# These must be given in the form of a dictionary
options = {}
# While this problem should solve without changing the deault options, example code is
# given commented out below. See Section 5.6 for more options and advice.
# options['bound_push'] = 1e-8
# options['tol'] = 1e-9
# The set A_set is then decided. This set, explained in Section 4.3.3 is used to make the
# variance estimation run faster and has been shown to not decrease the accuracy of the variance
# prediction for large noisey data sets.
A_set = [l for i, l in enumerate(opt_model.meas_lambdas) if (i % 4 == 0)]
# Finally we run the variance estimatator using the arguments shown in Seciton 4.3.3
results_variances = v_estimator.run_opt('ipopt',
tee=True,
solver_options=options,
tolerance=1e-5,
max_iter=15,
subset_lambdas=A_set)
# Variances can then be displayed
print("\nThe estimated variances are:\n")
for k, v in six.iteritems(results_variances.sigma_sq):
print(k, v)
# and the sigmas for the parameter estimation step are now known and fixed
sigmas = results_variances.sigma_sq
#=========================================================================
# USER INPUT SECTION - PARAMETER ESTIMATION
#=========================================================================
# In order to run the paramter estimation we create a pyomo model as described in section 4.3.4
# given commented out below. See Section 5.6 for more options and advice.
# options['bound_push'] = 1e-8
# options['tol'] = 1e-9
options['linear_solver'] = 'ma57'
options['max_iter'] = 2000
# The set A_set is then decided. This set, explained in Section 4.3.3 is used to make the
# variance estimation run faster and has been shown to not decrease the accuracy of the variance
# prediction for large noisey data sets.
init_sigmas = 1e-10
# This will provide a list of sigma values based on the different delta values evaluated.
results_variances = v_estimator.run_opt('ipopt',
method = 'alternate',
tee=False,
solver_opts=options,
secant_point = 1e-11,
initial_sigmas = init_sigmas)
# Variances can then be displayed
print("\nThe estimated variances are:\n")
for k,v in six.iteritems(results_variances.sigma_sq):
print(k,v)
# and the sigmas for the parameter estimation step are now known and fixed
# sigmas = sigmas
sigmas = results_variances.sigma_sq
#=========================================================================
# USER INPUT SECTION - PARAMETER ESTIMATION
v_estimator = VarianceEstimator(opt_model)
v_estimator.apply_discretization('dae.collocation',
nfe=4,
ncp=1,
scheme='LAGRANGE-RADAU')
v_estimator.initialize_from_trajectory('Z', results_sim.Z)
v_estimator.initialize_from_trajectory('S', results_sim.S)
v_estimator.scale_variables_from_trajectory('Z', results_sim.Z)
v_estimator.scale_variables_from_trajectory('S', results_sim.S)
options = {} #{'mu_init': 1e-6, 'bound_push': 1e-6}
results_variances = v_estimator.run_opt('ipopt',
tee=True,
solver_options=options,
tolerance=1e-6)
print("\nThe estimated variances are:\n")
for k, v in six.iteritems(results_variances.sigma_sq):
print(k, v)
sigmas = results_variances.sigma_sq #results_variances.sigma_sq
#################################################################################
builder = TemplateBuilder()
builder.add_mixture_component(concentrations)
builder.add_parameter('k', bounds=(0.0, 1.0))
builder.add_spectral_data(results_sim.D)
builder.set_odes_rule(rule_odes)
# If we do not wish to use the Chen et al. way of solving for variances, there is a simpler
# and often more reliable way of finding variances. This is done by first assuming we have no model
# variance and solving for the overall variance. See details in the documentation under Section 4.16
# This value will give us our worst possible device variance (i.e. all variance is explained using
# the device variance)
# Once the worst case device variance we solve the maximum likelihood
# problem with different values of sigma in order to converge upon the most likely
# split between the total device variance and the total model variance, we can then,
# based on this solution solve for the individual model variances if we wish.
# To do this we only need to provide an initial value for the variances.
init_sigmas = 1e-8
results_variances = v_estimator.run_opt('ipopt',
method='alternate',
tee=False,
initial_sigmas=init_sigmas,
solver_opts=options,
tolerance=1e-10,
secant_point=6e-8,
individual_species=False)
# other options that may needed include an option to provide the second point for
# the secant method to obtain good starting values, as well as the the tolerance for
# when the optimal solution is reached. Additionally, it may be useful to solve for the individual
# species' variances in addition to the overall model variance.
# Variances can then be displayed
print("\nThe estimated variances are:\n")
for k, v in six.iteritems(results_variances.sigma_sq):
print(k, v)
# and the sigmas for the parameter estimation step are now known and fixed
# While this problem should solve without changing the deault options, example code is
# given commented out below. See Section 5.6 for more options and advice.
# options['bound_push'] = 1e-8
# options['tol'] = 1e-9
# The set A_set is then decided. This set, explained in Section 4.3.3 is used to make the
# variance estimation run faster and has been shown to not decrease the accuracy of the variance
# prediction for large noisey data sets.
A_set = [l for i,l in enumerate(opt_model.meas_lambdas) if (i % 4 == 0)]
# Finally we run the variance estimatator using the arguments shown in Seciton 4.3.3
results_variances = v_estimator.run_opt('ipopt',
report_time = True,
lsq_ipopt = True,
tee=True,
fixed_device_variance = 3e-06,
solver_opts=options,
tolerance=1e-5,
max_iter=15,
subset_lambdas=A_set)
# Variances can then be displayed
print("\nThe estimated variances are:\n")
for k,v in six.iteritems(results_variances.sigma_sq):
print(k, v)
# and the sigmas for the parameter estimation step are now known and fixed
sigmas = results_variances.sigma_sq
#=========================================================================
# USER INPUT SECTION - PARAMETER ESTIMATION
# The set A_set is then decided. This set, explained in Section 4.3.3 is used to make the
# variance estimation run faster and has been shown to not decrease the accuracy of the variance
# prediction for large noisey data sets.
#A_set = [l for i,l in enumerate(opt_model.meas_lambdas) if (i % 4 == 0)]
# For this small problem we do not need this, however it should be set for larger problems
# This is the standard Chen et al. method used within KIPET and added here for comparison with
# alternative method. Once can see that the results are quite different and it is not obvious which
# method provides the correct results. On close inspection, the alternative method is closer,
# however this may be due to the fact that we were able to get the device variance fairly accurately
# This will provide a list of sigma values based on the different delta values evaluated.
results_variances = v_estimator.run_opt(
'ipopt',
method='Chen',
tee=False,
solver_opts=options,
#num_points = num_points,
tolerance=1e-10)
#device_range = search_range)
# Variances can then be displayed
print("\nThe estimated variances are:\n")
for k, v in six.iteritems(results_variances.P):
print(k, v)
sigmas = results_variances.sigma_sq
for k, v in six.iteritems(sigmas):
print(k, v)
#=========================================================================
v_estimator.initialize_from_trajectory('S', results.S)
options = {}
A_set = [l for i, l in enumerate(model.meas_lambdas) if (i % 4 == 0)]
# #: this will take a sweet-long time to solve.
results_variances = v_estimator.run_opt('ipopt',
tee=True,
solver_options=options,
tolerance=1e-5,
max_iter=15,
subset_lambdas=A_set,
inputs_sub=inputs_sub,
trajectories=trajs,
jump=True,
jump_times=jump_times,
jump_states=jump_states,
fixedy=True,
fixedtraj=True,
yfix=yfix,
yfixtraj=yfixtraj,
feed_times=feed_times
)
print("\nThe estimated variances are:\n")
for k, v in six.iteritems(results_variances.sigma_sq):
print(k, v)
sigmas = results_variances.sigma_sq
#subset_lambdas = A,
solver_opts=options)
# Now that we have the worst case device variance we wish to solve the maximum likelihood
# problem with different values of delta based on this information and device information
# for best and worst-case performance. We will solve for different values of model variance,
# known as sigma, at each value. We can provide a range, based on the value from above and
# device specifications and we can set a number of points to search within that range.
best_possible_accuracy = 1e-8
search_range = (best_possible_accuracy, worst_case_device_var)
num_points = 10
# This will provide a list of sigma values based on the different delta values evaluated.
results_variances = v_estimator.run_opt(
'ipopt',
method='direct_sigmas',
tee=False,
solver_opts=options,
num_points=num_points,
#subset_lambdas=A_set,
device_range=search_range)
# It is suggested that from this pool of solutions for different delta and sigma values, that the
# best choice for sigma and delta will then be which provided the parameter values closest to
# the initial guesses.
# it is also possible to solve directly for sigmas based on a specific value for delta using
delta = 1e-7
results_vest = v_estimator.solve_sigma_given_delta(
'ipopt',
#subset_lambdas= A,
solver_opts=options,
tee=False,
options = {}
# While this problem should solve without changing the deault options, example code is
# given commented out below. See Section 5.6 for more options and advice.
# options['bound_push'] = 1e-8
options['linear_solver'] = 'ma57'
# The set A_set is then decided. This set, explained in Section 4.3.3 is used to make the
# variance estimation run faster and has been shown to not decrease the accuracy of the variance
# prediction for large noisey data sets.
A_set = [l for i, l in enumerate(opt_model.meas_lambdas) if (i % 4 == 0)]
# Finally we run the variance estimator using the arguments shown in Section 4.3.3
results_variances = v_estimator.run_opt('ipopt',
tee=True,
solver_opts=options,
lsq_ipopt=True,
tolerance=1e-7,
max_iter=25,
report_time=True,
subset_lambdas=A_set)
# Variances can then be displayed
print("\nThe estimated variances are:\n")
for k, v in six.iteritems(results_variances.sigma_sq):
print(k, v)
# and the sigmas for the parameter estimation step are now known and fixed
sigmas = results_variances.sigma_sq
#=========================================================================
# USER INPUT SECTION - PARAMETER ESTIMATION
#=========================================================================
