.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b05d_normal_mixture_all_algos.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_swissmetro_plot_b05d_normal_mixture_all_algos.py: Mixture of logit ================ Example of the use of different algorithms to estimate the model. Michel Bierlaire, EPFL Wed Jun 18 2025, 12:31:43 .. GENERATED FROM PYTHON SOURCE LINES 11-25 .. code-block:: Python import itertools import pandas as pd from IPython.core.display_functions import display import biogeme.biogeme_logging as blog from biogeme.biogeme import BIOGEME from biogeme.exceptions import BiogemeError from biogeme.expressions import Beta, Draws, MonteCarlo, log from biogeme.models import logit from biogeme.results_processing import EstimationResults from biogeme.tools import format_timedelta .. GENERATED FROM PYTHON SOURCE LINES 26-27 See the data processing script: :ref:`swissmetro_data`. .. GENERATED FROM PYTHON SOURCE LINES 27-44 .. code-block:: Python from swissmetro_data import ( CAR_AV_SP, CAR_CO_SCALED, CAR_TT_SCALED, CHOICE, SM_AV, SM_COST_SCALED, SM_TT_SCALED, TRAIN_AV_SP, TRAIN_COST_SCALED, TRAIN_TT_SCALED, database, ) logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b05d_normal_mixture_all_algos.py') .. rst-class:: sphx-glr-script-out .. code-block:: none Example b05d_normal_mixture_all_algos.py .. GENERATED FROM PYTHON SOURCE LINES 45-46 Parameters to be estimated .. GENERATED FROM PYTHON SOURCE LINES 46-51 .. code-block:: Python asc_car = Beta('asc_car', 0, None, None, 0) asc_train = Beta('asc_train', 0, None, None, 0) asc_sm = Beta('asc_sm', 0, None, None, 1) b_cost = Beta('b_cost', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 52-54 Define a random parameter, normally distributed, designed to be used for Monte-Carlo simulation. .. GENERATED FROM PYTHON SOURCE LINES 54-56 .. code-block:: Python b_time = Beta('b_time', 0, None, None, 0) .. GENERATED FROM PYTHON SOURCE LINES 57-58 It is advised not to use 0 as starting value for the following parameter. .. GENERATED FROM PYTHON SOURCE LINES 58-61 .. code-block:: Python b_time_s = Beta('b_time_s', 1, None, None, 0) b_time_rnd = b_time + b_time_s * Draws('b_time_rnd', 'NORMAL') .. GENERATED FROM PYTHON SOURCE LINES 62-63 Definition of the utility functions. .. GENERATED FROM PYTHON SOURCE LINES 63-67 .. code-block:: Python v_train = asc_train + b_time_rnd * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED v_swissmetro = asc_sm + b_time_rnd * SM_TT_SCALED + b_cost * SM_COST_SCALED v_car = asc_car + b_time_rnd * CAR_TT_SCALED + b_cost * CAR_CO_SCALED .. GENERATED FROM PYTHON SOURCE LINES 68-69 Associate utility functions with the numbering of alternatives .. GENERATED FROM PYTHON SOURCE LINES 69-71 .. code-block:: Python v = {1: v_train, 2: v_swissmetro, 3: v_car} .. GENERATED FROM PYTHON SOURCE LINES 72-73 Associate the availability conditions with the alternatives .. GENERATED FROM PYTHON SOURCE LINES 73-75 .. code-block:: Python av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP} .. GENERATED FROM PYTHON SOURCE LINES 76-77 Conditional to b_time_rnd, we have a logit model (called the kernel) .. GENERATED FROM PYTHON SOURCE LINES 77-79 .. code-block:: Python prob = logit(v, av, CHOICE) .. GENERATED FROM PYTHON SOURCE LINES 80-81 We integrate over b_time_rnd using Monte-Carlo .. GENERATED FROM PYTHON SOURCE LINES 81-83 .. code-block:: Python logprob = log(MonteCarlo(prob)) .. GENERATED FROM PYTHON SOURCE LINES 84-86 Options for the optimization algorithm -------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 88-89 The conjugate gradient iteration can be constrained to stay feasible, or not. .. GENERATED FROM PYTHON SOURCE LINES 89-91 .. code-block:: Python infeasible_cg_values = [True, False] .. GENERATED FROM PYTHON SOURCE LINES 92-93 The radius of the first trust region is tested with three different values. .. GENERATED FROM PYTHON SOURCE LINES 93-95 .. code-block:: Python initial_radius_values = [0.1, 1.0, 10.0] .. GENERATED FROM PYTHON SOURCE LINES 96-97 The percentage of iterations such that the analytical second derivatives is evaluated. .. GENERATED FROM PYTHON SOURCE LINES 97-100 .. code-block:: Python second_derivatives_values = [0.0, 0.5, 1.0] .. GENERATED FROM PYTHON SOURCE LINES 101-102 If the result files are already available, they are recycled. .. GENERATED FROM PYTHON SOURCE LINES 102-111 .. code-block:: Python def read_or_estimate(biogeme_object: BIOGEME) -> EstimationResults: try: return EstimationResults.from_yaml_file( filename=f'saved_results/{biogeme_object.model_name}.yaml' ) except FileNotFoundError: return biogeme_object.estimate() .. GENERATED FROM PYTHON SOURCE LINES 112-114 We run the optimization algorithm with all possible combinations of the parameters. The results are stored in a Pandas DataFrame called ``summary``. .. GENERATED FROM PYTHON SOURCE LINES 114-117 .. code-block:: Python results = {} summary_data = [] .. GENERATED FROM PYTHON SOURCE LINES 118-119 The first estimation is performed twice, to warm up the python code, so that the execution times are comparable .. GENERATED FROM PYTHON SOURCE LINES 119-186 .. code-block:: Python first = True for infeasible_cg, initial_radius, second_derivatives in itertools.product( infeasible_cg_values, initial_radius_values, second_derivatives_values ): # Create the Biogeme object the_biogeme = BIOGEME( database, logprob, number_of_draws=10000, seed=1223, infeasible_cg=infeasible_cg, initial_radius=initial_radius, second_derivatives=second_derivatives, generate_html=False, ) name = ( f'cg_{infeasible_cg}_radius_{initial_radius}_second_deriv_{second_derivatives}' ) the_biogeme.model_name = f'b05normal_mixture_algo_{name}'.strip() result_data = { 'InfeasibleCG': infeasible_cg, 'InitialRadius': initial_radius, 'SecondDerivatives': second_derivatives, 'Status': 'Success', # Assume success unless an exception is caught } try: results[name] = read_or_estimate(biogeme_object=the_biogeme) if first: results[name] = read_or_estimate(biogeme_object=the_biogeme) first = False opt_time = format_timedelta( results[name].optimization_messages["Optimization time"] ) result_data.update( { 'LogLikelihood': results[name].final_log_likelihood, 'GradientNorm': results[name].gradient_norm, 'Number of draws': results[name].number_of_draws, 'Optimization time': opt_time, 'TerminationCause': results[name].optimization_messages[ "Cause of termination" ], } ) except BiogemeError as e: print(e) result_data.update( { 'Status': 'Failed', 'LogLikelihood': None, 'GradientNorm': None, 'Number of draws': None, 'Optimization time': None, 'TerminationCause': str(e), } ) results[name] = None summary_data.append(result_data) summary = pd.DataFrame(summary_data) .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_0.0.iter Parameter values restored from __b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_0.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.05 0.097 - 1 -0.65 -1.2 0.95 -1.1 -0.1 7.1e+03 0.16 0.05 0.12 + 2 -0.7 -1.2 0.9 -1.2 -0.055 7.1e+03 0.16 0.05 0.12 + 3 -0.75 -1.1 0.85 -1.2 -0.0046 7.1e+03 0.17 0.05 0.13 + 4 -0.75 -1.1 0.85 -1.2 -0.0046 7.1e+03 0.17 0.025 -0.2 - 5 -0.75 -1.1 0.85 -1.2 -0.0046 7.1e+03 0.17 0.013 -0.12 - 6 -0.75 -1.1 0.85 -1.2 -0.0046 7.1e+03 0.17 0.0063 -0.1 - 7 -0.75 -1.1 0.85 -1.2 -0.0046 7.1e+03 0.17 0.0031 0.043 - 8 -0.75 -1.1 0.85 -1.2 -0.0015 7.1e+03 0.17 0.0031 0.13 + 9 -0.75 -1.1 0.85 -1.2 -0.0015 7.1e+03 0.17 0.0016 -0.02 - 10 -0.76 -1.1 0.85 -1.2 5.5e-05 7.1e+03 0.17 0.0016 0.13 + 11 -0.76 -1.1 0.85 -1.2 5.5e-05 7.1e+03 0.17 0.00078 -0.16 - 12 -0.76 -1.1 0.85 -1.2 5.5e-05 7.1e+03 0.17 0.00039 -0.082 - 13 -0.76 -1.1 0.85 -1.2 5.5e-05 7.1e+03 0.17 0.0002 0.08 - 14 -0.76 -1.1 0.85 -1.2 0.00025 7.1e+03 0.17 0.0002 0.13 + 15 -0.76 -1.1 0.85 -1.2 0.00025 7.1e+03 0.17 9.8e-05 0.037 - 16 -0.76 -1.1 0.85 -1.2 0.00035 7.1e+03 0.17 9.8e-05 0.13 + 17 -0.76 -1.1 0.85 -1.2 0.00035 7.1e+03 0.17 4.9e-05 -0.049 - 18 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 4.9e-05 0.13 + 19 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 2.4e-05 -0.22 - 20 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 1.2e-05 -0.2 - 21 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 6.1e-06 -0.16 - 22 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 3.1e-06 -0.073 - 23 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 1.5e-06 0.097 - 24 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 1.5e-06 0.13 + 25 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 7.6e-07 0.071 - 26 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 7.6e-07 0.13 + 27 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 3.8e-07 0.02 - 28 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 3.8e-07 0.13 + 29 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 1.9e-07 -0.084 - 30 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 9.5e-08 0.075 - 31 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 9.5e-08 0.13 + 32 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 4.8e-08 0.027 - 33 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 4.8e-08 0.13 + 34 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 2.4e-08 -0.07 - 35 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 2.4e-08 0.1 + 36 -0.76 -1.1 0.84 -1.2 0.0004 7.1e+03 0.17 1.2e-08 -0.24 + Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.1920928955077447e-08 Number of iterations: 37 Proportion of Hessian calculation: 0/15 = 0.0% Optimization time: 0:01:00.389863 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_0.0.yaml has been generated. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_0.0.iter Parameter values restored from __b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_0.0.iter Starting values for the algorithm: {'asc_train': -0.7562190257417825, 'b_time': -1.122827664315102, 'b_time_s': 0.8449678678624302, 'b_cost': -1.2388225789271832, 'asc_car': 0.00039961306525385397} Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.86 -1.2 0.74 -1.1 -0.1 5.3e+03 0.033 0.1 0.66 + 1 -0.76 -1.3 0.84 -1 -0.2 5.3e+03 0.022 0.1 0.54 + 2 -0.76 -1.4 0.86 -1.1 -0.16 5.2e+03 0.014 0.1 0.79 + 3 -0.66 -1.5 0.96 -1.2 -0.063 5.2e+03 0.025 0.1 0.69 + 4 -0.61 -1.6 1.1 -1.1 -0.14 5.2e+03 0.017 0.1 0.3 + 5 -0.71 -1.7 1.2 -1.2 -0.036 5.2e+03 0.014 0.1 0.45 + 6 -0.61 -1.7 1.3 -1.2 -0.11 5.2e+03 0.014 0.1 0.54 + 7 -0.65 -1.8 1.2 -1.2 -0.011 5.2e+03 0.012 0.1 0.82 + 8 -0.55 -1.8 1.3 -1.2 -0.034 5.2e+03 0.019 0.1 0.49 + 9 -0.56 -1.9 1.3 -1.2 0.024 5.2e+03 0.0051 0.1 0.88 + 10 -0.46 -2 1.4 -1.2 0.031 5.2e+03 0.012 0.1 0.43 + 11 -0.47 -2.1 1.4 -1.2 0.088 5.2e+03 0.0045 0.1 0.65 + 12 -0.43 -2.1 1.5 -1.2 0.085 5.2e+03 0.0026 0.1 0.76 + 13 -0.43 -2.1 1.5 -1.2 0.085 5.2e+03 0.0026 0.05 -0.65 - 14 -0.43 -2.1 1.5 -1.2 0.085 5.2e+03 0.0026 0.025 0.025 - 15 -0.46 -2.1 1.5 -1.3 0.11 5.2e+03 0.0034 0.025 0.13 + 16 -0.43 -2.1 1.5 -1.3 0.1 5.2e+03 0.0031 0.025 0.87 + 17 -0.44 -2.2 1.5 -1.3 0.1 5.2e+03 0.0021 0.025 0.72 + 18 -0.43 -2.2 1.6 -1.3 0.12 5.2e+03 0.0028 0.025 0.82 + 19 -0.42 -2.2 1.6 -1.3 0.11 5.2e+03 0.00099 0.025 0.89 + 20 -0.42 -2.2 1.6 -1.3 0.13 5.2e+03 0.0018 0.025 0.32 + 21 -0.41 -2.2 1.6 -1.3 0.13 5.2e+03 0.0011 0.25 0.93 ++ 22 -0.41 -2.2 1.6 -1.3 0.13 5.2e+03 0.0011 0.087 -64 - 23 -0.41 -2.2 1.6 -1.3 0.13 5.2e+03 0.0011 0.044 -20 - 24 -0.41 -2.2 1.6 -1.3 0.13 5.2e+03 0.0011 0.022 -1.3 - 25 -0.41 -2.2 1.6 -1.3 0.13 5.2e+03 0.00056 0.022 0.8 + 26 -0.4 -2.3 1.7 -1.3 0.13 5.2e+03 0.00052 0.022 0.16 + 27 -0.4 -2.3 1.7 -1.3 0.13 5.2e+03 0.00052 0.011 -0.71 - 28 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 0.0004 0.011 0.4 + 29 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 0.0004 0.0054 -0.82 - 30 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 0.00061 0.0054 0.22 + 31 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 0.00061 0.0027 -1.2 - 32 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 0.00061 0.0014 0.061 - 33 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 7.1e-05 0.0014 0.71 + 34 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 6.6e-05 0.0014 0.37 + 35 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 6.6e-05 0.00068 -0.33 - 36 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 6.8e-05 0.00068 0.26 + 37 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 1.7e-05 0.00068 0.6 + 38 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 1.7e-05 0.00034 -0.66 - 39 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 1.3e-05 0.00034 0.74 + 40 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 1.3e-05 0.00012 -1.9 - 41 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 1.3e-05 5.8e-05 -0.25 - 42 -0.4 -2.3 1.7 -1.3 0.14 5.2e+03 4.9e-06 5.8e-05 0.45 - Optimization algorithm has converged. Relative gradient: 4.896497511279725e-06 Cause of termination: Relative gradient = 4.9e-06 <= 6.1e-06 Number of function evaluations: 104 Number of gradient evaluations: 61 Number of hessian evaluations: 0 Algorithm: BFGS with trust region for simple bound constraints Number of iterations: 43 Proportion of Hessian calculation: 0/30 = 0.0% Optimization time: 0:01:45.321248 Calculate second derivatives and BHHH File b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_0.0~00.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_0.5.iter Parameter values restored from __b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_0.5.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.6 -1.2 1.6 -1.2 -0.055 7.8e+03 0.17 0.1 0.18 + 1 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 0.1 0.18 + 2 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 0.05 -0.39 - 3 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 0.025 -0.56 - 4 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 0.013 -0.62 - 5 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 0.0062 -0.62 - 6 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 0.0031 -0.62 - 7 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 0.0016 -0.62 - 8 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 0.00078 -0.62 - 9 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 0.00039 -0.62 - 10 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 0.0002 -0.62 - 11 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 9.8e-05 -0.62 - 12 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 4.9e-05 -0.62 - 13 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 2.4e-05 -0.62 - 14 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 1.2e-05 -0.62 - 15 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 6.1e-06 -0.62 - 16 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 3.1e-06 -0.62 - 17 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 1.5e-06 -0.62 - 18 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 7.6e-07 -0.62 - 19 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 3.8e-07 -0.62 - 20 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 1.9e-07 -0.62 - 21 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 9.5e-08 -0.62 - 22 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 4.8e-08 -0.62 - 23 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 2.4e-08 -0.62 - 24 -0.7 -1.1 1.5 -1.3 0.045 7.7e+03 0.18 1.2e-08 -0.62 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.1920928954904653e-08 Number of iterations: 25 Proportion of Hessian calculation: 0/3 = 0.0% Optimization time: 0:00:19.603331 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_0.5.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_1.0.iter Parameter values restored from __b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_1.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.6 -1.2 1.4 -1.2 -0.055 7.5e+03 0.16 0.1 0.16 + 1 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 0.1 0.17 + 2 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 0.05 -0.44 - 3 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 0.025 -0.62 - 4 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 0.013 -0.61 - 5 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 0.0062 -0.61 - 6 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 0.0031 -0.61 - 7 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 0.0016 -0.61 - 8 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 0.00078 -0.61 - 9 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 0.00039 -0.61 - 10 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 0.0002 -0.61 - 11 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 9.8e-05 -0.61 - 12 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 4.9e-05 -0.61 - 13 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 2.4e-05 -0.61 - 14 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 1.2e-05 -0.61 - 15 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 6.1e-06 -0.61 - 16 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 3.1e-06 -0.61 - 17 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 1.5e-06 -0.61 - 18 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 7.6e-07 -0.61 - 19 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 3.8e-07 -0.61 - 20 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 1.9e-07 -0.61 - 21 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 9.5e-08 -0.61 - 22 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 4.8e-08 -0.61 - 23 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 2.4e-08 -0.61 - 24 -0.7 -1.1 1.3 -1.3 0.045 7.5e+03 0.18 1.2e-08 -0.61 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.1920928954904653e-08 Number of iterations: 25 Proportion of Hessian calculation: 0/3 = 0.0% Optimization time: 0:00:19.659805 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_True_radius_0.1_second_deriv_1.0.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_True_radius_1.0_second_deriv_0.0.iter Parameter values restored from __b05normal_mixture_algo_cg_True_radius_1.0_second_deriv_0.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 1.3 -1.1 -0.15 7.4e+03 0.16 0.5 -0.61 - 1 -0.7 -1.3 1.3 -1.1 -0.15 7.4e+03 0.16 0.25 -0.11 - 2 -0.7 -1.3 1.3 -1.1 -0.15 7.4e+03 0.16 0.12 0.065 - 3 -0.58 -1.2 1.1 -1.2 -0.03 7.3e+03 0.16 0.12 0.12 + 4 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 0.12 0.16 + 5 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 0.062 -0.57 - 6 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 0.031 -0.57 - 7 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 0.016 -0.57 - 8 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 0.0078 -0.56 - 9 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 0.0039 -0.56 - 10 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 0.002 -0.56 - 11 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 0.00098 -0.56 - 12 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 0.00049 -0.56 - 13 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 0.00024 -0.56 - 14 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 0.00012 -0.56 - 15 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 6.1e-05 -0.56 - 16 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 3.1e-05 -0.56 - 17 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 1.5e-05 -0.56 - 18 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 7.6e-06 -0.56 - 19 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 3.8e-06 -0.56 - 20 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 1.9e-06 -0.56 - 21 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 9.5e-07 -0.56 - 22 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 4.8e-07 -0.56 - 23 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 2.4e-07 -0.56 - 24 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 1.2e-07 -0.56 - 25 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 6e-08 -0.56 - 26 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 3e-08 -0.56 - 27 -0.7 -1 1 -1.3 0.095 7.3e+03 0.18 1.5e-08 -0.56 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.4901161193847656e-08 Number of iterations: 28 Proportion of Hessian calculation: 0/3 = 0.0% Optimization time: 0:00:20.949426 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_True_radius_1.0_second_deriv_0.0.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_True_radius_1.0_second_deriv_0.5.iter Parameter values restored from __b05normal_mixture_algo_cg_True_radius_1.0_second_deriv_0.5.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.5 -0.69 - 1 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.25 -0.16 - 2 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.12 0.024 - 3 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.062 0.087 - 4 -0.64 -1.2 0.94 -1.1 -0.092 7.1e+03 0.16 0.062 0.11 + 5 -0.7 -1.2 0.88 -1.2 -0.03 7.1e+03 0.16 0.062 0.12 + 6 -0.7 -1.2 0.88 -1.2 -0.03 7.1e+03 0.16 0.031 0.0036 - 7 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 0.031 0.13 + 8 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 0.016 -0.25 - 9 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 0.0078 -0.27 - 10 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 0.0039 -0.29 - 11 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 0.002 -0.35 - 12 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 0.00098 -0.46 - 13 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 0.00049 -0.62 - 14 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 0.00024 -0.62 - 15 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 0.00012 -0.62 - 16 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 6.1e-05 -0.62 - 17 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 3.1e-05 -0.62 - 18 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 1.5e-05 -0.62 - 19 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 7.6e-06 -0.62 - 20 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 3.8e-06 -0.62 - 21 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 1.9e-06 -0.62 - 22 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 9.5e-07 -0.62 - 23 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 4.8e-07 -0.62 - 24 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 2.4e-07 -0.62 - 25 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 1.2e-07 -0.62 - 26 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 6e-08 -0.62 - 27 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 3e-08 -0.62 - 28 -0.73 -1.1 0.85 -1.2 0.0016 7.1e+03 0.17 1.5e-08 -0.62 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.4901161193847656e-08 Number of iterations: 29 Proportion of Hessian calculation: 0/4 = 0.0% Optimization time: 0:00:24.602564 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_True_radius_1.0_second_deriv_0.5.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_True_radius_1.0_second_deriv_1.0.iter Parameter values restored from __b05normal_mixture_algo_cg_True_radius_1.0_second_deriv_1.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.85 -1.1 -0.15 7e+03 0.15 0.5 -0.74 - 1 -0.7 -1.3 0.85 -1.1 -0.15 7e+03 0.15 0.25 -0.2 - 2 -0.7 -1.3 0.85 -1.1 -0.15 7e+03 0.15 0.12 -0.0043 - 3 -0.7 -1.3 0.85 -1.1 -0.15 7e+03 0.15 0.062 0.062 - 4 -0.7 -1.3 0.85 -1.1 -0.15 7e+03 0.15 0.031 0.091 - 5 -0.67 -1.2 0.82 -1.1 -0.12 6.9e+03 0.15 0.031 0.1 + 6 -0.7 -1.2 0.79 -1.1 -0.092 6.9e+03 0.16 0.031 0.1 + 7 -0.73 -1.2 0.75 -1.2 -0.061 6.9e+03 0.16 0.031 0.11 + 8 -0.73 -1.2 0.75 -1.2 -0.061 6.9e+03 0.16 0.016 0.096 - 9 -0.72 -1.2 0.74 -1.2 -0.045 6.9e+03 0.16 0.016 0.1 + 10 -0.73 -1.2 0.72 -1.2 -0.03 6.9e+03 0.16 0.016 0.11 + 11 -0.75 -1.1 0.71 -1.2 -0.014 6.9e+03 0.16 0.016 0.12 + 12 -0.75 -1.1 0.71 -1.2 -0.014 6.9e+03 0.16 0.0078 0.065 - 13 -0.76 -1.1 0.7 -1.2 -0.0062 6.9e+03 0.16 0.0078 0.12 + 14 -0.76 -1.1 0.7 -1.2 -0.0062 6.9e+03 0.16 0.0039 0.042 - 15 -0.76 -1.1 0.7 -1.2 -0.0023 6.9e+03 0.16 0.0039 0.12 + 16 -0.76 -1.1 0.7 -1.2 -0.0023 6.9e+03 0.16 0.002 -0.0089 - 17 -0.76 -1.1 0.69 -1.2 -0.00034 6.9e+03 0.16 0.002 0.12 + 18 -0.76 -1.1 0.69 -1.2 -0.00034 6.9e+03 0.16 0.00098 -0.11 - 19 -0.76 -1.1 0.69 -1.2 -0.00034 6.9e+03 0.16 0.00049 0.015 - 20 -0.76 -1.1 0.69 -1.2 0.00015 6.9e+03 0.16 0.00049 0.12 + 21 -0.76 -1.1 0.69 -1.2 0.00015 6.9e+03 0.16 0.00024 -0.068 - 22 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 0.00024 0.12 + 23 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 0.00012 -0.23 - 24 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 6.1e-05 -0.22 - 25 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 3.1e-05 -0.2 - 26 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 1.5e-05 -0.16 - 27 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 7.6e-06 -0.076 - 28 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 3.8e-06 0.093 - 29 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 3.8e-06 0.12 + 30 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 1.9e-06 0.086 - 31 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 1.9e-06 0.12 + 32 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 9.5e-07 0.073 - 33 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 9.5e-07 0.12 + 34 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 4.8e-07 0.047 - 35 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 4.8e-07 0.12 + 36 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 2.4e-07 -0.0055 - 37 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 2.4e-07 0.12 + 38 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 1.2e-07 -0.11 - 39 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 6e-08 0.024 - 40 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 6e-08 0.12 + 41 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 3e-08 -0.051 - 42 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 3e-08 0.12 + 43 -0.76 -1.1 0.69 -1.2 0.0004 6.9e+03 0.16 1.5e-08 -0.24 + Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.4901161193847656e-08 Number of iterations: 44 Proportion of Hessian calculation: 0/19 = 0.0% Optimization time: 0:01:11.780251 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_True_radius_1.0_second_deriv_1.0.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_True_radius_10.0_second_deriv_0.0.iter Parameter values restored from __b05normal_mixture_algo_cg_True_radius_10.0_second_deriv_0.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 5 -1.5 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.5 -1.8 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2 -1.7 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.62 -1 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.31 -0.37 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.16 -0.075 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.078 0.02 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.039 0.059 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.02 0.077 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0098 0.086 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0049 0.09 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0024 0.092 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0012 0.093 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00061 0.093 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00031 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00015 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-05 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-05 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-05 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-06 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-06 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-06 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-06 0.094 - 23 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6e-07 0.094 - 24 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3e-07 0.094 - 25 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-07 0.094 - 26 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.5e-08 0.094 - 27 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.7e-08 0.094 - 28 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-08 0.094 - 29 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.3e-09 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 9.313225746154785e-09 Number of iterations: 30 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:17.331607 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_True_radius_10.0_second_deriv_0.0.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_True_radius_10.0_second_deriv_0.5.iter Parameter values restored from __b05normal_mixture_algo_cg_True_radius_10.0_second_deriv_0.5.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 5 -1.5 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.5 -1.8 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2 -1.7 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.62 -1 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.31 -0.37 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.16 -0.075 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.078 0.02 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.039 0.059 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.02 0.077 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0098 0.086 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0049 0.09 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0024 0.092 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0012 0.093 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00061 0.093 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00031 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00015 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-05 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-05 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-05 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-06 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-06 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-06 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-06 0.094 - 23 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6e-07 0.094 - 24 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3e-07 0.094 - 25 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-07 0.094 - 26 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.5e-08 0.094 - 27 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.7e-08 0.094 - 28 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-08 0.094 - 29 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.3e-09 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 9.313225746154785e-09 Number of iterations: 30 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:16.475885 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_True_radius_10.0_second_deriv_0.5.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_True_radius_10.0_second_deriv_1.0.iter Parameter values restored from __b05normal_mixture_algo_cg_True_radius_10.0_second_deriv_1.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 5 -1.5 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.5 -1.8 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2 -1.7 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.62 -1 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.31 -0.37 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.16 -0.075 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.078 0.02 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.039 0.059 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.02 0.077 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0098 0.086 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0049 0.09 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0024 0.092 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0012 0.093 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00061 0.093 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00031 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00015 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-05 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-05 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-05 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-06 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-06 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-06 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-06 0.094 - 23 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6e-07 0.094 - 24 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3e-07 0.094 - 25 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-07 0.094 - 26 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.5e-08 0.094 - 27 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.7e-08 0.094 - 28 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-08 0.094 - 29 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.3e-09 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 9.313225746154785e-09 Number of iterations: 30 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:16.306208 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_True_radius_10.0_second_deriv_1.0.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_False_radius_0.1_second_deriv_0.0.iter Parameter values restored from __b05normal_mixture_algo_cg_False_radius_0.1_second_deriv_0.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.05 0.049 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.025 0.072 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.013 0.083 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0063 0.089 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0031 0.091 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0016 0.093 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00078 0.093 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00039 0.094 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0002 0.094 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.8e-05 0.094 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.9e-05 0.094 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-05 0.094 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-05 0.094 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6.1e-06 0.094 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.1e-06 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-06 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-07 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-07 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-07 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-08 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-08 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-08 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-08 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.1920928955078126e-08 Number of iterations: 23 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:13.426204 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_False_radius_0.1_second_deriv_0.0.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_False_radius_0.1_second_deriv_0.5.iter Parameter values restored from __b05normal_mixture_algo_cg_False_radius_0.1_second_deriv_0.5.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.05 0.049 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.025 0.072 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.013 0.083 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0063 0.089 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0031 0.091 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0016 0.093 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00078 0.093 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00039 0.094 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0002 0.094 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.8e-05 0.094 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.9e-05 0.094 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-05 0.094 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-05 0.094 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6.1e-06 0.094 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.1e-06 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-06 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-07 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-07 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-07 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-08 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-08 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-08 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-08 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.1920928955078126e-08 Number of iterations: 23 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:13.284322 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_False_radius_0.1_second_deriv_0.5.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_False_radius_0.1_second_deriv_1.0.iter Parameter values restored from __b05normal_mixture_algo_cg_False_radius_0.1_second_deriv_1.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.05 0.049 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.025 0.072 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.013 0.083 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0063 0.089 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0031 0.091 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0016 0.093 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00078 0.093 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00039 0.094 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0002 0.094 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.8e-05 0.094 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.9e-05 0.094 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-05 0.094 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-05 0.094 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6.1e-06 0.094 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.1e-06 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-06 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-07 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-07 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-07 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-08 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-08 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-08 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-08 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.1920928955078126e-08 Number of iterations: 23 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:13.081005 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_False_radius_0.1_second_deriv_1.0.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_False_radius_1.0_second_deriv_0.0.iter Parameter values restored from __b05normal_mixture_algo_cg_False_radius_1.0_second_deriv_0.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.5 -0.79 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.25 -0.23 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.12 -0.034 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.062 0.036 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.031 0.066 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.016 0.081 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0078 0.087 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0039 0.091 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.002 0.092 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00098 0.093 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00049 0.094 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00024 0.094 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00012 0.094 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6.1e-05 0.094 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.1e-05 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-05 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-06 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-06 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-06 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-07 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-07 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-07 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-07 0.094 - 23 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6e-08 0.094 - 24 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3e-08 0.094 - 25 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-08 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.4901161193847656e-08 Number of iterations: 26 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:14.545461 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_False_radius_1.0_second_deriv_0.0.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_False_radius_1.0_second_deriv_0.5.iter Parameter values restored from __b05normal_mixture_algo_cg_False_radius_1.0_second_deriv_0.5.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.5 -0.79 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.25 -0.23 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.12 -0.034 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.062 0.036 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.031 0.066 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.016 0.081 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0078 0.087 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0039 0.091 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.002 0.092 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00098 0.093 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00049 0.094 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00024 0.094 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00012 0.094 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6.1e-05 0.094 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.1e-05 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-05 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-06 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-06 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-06 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-07 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-07 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-07 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-07 0.094 - 23 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6e-08 0.094 - 24 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3e-08 0.094 - 25 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-08 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.4901161193847656e-08 Number of iterations: 26 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:14.993969 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_False_radius_1.0_second_deriv_0.5.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_False_radius_1.0_second_deriv_1.0.iter Parameter values restored from __b05normal_mixture_algo_cg_False_radius_1.0_second_deriv_1.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.5 -0.79 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.25 -0.23 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.12 -0.034 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.062 0.036 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.031 0.066 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.016 0.081 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0078 0.087 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0039 0.091 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.002 0.092 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00098 0.093 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00049 0.094 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00024 0.094 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00012 0.094 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6.1e-05 0.094 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.1e-05 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-05 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-06 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-06 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-06 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-07 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-07 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-07 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-07 0.094 - 23 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6e-08 0.094 - 24 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3e-08 0.094 - 25 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-08 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 1.4901161193847656e-08 Number of iterations: 26 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:14.676557 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_False_radius_1.0_second_deriv_1.0.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_False_radius_10.0_second_deriv_0.0.iter Parameter values restored from __b05normal_mixture_algo_cg_False_radius_10.0_second_deriv_0.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 5 -1.5 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.5 -1.8 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2 -1.7 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.62 -1 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.31 -0.37 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.16 -0.075 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.078 0.02 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.039 0.059 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.02 0.077 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0098 0.086 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0049 0.09 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0024 0.092 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0012 0.093 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00061 0.093 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00031 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00015 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-05 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-05 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-05 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-06 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-06 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-06 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-06 0.094 - 23 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6e-07 0.094 - 24 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3e-07 0.094 - 25 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-07 0.094 - 26 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.5e-08 0.094 - 27 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.7e-08 0.094 - 28 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-08 0.094 - 29 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.3e-09 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 9.313225746154785e-09 Number of iterations: 30 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:16.695333 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_False_radius_10.0_second_deriv_0.0.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_False_radius_10.0_second_deriv_0.5.iter Parameter values restored from __b05normal_mixture_algo_cg_False_radius_10.0_second_deriv_0.5.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 5 -1.5 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.5 -1.8 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2 -1.7 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.62 -1 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.31 -0.37 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.16 -0.075 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.078 0.02 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.039 0.059 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.02 0.077 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0098 0.086 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0049 0.09 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0024 0.092 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0012 0.093 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00061 0.093 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00031 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00015 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-05 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-05 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-05 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-06 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-06 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-06 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-06 0.094 - 23 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6e-07 0.094 - 24 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3e-07 0.094 - 25 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-07 0.094 - 26 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.5e-08 0.094 - 27 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.7e-08 0.094 - 28 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-08 0.094 - 29 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.3e-09 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 9.313225746154785e-09 Number of iterations: 30 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:17.274356 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_False_radius_10.0_second_deriv_0.5.yaml has been generated. Biogeme parameters read from biogeme.toml. *** Initial values of the parameters are obtained from the file __b05normal_mixture_algo_cg_False_radius_10.0_second_deriv_1.0.iter Parameter values restored from __b05normal_mixture_algo_cg_False_radius_10.0_second_deriv_1.0.iter Starting values for the algorithm: {'asc_train': -0.7011868916856909, 'b_time': -1.2778597983711935, 'b_cost': -1.0837904448710918, 'asc_car': -0.15463252099083746} As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: BFGS with trust region for simple bounds Iter. asc_train b_time b_time_s b_cost asc_car Function Relgrad Radius Rho 0 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 5 -1.5 - 1 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.5 -1.8 - 2 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2 -1.7 - 3 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.62 -1 - 4 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.31 -0.37 - 5 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.16 -0.075 - 6 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.078 0.02 - 7 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.039 0.059 - 8 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.02 0.077 - 9 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0098 0.086 - 10 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0049 0.09 - 11 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0024 0.092 - 12 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.0012 0.093 - 13 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00061 0.093 - 14 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00031 0.094 - 15 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 0.00015 0.094 - 16 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.6e-05 0.094 - 17 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.8e-05 0.094 - 18 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-05 0.094 - 19 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.5e-06 0.094 - 20 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 4.8e-06 0.094 - 21 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 2.4e-06 0.094 - 22 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.2e-06 0.094 - 23 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 6e-07 0.094 - 24 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3e-07 0.094 - 25 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.5e-07 0.094 - 26 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 7.5e-08 0.094 - 27 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 3.7e-08 0.094 - 28 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 1.9e-08 0.094 - 29 -0.7 -1.3 0.69 -1.1 -0.15 6.8e+03 0.15 9.3e-09 0.094 - Optimization algorithm has *not* converged. Algorithm: BFGS with trust region for simple bound constraints Cause of termination: Trust region is too small: 9.313225746154785e-09 Number of iterations: 30 Proportion of Hessian calculation: 0/1 = 0.0% Optimization time: 0:00:16.961922 Calculate second derivatives and BHHH It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm. File b05normal_mixture_algo_cg_False_radius_10.0_second_deriv_1.0.yaml has been generated. .. GENERATED FROM PYTHON SOURCE LINES 187-189 .. code-block:: Python display(summary) .. rst-class:: sphx-glr-script-out .. code-block:: none InfeasibleCG ... TerminationCause 0 True ... Relative gradient = 4.9e-06 <= 6.1e-06 1 True ... Trust region is too small: 1.1920928954904653e-08 2 True ... Trust region is too small: 1.1920928954904653e-08 3 True ... Trust region is too small: 1.4901161193847656e-08 4 True ... Trust region is too small: 1.4901161193847656e-08 5 True ... Trust region is too small: 1.4901161193847656e-08 6 True ... Trust region is too small: 9.313225746154785e-09 7 True ... Trust region is too small: 9.313225746154785e-09 8 True ... Trust region is too small: 9.313225746154785e-09 9 False ... Trust region is too small: 1.1920928955078126e-08 10 False ... Trust region is too small: 1.1920928955078126e-08 11 False ... Trust region is too small: 1.1920928955078126e-08 12 False ... Trust region is too small: 1.4901161193847656e-08 13 False ... Trust region is too small: 1.4901161193847656e-08 14 False ... Trust region is too small: 1.4901161193847656e-08 15 False ... Trust region is too small: 9.313225746154785e-09 16 False ... Trust region is too small: 9.313225746154785e-09 17 False ... Trust region is too small: 9.313225746154785e-09 [18 rows x 9 columns] .. GENERATED FROM PYTHON SOURCE LINES 190-193 .. code-block:: Python SUMMARY_FILE = '05d_normal_mixture_all_algos.csv' summary.to_csv(SUMMARY_FILE, index=False) print(f'Summary reported in file {SUMMARY_FILE}') .. rst-class:: sphx-glr-script-out .. code-block:: none Summary reported in file 05d_normal_mixture_all_algos.csv .. rst-class:: sphx-glr-timing **Total running time of the script:** (41 minutes 28.546 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b05d_normal_mixture_all_algos.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b05d_normal_mixture_all_algos.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b05d_normal_mixture_all_algos.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b05d_normal_mixture_all_algos.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_