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[-0.0643973]

+

[1.18328]



@@ -150,7 +150,7 @@ load the generator state .. raw:: html
-

[-0.0643973]

+

[1.18328]



diff --git a/openturns/master/_sources/auto_numerical_methods/general_methods/sg_execution_times.rst.txt b/openturns/master/_sources/auto_numerical_methods/general_methods/sg_execution_times.rst.txt index a8c05a01369..13f33b63222 100644 --- a/openturns/master/_sources/auto_numerical_methods/general_methods/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/general_methods/sg_execution_times.rst.txt @@ -6,22 +6,22 @@ Computation times ================= -**00:08.160** total execution time for **auto_numerical_methods_general_methods** files: +**00:08.853** total execution time for **auto_numerical_methods_general_methods** files: +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_ifs.py` (``plot_ifs.py``) | 00:07.215 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_ifs.py` (``plot_ifs.py``) | 00:07.742 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_pce_design.py` (``plot_pce_design.py``) | 00:00.362 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_sinus.py` (``plot_regression_sinus.py``) | 00:00.419 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_sinus.py` (``plot_regression_sinus.py``) | 00:00.359 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_pce_design.py` (``plot_pce_design.py``) | 00:00.408 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_estimate_integral_iterated_quadrature.py` (``plot_estimate_integral_iterated_quadrature.py``) | 00:00.125 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_estimate_integral_iterated_quadrature.py` (``plot_estimate_integral_iterated_quadrature.py``) | 00:00.160 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_interval.py` (``plot_regression_interval.py``) | 00:00.086 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_interval.py` (``plot_regression_interval.py``) | 00:00.102 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_study_save_load.py` (``plot_study_save_load.py``) | 00:00.011 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_study_save_load.py` (``plot_study_save_load.py``) | 00:00.018 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_random_generator.py` (``plot_random_generator.py``) | 00:00.001 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_combinatorial_generator.py` (``plot_combinatorial_generator.py``) | 00:00.002 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_combinatorial_generator.py` (``plot_combinatorial_generator.py``) | 00:00.001 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_random_generator.py` (``plot_random_generator.py``) | 00:00.001 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/auto_numerical_methods/iterative_statistics/sg_execution_times.rst.txt b/openturns/master/_sources/auto_numerical_methods/iterative_statistics/sg_execution_times.rst.txt index cdc471bca88..3132e0f9059 100644 --- a/openturns/master/_sources/auto_numerical_methods/iterative_statistics/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/iterative_statistics/sg_execution_times.rst.txt @@ -6,12 +6,12 @@ Computation times ================= -**00:00.577** total execution time for **auto_numerical_methods_iterative_statistics** files: +**00:00.646** total execution time for **auto_numerical_methods_iterative_statistics** files: +---------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_threshold.py` (``plot_iterative_threshold.py``) | 00:00.279 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_threshold.py` (``plot_iterative_threshold.py``) | 00:00.321 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_extrema.py` (``plot_iterative_extrema.py``) | 00:00.159 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_extrema.py` (``plot_iterative_extrema.py``) | 00:00.166 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_moments.py` (``plot_iterative_moments.py``) | 00:00.139 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_moments.py` (``plot_iterative_moments.py``) | 00:00.158 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/auto_numerical_methods/optimization/plot_control_termination.rst.txt b/openturns/master/_sources/auto_numerical_methods/optimization/plot_control_termination.rst.txt index e2d0e05677c..fc234257d15 100644 --- a/openturns/master/_sources/auto_numerical_methods/optimization/plot_control_termination.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/optimization/plot_control_termination.rst.txt @@ -210,8 +210,8 @@ Run algorithm .. code-block:: none - event probability: 0.13933077345035633 - calls number: 3748 + event probability: 0.13874558783600302 + calls number: 3785 diff --git a/openturns/master/_sources/auto_numerical_methods/optimization/plot_ego.rst.txt b/openturns/master/_sources/auto_numerical_methods/optimization/plot_ego.rst.txt index 1df29aacf06..48750eb81b5 100644 --- a/openturns/master/_sources/auto_numerical_methods/optimization/plot_ego.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/optimization/plot_ego.rst.txt @@ -840,7 +840,7 @@ We run the algorithm and get the result: .. raw:: html
-

[0.124456,0.803571]

+

[0.124444,0.803607]



@@ -859,7 +859,7 @@ We run the algorithm and get the result: .. raw:: html
-

[-1.04662]

+

[-1.04663]



@@ -974,7 +974,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 4.477 seconds) + **Total running time of the script:** (0 minutes 4.814 seconds) .. _sphx_glr_download_auto_numerical_methods_optimization_plot_ego.py: diff --git a/openturns/master/_sources/auto_numerical_methods/optimization/plot_optimization_dlib.rst.txt b/openturns/master/_sources/auto_numerical_methods/optimization/plot_optimization_dlib.rst.txt index 7c061d85cd2..e6ab35787ea 100644 --- a/openturns/master/_sources/auto_numerical_methods/optimization/plot_optimization_dlib.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/optimization/plot_optimization_dlib.rst.txt @@ -450,13 +450,13 @@ Retrieve results .. code-block:: none - x^ = [3.0398,1.30277,0.5] - f(x^) = [2.77699e-27] + x^ = [2.66928,1.14398,0.5] + f(x^) = [1.0387e-23] Iteration number: 7 Evaluation number: 8 - Absolute error: 1.8329612019352505e-07 - Relative error: 5.4800485422277403e-08 - Residual error: 1.830298897866633e-14 + Absolute error: 1.266046219980731e-06 + Relative error: 4.296315324200083e-07 + Residual error: 1.2764810781704099e-12 Constraint error: 0.0 diff --git a/openturns/master/_sources/auto_numerical_methods/optimization/sg_execution_times.rst.txt b/openturns/master/_sources/auto_numerical_methods/optimization/sg_execution_times.rst.txt index 13ac756c9e0..0151f0f5f61 100644 --- a/openturns/master/_sources/auto_numerical_methods/optimization/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_numerical_methods/optimization/sg_execution_times.rst.txt @@ -6,28 +6,28 @@ Computation times ================= -**00:06.727** total execution time for **auto_numerical_methods_optimization** files: +**00:07.230** total execution time for **auto_numerical_methods_optimization** files: +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_ego.py` (``plot_ego.py``) | 00:04.477 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_ego.py` (``plot_ego.py``) | 00:04.814 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rastrigin.py` (``plot_optimization_rastrigin.py``) | 00:00.940 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rastrigin.py` (``plot_optimization_rastrigin.py``) | 00:01.011 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rosenbrock.py` (``plot_optimization_rosenbrock.py``) | 00:00.592 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rosenbrock.py` (``plot_optimization_rosenbrock.py``) | 00:00.634 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_dlib.py` (``plot_optimization_dlib.py``) | 00:00.346 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_dlib.py` (``plot_optimization_dlib.py``) | 00:00.383 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_pagmo.py` (``plot_optimization_pagmo.py``) | 00:00.158 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_pagmo.py` (``plot_optimization_pagmo.py``) | 00:00.165 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_constraints.py` (``plot_optimization_constraints.py``) | 00:00.067 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_constraints.py` (``plot_optimization_constraints.py``) | 00:00.071 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_nlopt.py` (``plot_optimization_nlopt.py``) | 00:00.066 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_nlopt.py` (``plot_optimization_nlopt.py``) | 00:00.069 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_bonmin.py` (``plot_optimization_bonmin.py``) | 00:00.059 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_bonmin.py` (``plot_optimization_bonmin.py``) | 00:00.060 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_numerical_methods_optimization_plot_control_termination.py` (``plot_control_termination.py``) | 00:00.014 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_minmax_optimization.py` (``plot_minmax_optimization.py``) | 00:00.004 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_minmax_optimization.py` (``plot_minmax_optimization.py``) | 00:00.006 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_numerical_methods_optimization_plot_minmax_by_random_design.py` (``plot_minmax_by_random_design.py``) | 00:00.003 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/auto_probabilistic_modeling/copulas/sg_execution_times.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/copulas/sg_execution_times.rst.txt index 45bb5535a55..8130d7e433a 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/copulas/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/copulas/sg_execution_times.rst.txt @@ -6,14 +6,14 @@ Computation times ================= -**00:00.455** total execution time for **auto_probabilistic_modeling_copulas** files: +**00:00.394** total execution time for **auto_probabilistic_modeling_copulas** files: +-----------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_ordinal_sum_copula.py` (``plot_ordinal_sum_copula.py``) | 00:00.451 | 0.0 MB | -+-----------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_create_copula.py` (``plot_create_copula.py``) | 00:00.001 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_ordinal_sum_copula.py` (``plot_ordinal_sum_copula.py``) | 00:00.391 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_extract_copula.py` (``plot_extract_copula.py``) | 00:00.001 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_composed_copula.py` (``plot_composed_copula.py``) | 00:00.001 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_create_copula.py` (``plot_create_copula.py``) | 00:00.001 | 0.0 MB | ++-----------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/auto_probabilistic_modeling/distributions/sg_execution_times.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/distributions/sg_execution_times.rst.txt index 8cb7b1bd074..3432fda693c 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/distributions/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/distributions/sg_execution_times.rst.txt @@ -6,44 +6,44 @@ Computation times ================= -**00:06.818** total execution time for **auto_probabilistic_modeling_distributions** files: +**00:05.963** total execution time for **auto_probabilistic_modeling_distributions** files: +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_quick_start_guide_distributions.py` (``plot_quick_start_guide_distributions.py``) | 00:01.075 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_quick_start_guide_distributions.py` (``plot_quick_start_guide_distributions.py``) | 00:00.864 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_draw_multivariate_distributions.py` (``plot_create_draw_multivariate_distributions.py``) | 00:00.892 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_draw_multivariate_distributions.py` (``plot_create_draw_multivariate_distributions.py``) | 00:00.822 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_minimum_volume_level_sets.py` (``plot_minimum_volume_level_sets.py``) | 00:00.717 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_minimum_volume_level_sets.py` (``plot_minimum_volume_level_sets.py``) | 00:00.612 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_transformation.py` (``plot_distribution_transformation.py``) | 00:00.672 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_transformation.py` (``plot_distribution_transformation.py``) | 00:00.602 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_order_statistics_distribution.py` (``plot_order_statistics_distribution.py``) | 00:00.540 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_order_statistics_distribution.py` (``plot_order_statistics_distribution.py``) | 00:00.498 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_truncated_distribution.py` (``plot_truncated_distribution.py``) | 00:00.416 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_truncated_distribution.py` (``plot_truncated_distribution.py``) | 00:00.370 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_overview_univariate_distributions.py` (``plot_overview_univariate_distributions.py``) | 00:00.405 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_overview_univariate_distributions.py` (``plot_overview_univariate_distributions.py``) | 00:00.362 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_manipulation.py` (``plot_distribution_manipulation.py``) | 00:00.320 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_manipulation.py` (``plot_distribution_manipulation.py``) | 00:00.276 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_extreme_value_distribution.py` (``plot_create_extreme_value_distribution.py``) | 00:00.315 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_extreme_value_distribution.py` (``plot_create_extreme_value_distribution.py``) | 00:00.259 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_and_draw_scalar_distributions.py` (``plot_create_and_draw_scalar_distributions.py``) | 00:00.267 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_and_draw_scalar_distributions.py` (``plot_create_and_draw_scalar_distributions.py``) | 00:00.243 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_random_mixture.py` (``plot_create_random_mixture.py``) | 00:00.265 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_random_mixture.py` (``plot_create_random_mixture.py``) | 00:00.230 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_bayes_distribution.py` (``plot_bayes_distribution.py``) | 00:00.214 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_bayes_distribution.py` (``plot_bayes_distribution.py``) | 00:00.188 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_mixture_distribution.py` (``plot_mixture_distribution.py``) | 00:00.195 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_mixture_distribution.py` (``plot_mixture_distribution.py``) | 00:00.177 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_generate_by_inversion.py` (``plot_generate_by_inversion.py``) | 00:00.176 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_generate_by_inversion.py` (``plot_generate_by_inversion.py``) | 00:00.156 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_python_distribution.py` (``plot_python_distribution.py``) | 00:00.126 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_python_distribution.py` (``plot_python_distribution.py``) | 00:00.101 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_conditional_distribution.py` (``plot_conditional_distribution.py``) | 00:00.096 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_conditional_distribution.py` (``plot_conditional_distribution.py``) | 00:00.087 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_your_own_dist.py` (``plot_create_your_own_dist.py``) | 00:00.069 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_your_own_dist.py` (``plot_create_your_own_dist.py``) | 00:00.060 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_maximum_distribution.py` (``plot_maximum_distribution.py``) | 00:00.059 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_maximum_distribution.py` (``plot_maximum_distribution.py``) | 00:00.056 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_conditional_random_vector.py` (``plot_conditional_random_vector.py``) | 00:00.001 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/auto_probabilistic_modeling/random_vectors/sg_execution_times.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/random_vectors/sg_execution_times.rst.txt index d7e616524da..a786dfc642a 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/random_vectors/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/random_vectors/sg_execution_times.rst.txt @@ -6,12 +6,12 @@ Computation times ================= -**00:00.007** total execution time for **auto_probabilistic_modeling_random_vectors** files: +**00:00.005** total execution time for **auto_probabilistic_modeling_random_vectors** files: +----------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_random_vectors_plot_python_randomvector.py` (``plot_python_randomvector.py``) | 00:00.003 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_random_vectors_plot_random_vector_manipulation.py` (``plot_random_vector_manipulation.py``) | 00:00.002 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_random_vectors_plot_random_vector_manipulation.py` (``plot_random_vector_manipulation.py``) | 00:00.003 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_random_vectors_plot_python_randomvector.py` (``plot_python_randomvector.py``) | 00:00.002 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_probabilistic_modeling_random_vectors_plot_composite_random_vector.py` (``plot_composite_random_vector.py``) | 00:00.002 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_create_mesh.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_create_mesh.rst.txt index 430de0352ce..a3e7e2a4ef7 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_create_mesh.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_create_mesh.rst.txt @@ -386,11 +386,6 @@ Display figures -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** (0 minutes 2.205 seconds) - - .. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_create_mesh.py: .. only:: html diff --git a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_gaussian_process_covariance_hmat.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_gaussian_process_covariance_hmat.rst.txt index 09d6e6d6bf6..21791a91664 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_gaussian_process_covariance_hmat.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_gaussian_process_covariance_hmat.rst.txt @@ -228,7 +228,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.345 seconds) + **Total running time of the script:** (0 minutes 2.129 seconds) .. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_covariance_hmat.py: diff --git a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_userdefined_covariance_model.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_userdefined_covariance_model.rst.txt index b9806ad615a..58021da69e7 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_userdefined_covariance_model.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/plot_userdefined_covariance_model.rst.txt @@ -157,7 +157,7 @@ Draw the covariance model .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.260 seconds) + **Total running time of the script:** (0 minutes 2.024 seconds) .. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py: diff --git a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/sg_execution_times.rst.txt b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/sg_execution_times.rst.txt index 037638744ba..30a5ae24980 100644 --- a/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_probabilistic_modeling/stochastic_processes/sg_execution_times.rst.txt @@ -6,54 +6,54 @@ Computation times ================= -**00:13.554** total execution time for **auto_probabilistic_modeling_stochastic_processes** files: +**00:11.931** total execution time for **auto_probabilistic_modeling_stochastic_processes** files: +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_covariance_hmat.py` (``plot_gaussian_process_covariance_hmat.py``) | 00:02.345 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_covariance_hmat.py` (``plot_gaussian_process_covariance_hmat.py``) | 00:02.129 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py` (``plot_userdefined_covariance_model.py``) | 00:02.260 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py` (``plot_userdefined_covariance_model.py``) | 00:02.024 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_mesh.py` (``plot_create_mesh.py``) | 00:02.205 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_mesh.py` (``plot_create_mesh.py``) | 00:01.944 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_field_manipulation.py` (``plot_field_manipulation.py``) | 00:01.874 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_field_manipulation.py` (``plot_field_manipulation.py``) | 00:01.574 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_box_cox_transform.py` (``plot_box_cox_transform.py``) | 00:01.070 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_box_cox_transform.py` (``plot_box_cox_transform.py``) | 00:00.909 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_processes_comparison.py` (``plot_gaussian_processes_comparison.py``) | 00:00.776 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_processes_comparison.py` (``plot_gaussian_processes_comparison.py``) | 00:00.670 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_process_manipulation.py` (``plot_process_manipulation.py``) | 00:00.471 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_process_manipulation.py` (``plot_process_manipulation.py``) | 00:00.424 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_random_walk_process.py` (``plot_random_walk_process.py``) | 00:00.308 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_random_walk_process.py` (``plot_random_walk_process.py``) | 00:00.284 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_and_manipulate_arma_process.py` (``plot_create_and_manipulate_arma_process.py``) | 00:00.298 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_and_manipulate_arma_process.py` (``plot_create_and_manipulate_arma_process.py``) | 00:00.266 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_discrete_markov_chain_process.py` (``plot_discrete_markov_chain_process.py``) | 00:00.293 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_discrete_markov_chain_process.py` (``plot_discrete_markov_chain_process.py``) | 00:00.253 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_kronecker_covmodel.py` (``plot_kronecker_covmodel.py``) | 00:00.268 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_kronecker_covmodel.py` (``plot_kronecker_covmodel.py``) | 00:00.249 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_export_field_vtk.py` (``plot_export_field_vtk.py``) | 00:00.173 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_mix_rv_process.py` (``plot_mix_rv_process.py``) | 00:00.156 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_mix_rv_process.py` (``plot_mix_rv_process.py``) | 00:00.162 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_white_noise_process.py` (``plot_white_noise_process.py``) | 00:00.148 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_white_noise_process.py` (``plot_white_noise_process.py``) | 00:00.160 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_export_field_vtk.py` (``plot_export_field_vtk.py``) | 00:00.128 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_normal_process.py` (``plot_create_normal_process.py``) | 00:00.149 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_add_trend.py` (``plot_add_trend.py``) | 00:00.125 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_add_trend.py` (``plot_add_trend.py``) | 00:00.146 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_normal_process.py` (``plot_create_normal_process.py``) | 00:00.124 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_trend_transform.py` (``plot_trend_transform.py``) | 00:00.129 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_trend_transform.py` (``plot_trend_transform.py``) | 00:00.119 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_aggregated_process.py` (``plot_aggregated_process.py``) | 00:00.124 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_timeseries_manipulation.py` (``plot_timeseries_manipulation.py``) | 00:00.107 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_timeseries_manipulation.py` (``plot_timeseries_manipulation.py``) | 00:00.114 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_aggregated_process.py` (``plot_aggregated_process.py``) | 00:00.106 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_functional_basis_process.py` (``plot_functional_basis_process.py``) | 00:00.086 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_functional_basis_process.py` (``plot_functional_basis_process.py``) | 00:00.068 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_user_stationary_covmodel.py` (``plot_user_stationary_covmodel.py``) | 00:00.071 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_user_stationary_covmodel.py` (``plot_user_stationary_covmodel.py``) | 00:00.064 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_spectral_model.py` (``plot_userdefined_spectral_model.py``) | 00:00.069 | 0.0 MB | -+--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_parametric_spectral_density.py` (``plot_parametric_spectral_density.py``) | 00:00.002 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_spectral_model.py` (``plot_userdefined_spectral_model.py``) | 00:00.058 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_stationary_covmodel.py` (``plot_create_stationary_covmodel.py``) | 00:00.001 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_parametric_spectral_density.py` (``plot_parametric_spectral_density.py``) | 00:00.001 | 0.0 MB | ++--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/auto_reliability_sensitivity/central_dispersion/sg_execution_times.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/central_dispersion/sg_execution_times.rst.txt index 2bd7dfd89b4..8302b51d177 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/central_dispersion/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/central_dispersion/sg_execution_times.rst.txt @@ -6,12 +6,12 @@ Computation times ================= -**00:00.636** total execution time for **auto_reliability_sensitivity_central_dispersion** files: +**00:00.597** total execution time for **auto_reliability_sensitivity_central_dispersion** files: +---------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_expectation_simulation_algorithm.py` (``plot_expectation_simulation_algorithm.py``) | 00:00.461 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_expectation_simulation_algorithm.py` (``plot_expectation_simulation_algorithm.py``) | 00:00.427 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_central_tendency.py` (``plot_central_tendency.py``) | 00:00.126 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_central_tendency.py` (``plot_central_tendency.py``) | 00:00.124 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_estimate_moments_taylor.py` (``plot_estimate_moments_taylor.py``) | 00:00.048 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_estimate_moments_taylor.py` (``plot_estimate_moments_taylor.py``) | 00:00.046 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_experiment.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_experiment.rst.txt index 709f791ad9d..ccf84d9f138 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_experiment.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_experiment.rst.txt @@ -294,7 +294,7 @@ This growth depends on the dimension of the problem. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.111 seconds) + **Total running time of the script:** (0 minutes 2.575 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_experiment.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_quadrature.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_quadrature.rst.txt index 87b6b27fa1e..7e8bfe6785d 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_quadrature.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/plot_smolyak_quadrature.rst.txt @@ -584,7 +584,7 @@ We can finally create the graph. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 7.411 seconds) + **Total running time of the script:** (0 minutes 8.529 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_quadrature.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/sg_execution_times.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/sg_execution_times.rst.txt index a19ccf998df..79f028e5620 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/design_of_experiments/sg_execution_times.rst.txt @@ -6,40 +6,40 @@ Computation times ================= -**00:14.663** total execution time for **auto_reliability_sensitivity_design_of_experiments** files: +**00:16.930** total execution time for **auto_reliability_sensitivity_design_of_experiments** files: +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_quadrature.py` (``plot_smolyak_quadrature.py``) | 00:07.411 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_quadrature.py` (``plot_smolyak_quadrature.py``) | 00:08.529 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_experiment.py` (``plot_smolyak_experiment.py``) | 00:02.111 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_experiment.py` (``plot_smolyak_experiment.py``) | 00:02.575 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_plot_design.py` (``plot_plot_design.py``) | 00:01.247 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_plot_design.py` (``plot_plot_design.py``) | 00:01.361 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiments.py` (``plot_design_of_experiments.py``) | 00:01.031 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiments.py` (``plot_design_of_experiments.py``) | 00:01.168 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_low_discrepancy_sequence.py` (``plot_low_discrepancy_sequence.py``) | 00:00.550 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_low_discrepancy_sequence.py` (``plot_low_discrepancy_sequence.py``) | 00:00.697 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_optimal_lhs.py` (``plot_optimal_lhs.py``) | 00:00.469 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_merge.py` (``plot_smolyak_merge.py``) | 00:00.563 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_merge.py` (``plot_smolyak_merge.py``) | 00:00.468 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_optimal_lhs.py` (``plot_optimal_lhs.py``) | 00:00.532 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_deterministic_doe.py` (``plot_create_deterministic_doe.py``) | 00:00.292 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_deterministic_doe.py` (``plot_create_deterministic_doe.py``) | 00:00.310 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_deterministic_design.py` (``plot_deterministic_design.py``) | 00:00.258 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_deterministic_design.py` (``plot_deterministic_design.py``) | 00:00.298 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_indices.py` (``plot_smolyak_indices.py``) | 00:00.240 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_indices.py` (``plot_smolyak_indices.py``) | 00:00.277 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_mixed_design.py` (``plot_mixed_design.py``) | 00:00.130 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_mixed_design.py` (``plot_mixed_design.py``) | 00:00.143 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiment_continuous_discrete.py` (``plot_design_of_experiment_continuous_discrete.py``) | 00:00.115 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_random_doe.py` (``plot_create_random_doe.py``) | 00:00.122 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_random_doe.py` (``plot_create_random_doe.py``) | 00:00.114 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiment_continuous_discrete.py` (``plot_design_of_experiment_continuous_discrete.py``) | 00:00.120 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_monte_carlo_experiment.py` (``plot_monte_carlo_experiment.py``) | 00:00.063 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_gauss_product_experiment.py` (``plot_gauss_product_experiment.py``) | 00:00.062 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_gauss_product_experiment.py` (``plot_gauss_product_experiment.py``) | 00:00.057 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_probabilistic_design.py` (``plot_probabilistic_design.py``) | 00:00.060 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_probabilistic_design.py` (``plot_probabilistic_design.py``) | 00:00.056 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_composite_experiment.py` (``plot_composite_experiment.py``) | 00:00.060 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_composite_experiment.py` (``plot_composite_experiment.py``) | 00:00.052 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_monte_carlo_experiment.py` (``plot_monte_carlo_experiment.py``) | 00:00.054 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_adaptive_directional_sampling.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_adaptive_directional_sampling.rst.txt index e4c3aac1ade..8340a73df51 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_adaptive_directional_sampling.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_adaptive_directional_sampling.rst.txt @@ -218,7 +218,7 @@ Retrieve results. .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.078 seconds) + **Total running time of the script:** (0 minutes 2.117 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_estimate_probability_adaptive_directional_sampling.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_form_oscillator.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_form_oscillator.rst.txt index 87b8979b1c6..c8a2be23b43 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_form_oscillator.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_estimate_probability_form_oscillator.rst.txt @@ -725,7 +725,7 @@ We can see that this post-treatment of FORM result allows one to greatly improve .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 5.586 seconds) + **Total running time of the script:** (0 minutes 5.350 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_estimate_probability_form_oscillator.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability/sg_execution_times.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability/sg_execution_times.rst.txt index 9040b4c4043..661d0f8663b 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability/sg_execution_times.rst.txt @@ -6,56 +6,56 @@ Computation times ================= -**00:18.179** total execution time for **auto_reliability_sensitivity_reliability** files: +**00:17.970** total execution time for **auto_reliability_sensitivity_reliability** files: +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form_oscillator.py` (``plot_estimate_probability_form_oscillator.py``) | 00:05.586 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form_oscillator.py` (``plot_estimate_probability_form_oscillator.py``) | 00:05.350 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_adaptive_directional_sampling.py` (``plot_estimate_probability_adaptive_directional_sampling.py``) | 00:02.078 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_adaptive_directional_sampling.py` (``plot_estimate_probability_adaptive_directional_sampling.py``) | 00:02.117 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_proba_system_event.py` (``plot_proba_system_event.py``) | 00:01.749 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_proba_system_event.py` (``plot_proba_system_event.py``) | 00:01.797 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_crossentropy.py` (``plot_crossentropy.py``) | 00:01.406 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_crossentropy.py` (``plot_crossentropy.py``) | 00:01.497 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py` (``plot_estimate_probability_randomized_qmc.py``) | 00:00.934 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py` (``plot_estimate_probability_randomized_qmc.py``) | 00:00.925 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_form_explained.py` (``plot_form_explained.py``) | 00:00.831 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_form_explained.py` (``plot_form_explained.py``) | 00:00.802 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_subset_sampling.py` (``plot_subset_sampling.py``) | 00:00.752 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_subset_sampling.py` (``plot_subset_sampling.py``) | 00:00.727 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_event_system.py` (``plot_event_system.py``) | 00:00.654 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_event_system.py` (``plot_event_system.py``) | 00:00.688 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_domain_event.py` (``plot_create_domain_event.py``) | 00:00.643 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_directional_sampling.py` (``plot_estimate_probability_directional_sampling.py``) | 00:00.630 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_directional_sampling.py` (``plot_estimate_probability_directional_sampling.py``) | 00:00.616 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_domain_event.py` (``plot_create_domain_event.py``) | 00:00.627 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam.py` (``plot_axial_stressed_beam.py``) | 00:00.551 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam.py` (``plot_axial_stressed_beam.py``) | 00:00.533 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_multi_form.py` (``plot_multi_form.py``) | 00:00.517 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_multi_form.py` (``plot_multi_form.py``) | 00:00.480 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_nais.py` (``plot_nais.py``) | 00:00.441 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_nais.py` (``plot_nais.py``) | 00:00.436 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam_quickstart.py` (``plot_axial_stressed_beam_quickstart.py``) | 00:00.397 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam_quickstart.py` (``plot_axial_stressed_beam_quickstart.py``) | 00:00.385 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form.py` (``plot_estimate_probability_form.py``) | 00:00.373 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form.py` (``plot_estimate_probability_form.py``) | 00:00.347 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_importance_sampling.py` (``plot_estimate_probability_importance_sampling.py``) | 00:00.153 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_importance_sampling.py` (``plot_estimate_probability_importance_sampling.py``) | 00:00.148 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_results.py` (``plot_probability_simulation_results.py``) | 00:00.146 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_results.py` (``plot_probability_simulation_results.py``) | 00:00.144 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_flood_model.py` (``plot_flood_model.py``) | 00:00.125 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_flood_model.py` (``plot_flood_model.py``) | 00:00.121 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_threshold_event.py` (``plot_create_threshold_event.py``) | 00:00.082 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_threshold_event.py` (``plot_create_threshold_event.py``) | 00:00.076 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_monte_carlo.py` (``plot_estimate_probability_monte_carlo.py``) | 00:00.047 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_monte_carlo.py` (``plot_estimate_probability_monte_carlo.py``) | 00:00.046 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_parametrization.py` (``plot_probability_simulation_parametrization.py``) | 00:00.044 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_parametrization.py` (``plot_probability_simulation_parametrization.py``) | 00:00.042 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_lhs.py` (``plot_estimate_probability_lhs.py``) | 00:00.042 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_lhs.py` (``plot_estimate_probability_lhs.py``) | 00:00.041 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_strong_maximum_test.py` (``plot_strong_maximum_test.py``) | 00:00.005 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_post_analytical_importance_sampling.py` (``plot_post_analytical_importance_sampling.py``) | 00:00.005 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_post_analytical_importance_sampling.py` (``plot_post_analytical_importance_sampling.py``) | 00:00.004 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_event_manipulation.py` (``plot_event_manipulation.py``) | 00:00.002 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/plot_field_fca_sobol.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/plot_field_fca_sobol.rst.txt index 0e204641e50..fec1d681f0a 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/plot_field_fca_sobol.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/plot_field_fca_sobol.rst.txt @@ -521,7 +521,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 6.588 seconds) + **Total running time of the script:** (0 minutes 6.915 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_reliability_processes_plot_field_fca_sobol.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/sg_execution_times.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/sg_execution_times.rst.txt index ddef827f78d..dabde49f7a1 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability_processes/sg_execution_times.rst.txt @@ -6,12 +6,12 @@ Computation times ================= -**00:06.770** total execution time for **auto_reliability_sensitivity_reliability_processes** files: +**00:07.102** total execution time for **auto_reliability_sensitivity_reliability_processes** files: +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_field_fca_sobol.py` (``plot_field_fca_sobol.py``) | 00:06.588 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_field_fca_sobol.py` (``plot_field_fca_sobol.py``) | 00:06.915 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_estimate_probability_monte_carlo_process.py` (``plot_estimate_probability_monte_carlo_process.py``) | 00:00.179 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_estimate_probability_monte_carlo_process.py` (``plot_estimate_probability_monte_carlo_process.py``) | 00:00.186 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_event_process.py` (``plot_event_process.py``) | 00:00.002 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_wingweight.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_wingweight.rst.txt index 56072bfe0af..b71c5d071ee 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_wingweight.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_wingweight.rst.txt @@ -1188,7 +1188,7 @@ We can also see that the asymptotic p-values and p-values estimated by permutati .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 5.525 seconds) + **Total running time of the script:** (0 minutes 6.281 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_wingweight.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/sg_execution_times.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/sg_execution_times.rst.txt index dc0ddbfcfc0..1d7a44b20c4 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/sg_execution_times.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/sensitivity_analysis/sg_execution_times.rst.txt @@ -6,22 +6,22 @@ Computation times ================= -**00:08.733** total execution time for **auto_reliability_sensitivity_sensitivity_analysis** files: +**00:09.585** total execution time for **auto_reliability_sensitivity_sensitivity_analysis** files: +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_wingweight.py` (``plot_sensitivity_wingweight.py``) | 00:05.525 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_wingweight.py` (``plot_sensitivity_wingweight.py``) | 00:06.281 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_functional_chaos_sensitivity.py` (``plot_functional_chaos_sensitivity.py``) | 00:00.960 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_functional_chaos_sensitivity.py` (``plot_functional_chaos_sensitivity.py``) | 00:00.920 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_par_coo.py` (``plot_sensitivity_par_coo.py``) | 00:00.801 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_par_coo.py` (``plot_sensitivity_par_coo.py``) | 00:00.821 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_hsic_estimators_ishigami.py` (``plot_hsic_estimators_ishigami.py``) | 00:00.728 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_hsic_estimators_ishigami.py` (``plot_hsic_estimators_ishigami.py``) | 00:00.770 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol.py` (``plot_sensitivity_sobol.py``) | 00:00.422 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol.py` (``plot_sensitivity_sobol.py``) | 00:00.452 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_ancova.py` (``plot_sensitivity_ancova.py``) | 00:00.117 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_ancova.py` (``plot_sensitivity_ancova.py``) | 00:00.132 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol_multivariate.py` (``plot_sensitivity_sobol_multivariate.py``) | 00:00.104 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_fast.py` (``plot_sensitivity_fast.py``) | 00:00.106 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_fast.py` (``plot_sensitivity_fast.py``) | 00:00.077 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol_multivariate.py` (``plot_sensitivity_sobol_multivariate.py``) | 00:00.103 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/theory/meta_modeling/taylor_expansion.rst.txt b/openturns/master/_sources/theory/meta_modeling/taylor_expansion.rst.txt index 68da2d9cd0a..f202e3193d3 100644 --- a/openturns/master/_sources/theory/meta_modeling/taylor_expansion.rst.txt +++ b/openturns/master/_sources/theory/meta_modeling/taylor_expansion.rst.txt @@ -1,57 +1,73 @@ .. _taylor_expansion: -Linear and Quadratic Taylor Expansions --------------------------------------- -| The approximation of the model response - :math:`\underline{y} = h(\underline{x})` around a specific set - :math:`\underline{x}_0 = (x_{0,1},\dots,x_{0,n_{X}})` of input - parameters may be of interest. One may then substitute :math:`h` for - its Taylor expansion at point :math:`\underline{x}_0`. Hence :math:`h` - is replaced with a first or second-order polynomial - :math:`\widehat{h}` whose evaluation is inexpensive, allowing the - analyst to apply the uncertainty propagation methods. -| We consider the first and second order Taylor expansions around - :math:`\ux=\underline{x}_0`. +Let :math:`h: \Rset^d \rightarrow \Rset^q` be a function, let :math:`\ux \in \Rset^{n_X}` +be an input point and let :math:`\uy=h(\ux)` be the corresponding output. - .. math:: +First-order Taylor expansion +---------------------------- - \underline{y} \, \, \approx \, \, \widehat{h}(\underline{x}) \, \, = \, \, h(\underline{x}_0) \, + \, \sum_{i=1}^{n_{X}} \; \frac{\partial h}{\partial x_i}(\underline{x}_0).\left(x_i - x_{0,i} \right) +The first-order Taylor expansion of :math:`h` at the point :math:`\ux_0` is the function +:math:`\widehat{h}: \Rset^d \rightarrow \Rset^q` defined for each marginal function +:math:`h_k` of :math:`h` by the equation: -Introducing a vector notation, the previous equation rewrites: +.. math:: + + \widehat{h}_k(\ux) = h_k(\ux_0) + \sum_{i=1}^{d} \left(\frac{\partial h_k}{\partial x_i}\right)(\ux_0)\left(x_i - x_{0,i} \right) + +for :math:`k \in \{1, ..., q\}` which can be written as: + +.. math:: + + \widehat{h}(\ux) = h(\ux_0) + \mat{L} (\ux-\ux_0) + + +where :math:`\mat{L} = (L_{ij})_{1 \leq i \leq q, 1\leq j \leq d}` is the Jacobian +matrix evaluated at the point :math:`\ux_0`: + +.. math:: + + L_{ij} = \left(\frac{\partial h_i}{\partial x_i}\right)(\ux_0) + +for :math:`i \in \{1, ..., q\}` and :math:`j \in \{1, ..., d\}`. + + +Second-order Taylor expansion +----------------------------- + +The second-order Taylor expansion of :math:`h` at the point :math:`\ux_0` is the function +:math:`\widehat{h}: \Rset^d \rightarrow \Rset^q` defined for each marginal function +:math:`h_k` of :math:`h` by the equation: .. math:: - \underline{y} \, \, \approx \, \, \underline{y}_0 \, + \, \underline{\underline{L}} \: \left(\underline{x}-\underline{x}_0\right) + \widehat{h}_k(\ux) = h_k(\ux_0) + \sum_{i=1}^{d} \left(\frac{\partial h_k}{\partial x_i}\right)(\ux_0) + \left(x_i - x_{0,i} \right) + \frac{1}{2} \sum_{i,j = 1}^d \left( \frac{\partial^2 h_k}{\partial x_i + \partial x_j}\right)(\ux_0)(x_i-x_{0,i})(x_j-x_{0,j}) -where: -- :math:`\underline{y_0} = (y_{0,1} , \dots, y_{0,n_Y})^{\textsf{T}}= h(\underline{x}_0)` - is the vector model response evaluated at :math:`\underline{x}_0`; +which can be written as: -- :math:`\underline{x}` is the current set of input parameters; +.. math:: -- :math:`\underline{\underline{L}} = \left( \frac{\partial y_{0,j}}{\partial x_i} \, \, , \, \, i=1,\ldots, n_X \, \, , \, \, j=1, \ldots, n_Y \right)` - is the transposed Jacobian matrix evaluated at - :math:`\underline{x}_0`. + \widehat{h}(\ux) = h(\ux_0) + \mat{L} (\ux-\ux_0) + \frac{1}{2} \left\langle \left\langle\mat{Q},\ux- + \ux_0 \right \rangle, \ux-\ux_0 \right \rangle - .. math:: - \begin{aligned} - \underline{y} \, \, \approx \, \, \widehat{h}(\underline{x}) \, \, = \, \, - h(\underline{x}_0) \, + \, \sum_{i=1}^{n_{X}} \; \frac{\partial h}{\partial x_i}(\underline{x}_0).\left(x_i - x_{0,i} \right) \, + \, \frac{1}{2} \; \sum_{i,j=1}^{n_X} \; \frac{\partial^2 h}{\partial x_i \partial x_j}(\underline{x}_0).\left(x_i - x_{0,i} \right).\left(x_j - x_{0,j} \right) - \end{aligned} +where :math:`\mat{Q} = (Q_{ijk})_{1 \leq i,j \leq d, 1\leq k \leq q}` is the Hessian tensor of order 3 evaluated at :math:`\ux_0`: -Introducing a vector notation, the previous equation rewrites: .. math:: - \underline{y} \, \, \approx \, \, \underline{y}_0 \, + \, \underline{\underline{L}} \: \left(\underline{x}-\underline{x}_0\right) \, + \, \frac{1}{2} \; \left\langle \left\langle\underline{\underline{\underline{Q}}}\:,\underline{x}-\underline{x}_0 \right\rangle,\:\underline{x}-\underline{x}_0 \right\rangle + Q_{ijk} = \left(\frac{\partial^2 h_k}{\partial x_i\partial x_j}\right)(\ux_0) + +for :math:`i, j \in \{1, ..., d\}` and :math:`k \in \{1, ..., q\}`. + +The first and second order Taylor expansions are used in the following cases: -where -:math:`\underline{\underline{Q}} = \left\{ \frac{\partial^2 y_{0,k}}{\partial x_i \partial x_j} \, \, , \, \, i,j=1,\ldots, n_X \, \, , \, \, k=1, \ldots, n_Y \right\}` -is the transposed Hessian matrix. +- to evaluate the importance factors of the input point on the output: refer to :ref:`taylor_importance_factors`, +- to get an approximation of the mean and the variance of the output: refer to :ref:`taylor_expansion_moments`. .. topic:: API: diff --git a/openturns/master/_sources/theory/numerical_methods/nataf_transformation.rst.txt b/openturns/master/_sources/theory/numerical_methods/nataf_transformation.rst.txt index 74fb084107d..8be49bb8267 100644 --- a/openturns/master/_sources/theory/numerical_methods/nataf_transformation.rst.txt +++ b/openturns/master/_sources/theory/numerical_methods/nataf_transformation.rst.txt @@ -135,7 +135,7 @@ the standard normal distribution with independent components. .. topic:: API: - - See the available :ref:`Nataf transformations `. + - See the available :ref:`Nataf transformations `. .. topic:: References: diff --git a/openturns/master/_sources/theory/reliability_sensitivity/importance_form.rst.txt b/openturns/master/_sources/theory/reliability_sensitivity/importance_form.rst.txt index 661c0ee249e..b460ebb0d16 100644 --- a/openturns/master/_sources/theory/reliability_sensitivity/importance_form.rst.txt +++ b/openturns/master/_sources/theory/reliability_sensitivity/importance_form.rst.txt @@ -23,7 +23,7 @@ input components with respect to the realization of the event. They are often se of the impact of modeling the input components as random variables rather than fixed values. FORM importance factors are defined as follows. -The :ref:`isoprobabilistic transformation ` :math:`T` used in the FORM and +The :ref:`isoprobabilistic transformation ` :math:`T` used in the FORM and SORM approximation is a diffeomorphism from :math:`\supp{\vect{X}}` into :math:`\Rset^n`, such that the distribution of the random vector :math:`\vect{U}=T(\vect{X})` has the diff --git a/openturns/master/_sources/theory/reliability_sensitivity/taylor_importance_factors.rst.txt b/openturns/master/_sources/theory/reliability_sensitivity/taylor_importance_factors.rst.txt index 0a03e88a150..d8b57636b77 100644 --- a/openturns/master/_sources/theory/reliability_sensitivity/taylor_importance_factors.rst.txt +++ b/openturns/master/_sources/theory/reliability_sensitivity/taylor_importance_factors.rst.txt @@ -1,79 +1,35 @@ .. _taylor_importance_factors: -Taylor decomposition importance factors ---------------------------------------- +Taylor importance factors +------------------------- The importance factors derived from a Taylor expansion are -defined to rank the sensitivity of the inputs to -the output for central dispersion analysis. +defined to rank the sensitivity of the output to +the inputs for central dispersion analysis. -Let us denote by :math:`\uX` the input random vector. -Assume that the marginals of :math:`\uX` are independent. -Suppose that :math:`Z = h(\ux)` is a real function of the -input, i.e. :math:`n_Z = 1`. -Assume that the order 1 Taylor expansion of the function :math:`h` -at the point :math:`\ux = \muX` is exact, i.e.: +We consider the Taylor expansion of a function. We use the notations introduced in +:ref:`Taylor Expansion `. Let :math:`\uX` be the input random vector. We assume that +the marginals of :math:`\uX` are independent. Let :math:`Y = h(\ux)` with +:math:`h: \Rset^d \rightarrow \Rset` be a function with a scalar output. -.. math:: - h(\ux) = h(\muX) - + \sum_{i=1}^{n_X} \frac{\partial h}{\partial x_i} (\muX) (x_i - \mu_i) - -where: - -- :math:`\muX` is the mean of the input random vector, - -- :math:`\frac{\partial h}{\partial x_i} (\muX)` - is the partial derivative of the model :math:`h` - with respect to the i-th input variable, - evaluated at the point :math:`\ux`. - -Therefore the expectation of :math:`Z` is: +Refer to :ref:`Taylor Expansion ` for details on the expressions +of the first-order and second-order Taylor expansions and to +:ref:`Taylor Expansion Moments ` for +details on the approximations of the mean and the variance of :math:`Y`. -.. math:: - \Expect{Z} = h(\muX). - -The independence of the marginals implies: +The importance factor of :math:`X_i` is defined by: .. math:: - \Var Z = \sum_{i=1}^{n_X} \left(\frac{\partial h}{\partial x_i} (\muX)\right)^2 \sigma_i^2 - -where: -- :math:`\Var Z` is the variance of the output variable, + \eta_i = \frac{ \left(\frac{\partial h}{\partial x_i}(\vect{\mu})\right)^2 \sigma_i^2}{\Var Y}. -- :math:`\sigma_i^2 = \Var X_i` is the variance of the i-th input variable. - -Let :math:`\eta_i` be the importance factor of the i-th input -variable, defined by: +If the model is linear (i.e. if the model is equal to its first-order Taylor expansion), then the importance factors sum to one: .. math:: - \eta_i = \frac{\left(\frac{\partial h}{\partial x_i} (\muX)\right)^2 \sigma_i^2}{\Var Z}. -Therefore, the importance factors sum to one: + \eta_1 + \eta_2 + \ldots + \eta_{d} = 1 -.. math:: - \eta_1 + \eta_2 + \ldots + \eta_{n_X} = 1 - -| Each coefficient :math:`\frac{\partial h(\ux)}{\partial x^i}` is a - linear estimate of the number of units change in the variable - :math:`y=h(\ux)` as a result of a unit change in the variable - :math:`x^i`. This first term depends on the physical units of the - variables and is meaningful only when the units of the model are - known. In the general case, as the variables have different physical - units, if :math:`i\neq j`, it is not possible to compare - :math:`\frac{\partial h(\ux)}{\partial x_i}` with - :math:`\frac{\partial h(\ux)}{\partial x_j}`. - This is the reason why the importance factor are - normalized. These factors enable to make the results - comparable independently of the original units of the inputs of the - model. -| To summarize, the coefficients :math:`\cF_1, ..., \cF_{n_X}` - represent a linear estimate of the change in the output variable - :math:`z = h(\ux)` caused by a small change in the input variable - :math:`x_i`. The importance factors are independent of the original - units of the model, and are comparable with each other. - -These are also called importance factors derived from perturbation methods. +These importance factors are also called *importance factors derived from perturbation methods*. .. topic:: API: diff --git a/openturns/master/_sources/theory/reliability_sensitivity/taylor_moments.rst.txt b/openturns/master/_sources/theory/reliability_sensitivity/taylor_moments.rst.txt index c785acd92eb..84ffcf5847d 100644 --- a/openturns/master/_sources/theory/reliability_sensitivity/taylor_moments.rst.txt +++ b/openturns/master/_sources/theory/reliability_sensitivity/taylor_moments.rst.txt @@ -1,144 +1,105 @@ -Taylor variance decomposition ------------------------------ - -| The Taylor variance decomposition (also referred as quadratic cumul method - or perturbation method) is a probabilistic approach designed to propagate - the uncertainties of the input variables :math:`\uX` through the model - :math:`h` towards the output variables :math:`\uY`. It enables to - access the central dispersion (expectation and variance) of the output - variables. -| This method is based on a Taylor decomposition of the output variable - :math:`\uY` towards the :math:`\uX` random vectors around the mean - point :math:`\muX`. Depending on the order of the Taylor decomposition - (classically first order or second order), one can obtain different - formulas. For easiness of the reading, we first present the formulas - with :math:`n_Y=1` before the ones obtained for :math:`n_Y > 1`. -| As :math:`Y=h(\uX)`, the Taylor decomposition around - :math:`\ux = \muX` at the second order yields to: - -| **Case** :math:`n_Y=1` +.. _taylor_expansion_moments: -.. math:: +Taylor expansion moments +------------------------ - Y = h(\muX) + < \underline{\nabla} h(\muX) , \: \uX - \muX> + \frac{1}{2}<<\underline{\underline{\nabla }}^2 h(\muX,\: \underline{\mu}_{\:X}),\: \uX - \muX>,\: \uX - \muX> + o(\Cov \uX) +In this page, we consider the Taylor expansion of a function. +One way to evaluate the central dispersion (expectation and variance) of the variable :math:`\uY=h(\uX)` +is to use the Taylor expansion of the function :math:`h: \Rset^d \rightarrow \Rset^q` at +the mean point :math:`\vect{\mu} = \Expect{\uX}`. Depending on the order of the Taylor expansion (classically first or second order), we get different approximations +of the mean and variance of :math:`Y`. -where: +We use the notations introduced in :ref:`Taylor Expansion `. -- :math:`\muX = \Expect{\uX}` is the vector of the input variables at - the mean values of each component. +In the remainder, let :math:`\Cov \uX` be the covariance matrix of :math:`\uX`, defined by: -- :math:`\Cov \uX` is the covariance matrix of the random vector - :math:`\uX`. The elements are the followings : - :math:`(\Cov \uX)_{ij} = \Expect{\left(X^i - \Expect{X^i} \right)\times\left(X^j - \Expect{X^j} \right)}` +.. math:: -- :math:`\underline{\nabla} h(\muX) = \: ^t \left( \frac{\partial y}{\partial x^j}\right)_{\ux\: =\: \muX} = \: ^t \left( \frac{\partial h(\ux)}{\partial x^j}\right)_{\ux\: =\: \muX}` - is the gradient vector taken at the value :math:`\ux = \muX` and - :math:`j=1,\ldots,n_X`. + \Cov \uX = \mat{C} -- :math:`\underline{\underline{\nabla}}^2 h(\ux,\ux)` is a matrix. It - is composed by the second order derivative of the output variable - towards the :math:`i^\textrm{th}` and :math:`j^\textrm{th}` - components of :math:`\ux` taken around :math:`\ux = \muX`. It yields - to: - :math:`\left( \nabla^2 h(\muX,\muX) \right)_{ij} =\left( \frac{\partial^2 h(\ux,\ux)}{\partial x^i \partial x^j}\right)_{\ux\: =\: \muX}` -- :math:`<,>` is a scalar product between two vectors. +where :math:`\mat{C} \in \Rset^{n_X \times n_X}` is the input covariance matrix: -| **Approximation at the order 1 - Case** :math:`n_Y=1` +.. math:: - .. math:: + c_{ij} = \Expect{\left(X_i - \Expect{X_i}\right)\left(X_j - \Expect{X_j} \right)} - \Expect{Y} = h(\muX) +with :math:`c_{ii} = \sigma_i^2`. - .. math:: - \Var{Y} = \sum_{i,j=1}^{n_X} \frac{\partial h(\muX)}{\partial X^i} . \frac{\partial h(\muX)}{\partial X^j}.(\Cov \uX)_{ij} +Case 1: :math:`q=1`, :math:`Y = h(\vect{X}) \in \Rset` +------------------------------------------------------ -| **Approximation at the order 2 - Case** :math:`n_Y=1` +The second-order Taylor expansion of :math:`h` at the point :math:`\ux = \vect{\mu}` is: - .. math:: +.. math:: - \begin{aligned} - \begin{split} - \Expect{Y} = h(\muX) + \frac{1}{2}. \sum_{i,j=1}^{n_X} \frac{\partial^2 h(\muX,\muX)}{\partial x^i \partial x^j} . (\Cov \uX)_{ij} - \end{split} - \end{aligned} + y = h(\vect{\mu}) + \sum_{i = 1}^d \left( \frac{\partial h}{\partial x_i }\right)(\vect{\mu})(x_i-\mu_i) + + \frac{1}{2} \sum_{i,j = 1}^d \left(\frac{\partial^2 h}{\partial x_i \partial x_j}\right)(\vect{\mu}) + (x_i-\mu_i)(x_j-\mu_j) + o\left(\|\vect{x}\|^2\right). -| The decomposition of the variance at the order 2 is not implemented. - It requires both the knowledge of higher order derivatives of the model - and the knowledge of moments of order strictly greater than 2 of the pdf. -| **Case** :math:`n_Y>1` +The expectation and variance of the first-order expansion are: + .. math:: -| The perturbation approach can be developed at different orders - from the Taylor decomposition of the random vector :math:`\uY`. As - :math:`\uY=h(\uX)`, the Taylor decomposition around :math:`\ux = \muX` - at the second order yields to: + \Expect{Y} \approx h(\vect{\mu})\\ + \Var{Y} \approx \sum_{i=1}^{d} \sigma_i^2 \left(\left(\frac{\partial h}{\partial x_i} + \right)(\vect{\mu}) \right)^2 - .. math:: - \uY = h(\muX) + <\underline{\underline{\nabla}}h(\muX) , \: \uX - \muX> + \frac{1}{2}<<\underline{\underline{\underline{\nabla }}}^2 h(\muX,\: \underline{\mu}_{\:X}),\: \uX - \muX>,\: \uX - \muX> + o(\Cov \uX) +The expectation of the second-order expansion is: -where: + .. math:: -- :math:`\muX = \Expect{\uX}` is the vector of the input variables at - the mean values of each component. + \Expect{Y} \approx h (\vect{\mu}) + \frac{1}{2} \sum_{i,j=1}^{d} c_{ij}\left(\frac{\partial^2 h} + {\partial x_i \partial x_j}\right)(\vect{\mu}). -- :math:`\Cov \uX` is the covariance matrix of the random vector - :math:`\uX`. The elements are the followings : - :math:`(\Cov \uX)_{ij} = \Expect{\left(X^i - \Expect{X^i} \right)^2}` -- :math:`\underline{\underline{\nabla}} h(\muX) = \: ^t \left( \frac{\partial y^i}{\partial x^j}\right)_{\ux\: =\: \muX} = \: ^t \left( \frac{\partial h^i(\ux)}{\partial x^j}\right)_{\ux\: =\: \muX}` - is the transposed Jacobian matrix with :math:`i=1,\ldots,n_Y` and - :math:`j=1,\ldots,n_X`. +The second-order approximation of the variance is not implemented because it requires both the knowledge of higher +order derivatives of :math:`h` and the knowledge of moments of order strictly greater +than 2 of the distribution of :math:`\uX`. -- :math:`\underline{\underline{\underline{\nabla^2}}} h(\ux\:,\ux)` is - a tensor of order 3. It is composed by the second order derivative - towards the :math:`i^\textrm{th}` and :math:`j^\textrm{th}` - components of :math:`\ux` of the :math:`k^\textrm{th}` component of - the output vector :math:`h(\ux)`. It yields to: - :math:`\left( \nabla^2 h(\ux) \right)_{ijk} = \frac{\partial^2 (h^k(\ux))}{\partial x^i \partial x^j}` -- :math:`<\underline{\underline{\nabla}}h(\muX) , \: \uX - \muX> = \sum_{j=1}^{n_X} \left( \frac{\partial {\uy}}{\partial {x^j}}\right)_{\ux = \muX} . \left( X^j-\muX^j \right)` +Case 2: :math:`q>1`, :math:`Y =(Y_1, \dots, Y_q) \in \Rset^q` +------------------------------------------------------------- -- :math:`<<\underline{\underline{\underline{\nabla }}}^2 h(\muX,\: \underline{\mu}_{X}),\: \uX - \muX>,\: \uX - \muX> = - \left( ^t (\uX^i - \muX^i). \left(\frac{\partial^2 y^k}{\partial x^i \partial x^k}\right)_{\ux = \muX}. (\uX^j - \muX^j) \right)_{ijk}` +The second-order Taylor expansion of :math:`h = (h_1, \dots, h_q)` at the point +:math:`\ux = \vect{\mu}` for each marginal function :math:`h_k` is: -| **Approximation at the order 1 - Case** :math:`n_Y>1` +.. math:: - .. math:: + y_k = h_k(\vect{\mu}) + \sum_{i = 1}^d \left( \frac{\partial h_k}{\partial x_i }\right)(\vect{\mu}) + (x_i-\mu_i)+ \frac{1}{2} \sum_{i,j = 1}^d \left( \frac{\partial^2 h_k}{\partial x_i \partial + x_j}\right)(\vect{\mu})(x_i-\mu_i)(x_j-\mu_j) + o(\|\vect{x}\|^2). - \Expect{\uY} \approx \underline{h}(\muX) - Pay attention that :math:`\Expect{\uY}` is a vector. The - :math:`k^\textrm{th}` component of this vector is equal to the - :math:`k^\textrm{th}` component of the output vector computed by the - model :math:`h` at the mean value. :math:`\Expect{\uY}` is thus the - computation of the model at mean. +where :math:`1\leq k \leq q`. -.. math:: +The expectation and covariance matrix of the first-order expansion are: - \Cov \uY \approx ^t\underline{\underline{\nabla}}\:\underline{h}(\muX).\Cov \uX.\underline{\underline{\nabla}}\:\underline{h}(\muX) -| **Approximation at the order 2 - Case** :math:`n_Y>1` + .. math:: -.. math:: + \Expect{\uY} \approx h(\vect{\mu})\\ + \Cov \uY \approx \left( \sum_{i,j=1}^{d} c_{ij} \left( \frac{\partial h_k}{\partial x_i } + \right)(\vect{\mu})\left( \frac{\partial h_\ell}{\partial x_j }\right)(\vect{\mu})\right)_{k, + \ell} - \Expect{\uY} \approx \underline{h}(\muX) + \frac{1}{2}.\underline{\underline{\underline{\nabla}}}^2 \underline{\underline{h}}(\muX,\muX) \odot \Cov \uX -This last formulation is the reduced writing of the following -expression: +The expectation of the second-order expansion is: .. math:: - (\Expect{\uY})_k \approx (\underline{h}(\muX))_k + \left( \sum_{i=1}^{n_X}\frac{1}{2} (\Cov \uX)_{ii}.{(\nabla^2\:h(\uX))}_{iik} + \sum_{i=1}^{n_X} \sum_{j=1}^{i-1} (\Cov X)_{ij}.{(\nabla^2\:h(\uX))}_{ijk} \right)_k + (\Expect{\uY})_k \approx \Expect{Y_k} \approx h_k(\vect{\mu}) + \frac{1}{2} \sum_{i,j=1}^{d} c_{ij}\left( + \frac{\partial^2 h_k}{\partial x_i \partial x_j}\right)(\vect{\mu}) + + +The second-order approximation of the variance is not implemented because it requires both the +knowledge of higher order derivatives of :math:`h` and the knowledge of moments of order strictly greater +than 2 of the probability density function. -The decomposition of the variance at the order 2 is not implemented. -It requires both the knowledge of -higher order derivatives of the model and the knowledge of moments of -order strictly greater than 2 of the pdf. .. topic:: API: diff --git a/openturns/master/_sources/user_manual/response_surface/parametric_approximation.rst.txt b/openturns/master/_sources/user_manual/response_surface/parametric_approximation.rst.txt index 803eb69405e..280a1aee546 100644 --- a/openturns/master/_sources/user_manual/response_surface/parametric_approximation.rst.txt +++ b/openturns/master/_sources/user_manual/response_surface/parametric_approximation.rst.txt @@ -7,7 +7,7 @@ Response surface: Parametric approximation Taylor approximation ==================== -Refer to :ref:`taylor_expansion`. +Refer to :ref:`Taylor expansion `. .. autosummary:: :toctree: _generated/ diff --git a/openturns/master/auto_calibration/bayesian_calibration/plot_gibbs.html b/openturns/master/auto_calibration/bayesian_calibration/plot_gibbs.html index 99933484bd0..9bafab5aa30 100644 --- a/openturns/master/auto_calibration/bayesian_calibration/plot_gibbs.html +++ b/openturns/master/auto_calibration/bayesian_calibration/plot_gibbs.html @@ -245,7 +245,7 @@

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Total running time of the script: (0 minutes 6.231 seconds)

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