def setUp(self):
"""
Set up problem.
"""
super(Test_prob_1to1, self).setUp()
self.disc._input_sample_set.estimate_volume_mc()
calcP.prob(self.disc)
def postprocess(station_nums, ref_num):
filename = 'P_q'+str(station_nums[0]+1)+'_q'+str(station_nums[1]+1)
if len(station_nums) == 3:
filename += '_q'+str(station_nums[2]+1)
filename += '_ref_'+str(ref_num+1)
data = Q[:, station_nums]
output_sample_set = sample.sample_set(data.shape[1])
output_sample_set.set_values(data)
q_ref = Q_ref[ref_num, station_nums]
# Create Simple function approximation
# Save points used to parition D for simple function approximation and the
# approximation itself (this can be used to make close comparisions...)
output_probability_set = sfun.regular_partition_uniform_distribution_rectangle_scaled(\
output_sample_set, q_ref, rect_scale=0.15,
cells_per_dimension=np.ones((data.shape[1],)))
my_disc = sample.discretization(input_sample_set, output_sample_set,
output_probability_set)
# Calclate P on the actual samples with assumption that voronoi cells have
# equal size
input_sample_set.estimate_volume_mc()
print "Calculating prob"
calcP.prob(my_disc)
sample.save_discretization(my_disc, filename, "prob_solution")
def postprocess(station_nums, ref_num):
filename = 'P_q' + str(station_nums[0] + 1) + '_q' + str(station_nums[1] +
1)
if len(station_nums) == 3:
filename += '_q' + str(station_nums[2] + 1)
filename += '_ref_' + str(ref_num + 1)
data = Q[:, station_nums]
output_sample_set = sample.sample_set(data.shape[1])
output_sample_set.set_values(data)
q_ref = Q_ref[ref_num, station_nums]
# Create Simple function approximation
# Save points used to parition D for simple function approximation and the
# approximation itself (this can be used to make close comparisions...)
output_probability_set = sfun.regular_partition_uniform_distribution_rectangle_scaled(\
output_sample_set, q_ref, rect_scale=0.15,
cells_per_dimension=np.ones((data.shape[1],)))
my_disc = sample.discretization(input_sample_set, output_sample_set,
output_probability_set)
# Calclate P on the actual samples with assumption that voronoi cells have
# equal size
input_sample_set.estimate_volume_mc()
print "Calculating prob"
calcP.prob(my_disc)
sample.save_discretization(my_disc, filename, "prob_solution")
def setUp(self):
"""
Set up problem.
"""
super(Test_prob_1to1, self).setUp()
self.disc._input_sample_set.estimate_volume_mc()
calcP.prob(self.disc)
def setUp(self):
"""
Set up problem.
"""
super(Test_prob_3to1, self).setUp()
self.disc._input_sample_set.estimate_volume_mc()
calcP.prob(self.disc)
self.P_ref = np.loadtxt(data_path + "/3to1_prob.txt.gz")
def setUp(self):
"""
Set up problem.
"""
super(Test_prob_3to1, self).setUp()
self.disc._input_sample_set.estimate_volume_mc()
calcP.prob(self.disc)
self.P_ref = np.loadtxt(data_path + "/3to1_prob.txt.gz")
def postprocess(station_nums, ref_num):
filename = 'P_q' + str(station_nums[0] + 1) + \
'_q' + str(station_nums[1] + 1)
if len(station_nums) == 3:
filename += '_q' + str(station_nums[2] + 1)
filename += '_ref_' + str(ref_num + 1)
data = Q[:, station_nums]
output_sample_set = sample.sample_set(data.shape[1])
output_sample_set.set_values(data)
q_ref = Q_ref[ref_num, station_nums]
# Create Simple function approximation
# Save points used to parition D for simple function approximation and the
# approximation itself (this can be used to make close comparisions...)
output_probability_set = sfun.regular_partition_uniform_distribution_rectangle_scaled(
output_sample_set,
q_ref,
rect_scale=0.15,
cells_per_dimension=np.ones((data.shape[1], )))
num_l_emulate = 1e4
set_emulated = bsam.random_sample_set('r', lam_domain, num_l_emulate)
my_disc = sample.discretization(input_sample_set,
output_sample_set,
output_probability_set,
emulated_input_sample_set=set_emulated)
print("Finished emulating lambda samples")
# Calculate P on lambda emulate
print("Calculating prob_on_emulated_samples")
calcP.prob_on_emulated_samples(my_disc)
sample.save_discretization(my_disc, filename,
"prob_on_emulated_samples_solution")
# Calclate P on the actual samples with assumption that voronoi cells have
# equal size
input_sample_set.estimate_volume_mc()
print("Calculating prob")
calcP.prob(my_disc)
sample.save_discretization(my_disc, filename, "prob_solution")
# Calculate P on the actual samples estimating voronoi cell volume with MC
# integration
calcP.prob_with_emulated_volumes(my_disc)
print("Calculating prob_with_emulated_volumes")
sample.save_discretization(my_disc, filename,
"prob_with_emulated_volumes_solution")
def postprocess(station_nums, ref_num):
filename = 'P_q'+str(station_nums[0]+1)+'_q'+str(station_nums[1]+1)
if len(station_nums) == 3:
filename += '_q'+str(station_nums[2]+1)
filename += '_ref_'+str(ref_num+1)
data = Q[:, station_nums]
q_ref = Q_ref[ref_num, station_nums]
# Create Simple function approximation
# Save points used to parition D for simple function approximation and the
# approximation itself (this can be used to make close comparisions...)
(rho_D_M, d_distr_samples, d_Tree) = sfun.uniform_hyperrectangle(data,
q_ref, bin_ratio=0.15,
center_pts_per_edge=np.ones((data.shape[1],)))
mdict = dict()
mdict['rho_D_M'] = rho_D_M
mdict['d_distr_samples'] = d_distr_samples
# Calclate P on the actual samples with assumption that voronoi cells have
# equal size
(P1, lam_vol1, io_ptr1) = calcP.prob(samples, data, rho_D_M,
d_distr_samples, d_Tree)
print "Calculating prob"
mdict['P1'] = P1
mdict['lam_vol1'] = lam_vol1
mdict['lem1'] = samples
mdict['io_ptr1'] = io_ptr1
# Export P and compare to MATLAB solution visually
sio.savemat(filename, mdict, do_compression=True)
def postprocess(station_nums, ref_num):
filename = 'P_q'+str(station_nums[0]+1)+'_q'+str(station_nums[1]+1)
if len(station_nums) == 3:
filename += '_q'+str(station_nums[2]+1)
filename += '_ref_'+str(ref_num+1)
data = Q[:, station_nums]
q_ref = Q_ref[ref_num, station_nums]
# Create Simple function approximation
# Save points used to parition D for simple function approximation and the
# approximation itself (this can be used to make close comparisions...)
(rho_D_M, d_distr_samples, d_Tree) = sfun.uniform_hyperrectangle(data,
q_ref, bin_ratio=0.15,
center_pts_per_edge=np.ones((data.shape[1],)))
num_l_emulate = 1e6
lambda_emulate = calcP.emulate_iid_lebesgue(lam_domain, num_l_emulate)
if comm.rank == 0:
print "Finished emulating lambda samples"
mdict = dict()
mdict['rho_D_M'] = rho_D_M
mdict['d_distr_samples'] = d_distr_samples
mdict['num_l_emulate'] = num_l_emulate
# Calculate P on lambda emulate
(P0, lem0, io_ptr0, emulate_ptr0) = calcP.prob_emulated(samples, data,
rho_D_M, d_distr_samples, lambda_emulate, d_Tree)
if comm.rank == 0:
print "Calculating prob_emulated"
mdict['P0'] = P0
mdict['lem0'] = lem0
mdict['io_ptr0'] = io_ptr0
mdict['emulate_ptr0'] = emulate_ptr0
# Calclate P on the actual samples with assumption that voronoi cells have
# equal size
(P1, lam_vol1, io_ptr1) = calcP.prob(samples, data,
rho_D_M, d_distr_samples, d_Tree)
if comm.rank == 0:
print "Calculating prob"
mdict['P1'] = P1
mdict['lam_vol1'] = lam_vol1
mdict['lem1'] = samples
mdict['io_ptr1'] = io_ptr1
# Calculate P on the actual samples estimating voronoi cell volume with MC
# integration
(P3, lam_vol3, lambda_emulate3, io_ptr3, emulate_ptr3) = calcP.prob_mc(samples,
data, rho_D_M, d_distr_samples, lambda_emulate, d_Tree)
if comm.rank == 0:
print "Calculating prob_mc"
mdict['P3'] = P3
mdict['lam_vol3'] = lam_vol3
mdict['io_ptr3'] = io_ptr3
mdict['emulate_ptr3'] = emulate_ptr3
# Export P
sio.savemat(filename, mdict, do_compression=True)
def setUp(self):
"""
Set up problem.
"""
super(Test_prob_10to4, self).setUp()
(self.P, self.lam_vol, _) = calcP.prob(samples=self.samples,
data=self.data, rho_D_M=self.d_distr_prob,
d_distr_samples=self.d_distr_samples, d_Tree=self.d_Tree)
def setUp(self):
"""
Set up problem.
"""
super(Test_prob_3to1, self).setUp()
(self.P, self.lam_vol, _) = calcP.prob(samples=self.samples,
data=self.data, rho_D_M=self.d_distr_prob,
d_distr_samples=self.d_distr_samples, d_Tree=self.d_Tree)
self.P_ref = np.loadtxt(data_path + "/3to1_prob.txt.gz")
def postprocess(station_nums, ref_num):
filename = 'P_q'+str(station_nums[0]+1)+'_q'
if len(station_nums) == 3:
filename += '_q'+str(station_nums[2]+1)
filename += '_ref_'+str(ref_num+1)
data = Q[:, station_nums]
q_ref = Q_ref[ref_num, station_nums]
# Create Simple function approximation
# Save points used to parition D for simple function approximation and the
# approximation itself (this can be used to make close comparisions...)
(rho_D_M, d_distr_samples, d_Tree) = sfun.uniform_hyperrectangle(data,
q_ref, bin_ratio=0.15,
center_pts_per_edge=np.ones((data.shape[1],)))
num_l_emulate = 1e6
lambda_emulate = calcP.emulate_iid_lebesgue(lam_domain, num_l_emulate)
print "Finished emulating lambda samples"
mdict = dict()
mdict['rho_D_M'] = rho_D_M
mdict['d_distr_samples'] = d_distr_samples
mdict['num_l_emulate'] = num_l_emulate
mdict['lambda_emulate'] = lambda_emulate
# Calculate P on lambda emulate
(P0, lem0, io_ptr0, emulate_ptr0) = calcP.prob_emulated(samples, data,
rho_D_M, d_distr_samples, lambda_emulate, d_Tree)
print "Calculating prob_emulated"
mdict['P0'] = P0
mdict['lem0'] = lem0
mdict['io_ptr0'] = io_ptr0
mdict['emulate_ptr0'] = emulate_ptr0
# Calclate P on the actual samples with assumption that voronoi cells have
# equal size
(P1, lam_vol1, io_ptr1) = calcP.prob(samples, data,
rho_D_M, d_distr_samples, d_Tree)
print "Calculating prob"
mdict['P1'] = P1
mdict['lam_vol1'] = lam_vol1
mdict['lem1'] = samples
mdict['io_ptr1'] = io_ptr1
# Calculate P on the actual samples estimating voronoi cell volume with MC
# integration
(P3, lam_vol3, lambda_emulate3, io_ptr3, emulate_ptr3) = calcP.prob_mc(samples,
data, rho_D_M, d_distr_samples, lambda_emulate, d_Tree)
print "Calculating prob_mc"
mdict['P3'] = P3
mdict['lam_vol3'] = lam_vol3
mdict['io_ptr3'] = io_ptr3
mdict['emulate_ptr3'] = emulate_ptr3
# Export P
sio.savemat(filename, mdict, do_compression=True)
def setUp(self):
"""
Set up problem.
"""
super(Test_prob_1to1, self).setUp()
(self.P, self.lam_vol,
_) = calcP.prob(samples=self.samples,
data=self.data,
rho_D_M=self.d_distr_prob,
d_distr_samples=self.d_distr_samples,
d_Tree=self.d_Tree)
def setUp(self):
"""
Set up problem.
"""
super(Test_prob_3to1, self).setUp()
(self.P, self.lam_vol,
_) = calcP.prob(samples=self.samples,
data=self.data,
rho_D_M=self.d_distr_prob,
d_distr_samples=self.d_distr_samples,
d_Tree=self.d_Tree)
self.P_ref = np.loadtxt(data_path + "/3to1_prob.txt.gz")
def postprocess(station_nums, ref_num):
filename = 'P_q' + str(station_nums[0] + 1) + '_q' + str(station_nums[1] +
1)
if len(station_nums) == 3:
filename += '_q' + str(station_nums[2] + 1)
filename += '_ref_' + str(ref_num + 1)
data = Q[:, station_nums]
q_ref = Q_ref[ref_num, station_nums]
# Create Simple function approximation
# Save points used to parition D for simple function approximation and the
# approximation itself (this can be used to make close comparisions...)
(rho_D_M, d_distr_samples,
d_Tree) = sfun.uniform_hyperrectangle(data,
q_ref,
bin_ratio=0.15,
center_pts_per_edge=np.ones(
(data.shape[1], )))
mdict = dict()
mdict['rho_D_M'] = rho_D_M
mdict['d_distr_samples'] = d_distr_samples
# Calclate P on the actual samples with assumption that voronoi cells have
# equal size
(P1, lam_vol1, io_ptr1) = calcP.prob(samples, data, rho_D_M,
d_distr_samples, d_Tree)
print "Calculating prob"
mdict['P1'] = P1
mdict['lam_vol1'] = lam_vol1
mdict['lem1'] = samples
mdict['io_ptr1'] = io_ptr1
# Export P and compare to MATLAB solution visually
sio.savemat(filename, mdict, do_compression=True)
Partition_discretization = sampler.create_random_discretization('random',
Partition_set,
num_samples=num_samples_discretize_D)
Monte_Carlo_discretization = sampler.create_random_discretization('random',
Monte_Carlo_set,
num_samples=num_iid_samples)
# Compute the simple function approximation to the distribution on the data space
simpleFunP.user_partition_user_distribution(my_discretization,
Partition_discretization,
Monte_Carlo_discretization)
# Calculate probabilities
calculateP.prob(my_discretization)
########################################
# Post-process the results (optional)
########################################
# Show some plots of the different sample sets
plotD.scatter_2D(my_discretization._input_sample_set,
filename = 'Parameter_Samples',
file_extension = '.eps')
plotD.scatter_2D(my_discretization._output_sample_set,
filename = 'QoI_Samples',
file_extension = '.eps')
plotD.scatter_2D(my_discretization._output_probability_set,
filename = 'Data_Space_Discretization',
file_extension = '.eps')
'''
def calculate_prob_for_sample_set_region(self,
s_set,
regions,
update_input=True):
"""
Solves stochastic inverse problem based on surrogate points and the
MC assumption. Calculates the probability of a regions of input space
and error estimates for those probabilities.
:param: s_set: sample set for which to calculate error
:type s_set: :class:`bet.sample.sample_set_base`
:param region: list of regions of s_set for which to calculate error
:type region: list
:param update_input: whether or not to update probabilities and
errror identifiers for input discretization
:type update_input: bool
:rtype: tuple
:returns: (probabilities, ``error_estimates``), the probability and
error estimates for the region
"""
if not hasattr(self, 'surrogate_discretization'):
msg = "surrogate discretization has not been created"
raise calculateError.wrong_argument_type(msg)
if not isinstance(s_set, sample.sample_set_base):
msg = "s_set must be of type bet.sample.sample_set_base"
raise calculateError.wrong_argument_type(msg)
# Calculate probability of region
if self.surrogate_discretization._input_sample_set._volumes_local\
is None:
self.surrogate_discretization._input_sample_set.\
estimate_volume_mc(globalize=False)
calculateP.prob(self.surrogate_discretization, globalize=False)
prob_new_values = calculateP.prob_from_sample_set(\
self.surrogate_discretization._input_sample_set, s_set)
# Calculate for each region
probabilities = []
error_estimates = []
for region in regions:
marker = np.equal(s_set._region, region)
probability = np.sum(prob_new_values[marker])
# Calculate error estimate for region
model_error = calculateError.model_error(\
self.surrogate_discretization)
error_estimate = model_error.calculate_for_sample_set_region_mc(\
s_set, region)
probabilities.append(probability)
error_estimates.append(error_estimate)
# Update input only if 1 region is given
if update_input:
num = self.input_disc._input_sample_set.check_num()
prob = np.zeros((num, ))
error_id = np.zeros((num, ))
for i in range(num):
Itemp = np.equal(self.dummy_disc._emulated_ii_ptr_local, i)
prob_sum = np.sum(self.surrogate_discretization.\
_input_sample_set._probabilities_local[Itemp])
prob[i] = comm.allreduce(prob_sum, op=MPI.SUM)
error_id_sum = np.sum(self.surrogate_discretization.\
_input_sample_set._error_id_local[Itemp])
error_id[i] = comm.allreduce(error_id_sum, op=MPI.SUM)
self.input_disc._input_sample_set.set_probabilities(prob)
self.input_disc._input_sample_set.set_error_id(error_id)
return (probabilities, error_estimates)
# RESULTS WHERE SAMPLES = LAMBDA_EMULATE
# samples are on a regular grid
# result_wtree, result_wsamples, result_emulated_rg
self.result_emulated_rg = calcP.prob_emulated(self.r_samples, self.r_data,
self.rho_D_M, self.d_distr_samples, self.lam_domain,
self.r_samples, self.d_Tree)
self.result_wtree = result_emulated_rg
self.result_wsamples = result_emulated_rg
self.result_wotree = calcP.prob_emulated(self.r_samples, self.r_data,
self.rho_D_M, self.d_distr_samples, self.lam_domain,
self.r_samples)
self.result_wosamples = calcP.prob_emulated(self.r_samples, self.r_data,
self.rho_D_M, self.d_distr_samples, self.lam_domain)
self.result_prob_rg = calcP.prob(self.r_samples, self.r_data,
self.rho_D_M, self.d_distr_samples, self.lam_domain,
self.d_Tree)
self.result_mc_rg = calcP.prob_mc(self.r_samples, self.r_data,
self.rho_D_M, self.d_distr_samples, self.lam_domain,
self.r_samples, self.d_Tree)
# samples are iid
self.result_emulated_iid = calcP.prob_emulated(self.u_samples, self.u_data,
self.rho_D_M, self.d_distr_samples, self.lam_domain,
self.u_samples, self.d_Tree)
self.result_prob_iid = calcP.prob(self.u_samples, self.u_data,
self.rho_D_M, self.d_distr_samples, self.lam_domain,
self.d_Tree)
self.result_mc_iid = calcP.prob_mc(self.u_samples, self.u_data,
self.rho_D_M, self.d_distr_samples, self.lam_domain,
#QoI_indices = [0, 3, 5, 8, 9]
#QoI_indices = [3, 4, 5, 8, 9]
#QoI_indices = [2, 3, 5, 6, 9]
# Restrict the data to have just QoI_indices
data = data[:, QoI_indices]
Q_ref = Q[QoI_indices, :].dot(0.5 * np.ones(Lambda_dim))
# bin_ratio defines the uncertainty in our data
bin_ratio = 0.25
# Find the simple function approximation
(d_distr_prob, d_distr_samples, d_Tree) = simpleFunP.uniform_hyperrectangle(\
data=data, Q_ref=Q_ref, bin_ratio=bin_ratio, center_pts_per_edge = 1)
# Calculate probablities making the Monte Carlo assumption
(P, lam_vol, io_ptr) = calculateP.prob(samples=samples, data=data,
rho_D_M=d_distr_prob, d_distr_samples=d_distr_samples)
percentile = 1.0
# Sort samples by highest probability density and find how many samples lie in
# the support of the inverse solution. With the Monte Carlo assumption, this
# also tells us the approximate volume of this support.
(num_samples, P_high, samples_high, lam_vol_high, data_high) =\
postTools.sample_highest_prob(top_percentile=percentile, P_samples=P,
samples=samples, lam_vol=lam_vol,data = data,sort=True)
# Print the number of samples that make up the highest percentile percent
# samples and ratio of the volume of the parameter domain they take up
if comm.rank == 0:
print (num_samples, np.sum(lam_vol_high))
def calculate_prob_for_sample_set_region(self, s_set,
regions, update_input=True):
"""
Solves stochastic inverse problem based on surrogate points and the
MC assumption. Calculates the probability of a regions of input space
and error estimates for those probabilities.
:param: s_set: sample set for which to calculate error
:type s_set: :class:`bet.sample.sample_set_base`
:param region: list of regions of s_set for which to calculate error
:type region: list
:param update_input: whether or not to update probabilities and
errror identifiers for input discretization
:type update_input: bool
:rtype: tuple
:returns: (probabilities, ``error_estimates``), the probability and
error estimates for the region
"""
if not hasattr(self, 'surrogate_discretization'):
msg = "surrogate discretization has not been created"
raise calculateError.wrong_argument_type(msg)
if not isinstance(s_set, sample.sample_set_base):
msg = "s_set must be of type bet.sample.sample_set_base"
raise calculateError.wrong_argument_type(msg)
# Calculate probability of region
if self.surrogate_discretization._input_sample_set._volumes_local\
is None:
self.surrogate_discretization._input_sample_set.\
estimate_volume_mc(globalize=False)
calculateP.prob(self.surrogate_discretization, globalize=False)
prob_new_values = calculateP.prob_from_sample_set(\
self.surrogate_discretization._input_sample_set, s_set)
# Calculate for each region
probabilities = []
error_estimates = []
for region in regions:
marker = np.equal(s_set._region, region)
probability = np.sum(prob_new_values[marker])
# Calculate error estimate for region
model_error = calculateError.model_error(\
self.surrogate_discretization)
error_estimate = model_error.calculate_for_sample_set_region_mc(\
s_set, region)
probabilities.append(probability)
error_estimates.append(error_estimate)
# Update input only if 1 region is given
if update_input:
num = self.input_disc._input_sample_set.check_num()
prob = np.zeros((num,))
error_id = np.zeros((num,))
for i in range(num):
Itemp = np.equal(self.dummy_disc._emulated_ii_ptr_local, i)
prob_sum = np.sum(self.surrogate_discretization.\
_input_sample_set._probabilities_local[Itemp])
prob[i] = comm.allreduce(prob_sum, op=MPI.SUM)
error_id_sum = np.sum(self.surrogate_discretization.\
_input_sample_set._error_id_local[Itemp])
error_id[i] = comm.allreduce(error_id_sum, op=MPI.SUM)
self.input_disc._input_sample_set.set_probabilities(prob)
self.input_disc._input_sample_set.set_error_id(error_id)
return (probabilities, error_estimates)
'''
# Restrict the data to have just QoI_indices
data = data[:, QoI_indices]
Q_ref = Q[QoI_indices, :].dot(0.5 * np.ones(Lambda_dim))
# bin_ratio defines the uncertainty in our data
bin_ratio = 0.25
# Find the simple function approximation
(d_distr_prob, d_distr_samples, d_Tree) = simpleFunP.uniform_hyperrectangle(\
data=data, Q_ref=Q_ref, bin_ratio=bin_ratio, center_pts_per_edge = 1)
# Calculate probablities making the Monte Carlo assumption
(P, lam_vol, io_ptr) = calculateP.prob(samples=samples,
data=data,
rho_D_M=d_distr_prob,
d_distr_samples=d_distr_samples)
percentile = 1.0
# Sort samples by highest probability density and find how many samples lie in
# the support of the inverse solution. With the Monte Carlo assumption, this
# also tells us the approximate volume of this support.
(num_samples, P_high, samples_high, lam_vol_high, data_high) =\
postTools.sample_highest_prob(top_percentile=percentile, P_samples=P,
samples=samples, lam_vol=lam_vol,data = data,sort=True)
# Print the number of samples that make up the highest percentile percent
# samples and ratio of the volume of the parameter domain they take up
if comm.rank == 0:
print(num_samples, np.sum(lam_vol_high))