,signal,n_pow):
s_spec = sp.fft(signal*self._window)
s_amp = sp.absolute(s_spec)
s_phase = sp.angle(s_spec)
gamma = self._calc_aposteriori_snr(s_amp,n_pow)
xi = self._calc_apriori_snr(gamma)
self._prevGamma = gamma
nu = gamma * xi / (1.0+xi)
self._G = (self._gamma15*sp.sqrt(nu)/gamma)*sp.exp(-nu/2.0)* ((1.0+nu)*spc.i0(nu/2.0)+nu*spc.i1(nu/2.0))
idx = sp.less(s_amp**2.0,n_pow)
self._G[idx] = self._constant
idx = sp.isnan(self._G) + sp.isinf(self._G)
self._G[idx] = xi[idx] / ( xi[idx] + 1.0)
idx = sp.isnan(self._G) + sp.isinf(self._G)
self._G[idx] = self._constant
self._G = sp.maximum(self._G,0.0)
amp = self._G * s_amp
amp = sp.maximum(amp,0.0)
amp2 = self._ratio*amp + (1.0-self._ratio)*s_amp
self._prevAmp = amp
spec = amp2 * sp.exp(s_phase*1j)
return sp.real(sp.ifft(spec))
def plot(self, func, interp=True, plotter='imshow'):
import matplotlib as mpl
from matplotlib import pylab as pl
if interp:
lpi = self.interpolator(func)
z = lpi[self.yrange[0]:self.yrange[1]:complex(0, self.nrange),
self.xrange[0]:self.xrange[1]:complex(0, self.nrange)]
else:
y, x = sp.mgrid[
self.yrange[0]:self.yrange[1]:complex(0, self.nrange),
self.xrange[0]:self.xrange[1]:complex(0, self.nrange)]
z = func(x, y)
z = sp.where(sp.isinf(z), 0.0, z)
extent = (self.xrange[0], self.xrange[1], self.yrange[0],
self.yrange[1])
pl.ioff()
pl.clf()
pl.hot() # Some like it hot
if plotter == 'imshow':
pl.imshow(sp.nan_to_num(z),
interpolation='nearest',
extent=extent,
origin='lower')
elif plotter == 'contour':
Y, X = sp.ogrid[
self.yrange[0]:self.yrange[1]:complex(0, self.nrange),
self.xrange[0]:self.xrange[1]:complex(0, self.nrange)]
pl.contour(sp.ravel(X), sp.ravel(Y), z, 20)
x = self.x
y = self.y
lc = mpl.collections.LineCollection(sp.array([
((x[i], y[i]), (x[j], y[j])) for i, j in self.tri.edge_db
]),
colors=[(0, 0, 0, 0.2)])
ax = pl.gca()
ax.add_collection(lc)
if interp:
title = '%s Interpolant' % self.name
else:
title = 'Reference'
if hasattr(func, 'title'):
pl.title('%s: %s' % (func.title, title))
else:
pl.title(title)
pl.show()
pl.ion()
def to_mallet_dataset(obs):
"""
Convert to mallet in svmlight format, which also supports continuous features
"""
mystr = ""
for d in obs.observations:
mystr += str(d.label) + " "
for fname, fvalue in d.features_obs.iteritems():
if isnan(fvalue) or isinf(fvalue):
fvalue = 0.0
mystr += str(fname) + ":%.10f " % fvalue
mystr += "\n"
mystr += "\n"
return mystr
def learn_embeddings(self):
n, m = self.adj_matrix.shape
diags = self.adj_matrix.sum(axis=1).flatten()
D = sparse.spdiags(diags, [0], m, n, format='csr')
L = D - self.adj_matrix
with scipy.errstate(divide='ignore'):
diags_sqrt = 1.0 / scipy.sqrt(diags)
diags_sqrt[scipy.isinf(diags_sqrt)] = 0
DH = sparse.spdiags(diags_sqrt, [0], m, n, format='csr')
laplacian = DH.dot(L.dot(DH))
_, v = sparse.linalg.eigs(laplacian, k=self.dim + 1, which='SM')
embeddings = v[:, 1:].real
return embeddings
def compute_by_noise_pow(self,signal,n_pow):
s_spec = sp.fft(signal *self._window)
s_amp = sp.absolute(s_spec)
s_phase = sp.angle(s_spec)
gamma = self._calc_aposteriori_snr(s_amp,n_pow)
#xi = self._calc_apriori_snr2(gamma,n_pow)
xi = self._calc_apriori_snr(gamma)
self._prevGamma = gamma
u = 0.5 - self._mu/(4.0*sp.sqrt(gamma*xi))
self._G = u + sp.sqrt(u**2.0 + self._tau/(gamma*2.0))
idx = sp.less(s_amp**2.0,n_pow)
self._G[idx] = self._constant
idx = sp.isnan(self._G) + sp.isinf(self._G)
self._G[idx] = xi[idx] / ( xi[idx] + 1.0)
idx = sp.isnan(self._G) + sp.isinf(self._G)
self._G[idx] = self._constant
self._G = sp.maximum(self._G,0.0)
amp = self._G * s_amp
amp = sp.maximum(amp,0.0)
amp2 = self._ratio*amp + (1.0-self._ratio)*s_amp
self._prevAmp = amp
spec = amp2 * sp.exp(s_phase*1j)
return sp.real(sp.ifft(spec))
def lapnormadj(A):
import scipy
import numpy as np
from scipy.sparse import csgraph
n,m = A.shape
d1 = A.sum(axis=1).flatten()
d2 = A.sum(axis=0).flatten()
d1_sqrt = 1.0/scipy.sqrt(d1)
d2_sqrt = 1.0/scipy.sqrt(d2)
d1_sqrt[scipy.isinf(d1_sqrt)] = 0
d2_sqrt[scipy.isinf(d2_sqrt)] = 0
la = np.zeros(shape=(n,m))
for i in range(0,n):
for j in range(0,m):
la[i,j] = A[i,j]/(d1_sqrt[i]*d2_sqrt[j])
#D1 = scipy.sparse.spdiags(d1_sqrt, [0], n,m, format='coo')
#D2 = scipy.sparse.spdiags(d2_sqrt, [0], n,m, format='coo')
return scipy.sparse.coo_matrix(la)
def Update(self, s, y, s_dot_y=None):
if len(self.s) == self.maxnumvecs:
self.s.pop(0)
self.y.pop(0)
self.rho.pop(0)
if s_dot_y is None: s_dot_y = dot(s, y)
rho = 1.0 / s_dot_y
if isinf(rho):
print 'Warning, s . y = 0; ignoring pair'
else:
self.s.append(s)
self.y.append(y)
self.rho.append(rho)
def laplaceNorm(A):
"""
:param mat: Adjacency matrix
:return: laplacian normalized matrix
"""
import scipy
from scipy.sparse import csgraph
n,m = A.shape
diags = A.sum(axis=1).flatten()
diags_sqrt = 1.0/scipy.sqrt(diags)
diags_sqrt[scipy.isinf(diags_sqrt)] = 0
#print diags_sqrt
DH = scipy.sparse.spdiags(diags_sqrt, [0], m,n, format='coo')
return scipy.sparse.coo_matrix(DH * A * DH)
def laplaceNorm(A):
"""
Function to perform laplcian normalization of mxm matrix
:param mat: Adjacency matrix
:return: laplacian normalized matrix
"""
import scipy
from scipy.sparse import csgraph
n,m = A.shape
diags = A.sum(axis=1).flatten()
diags_sqrt = 1.0/scipy.sqrt(diags)
diags_sqrt[scipy.isinf(diags_sqrt)] = 0
#print diags_sqrt
DH = scipy.sparse.spdiags(diags_sqrt, [0], m,n, format='coo')
return scipy.sparse.coo_matrix(DH * A * DH)
def sample(self, model, evidence):
z = evidence['z']
g = evidence['g']
h = evidence['h']
T = evidence['T']
phi = evidence['phi']
transition_var_h = evidence['transition_var_h']
shot_id = evidence['shot_id']
observation_var_h = model.known_params['observation_var_h']
mu_h = model.known_params['mu_h']
prior_mu_h = model.hyper_params['h']['mu']
prior_cov_h = model.hyper_params['h']['cov']
n = len(h)
N = len(z)
# Making g, h, and z vector valued to avoid ambiguity
z_h = ma.asarray(nan + zeros(n))
obs_cov = ma.asarray(inf + zeros(n))
if 2 in T:
z_h[T==2] = z[T==2]
obs_cov[T==2] = observation_var_h
pdb.set_trace()
#for i in xrange(n):
# z_i = z[shot_id == i]
# T_i = T[shot_id == i]
# if 2 in T_i:
# # Sample mean and variance for multiple observations
# n_obs = sum(T_i == 2)
# z_h[i] = mean(z_i[T_i == 2])
# obs_cov[i] = observation_var_h/n_obs
z_h[isnan(z_h)] = ma.masked
obs_cov[isinf(obs_cov)] = ma.masked
kalman = self._kalman
kalman.initial_state_mean = array([prior_mu_h[0],])
kalman.initial_state_covariance = array([prior_cov_h[0],])
kalman.transition_matrices = array([phi,])
kalman.transition_covariance = array([transition_var_h,])
kalman.transition_offsets = mu_h*(1-phi)*ones((n, 1))
kalman.observation_matrices = eye(1)
kalman.observation_offsets = g
kalman.observation_covariance = obs_cov
sampled_h = forward_filter_backward_sample(kalman, z_h, prior_mu_h, prior_cov_h)
return sampled_h.reshape((n,))
def lnposteriorargs(self,args,**fixed):
kwargs = {}
kwargs.update({key:val for key,val in zip(self.fitted,args)})
kwargs.update(fixed)
kwargs.update({par:scipy.nan for par in self.solved()})
lnpriors = self.lnpriors(**kwargs)
if scipy.isinf(sum(lnpriors)): return -scipy.inf,{}
solved = self.solve_update_analytic(**kwargs)
kwargs.update(solved)
solved.update(fixed)
lnpriors = self.lnpriors(**kwargs)
lnlkls = self.lnlkls(**kwargs)
lnposteriors = [lnlkl + lnprior for lnlkl,lnprior in zip(lnlkls,lnpriors)]
for id,lnposterior in zip(self.ids,lnposteriors):
solved['lnposterior_{}'.format(id)] = lnposterior
#print id,solved['lnposterior_{}'.format(id)]
return sum(lnposteriors),solved
def fit(self, adjacency_matrix):
"""Fits the model from data in adjacency_matrix
Parameters
----------
adjacency_matrix : Scipy csr matrix or numpy ndarray
Adjacency matrix of the graph
node_weights : {'uniform', 'degree', array of length n_nodes with positive entries}
Node weights
"""
if type(adjacency_matrix) == sparse.csr_matrix:
adj_matrix = adjacency_matrix
elif sparse.isspmatrix(adjacency_matrix) or type(adjacency_matrix) == np.ndarray:
adj_matrix = sparse.csr_matrix(adjacency_matrix)
else:
raise TypeError(
"The argument must be a NumPy array or a SciPy Sparse matrix.")
n_nodes, m_nodes = adj_matrix.shape
if n_nodes != m_nodes:
raise ValueError("The adjacency matrix must be a square matrix.")
#if csgraph.connected_components(adj_matrix, directed=False)[0] > 1:
#raise ValueError("The graph must be connected.")
if (adj_matrix != adj_matrix.maximum(adj_matrix.T)).nnz != 0:
raise ValueError("The adjacency matrix is not symmetric.")
# builds standard laplacian
degrees = adj_matrix.dot(np.ones(n_nodes))
degree_matrix = sparse.diags(degrees, format='csr')
laplacian = degree_matrix - adj_matrix
# applies normalization by node weights
with errstate(divide='ignore'):
degrees_inv_sqrt = 1.0 / sqrt(degrees)
degrees_inv_sqrt[isinf(degrees_inv_sqrt)] = 0
weight_matrix = sparse.diags(degrees_inv_sqrt, format='csr')
laplacian = weight_matrix.dot(laplacian.dot(weight_matrix))
# spectral decomposition
eigenvalues, eigenvectors = eigsh(laplacian, min(self.embedding_dimension + 1, n_nodes - 1), which='SM')
self.eigenvalues_ = eigenvalues[1:]
self.embedding_ = np.array(weight_matrix.dot(eigenvectors[:, 1:]))
return self
def plot(self, func, interp=True, plotter='imshow'):
import matplotlib as mpl
from matplotlib import pylab as pl
if interp:
lpi = self.interpolator(func)
z = lpi[self.yrange[0]:self.yrange[1]:complex(0,self.nrange),
self.xrange[0]:self.xrange[1]:complex(0,self.nrange)]
else:
y, x = sp.mgrid[self.yrange[0]:self.yrange[1]:complex(0,self.nrange),
self.xrange[0]:self.xrange[1]:complex(0,self.nrange)]
z = func(x, y)
z = sp.where(sp.isinf(z), 0.0, z)
extent = (self.xrange[0], self.xrange[1],
self.yrange[0], self.yrange[1])
pl.ioff()
pl.clf()
pl.hot() # Some like it hot
if plotter == 'imshow':
pl.imshow(sp.nan_to_num(z), interpolation='nearest', extent=extent, origin='lower')
elif plotter == 'contour':
Y, X = sp.ogrid[self.yrange[0]:self.yrange[1]:complex(0,self.nrange),
self.xrange[0]:self.xrange[1]:complex(0,self.nrange)]
pl.contour(sp.ravel(X), sp.ravel(Y), z, 20)
x = self.x
y = self.y
lc = mpl.collections.LineCollection(sp.array([((x[i], y[i]), (x[j], y[j]))
for i, j in self.tri.edge_db]), colors=[(0,0,0,0.2)])
ax = pl.gca()
ax.add_collection(lc)
if interp:
title = '%s Interpolant' % self.name
else:
title = 'Reference'
if hasattr(func, 'title'):
pl.title('%s: %s' % (func.title, title))
else:
pl.title(title)
pl.show()
pl.ion()
def makehist(testpath,npulses):
""" This functions are will create histogram from data made in the testpath.
Inputs
testpath - The path that the data is located.
npulses - The number of pulses in the sim.
"""
sns.set_style("whitegrid")
sns.set_context("notebook")
params = ['Ne','Te','Ti','Vi']
pvals = [1e11,1e11,2.1e3,1.1e3,0.]
errdict = makehistdata(params,testpath)[:4]
ernames = ['Data','Error','Error Percent']
sig1 = sp.sqrt(1./npulses)
for ierr, iername in enumerate(ernames):
filetemplate= str(Path(testpath).join('AnalysisPlots',iername))
(figmplf, axmat) = plt.subplots(2, 2,figsize=(20, 15), facecolor='w')
axvec = axmat.flatten()
for ipn, iparam in enumerate(params):
plt.sca(axvec[ipn])
if sp.any(sp.isinf(errdict[ierr][iparam])):
continue
histhand = sns.distplot(errdict[ierr][iparam], bins=100, kde=True, rug=False)
xlim = histhand.get_xlim()
if ierr==0:
x0=pvals[ipn]
else:
x0=0
if ierr==2:
sig=sig1*100.
else:
sig=sig1*pvals[ipn]
x = sp.linspace(xlim[0],xlim[1],100)
den1 = sp.stats.norm(x0,sig).pdf(x)
#plt.plot(x,den1,'g--')
axvec[ipn].set_title(iparam)
figmplf.suptitle(iername +' Pulses: {0}'.format(npulses), fontsize=20)
fname= filetemplate+'_{0:0>5}Pulses.png'.format(npulses)
plt.savefig(fname)
plt.close(figmplf)
def _unbounded_set_value(self, uvalue):
"""Set a varying param's value via a transformed parameter that has
its range mapped to (-inf,inf)."""
if self.status != varying:
raise ParamError, 'Unbounded access valid only for varying parameter!'
# *** Is this test redundant?
if not self.bounded:
raise ParamError, 'No bounds defined for parameter!'
else:
expv = exp(uvalue)
if isinf(expv) or isnan(expv):
if uvalue > 0:
self._set_value(self.hi)
else:
self._set_value(self.lo)
else:
# Use _set_value, since this should be in range. In fact,
# I've found just-barely out-of-range results (presumably due
# to roundoff at limits) that trigger exceptions using set_value.
self._set_value( (self.lo + self.hi*expv)/(1. + expv) )
def with_walking(time_arr, mins_per_square=1.3, transfer_constant=5):
arr = time_arr.copy()
cross_footprint = sp.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]]).astype(bool)
diag_footprint = sp.array([[1, 0, 1],[0, 1, 0], [1, 0, 1]]).astype(bool)
arr[sp.isnan(arr)] = sp.inf
for i in range(60):
cross_arr = sp.ndimage.minimum_filter(arr, footprint=cross_footprint)
cross_arr[sp.isnan(cross_arr)] = sp.inf
cross_changes = (cross_arr != arr)
cross_arr[cross_changes] += 1*mins_per_square
diag_arr = sp.ndimage.minimum_filter(arr, footprint=diag_footprint)
diag_arr[sp.isnan(diag_arr)] = sp.inf
diag_changes = (diag_arr != arr)
diag_arr[diag_changes] += 1.4*mins_per_square
arr = sp.minimum(cross_arr, diag_arr)
arr[sp.isinf(arr)] = sp.nan
return arr + transfer_constant
def gmres(A, b, x0=None, tol=1e-5, restrt=None, maxiter=None, xtype=None, M=None, callback=None, residuals=None):
'''
Generalized Minimum Residual Method (GMRES)
GMRES iteratively refines the initial solution guess to the system Ax = b
For robustness, Householder reflections are used to orthonormalize the Krylov Space
Givens Rotations are used to provide the residual norm each iteration
Parameters
----------
A : array, matrix or sparse matrix
n x n, linear system to solve
b : array
n x 1, right hand side
x0 : array
n x 1, initial guess
default is a vector of zeros
tol : float
convergence tolerance
restrt : int
number of restarts
total iterations = restrt*maxiter
maxiter : int
maximum number of allowed inner iterations
xtype : type
dtype for the solution
M : matrix-like
n x n, inverted preconditioner, i.e. solve M A x = b.
For preconditioning with a mat-vec routine, set
A.psolve = func, where func := M y
callback : function
callback( ||resid||_2 ) is called each iteration,
residuals : {None, empty-list}
If empty-list, residuals holds the residual norm history,
including the initial residual, upon completion
Returns
-------
(xNew, info)
xNew -- an updated guess to the solution of Ax = b
info -- halting status of gmres
0 : successful exit
>0 : convergence to tolerance not achieved,
return iteration count instead. This value
is precisely the order of the Krylov space.
<0 : numerical breakdown, or illegal input
Notes
-----
Examples
--------
>>>from pyamg.krylov import *
>>>from scipy import rand
>>>import pyamg
>>>A = pyamg.poisson((50,50))
>>>b = rand(A.shape[0],)
>>>(x,flag) = gmres(A,b)
>>>print pyamg.util.linalg.norm(b - A*x)
References
----------
Yousef Saad, "Iterative Methods for Sparse Linear Systems,
Second Edition", SIAM, pp. 151-172, pp. 272-275, 2003
'''
# Convert inputs to linear system, with error checking
A,M,x,b,postprocess = make_system(A,M,x0,b,xtype)
dimen = A.shape[0]
# Choose type
xtype = upcast(A.dtype, x.dtype, b.dtype, M.dtype)
# We assume henceforth that shape=(n,) for all arrays
b = ravel(array(b,xtype))
x = ravel(array(x,xtype))
# Should norm(r) be kept
if residuals == []:
keep_r = True
else:
keep_r = False
# check number of iterations
if restrt == None:
restrt = 1
elif restrt < 1:
raise ValueError('Number of restarts must be positive')
if maxiter == None:
maxiter = int(max(ceil(dimen/restrt)))
elif maxiter < 1:
raise ValueError('Number of iterations must be positive')
elif maxiter > dimen:
warn('maximimum allowed inner iterations (maxiter) are the number of degress of freedom')
maxiter = dimen
# Scale tol by normb
normb = linalg.norm(b)
if normb == 0:
pass
# if callback != None:
# callback(0.0)
#
# return (postprocess(zeros((dimen,)), dtype=xtype),0)
else:
tol = tol*normb
# Is this a one dimensional matrix?
if dimen == 1:
entry = ravel(A*array([1.0], dtype=xtype))
return (postprocess(b/entry), 0)
# Prep for method
r = b - ravel(A*x)
normr = linalg.norm(r)
if keep_r:
residuals.append(normr)
# Is initial guess sufficient?
if normr <= tol:
if callback != None:
callback(norm(r))
return (postprocess(x), 0)
#Apply preconditioner
r = ravel(M*r)
normr = linalg.norm(r)
# Check for nan, inf
if any(isnan(r)) or any(isinf(r)):
warn('inf or nan after application of preconditioner')
return(postprocess(x), -1)
# Use separate variable to track iterations. If convergence fails, we cannot
# simply report niter = (outer-1)*maxiter + inner. Numerical error could cause
# the inner loop to halt before reaching maxiter while the actual ||r|| > tol.
niter = 0
# Begin GMRES
for outer in range(restrt):
# Calculate vector w, which defines the Householder reflector
# Take shortcut in calculating,
# w = r + sign(r[1])*||r||_2*e_1
w = r
beta = mysign(w[0])*normr
w[0] += beta
w = w / linalg.norm(w)
# Preallocate for Krylov vectors, Householder reflectors and Hessenberg matrix
# Space required is O(dimen*maxiter)
H = zeros( (maxiter, maxiter), dtype=xtype) # upper Hessenberg matrix (actually made upper tri with Given's Rotations)
W = zeros( (dimen, maxiter), dtype=xtype) # Householder reflectors
W[:,0] = w
# Multiply r with (I - 2*w*w.T), i.e. apply the Householder reflector
# This is the RHS vector for the problem in the Krylov Space
g = zeros((dimen,), dtype=xtype)
g[0] = -beta
for inner in range(maxiter):
# Calcute Krylov vector in two steps
# (1) Calculate v = P_j = (I - 2*w*w.T)v, where k = inner
v = -2.0*conjugate(w[inner])*w
v[inner] += 1.0
# (2) Calculate the rest, v = P_1*P_2*P_3...P_{j-1}*ej.
for j in range(inner-1,-1,-1):
v = v - 2.0*dot(conjugate(W[:,j]), v)*W[:,j]
# Calculate new search direction
v = ravel(A*v)
#Apply preconditioner
v = ravel(M*v)
# Check for nan, inf
if any(isnan(v)) or any(isinf(v)):
warn('inf or nan after application of preconditioner')
return(postprocess(x), -1)
# Factor in all Householder orthogonal reflections on new search direction
for j in range(inner+1):
v = v - 2.0*dot(conjugate(W[:,j]), v)*W[:,j]
# Calculate next Householder reflector, w
# w = v[inner+1:] + sign(v[inner+1])*||v[inner+1:]||_2*e_{inner+1)
# Note that if maxiter = dimen, then this is unnecessary for the last inner
# iteration, when inner = dimen-1. Here we do not need to calculate a
# Householder reflector or Given's rotation because nnz(v) is already the
# desired length, i.e. we do not need to zero anything out.
if inner != dimen-1:
w = zeros((dimen,), dtype=xtype)
vslice = v[inner+1:]
alpha = linalg.norm(vslice)
if alpha != 0:
alpha = mysign(vslice[0])*alpha
# We do not need the final reflector for future calculations
if inner < (maxiter-1):
w[inner+1:] = vslice
w[inner+1] += alpha
w = w / linalg.norm(w)
W[:,inner+1] = w
# Apply new reflector to v
# v = v - 2.0*w*(w.T*v)
v[inner+1] = -alpha
v[inner+2:] = 0.0
# Apply all previous Given's Rotations to v
if inner == 0:
# Q will store the cumulative effect of all Given's Rotations
Q = scipy.sparse.eye(dimen, dimen, format='csr', dtype=xtype)
# Declare initial Qj, which will be the current Given's Rotation
rowptr = hstack( (array([0, 2, 4],int), arange(5,dimen+3,dtype=int)) )
colindices = hstack( (array([0, 1, 0, 1],int), arange(2, dimen,dtype=int)) )
data = ones((dimen+2,), dtype=xtype)
Qj = csr_matrix( (data, colindices, rowptr), shape=(dimen,dimen), dtype=xtype)
else:
# Could avoid building a global Given's Rotation, by storing
# and applying each 2x2 matrix individually.
# But that would require looping, the bane of wonderful Python
Q = Qj*Q
v = Q*v
# Calculate Qj, the next Given's rotation, where j = inner
# Note that if maxiter = dimen, then this is unnecessary for the last inner
# iteration, when inner = dimen-1. Here we do not need to calculate a
# Householder reflector or Given's rotation because nnz(v) is already the
# desired length, i.e. we do not need to zero anything out.
if inner != dimen-1:
if v[inner+1] != 0:
# Calculate terms for complex 2x2 Given's Rotation
# Note that abs(x) takes the complex modulus
h1 = v[inner]; h2 = v[inner+1];
h1_mag = abs(h1); h2_mag = abs(h2);
if h1_mag < h2_mag:
mu = h1/h2
tau = conjugate(mu)/abs(mu)
else:
mu = h2/h1
tau = mu/abs(mu)
denom = sqrt( h1_mag**2 + h2_mag**2 )
c = h1_mag/denom; s = h2_mag*tau/denom;
Qblock = array([[c, conjugate(s)], [-s, c]], dtype=xtype)
# Modify Qj in csr-format so that it represents the current
# global Given's Rotation equivalent to Qblock
if inner != 0:
Qj.data[inner-1] = 1.0
Qj.indices[inner-1] = inner-1
Qj.indptr[inner-1] = inner-1
Qj.data[inner:inner+4] = ravel(Qblock)
Qj.indices[inner:inner+4] = [inner, inner+1, inner, inner+1]
Qj.indptr[inner:inner+3] = [inner, inner+2, inner+4]
# Apply Given's Rotation to g,
# the RHS for the linear system in the Krylov Subspace.
# Note that this dot does a matrix multiply, not an actual
# dot product where a conjugate transpose is taken
g[inner:inner+2] = dot(Qblock, g[inner:inner+2])
# Apply effect of Given's Rotation to v
v[inner] = dot(Qblock[0,:], v[inner:inner+2])
v[inner+1] = 0.0
# Write to upper Hessenberg Matrix,
# the LHS for the linear system in the Krylov Subspace
H[:,inner] = v[0:maxiter]
# Don't update normr if last inner iteration, because
# normr is calculated directly after this loop ends.
if inner < maxiter-1:
normr = abs(g[inner+1])
if normr < tol:
break
# Allow user access to residual
if callback != None:
callback( normr )
if keep_r:
residuals.append(normr)
niter += 1
# end inner loop, back to outer loop
# Find best update to x in Krylov Space, V. Solve inner+1 x inner+1 system.
# Apparently this is the best way to solve a triangular
# system in the magical world of scipy
piv = arange(inner+1)
y = lu_solve((H[0:(inner+1),0:(inner+1)], piv), g[0:(inner+1)], trans=0)
# Use Horner like Scheme to map solution, y, back to original space.
# Note that we do not use the last reflector.
update = zeros(x.shape, dtype=xtype)
for j in range(inner,-1,-1):
update[j] += y[j]
# Apply j-th reflector, (I - 2.0*w_j*w_j.T)*upadate
update = update - 2.0*dot(conjugate(W[:,j]), update)*W[:,j]
x = x + update
r = b - ravel(A*x)
#Apply preconditioner
r = ravel(M*r)
normr = linalg.norm(r)
# Check for nan, inf
if any(isnan(r)) or any(isinf(r)):
warn('inf or nan after application of preconditioner')
return(postprocess(x), -1)
# Allow user access to residual
if callback != None:
callback( normr )
if keep_r:
residuals.append(normr)
# Has GMRES stagnated?
indices = (x != 0)
if indices.any():
change = max(abs( update[indices] / x[indices] ))
if change < 1e-12:
# No change, halt
return (postprocess(x), -1)
# test for convergence
if normr < tol:
return (postprocess(x),0)
# end outer loop
return (postprocess(x), niter)
def _oneEvaluation(self, evaluable):
""" This method should be called by all tabu optimizers for producing an evaluation.
This is nearly identical to BlackBoxOptimizer's _oneEvaluation except that it subtracts
the tabuPenalty from the evaluations of tabuEvaluables"""
if not self._setUp:
return BlackBoxOptimizer._oneEvaluation(self,evaluable)
if self._wasUnwrapped:
self.wrappingEvaluable._setParameters(evaluable)
res = self.evaluator(self.wrappingEvaluable)
elif self._wasWrapped:
res = self.evaluator(evaluable.params)
else:
res = self.evaluator(evaluable)
''' added by JPQ '''
if self.constrained :
self.feasible = self.evaluator.outfeasible
self.violation = self.evaluator.outviolation
# ---
if isscalar(res):
# detect numerical instability
if isnan(res) or isinf(res):
raise DivergenceError
#apply pentalty if tabu
for t in self.tabuList:
if t(evaluable):
res-=self.tabuPenalty
break
# always keep track of the best
if (self.numEvaluations == 0
or self.bestEvaluation is None
or (self.minimize and res <= self.bestEvaluation)
or (not self.minimize and res >= self.bestEvaluation)):
self.bestEvaluation = res
#update tabuList
self.tabuList.append(self.tabuGenerator(self.bestEvaluable,evaluable))
l=len(self.tabuList)
if l > self.maxTabuList:
self.tabuList=self.tabuList[(l-self.maxTabuList):l]
self.bestEvaluable = evaluable.copy()
self.numEvaluations += 1
# if desired, also keep track of all evaluables and/or their fitness.
if self.storeAllEvaluated:
if self._wasUnwrapped:
self._allEvaluated.append(self.wrappingEvaluable.copy())
elif self._wasWrapped:
self._allEvaluated.append(evaluable.params.copy())
else:
self._allEvaluated.append(evaluable.copy())
if self.storeAllEvaluations:
if self._wasOpposed and isscalar(res):
''' added by JPQ '''
if self.constrained :
self._allEvaluations.append([-res,self.feasible,self.violation])
# ---
else:
self._allEvaluations.append(-res)
else:
''' added by JPQ '''
if self.constrained :
self._allEvaluations.append([res,self.feasible,self.violation])
# ---
else:
self._allEvaluations.append(res)
''' added by JPQ '''
if self.constrained :
return [res,self.feasible,self.violation]
else:
# ---
return res
def yIsPoor(y):
"""Returns True if y is not usable"""
return max(scipy.isinf(y)) or max(scipy.isnan(y))
def _pathwiseLearn(self, ss, varnames, bases, X_orig, X_orig_regress, y_orig,
max_num_bases, target_nmse, verbose=False, **fit_params):
"""Adapted from enet_path() in sklearn.linear_model.
http://scikit-learn.sourceforge.net/modules/linear_model.html
Compute Elastic-Net path with coordinate descent.
Returns list of model (or None if failure)."""
if verbose:
print ' Pathwise learn: begin. max_num_bases=%d' % max_num_bases
max_iter = 5000 #default 5000. magic number.
#Condition X and y:
# -"unbias" = rescale so that (mean=0, stddev=1) -- subtract each row's mean, then divide by stddev
# -X transposed
# -X as fortran array
(X_unbiased, y_unbiased, X_avgs, X_stds, y_avg, y_std) = self._unbiasedXy(X_orig_regress, y_orig)
X_unbiased = numpy.asfortranarray(X_unbiased) # make data contiguous in memory
n_samples = X_unbiased.shape[0]
vals = numpy.dot(X_unbiased.T, y_unbiased)
vals = [val for val in vals if not scipy.isnan(val)]
if vals: alpha_max = numpy.abs(max(vals) / (n_samples * ss.l1_ratio()))
else: alpha_max = 1.0 #backup: pick a value from the air
#alphas = lotsa alphas at beginning, and usual rate for rest
st, fin = numpy.log10(alpha_max*ss.eps()), numpy.log10(alpha_max)
alphas1 = numpy.logspace(st, fin, num=ss.numAlphas()*10)[::-1][:ss.numAlphas()/4]
alphas2 = numpy.logspace(st, fin, num=ss.numAlphas())
alphas = sorted(set(alphas1).union(alphas2), reverse=True)
if not 'precompute' in fit_params or fit_params['precompute'] is True:
fit_params['precompute'] = numpy.dot(X_unbiased.T, X_unbiased)
#if not 'Xy' in fit_params or fit_params['Xy'] is None:
# fit_params['Xy'] = numpy.dot(X_unbiased.T, y_unbiased)
models = [] #build this up
nmses = [] #for detecting stagnation
cur_unbiased_coefs = None # init values for coefs
start_time = time.time()
for (alpha_i, alpha) in enumerate(alphas):
#compute (unbiased) coefficients. Recall that mean=0 so no intercept needed
clf = ElasticNetWithTimeout(alpha=alpha, l1_ratio=ss.l1_ratio(), fit_intercept=False,
max_iter=max_iter, **fit_params)
try:
clf.fit(X_unbiased, y_unbiased)
except TimeoutError:
print ' Regularized update failed. Returning None'
return None #failure
except ValueError:
print ' Regularized update failed with ValueError.'
print ' X_unbiased:'
print X_unbiased
print ' y_unbiased:'
print y_unbiased
sys.exit(1)
cur_unbiased_coefs = clf.coef_.copy()
if cur_unbiased_coefs.shape == tuple():
# This happens when we have only one variable because
# ElasticNet calls numpy.squeeze(), which reduces a
# single element array to a 0-d array. That would
# crash us below in list(cur_unbiased_coefs). We just
# undo the squeeze.
cur_unbiased_coefs = cur_unbiased_coefs.reshape((1,))
#compute model; update models
# -"rebias" means convert from (mean=0, stddev=1) to original (mean, stddev)
coefs = self._rebiasCoefs([0.0] + list(cur_unbiased_coefs), X_stds, X_avgs, y_std, y_avg)
(coefs_n, bases_n, coefs_d, bases_d) = self._allocateToNumerDenom(ss, bases, coefs)
model = FFXModel(coefs_n, bases_n, coefs_d, bases_d, varnames)
models.append(model)
#update nmses
nmse_unbiased = nmse(numpy.dot(cur_unbiased_coefs, X_unbiased.T), y_unbiased,
min(y_unbiased), max(y_unbiased))
nmses.append(nmse_unbiased)
#log
num_bases = len(numpy.nonzero(cur_unbiased_coefs)[0])
if verbose and ((alpha_i==0) or (alpha_i+1) % 50 == 0):
print ' alpha %d/%d (%3e): num_bases=%d, nmse=%.6f, time %.2f s' % \
(alpha_i+1, len(alphas), alpha, num_bases, nmse_unbiased, time.time() - start_time)
#maybe stop
if scipy.isinf(nmses[-1]):
if verbose:
print ' Pathwise learn: Early stop because nmse is inf'
return None
if nmse_unbiased < target_nmse:
if verbose:
print ' Pathwise learn: Early stop because nmse < target'
return models
if num_bases > max_num_bases:
if verbose:
print ' Pathwise learn: Early stop because num bases > %d' % max_num_bases
return models
if len(nmses) > 15 and round(nmses[-1], 4) == round(nmses[-15], 4):
if verbose:
print ' Pathwise learn: Early stop because nmses stagnated'
return models
if verbose:
print ' Pathwise learn: done'
return models