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b/openturns/master/_downloads/80fe3267b6620cf75a9db88be1d114e9/TruncatedOverMesh.py new file mode 100644 index 00000000000..782b2a72174 --- /dev/null +++ b/openturns/master/_downloads/80fe3267b6620cf75a9db88be1d114e9/TruncatedOverMesh.py @@ -0,0 +1,47 @@ +import openturns as ot +import openturns.experimental as otexp +from openturns.viewer import View + +ot.ResourceMap.SetAsUnsignedInteger("Distribution-DefaultIntegrationNodesNumber", 64) +ot.ResourceMap.SetAsUnsignedInteger("Mesh-LargeSize", 0) + +grid = ot.GridLayout(2, 2) +threshold = 0.2 +inVars = ["x1", "x2"] +formula = "sin(x1)*sin(x2)" +f = ot.SymbolicFunction(inVars, [formula]) +levelSet = ot.LevelSet(f, ot.Less(), threshold) +xMin = [-5.0] * 2 +xMax = [5.0] * 2 +box = ot.Interval(xMin, xMax) +mesh = ot.LevelSetMesher([51] * 2).build(levelSet, box, False) +pdf_2d = ot.Graph("Normal distribution over a mesh, PDF", "x1", "x2", True) +cdf_2d = ot.Graph("Normal distribution over a mesh, CDF", "x1", "x2", True) +dist = ot.Normal([0] * 2, [2] * 2) +distribution_2d = otexp.TruncatedOverMesh(dist, mesh) +mesh_g = mesh.draw() +mesh_g.setLegends([""]) +mesh_g.setTitle("Mesh of domain D={" + formula + "<=" + str(threshold) + "}") +mesh_g.setXTitle("x1") +mesh_g.setYTitle("x2") + +iso = f.draw(xMin, xMax) +iso.setTitle("Normal sample on D") +dr = iso.getDrawable(0) +dr.setLevels([threshold]) +iso.setDrawables([dr]) +iso.add(ot.Cloud(distribution_2d.getSample(1500))) +grid.setGraph(0, 0, mesh_g) +grid.setGraph(0, 1, iso) + +pdf_2d.add(distribution_2d.drawPDF(xMin, xMax)) +pdf_2d.setLegends([""]) +cdf_2d.add(distribution_2d.drawCDF(xMin, xMax, [41] * 2)) +cdf_2d.setLegends([""]) +grid.setGraph(1, 0, pdf_2d) +grid.setGraph(1, 1, cdf_2d) +grid.setTitle("TruncatedOverMesh") +grid.setLegendPosition("topright") +v = View(grid) +fig = v.getFigure() +fig.axes[1].legend(loc="best") diff --git a/openturns/master/_downloads/88d3828120a999fc8ca5897c5dd2db69/auto_graphs_python.zip 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    [0.184564]

    +

    [0.843059]



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

    [0.184564]

    +

    [0.843059]



    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 878ddbb602e..2deb9554676 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 @@ -6,20 +6,20 @@ Computation times ================= -**00:08.686** total execution time for **auto_numerical_methods_general_methods** files: +**00:08.378** total execution time for **auto_numerical_methods_general_methods** files: +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_ifs.py` (``plot_ifs.py``) | 00:07.606 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_ifs.py` (``plot_ifs.py``) | 00:07.382 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_sinus.py` (``plot_regression_sinus.py``) | 00:00.453 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_sinus.py` (``plot_regression_sinus.py``) | 00:00.390 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_pce_design.py` (``plot_pce_design.py``) | 00:00.393 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_pce_design.py` (``plot_pce_design.py``) | 00:00.373 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_estimate_integral_iterated_quadrature.py` (``plot_estimate_integral_iterated_quadrature.py``) | 00:00.130 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_estimate_integral_iterated_quadrature.py` (``plot_estimate_integral_iterated_quadrature.py``) | 00:00.129 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_interval.py` (``plot_regression_interval.py``) | 00:00.089 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_regression_interval.py` (``plot_regression_interval.py``) | 00:00.090 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_general_methods_plot_study_save_load.py` (``plot_study_save_load.py``) | 00:00.014 | 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_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 62ad1ecd3db..ba725e48711 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 ================= -**00:00.602** total execution time for **auto_numerical_methods_iterative_statistics** files: +**00:00.587** 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``) | 00:00.273 | 0.0 MB | +| :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_extrema.py` (``plot_iterative_extrema.py``) | 00:00.182 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_extrema.py` (``plot_iterative_extrema.py``) | 00:00.164 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_moments.py` (``plot_iterative_moments.py``) | 00:00.147 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_moments.py` (``plot_iterative_moments.py``) | 00:00.144 | 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 7af9ba517b8..03c77b2d3b5 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: 0.1419169760377995 - calls number: 6028 + event probability: 0.14246481290765534 + calls number: 5928 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 48139bdee3d..67da5d3158c 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
    -

    [0.124431,0.80366]

    +

    [0.124453,0.803588]



    @@ -974,7 +974,7 @@ Reset default settings .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 4.536 seconds) + **Total running time of the script:** (0 minutes 4.371 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 46133aeceb4..b2d68f71976 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^ = [2.82693,1.21154,0.5] - f(x^) = [9.11608e-24] - Iteration number: 10 - Evaluation number: 14 - Absolute error: 2.354434048876458e-06 - Relative error: 7.555978502116947e-07 - Residual error: 2.52374697952362e-11 + x^ = [3.0355,1.30093,0.5] + f(x^) = [3.06374e-27] + Iteration number: 7 + Evaluation number: 8 + Absolute error: 1.879043932354807e-07 + Relative error: 5.625602187319411e-08 + Residual error: 1.93598323593222e-14 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 9b4d0bb0bcf..737303b2ed2 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 @@ -6,24 +6,24 @@ Computation times ================= -**00:07.057** total execution time for **auto_numerical_methods_optimization** files: +**00:06.702** total execution time for **auto_numerical_methods_optimization** files: +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_ego.py` (``plot_ego.py``) | 00:04.536 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_ego.py` (``plot_ego.py``) | 00:04.371 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rastrigin.py` (``plot_optimization_rastrigin.py``) | 00:01.034 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rastrigin.py` (``plot_optimization_rastrigin.py``) | 00:00.973 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rosenbrock.py` (``plot_optimization_rosenbrock.py``) | 00:00.656 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_rosenbrock.py` (``plot_optimization_rosenbrock.py``) | 00:00.613 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_dlib.py` (``plot_optimization_dlib.py``) | 00:00.397 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_dlib.py` (``plot_optimization_dlib.py``) | 00:00.364 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_pagmo.py` (``plot_optimization_pagmo.py``) | 00:00.180 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_pagmo.py` (``plot_optimization_pagmo.py``) | 00:00.164 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_bonmin.py` (``plot_optimization_bonmin.py``) | 00:00.088 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_constraints.py` (``plot_optimization_constraints.py``) | 00:00.070 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_nlopt.py` (``plot_optimization_nlopt.py``) | 00:00.076 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_nlopt.py` (``plot_optimization_nlopt.py``) | 00:00.068 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_constraints.py` (``plot_optimization_constraints.py``) | 00:00.069 | 0.0 MB | +| :ref:`sphx_glr_auto_numerical_methods_optimization_plot_optimization_bonmin.py` (``plot_optimization_bonmin.py``) | 00:00.058 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_numerical_methods_optimization_plot_control_termination.py` (``plot_control_termination.py``) | 00:00.014 | 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 4148a611605..1e458eed17c 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 ================= -**00:00.417** total execution time for **auto_probabilistic_modeling_copulas** files: +**00:00.408** 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``) | 00:00.413 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_ordinal_sum_copula.py` (``plot_ordinal_sum_copula.py``) | 00:00.405 | 0.0 MB | +-----------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_copulas_plot_extract_copula.py` (``plot_extract_copula.py``) | 00:00.002 | 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``) | 00:00.002 | 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 75b7c85cf47..2d339e5c1a2 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 ================= -**00:07.405** total execution time for **auto_probabilistic_modeling_distributions** files: +**00:06.296** total execution time for **auto_probabilistic_modeling_distributions** files: +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_draw_multivariate_distributions.py` (``plot_create_draw_multivariate_distributions.py``) | 00:01.021 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_quick_start_guide_distributions.py` (``plot_quick_start_guide_distributions.py``) | 00:00.905 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_quick_start_guide_distributions.py` (``plot_quick_start_guide_distributions.py``) | 00:01.008 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_draw_multivariate_distributions.py` (``plot_create_draw_multivariate_distributions.py``) | 00:00.865 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_transformation.py` (``plot_distribution_transformation.py``) | 00:00.768 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_minimum_volume_level_sets.py` (``plot_minimum_volume_level_sets.py``) | 00:00.645 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_minimum_volume_level_sets.py` (``plot_minimum_volume_level_sets.py``) | 00:00.732 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_transformation.py` (``plot_distribution_transformation.py``) | 00:00.632 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_order_statistics_distribution.py` (``plot_order_statistics_distribution.py``) | 00:00.711 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_order_statistics_distribution.py` (``plot_order_statistics_distribution.py``) | 00:00.558 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_truncated_distribution.py` (``plot_truncated_distribution.py``) | 00:00.494 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_truncated_distribution.py` (``plot_truncated_distribution.py``) | 00:00.393 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_overview_univariate_distributions.py` (``plot_overview_univariate_distributions.py``) | 00:00.424 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_overview_univariate_distributions.py` (``plot_overview_univariate_distributions.py``) | 00:00.379 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_extreme_value_distribution.py` (``plot_create_extreme_value_distribution.py``) | 00:00.333 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_manipulation.py` (``plot_distribution_manipulation.py``) | 00:00.291 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_and_draw_scalar_distributions.py` (``plot_create_and_draw_scalar_distributions.py``) | 00:00.304 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_extreme_value_distribution.py` (``plot_create_extreme_value_distribution.py``) | 00:00.273 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_random_mixture.py` (``plot_create_random_mixture.py``) | 00:00.299 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_and_draw_scalar_distributions.py` (``plot_create_and_draw_scalar_distributions.py``) | 00:00.253 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_distribution_manipulation.py` (``plot_distribution_manipulation.py``) | 00:00.296 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_random_mixture.py` (``plot_create_random_mixture.py``) | 00:00.244 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_bayes_distribution.py` (``plot_bayes_distribution.py``) | 00:00.221 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_bayes_distribution.py` (``plot_bayes_distribution.py``) | 00:00.193 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_mixture_distribution.py` (``plot_mixture_distribution.py``) | 00:00.220 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_mixture_distribution.py` (``plot_mixture_distribution.py``) | 00:00.187 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_generate_by_inversion.py` (``plot_generate_by_inversion.py``) | 00:00.182 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_generate_by_inversion.py` (``plot_generate_by_inversion.py``) | 00:00.160 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_python_distribution.py` (``plot_python_distribution.py``) | 00:00.117 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_python_distribution.py` (``plot_python_distribution.py``) | 00:00.104 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_conditional_distribution.py` (``plot_conditional_distribution.py``) | 00:00.113 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_conditional_distribution.py` (``plot_conditional_distribution.py``) | 00:00.088 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_maximum_distribution.py` (``plot_maximum_distribution.py``) | 00:00.081 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_your_own_dist.py` (``plot_create_your_own_dist.py``) | 00:00.063 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_create_your_own_dist.py` (``plot_create_your_own_dist.py``) | 00:00.077 | 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_conditional_random_vector.py` (``plot_conditional_random_vector.py``) | 00:00.001 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_distributions_plot_conditional_random_vector.py` (``plot_conditional_random_vector.py``) | 00:00.002 | 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 8fa19099b91..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 @@ -6,7 +6,7 @@ Computation times ================= -**00:00.006** 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_random_vector_manipulation.py` (``plot_random_vector_manipulation.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 723d785b114..68ab84a8f53 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 @@ -388,7 +388,7 @@ Display figures .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.053 seconds) + **Total running time of the script:** (0 minutes 2.134 seconds) .. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_create_mesh.py: 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 e35d95d89cb..71bfbf01498 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 2.378 seconds) + **Total running time of the script:** (0 minutes 2.145 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 7d602101e87..8d8b304f6c1 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 2.521 seconds) + **Total running time of the script:** (0 minutes 2.226 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 919c3d95b25..06ad716f6ba 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 @@ -6,52 +6,52 @@ Computation times ================= -**00:13.839** total execution time for **auto_probabilistic_modeling_stochastic_processes** files: +**00:12.813** total execution time for **auto_probabilistic_modeling_stochastic_processes** files: +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py` (``plot_userdefined_covariance_model.py``) | 00:02.521 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py` (``plot_userdefined_covariance_model.py``) | 00:02.226 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_covariance_hmat.py` (``plot_gaussian_process_covariance_hmat.py``) | 00:02.378 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_covariance_hmat.py` (``plot_gaussian_process_covariance_hmat.py``) | 00:02.145 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_mesh.py` (``plot_create_mesh.py``) | 00:02.053 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_mesh.py` (``plot_create_mesh.py``) | 00:02.134 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_field_manipulation.py` (``plot_field_manipulation.py``) | 00:01.744 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_field_manipulation.py` (``plot_field_manipulation.py``) | 00:01.653 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_box_cox_transform.py` (``plot_box_cox_transform.py``) | 00:01.084 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_box_cox_transform.py` (``plot_box_cox_transform.py``) | 00:01.016 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_processes_comparison.py` (``plot_gaussian_processes_comparison.py``) | 00:00.800 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_processes_comparison.py` (``plot_gaussian_processes_comparison.py``) | 00:00.705 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_process_manipulation.py` (``plot_process_manipulation.py``) | 00:00.521 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_process_manipulation.py` (``plot_process_manipulation.py``) | 00:00.447 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_discrete_markov_chain_process.py` (``plot_discrete_markov_chain_process.py``) | 00:00.448 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_random_walk_process.py` (``plot_random_walk_process.py``) | 00:00.312 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_random_walk_process.py` (``plot_random_walk_process.py``) | 00:00.307 | 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``) | 00:00.301 | 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``) | 00:00.302 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_discrete_markov_chain_process.py` (``plot_discrete_markov_chain_process.py``) | 00:00.292 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_kronecker_covmodel.py` (``plot_kronecker_covmodel.py``) | 00:00.275 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_kronecker_covmodel.py` (``plot_kronecker_covmodel.py``) | 00:00.264 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_white_noise_process.py` (``plot_white_noise_process.py``) | 00:00.174 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_mix_rv_process.py` (``plot_mix_rv_process.py``) | 00:00.190 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_add_trend.py` (``plot_add_trend.py``) | 00:00.169 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_white_noise_process.py` (``plot_white_noise_process.py``) | 00:00.161 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_export_field_vtk.py` (``plot_export_field_vtk.py``) | 00:00.166 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_normal_process.py` (``plot_create_normal_process.py``) | 00:00.142 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_mix_rv_process.py` (``plot_mix_rv_process.py``) | 00:00.164 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_add_trend.py` (``plot_add_trend.py``) | 00:00.134 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_trend_transform.py` (``plot_trend_transform.py``) | 00:00.132 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_export_field_vtk.py` (``plot_export_field_vtk.py``) | 00:00.132 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_create_normal_process.py` (``plot_create_normal_process.py``) | 00:00.131 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_trend_transform.py` (``plot_trend_transform.py``) | 00:00.123 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_aggregated_process.py` (``plot_aggregated_process.py``) | 00:00.125 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_timeseries_manipulation.py` (``plot_timeseries_manipulation.py``) | 00:00.119 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_timeseries_manipulation.py` (``plot_timeseries_manipulation.py``) | 00:00.123 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_aggregated_process.py` (``plot_aggregated_process.py``) | 00:00.111 | 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_user_stationary_covmodel.py` (``plot_user_stationary_covmodel.py``) | 00:00.072 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_user_stationary_covmodel.py` (``plot_user_stationary_covmodel.py``) | 00:00.067 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_functional_basis_process.py` (``plot_functional_basis_process.py``) | 00:00.071 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_spectral_model.py` (``plot_userdefined_spectral_model.py``) | 00:00.066 | 0.0 MB | +| :ref:`sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_spectral_model.py` (``plot_userdefined_spectral_model.py``) | 00:00.061 | 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 | +--------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ 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 2bad092375f..7cf34467f5b 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 ================= -**00:00.614** total execution time for **auto_reliability_sensitivity_central_dispersion** files: +**00:00.642** 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``) | 00:00.437 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_expectation_simulation_algorithm.py` (``plot_expectation_simulation_algorithm.py``) | 00:00.466 | 0.0 MB | +---------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_central_tendency.py` (``plot_central_tendency.py``) | 00:00.129 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_central_dispersion_plot_central_tendency.py` (``plot_central_tendency.py``) | 00:00.128 | 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 | +---------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ 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 d4bfc78b7cc..f18e9610d97 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 2.125 seconds) + **Total running time of the script:** (0 minutes 2.056 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 7dc624ba54b..591947fe319 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 7.426 seconds) + **Total running time of the script:** (0 minutes 7.336 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 83db6d658f1..dadee48b877 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 @@ -6,38 +6,38 @@ Computation times ================= -**00:14.810** total execution time for **auto_reliability_sensitivity_design_of_experiments** files: +**00:14.485** 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``) | 00:07.426 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_quadrature.py` (``plot_smolyak_quadrature.py``) | 00:07.336 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_experiment.py` (``plot_smolyak_experiment.py``) | 00:02.125 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_experiment.py` (``plot_smolyak_experiment.py``) | 00:02.056 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_plot_design.py` (``plot_plot_design.py``) | 00:01.302 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_plot_design.py` (``plot_plot_design.py``) | 00:01.241 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiments.py` (``plot_design_of_experiments.py``) | 00:01.070 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiments.py` (``plot_design_of_experiments.py``) | 00:01.026 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_low_discrepancy_sequence.py` (``plot_low_discrepancy_sequence.py``) | 00:00.566 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_low_discrepancy_sequence.py` (``plot_low_discrepancy_sequence.py``) | 00:00.548 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_merge.py` (``plot_smolyak_merge.py``) | 00:00.471 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_merge.py` (``plot_smolyak_merge.py``) | 00:00.464 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_optimal_lhs.py` (``plot_optimal_lhs.py``) | 00:00.468 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_optimal_lhs.py` (``plot_optimal_lhs.py``) | 00:00.463 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_deterministic_doe.py` (``plot_create_deterministic_doe.py``) | 00:00.293 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_deterministic_doe.py` (``plot_create_deterministic_doe.py``) | 00:00.285 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_deterministic_design.py` (``plot_deterministic_design.py``) | 00:00.268 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_deterministic_design.py` (``plot_deterministic_design.py``) | 00:00.262 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_indices.py` (``plot_smolyak_indices.py``) | 00:00.236 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_smolyak_indices.py` (``plot_smolyak_indices.py``) | 00:00.232 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_mixed_design.py` (``plot_mixed_design.py``) | 00:00.133 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_mixed_design.py` (``plot_mixed_design.py``) | 00:00.129 | 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``) | 00:00.119 | 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``) | 00:00.117 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_create_random_doe.py` (``plot_create_random_doe.py``) | 00:00.115 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_gauss_product_experiment.py` (``plot_gauss_product_experiment.py``) | 00:00.058 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_gauss_product_experiment.py` (``plot_gauss_product_experiment.py``) | 00:00.056 | 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_probabilistic_design.py` (``plot_probabilistic_design.py``) | 00:00.055 | 0.0 MB | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_composite_experiment.py` (``plot_composite_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 0c212c24601..fc6e13987ad 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 2.039 seconds) + **Total running time of the script:** (0 minutes 2.107 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 3d769b95cb3..66403b351d7 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 5.902 seconds) + **Total running time of the script:** (0 minutes 5.173 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_estimate_probability_form_oscillator.py: diff --git a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_proba_system_event.rst.txt b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_proba_system_event.rst.txt index 88e7a4b2f60..6e20892ffeb 100644 --- a/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_proba_system_event.rst.txt +++ b/openturns/master/_sources/auto_reliability_sensitivity/reliability/plot_proba_system_event.rst.txt @@ -387,7 +387,7 @@ Draw the graphs! .. rst-class:: sphx-glr-timing - **Total running time of the script:** (0 minutes 2.251 seconds) + **Total running time of the script:** (0 minutes 2.200 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_proba_system_event.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 0dc1e160558..001d1aa261a 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 ================= -**00:18.694** total execution time for **auto_reliability_sensitivity_reliability** files: +**00:17.966** 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``) | 00:05.902 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form_oscillator.py` (``plot_estimate_probability_form_oscillator.py``) | 00:05.173 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_proba_system_event.py` (``plot_proba_system_event.py``) | 00:02.251 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_proba_system_event.py` (``plot_proba_system_event.py``) | 00:02.200 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_adaptive_directional_sampling.py` (``plot_estimate_probability_adaptive_directional_sampling.py``) | 00:02.039 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_adaptive_directional_sampling.py` (``plot_estimate_probability_adaptive_directional_sampling.py``) | 00:02.107 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_crossentropy.py` (``plot_crossentropy.py``) | 00:01.495 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_crossentropy.py` (``plot_crossentropy.py``) | 00:01.433 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_form_explained.py` (``plot_form_explained.py``) | 00:00.809 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py` (``plot_estimate_probability_randomized_qmc.py``) | 00:00.819 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py` (``plot_estimate_probability_randomized_qmc.py``) | 00:00.804 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_form_explained.py` (``plot_form_explained.py``) | 00:00.804 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_subset_sampling.py` (``plot_subset_sampling.py``) | 00:00.722 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_subset_sampling.py` (``plot_subset_sampling.py``) | 00:00.743 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_domain_event.py` (``plot_create_domain_event.py``) | 00:00.633 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_directional_sampling.py` (``plot_estimate_probability_directional_sampling.py``) | 00:00.629 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_event_system.py` (``plot_event_system.py``) | 00:00.630 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_event_system.py` (``plot_event_system.py``) | 00:00.620 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_directional_sampling.py` (``plot_estimate_probability_directional_sampling.py``) | 00:00.614 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_create_domain_event.py` (``plot_create_domain_event.py``) | 00:00.619 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam.py` (``plot_axial_stressed_beam.py``) | 00:00.522 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam.py` (``plot_axial_stressed_beam.py``) | 00:00.515 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_multi_form.py` (``plot_multi_form.py``) | 00:00.489 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_multi_form.py` (``plot_multi_form.py``) | 00:00.495 | 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``) | 00:00.455 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam_quickstart.py` (``plot_axial_stressed_beam_quickstart.py``) | 00:00.387 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_axial_stressed_beam_quickstart.py` (``plot_axial_stressed_beam_quickstart.py``) | 00:00.384 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form.py` (``plot_estimate_probability_form.py``) | 00:00.351 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_form.py` (``plot_estimate_probability_form.py``) | 00:00.349 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_importance_sampling.py` (``plot_estimate_probability_importance_sampling.py``) | 00:00.150 | 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_probability_simulation_results.py` (``plot_probability_simulation_results.py``) | 00:00.137 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_results.py` (``plot_probability_simulation_results.py``) | 00:00.142 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ | :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_flood_model.py` (``plot_flood_model.py``) | 00:00.117 | 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``) | 00:00.083 | 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_estimate_probability_lhs.py` (``plot_estimate_probability_lhs.py``) | 00:00.040 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_monte_carlo.py` (``plot_estimate_probability_monte_carlo.py``) | 00:00.032 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_parametrization.py` (``plot_probability_simulation_parametrization.py``) | 00:00.037 | 0.0 MB | +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_parametrization.py` (``plot_probability_simulation_parametrization.py``) | 00:00.032 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_monte_carlo.py` (``plot_estimate_probability_monte_carlo.py``) | 00:00.033 | 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``) | 00:00.007 | 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_strong_maximum_test.py` (``plot_strong_maximum_test.py``) | 00:00.005 | 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 d35fa300720..de34d08862c 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 6.974 seconds) + **Total running time of the script:** (0 minutes 6.458 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 3c717c2adb8..13a2dffa463 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 ================= -**00:07.206** total execution time for **auto_reliability_sensitivity_reliability_processes** files: +**00:06.637** 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``) | 00:06.974 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_field_fca_sobol.py` (``plot_field_fca_sobol.py``) | 00:06.458 | 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``) | 00:00.230 | 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``) | 00:00.177 | 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 462578d97b3..9165c6af93f 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 5.914 seconds) + **Total running time of the script:** (0 minutes 5.528 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 e75bda3e675..f4da8657e39 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 ================= -**00:09.307** total execution time for **auto_reliability_sensitivity_sensitivity_analysis** files: +**00:08.513** 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``) | 00:05.914 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_wingweight.py` (``plot_sensitivity_wingweight.py``) | 00:05.528 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_functional_chaos_sensitivity.py` (``plot_functional_chaos_sensitivity.py``) | 00:00.962 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_functional_chaos_sensitivity.py` (``plot_functional_chaos_sensitivity.py``) | 00:00.846 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_par_coo.py` (``plot_sensitivity_par_coo.py``) | 00:00.881 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_par_coo.py` (``plot_sensitivity_par_coo.py``) | 00:00.731 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_hsic_estimators_ishigami.py` (``plot_hsic_estimators_ishigami.py``) | 00:00.750 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_hsic_estimators_ishigami.py` (``plot_hsic_estimators_ishigami.py``) | 00:00.703 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol.py` (``plot_sensitivity_sobol.py``) | 00:00.474 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol.py` (``plot_sensitivity_sobol.py``) | 00:00.412 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_ancova.py` (``plot_sensitivity_ancova.py``) | 00:00.131 | 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_sobol_multivariate.py` (``plot_sensitivity_sobol_multivariate.py``) | 00:00.114 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_sobol_multivariate.py` (``plot_sensitivity_sobol_multivariate.py``) | 00:00.097 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_fast.py` (``plot_sensitivity_fast.py``) | 00:00.080 | 0.0 MB | +| :ref:`sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_fast.py` (``plot_sensitivity_fast.py``) | 00:00.078 | 0.0 MB | +-------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/openturns/master/_sources/bibliography.rst.txt b/openturns/master/_sources/bibliography.rst.txt index aabff29fe4f..77fd2f13835 100644 --- a/openturns/master/_sources/bibliography.rst.txt +++ b/openturns/master/_sources/bibliography.rst.txt @@ -113,6 +113,9 @@ Bibliography .. [gamboa2013] Gamboa, F., Janon, A., Klein, T. & Lagnoux, A. *Sensitivity analysis for multidimensional and functional outputs.* 2013. `pdf `__ +.. [genz2003] Genz A., Cools R., *An adaptive numerical cubature algorithm for simplices*, + ACM Transactions on Mathematical Software 29(3):297-308, September 2003 + `pdf `__ .. [gerstner1998] Gerstner, T., & Griebel, M. (1998). *Numerical integration using sparse grids.* Numerical algorithms, 18 (3), 209-232. `pdf `__ diff --git a/openturns/master/_sources/user_manual/_generated/openturns.experimental.SimplicialCubature.rst.txt b/openturns/master/_sources/user_manual/_generated/openturns.experimental.SimplicialCubature.rst.txt new file mode 100644 index 00000000000..a960d624d65 --- /dev/null +++ b/openturns/master/_sources/user_manual/_generated/openturns.experimental.SimplicialCubature.rst.txt @@ -0,0 +1,14 @@ +SimplicialCubature +========================================= + +.. currentmodule:: openturns.experimental + +.. autoclass:: SimplicialCubature + + + .. automethod:: __init__ + + + +.. minigallery:: openturns.experimental.SimplicialCubature + :add-heading: Examples using the class \ No newline at end of file diff --git a/openturns/master/_sources/user_manual/_generated/openturns.experimental.TruncatedOverMesh.rst.txt b/openturns/master/_sources/user_manual/_generated/openturns.experimental.TruncatedOverMesh.rst.txt new file mode 100644 index 00000000000..cc6dd121a3e --- /dev/null +++ b/openturns/master/_sources/user_manual/_generated/openturns.experimental.TruncatedOverMesh.rst.txt @@ -0,0 +1,16 @@ +TruncatedOverMesh +======================================== + +.. plot:: pyplots/TruncatedOverMesh.py + :include-source: False + +.. currentmodule:: openturns.experimental + +.. autoclass:: TruncatedOverMesh + + + .. automethod:: __init__ + + +.. minigallery:: openturns.experimental.TruncatedOverMesh + :add-heading: Examples using the class \ No newline at end of file diff --git a/openturns/master/_sources/user_manual/integration.rst.txt b/openturns/master/_sources/user_manual/integration.rst.txt index 12c26189a40..26ae2e3595c 100644 --- a/openturns/master/_sources/user_manual/integration.rst.txt +++ b/openturns/master/_sources/user_manual/integration.rst.txt @@ -10,6 +10,7 @@ Integration IntegrationAlgorithm FilonQuadrature + experimental.SimplicialCubature .. autosummary:: :toctree: _generated/ diff --git a/openturns/master/_sources/user_manual/probabilistic_modelling.rst.txt b/openturns/master/_sources/user_manual/probabilistic_modelling.rst.txt index f7d30342c09..3021977f832 100644 --- a/openturns/master/_sources/user_manual/probabilistic_modelling.rst.txt +++ b/openturns/master/_sources/user_manual/probabilistic_modelling.rst.txt @@ -82,6 +82,11 @@ Continuous parametric distributions Trapezoidal Triangular TruncatedNormal + + :template: classWithPlot.rst_t + experimental.TruncatedOverMesh + + :template: Distribution.rst_t Uniform :template: classWithPlot.rst_t diff --git a/openturns/master/auto_calibration/bayesian_calibration/plot_gibbs.html b/openturns/master/auto_calibration/bayesian_calibration/plot_gibbs.html index c4b38337ed6..a44b31cbfb3 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 @@

    Quick search

    View.ShowAll() -Posterior density

    Total running time of the script: (0 minutes 12.523 seconds)

    +Posterior density

    Total running time of the script: (0 minutes 11.922 seconds)

     -Bayesian inference (with log-pdf)

    Total running time of the script: (0 minutes 5.970 seconds)

    +Bayesian inference (with log-pdf)

    Total running time of the script: (0 minutes 5.532 seconds)

     + +
    + + + + + \ No newline at end of file diff --git a/openturns/master/user_manual/_generated/openturns.experimental.TruncatedOverMesh.html b/openturns/master/user_manual/_generated/openturns.experimental.TruncatedOverMesh.html new file mode 100644 index 00000000000..0cb07176bcc --- /dev/null +++ b/openturns/master/user_manual/_generated/openturns.experimental.TruncatedOverMesh.html @@ -0,0 +1,4300 @@ + + + + + + + + + TruncatedOverMesh — OpenTURNS 1.22dev documentation + + + + + + + + + + + + + + + + + + + + + + + + + +
    + + +

    + + OpenTURNS +

    +

    An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

    +     +
    + + + + +
    +
    +
    +
    + +
    +

    TruncatedOverMesh

    +

    (Source code, png)

    +
    +../../_images/TruncatedOverMesh.png +
    +
    +
    +class TruncatedOverMesh(*args)
    +

    Truncated distribution over a mesh.

    +
    +

    Warning

    +

    This class is experimental and likely to be modified in future releases. +To use it, import the openturns.experimental submodule.

    +
    +
    +
    Parameters:
    +
    +
    distDistribution

    Distribution to truncate

    +
    +
    meshMesh

    Mesh defining the domain of the distribution.

    +
    +
    +
    +
    +

    Notes

    +

    Its probability density function is defined as:

    +
    +

    f_X(x) = \frac{1}{|\cD|}, \quad x \in \cD

    +

    with \cD\subset\Rset^n a mesh of dimension n.

    +

    Examples

    +

    Create a distribution:

    +
    >>> import openturns as ot
+>>> import openturns.experimental as otexp
+>>> f = ot.SymbolicFunction(['x', 'y'], ['sin(x) * sin(y)'])
+>>> levelSet = ot.LevelSet(f, ot.Less(), 0.2)
+>>> box = ot.Interval([-5.0] * 2, [5.0] * 2)
+>>> mesh = ot.LevelSetMesher([50]*2).build(levelSet, box, False)
+>>> dist = ot.Normal([0] * 2, [2] * 2)
+>>> distribution = otexp.TruncatedOverMesh(dist, mesh)
+
    +
    +

    Draw a sample:

    +
    >>> sample = distribution.getSample(5)
+
    +
    +

    Methods

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    abs()

    Transform distribution by absolute value function.

    acos()

    Transform distribution by arccosine function.

    acosh()

    Transform distribution by acosh function.

    asin()

    Transform distribution by arcsine function.

    asinh()

    Transform distribution by asinh function.

    atan()

    Transform distribution by arctangent function.

    atanh()

    Transform distribution by atanh function.

    cbrt()

    Transform distribution by cubic root function.

    computeBilateralConfidenceInterval(prob)

    Compute a bilateral confidence interval.

    computeBilateralConfidenceIntervalWithMarginalProbability(prob)

    Compute a bilateral confidence interval.

    computeCDF(*args)

    Compute the cumulative distribution function.

    computeCDFGradient(*args)

    Compute the gradient of the cumulative distribution function.

    computeCharacteristicFunction(*args)

    Compute the characteristic function.

    computeComplementaryCDF(*args)

    Compute the complementary cumulative distribution function.

    computeConditionalCDF(*args)

    Compute the conditional cumulative distribution function.

    computeConditionalDDF(x, y)

    Compute the conditional derivative density function of the last component.

    computeConditionalPDF(*args)

    Compute the conditional probability density function.

    computeConditionalQuantile(*args)

    Compute the conditional quantile function of the last component.

    computeDDF(*args)

    Compute the derivative density function.

    computeDensityGenerator(betaSquare)

    Compute the density generator.

    computeDensityGeneratorDerivative(betaSquare)

    Compute the first-order derivative of the probability density function.

    computeDensityGeneratorSecondDerivative(...)

    Compute the second-order derivative of the probability density function.

    computeEntropy()

    Compute the entropy of the distribution.

    computeGeneratingFunction(*args)

    Compute the probability-generating function.

    computeInverseSurvivalFunction(point)

    Compute the inverse survival function.

    computeLogCharacteristicFunction(*args)

    Compute the logarithm of the characteristic function.

    computeLogGeneratingFunction(*args)

    Compute the logarithm of the probability-generating function.

    computeLogPDF(*args)

    Compute the logarithm of the probability density function.

    computeLogPDFGradient(*args)

    Compute the gradient of the log probability density function.

    computeLowerExtremalDependenceMatrix()

    Compute the lower extremal dependence coefficients.

    computeLowerTailDependenceMatrix()

    Compute the lower tail dependence coefficients.

    computeMinimumVolumeInterval(prob)

    Compute the confidence interval with minimum volume.

    computeMinimumVolumeIntervalWithMarginalProbability(prob)

    Compute the confidence interval with minimum volume.

    computeMinimumVolumeLevelSet(prob)

    Compute the confidence domain with minimum volume.

    computeMinimumVolumeLevelSetWithThreshold(prob)

    Compute the confidence domain with minimum volume.

    computePDF(*args)

    Compute the probability density function.

    computePDFGradient(*args)

    Compute the gradient of the probability density function.

    computeProbability(interval)

    Compute the interval probability.

    computeQuantile(*args)

    Compute the quantile function.

    computeRadialDistributionCDF(radius[, tail])

    Compute the cumulative distribution function of the squared radius.

    computeScalarQuantile(prob[, tail])

    Compute the quantile function for univariate distributions.

    computeSequentialConditionalCDF(x)

    Compute the sequential conditional cumulative distribution functions.

    computeSequentialConditionalDDF(x)

    Compute the sequential conditional derivative density function.

    computeSequentialConditionalPDF(x)

    Compute the sequential conditional probability density function.

    computeSequentialConditionalQuantile(q)

    Compute the conditional quantile function of the last component.

    computeSurvivalFunction(*args)

    Compute the survival function.

    computeUnilateralConfidenceInterval(prob[, tail])

    Compute a unilateral confidence interval.

    computeUnilateralConfidenceIntervalWithMarginalProbability(...)

    Compute a unilateral confidence interval.

    computeUpperExtremalDependenceMatrix()

    Compute the upper extremal dependence coefficients.

    computeUpperTailDependenceMatrix()

    Compute the upper tail dependence coefficients.

    cos()

    Transform distribution by cosine function.

    cosh()

    Transform distribution by cosh function.

    drawCDF(*args)

    Draw the cumulative distribution function.

    drawLogPDF(*args)

    Draw the graph or of iso-lines of log-probability density function.

    drawLowerExtremalDependenceFunction()

    Draw the lower extremal dependence function.

    drawLowerTailDependenceFunction()

    Draw the lower tail dependence function.

    drawMarginal1DCDF(marginalIndex, xMin, xMax, ...)

    Draw the cumulative distribution function of a margin.

    drawMarginal1DLogPDF(marginalIndex, xMin, ...)

    Draw the log-probability density function of a margin.

    drawMarginal1DPDF(marginalIndex, xMin, xMax, ...)

    Draw the probability density function of a margin.

    drawMarginal1DSurvivalFunction(...[, logScale])

    Draw the cumulative distribution function of a margin.

    drawMarginal2DCDF(firstMarginal, ...[, ...])

    Draw the cumulative distribution function of a couple of margins.

    drawMarginal2DLogPDF(firstMarginal, ...[, ...])

    Draw the log-probability density function of a couple of margins.

    drawMarginal2DPDF(firstMarginal, ...[, ...])

    Draw the probability density function of a couple of margins.

    drawMarginal2DSurvivalFunction(...[, ...])

    Draw the cumulative distribution function of a couple of margins.

    drawPDF(*args)

    Draw the graph or of iso-lines of probability density function.

    drawQuantile(*args)

    Draw the quantile function.

    drawSurvivalFunction(*args)

    Draw the cumulative distribution function.

    drawUpperExtremalDependenceFunction()

    Draw the upper extremal dependence function.

    drawUpperTailDependenceFunction()

    Draw the upper tail dependence function.

    exp()

    Transform distribution by exponential function.

    getCDFEpsilon()

    Accessor to the CDF computation precision.

    getCentralMoment(n)

    Accessor to the componentwise central moments.

    getCholesky()

    Accessor to the Cholesky factor of the covariance matrix.

    getClassName()

    Accessor to the object's name.

    getCopula()

    Accessor to the copula of the distribution.

    getCorrelation()

    Accessor to the correlation matrix.

    getCovariance()

    Accessor to the covariance matrix.

    getDescription()

    Accessor to the componentwise description.

    getDimension()

    Accessor to the dimension of the distribution.

    getDispersionIndicator()

    Dispersion indicator accessor.

    getId()

    Accessor to the object's id.

    getIntegrationNodesNumber()

    Accessor to the number of Gauss integration points.

    getInverseCholesky()

    Accessor to the inverse Cholesky factor of the covariance matrix.

    getInverseIsoProbabilisticTransformation()

    Accessor to the inverse iso-probabilistic transformation.

    getIsoProbabilisticTransformation()

    Accessor to the iso-probabilistic transformation.

    getKendallTau()

    Accessor to the Kendall coefficients matrix.

    getKurtosis()

    Accessor to the componentwise kurtosis.

    getMarginal(*args)

    Accessor to marginal distributions.

    getMean()

    Accessor to the mean.

    getMesh()

    Accessor to the distribution's mesh.

    getMoment(n)

    Accessor to the componentwise moments.

    getName()

    Accessor to the object's name.

    getPDFEpsilon()

    Accessor to the PDF computation precision.

    getParameter()

    Accessor to the parameter of the distribution.

    getParameterDescription()

    Accessor to the parameter description of the distribution.

    getParameterDimension()

    Accessor to the number of parameters in the distribution.

    getParametersCollection()

    Accessor to the parameter of the distribution.

    getPearsonCorrelation()

    Accessor to the Pearson correlation matrix.

    getPositionIndicator()

    Position indicator accessor.

    getProbabilities()

    Accessor to the discrete probability levels.

    getRange()

    Accessor to the range of the distribution.

    getRealization()

    Accessor to a pseudo-random realization from the distribution.

    getRoughness()

    Accessor to roughness of the distribution.

    getSample(size)

    Accessor to a pseudo-random sample from the distribution.

    getSampleByInversion(size)

    Accessor to a pseudo-random sample from the distribution.

    getSampleByQMC(size)

    Accessor to a low discrepancy sample from the distribution.

    getShadowedId()

    Accessor to the object's shadowed id.

    getShapeMatrix()

    Accessor to the shape matrix of the underlying copula if it is elliptical.

    getShiftedMoment(n, shift)

    Accessor to the componentwise shifted moments.

    getSingularities()

    Accessor to the singularities of the PDF function.

    getSkewness()

    Accessor to the componentwise skewness.

    getSpearmanCorrelation()

    Accessor to the Spearman correlation matrix.

    getStandardDeviation()

    Accessor to the componentwise standard deviation.

    getStandardDistribution()

    Accessor to the standard distribution.

    getStandardRepresentative()

    Accessor to the standard representative distribution in the parametric family.

    getSupport(*args)

    Accessor to the support of the distribution.

    getVisibility()

    Accessor to the object's visibility state.

    hasEllipticalCopula()

    Test whether the copula of the distribution is elliptical or not.

    hasIndependentCopula()

    Test whether the copula of the distribution is the independent one.

    hasName()

    Test if the object is named.

    hasVisibleName()

    Test if the object has a distinguishable name.

    inverse()

    Transform distribution by inverse function.

    isContinuous()

    Test whether the distribution is continuous or not.

    isCopula()

    Test whether the distribution is a copula or not.

    isDiscrete()

    Test whether the distribution is discrete or not.

    isElliptical()

    Test whether the distribution is elliptical or not.

    isIntegral()

    Test whether the distribution is integer-valued or not.

    ln()

    Transform distribution by natural logarithm function.

    log()

    Transform distribution by natural logarithm function.

    setDescription(description)

    Accessor to the componentwise description.

    setIntegrationNodesNumber(integrationNodesNumber)

    Accessor to the number of Gauss integration points.

    setMesh(mesh)

    Accessor to the distribution's mesh.

    setName(name)

    Accessor to the object's name.

    setParameter(parameters)

    Accessor to the parameter of the distribution.

    setParametersCollection(*args)

    Accessor to the parameter of the distribution.

    setShadowedId(id)

    Accessor to the object's shadowed id.

    setVisibility(visible)

    Accessor to the object's visibility state.

    sin()

    Transform distribution by sine function.

    sinh()

    Transform distribution by sinh function.

    sqr()

    Transform distribution by square function.

    sqrt()

    Transform distribution by square root function.

    tan()

    Transform distribution by tangent function.

    tanh()

    Transform distribution by tanh function.

    +
    +
    +__init__(*args)
    +
    + +
    +
    +abs()
    +

    Transform distribution by absolute value function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +acos()
    +

    Transform distribution by arccosine function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +acosh()
    +

    Transform distribution by acosh function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +asin()
    +

    Transform distribution by arcsine function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +asinh()
    +

    Transform distribution by asinh function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +atan()
    +

    Transform distribution by arctangent function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +atanh()
    +

    Transform distribution by atanh function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +cbrt()
    +

    Transform distribution by cubic root function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +computeBilateralConfidenceInterval(prob)
    +

    Compute a bilateral confidence interval.

    +
    +
    Parameters:
    +
    +
    alphafloat, \alpha \in [0,1]

    The confidence level.

    +
    +
    +
    +
    Returns:
    +
    +
    confIntervalInterval

    The confidence interval of level \alpha.

    +
    +
    +
    +
    +

    Notes

    +

    We consider an absolutely continuous measure \mu with density function p.

    +

    The bilateral confidence interval I^*_{\alpha} is the cartesian product I^*_{\alpha} = [a_1, b_1] \times \dots \times [a_d, b_d] where a_i = F_i^{-1}((1-\beta)/2) and b_i = F_i^{-1}((1+\beta)/2) for all i and which verifies \mu(I^*_{\alpha}) = \alpha.

    +

    Examples

    +

    Create a sample from a Normal distribution:

    +
    >>> import openturns as ot
+>>> sample = ot.Normal().getSample(10)
+>>> ot.ResourceMap.SetAsUnsignedInteger('DistributionFactory-DefaultBootstrapSize', 100)
+
    +
    +

    Fit a Normal distribution and extract the asymptotic parameters distribution:

    +
    >>> fittedRes = ot.NormalFactory().buildEstimator(sample)
+>>> paramDist = fittedRes.getParameterDistribution()
+
    +
    +

    Determine the bilateral confidence interval at level 0.9:

    +
    >>> confInt = paramDist.computeBilateralConfidenceInterval(0.9)
+
    +
    +
    + +
    +
    +computeBilateralConfidenceIntervalWithMarginalProbability(prob)
    +

    Compute a bilateral confidence interval.

    +

    Refer to computeBilateralConfidenceInterval()

    +
    +
    Parameters:
    +
    +
    alphafloat, \alpha \in [0,1]

    The confidence level.

    +
    +
    +
    +
    Returns:
    +
    +
    confIntervalInterval

    The confidence interval of level \alpha.

    +
    +
    marginalProbfloat

    The value \beta which is the common marginal probability of each marginal interval.

    +
    +
    +
    +
    +

    Examples

    +

    Create a sample from a Normal distribution:

    +
    >>> import openturns as ot
+>>> sample = ot.Normal().getSample(10)
+>>> ot.ResourceMap.SetAsUnsignedInteger('DistributionFactory-DefaultBootstrapSize', 100)
+
    +
    +

    Fit a Normal distribution and extract the asymptotic parameters distribution:

    +
    >>> fittedRes = ot.NormalFactory().buildEstimator(sample)
+>>> paramDist = fittedRes.getParameterDistribution()
+
    +
    +

    Determine the bilateral confidence interval at level 0.9 with marginal probability:

    +
    >>> confInt, marginalProb = paramDist.computeBilateralConfidenceIntervalWithMarginalProbability(0.9)
+
    +
    +
    + +
    +
    +computeCDF(*args)
    +

    Compute the cumulative distribution function.

    +
    +
    Parameters:
    +
    +
    Xsequence of float, 2-d sequence of float

    CDF input(s).

    +
    +
    +
    +
    Returns:
    +
    +
    Ffloat, Point

    CDF value(s) at input(s) X.

    +
    +
    +
    +
    +

    Notes

    +

    The cumulative distribution function is defined as:

    +
    +

    F_{\vect{X}}(\vect{x}) = \Prob{\bigcap_{i=1}^n X_i \leq x_i}, + \quad \vect{x} \in \supp{\vect{X}}

    +
    + +
    +
    +computeCDFGradient(*args)
    +

    Compute the gradient of the cumulative distribution function.

    +
    +
    Parameters:
    +
    +
    Xsequence of float

    CDF input.

    +
    +
    +
    +
    Returns:
    +
    +
    dFdthetaPoint

    Partial derivatives of the CDF with respect to the distribution +parameters at input X.

    +
    +
    +
    +
    +
    + +
    +
    +computeCharacteristicFunction(*args)
    +

    Compute the characteristic function.

    +
    +
    Parameters:
    +
    +
    tfloat

    Characteristic function input.

    +
    +
    +
    +
    Returns:
    +
    +
    phicomplex

    Characteristic function value at input t.

    +
    +
    +
    +
    +

    Notes

    +

    The characteristic function is defined as:

    +
    +

    \phi_X(t) = \mathbb{E}\left[\exp(- i t X)\right], + \quad t \in \Rset

    +

    OpenTURNS features a generic implementation of the characteristic function for +all its univariate distributions (both continuous and discrete). This default +implementation might be time consuming, especially as the modulus of t gets +high. Only some univariate distributions benefit from dedicated more efficient +implementations.

    +
    + +
    +
    +computeComplementaryCDF(*args)
    +

    Compute the complementary cumulative distribution function.

    +
    +
    Parameters:
    +
    +
    Xsequence of float, 2-d sequence of float

    Complementary CDF input(s).

    +
    +
    +
    +
    Returns:
    +
    +
    Cfloat, Point

    Complementary CDF value(s) at input(s) X.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeSurvivalFunction
    +
    +
    +

    Notes

    +

    The complementary cumulative distribution function.

    +
    +

    1 - F_{\vect{X}}(\vect{x}) = 1 - \Prob{\bigcap_{i=1}^n X_i \leq x_i}, \quad \vect{x} \in \supp{\vect{X}}

    +
    +

    Warning

    +

    This is not the survival function (except for 1-dimensional +distributions).

    +
    +
    + +
    +
    +computeConditionalCDF(*args)
    +

    Compute the conditional cumulative distribution function.

    +
    +
    Parameters:
    +
    +
    Xnfloat, sequence of float

    Conditional CDF input (last component).

    +
    +
    Xcondsequence of float, 2-d sequence of float with size n-1

    Conditionning values for the other components.

    +
    +
    +
    +
    Returns:
    +
    +
    Ffloat, sequence of float

    Conditional CDF value(s) at input X_n, X_{cond}.

    +
    +
    +
    +
    +

    Notes

    +

    The conditional cumulative distribution function of the last component with +respect to the other fixed components is defined as follows:

    +
    +

    F_{X_n \mid X_1, \ldots, X_{n - 1}}(x_n) = + \Prob{X_n \leq x_n \mid X_1=x_1, \ldots, X_{n-1}=x_{n-1}}, + \quad x_n \in \supp{X_n}

    +
    + +
    +
    +computeConditionalDDF(x, y)
    +

    Compute the conditional derivative density function of the last component.

    +

    With respect to the other fixed components.

    +
    +
    Parameters:
    +
    +
    Xnfloat

    Conditional DDF input (last component).

    +
    +
    Xcondsequence of float with dimension n-1

    Conditionning values for the other components.

    +
    +
    +
    +
    Returns:
    +
    +
    dfloat

    Conditional DDF value at input X_n, X_{cond}.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeDDF, computeConditionalCDF
    +
    +
    +
    + +
    +
    +computeConditionalPDF(*args)
    +

    Compute the conditional probability density function.

    +

    Conditional PDF of the last component with respect to the other fixed components.

    +
    +
    Parameters:
    +
    +
    Xnfloat, sequence of float

    Conditional PDF input (last component).

    +
    +
    Xcondsequence of float, 2-d sequence of float with size n-1

    Conditionning values for the other components.

    +
    +
    +
    +
    Returns:
    +
    +
    Ffloat, sequence of float

    Conditional PDF value(s) at input X_n, X_{cond}.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computePDF, computeConditionalCDF
    +
    +
    +
    + +
    +
    +computeConditionalQuantile(*args)
    +

    Compute the conditional quantile function of the last component.

    +

    Conditional quantile with respect to the other fixed components.

    +
    +
    Parameters:
    +
    +
    pfloat, sequence of float, 0 < p < 1

    Conditional quantile function input.

    +
    +
    Xcondsequence of float, 2-d sequence of float with size n-1

    Conditionning values for the other components.

    +
    +
    +
    +
    Returns:
    +
    +
    X1float

    Conditional quantile at input p, X_{cond}.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeQuantile, computeConditionalCDF
    +
    +
    +
    + +
    +
    +computeDDF(*args)
    +

    Compute the derivative density function.

    +
    +
    Parameters:
    +
    +
    Xsequence of float, 2-d sequence of float

    PDF input(s).

    +
    +
    +
    +
    Returns:
    +
    +
    dPoint, Sample

    DDF value(s) at input(s) X.

    +
    +
    +
    +
    +

    Notes

    +

    The derivative density function is the gradient of the probability density +function with respect to \vect{x}:

    +
    +

    \vect{\nabla}_{\vect{x}} f_{\vect{X}}(\vect{x}) = + \Tr{\left(\frac{\partial f_{\vect{X}}(\vect{x})}{\partial x_i}, + \quad i = 1, \ldots, n\right)}, + \quad \vect{x} \in \supp{\vect{X}}

    +
    + +
    +
    +computeDensityGenerator(betaSquare)
    +

    Compute the density generator.

    +
    +
    Parameters:
    +
    +
    yfloat

    Input.

    +
    +
    +
    +
    Returns:
    +
    +
    pfloat

    Value \varphi(y).

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    isElliptical, computePDF
    +
    +
    +

    Notes

    +

    The density generator is the function \varphi such that the probability density function +of the elliptical distribution rewrites:

    +
    +

    f_{\vect{X}}(\vect{x}) = + \varphi\left(\Tr{\left(\vect{x} - \vect{\mu}\right)} + \mat{\Sigma}^{-1} + \left(\vect{x} - \vect{\mu}\right) + \right), + \quad \vect{x} \in \supp{\vect{X}}

    +

    The density generator only exists for elliptical distributions.

    +
    + +
    +
    +computeDensityGeneratorDerivative(betaSquare)
    +

    Compute the first-order derivative of the probability density function.

    +

    PDF of the characteristic generator of the elliptical distribution.

    +
    +
    Parameters:
    +
    +
    beta2float

    Density generator input.

    +
    +
    +
    +
    Returns:
    +
    +
    pfloat

    Value \dfrac{d\varphi}{d\,t}(y).

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    isElliptical, computeDensityGenerator
    +
    +
    +

    Notes

    +

    This function only exists for elliptical distributions.

    +
    + +
    +
    +computeDensityGeneratorSecondDerivative(betaSquare)
    +

    Compute the second-order derivative of the probability density function.

    +

    PDF of the characteristic generator of the elliptical distribution.

    +
    +
    Parameters:
    +
    +
    beta2float

    Density generator input.

    +
    +
    +
    +
    Returns:
    +
    +
    pfloat

    Value \dfrac{d^2\varphi}{d\,t^2}(y).

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    isElliptical, computeDensityGenerator
    +
    +
    +

    Notes

    +

    This function only exists for elliptical distributions.

    +
    + +
    +
    +computeEntropy()
    +

    Compute the entropy of the distribution.

    +
    +
    Returns:
    +
    +
    efloat

    Entropy of the distribution.

    +
    +
    +
    +
    +

    Notes

    +

    The entropy of a distribution is defined by:

    +
    +

    \cE_X = \Expect{-\log(p_X(\vect{X}))}

    +

    Where the random vector \vect{X} follows the probability +distribution of interest, and p_X is either the probability +density function of \vect{X} if it is continuous or the +probability distribution function if it is discrete.

    +
    + +
    +
    +computeGeneratingFunction(*args)
    +

    Compute the probability-generating function.

    +
    +
    Parameters:
    +
    +
    zfloat or complex

    Probability-generating function input.

    +
    +
    +
    +
    Returns:
    +
    +
    gfloat

    Probability-generating function value at input X.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    isDiscrete
    +
    +
    +

    Notes

    +

    The probability-generating function is defined as follows:

    +
    +

    G_X(z) = \Expect{z^X}, \quad z \in \Cset

    +

    This function only exists for discrete distributions. OpenTURNS implements +this method for univariate distributions only.

    +
    + +
    +
    +computeInverseSurvivalFunction(point)
    +

    Compute the inverse survival function.

    +
    +
    Parameters:
    +
    +
    pfloat, p \in [0; 1]

    Level of the survival function.

    +
    +
    +
    +
    Returns:
    +
    +
    xPoint

    Point \vect{x} such that S_{\vect{X}}(\vect{x}) = p with iso-quantile components.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeQuantile, computeSurvivalFunction
    +
    +
    +

    Notes

    +

    The inverse survival function writes: S^{-1}(p) = \vect{x}^p where S( \vect{x}^p) = \Prob{\bigcap_{i=1}^d X_i > x_i^p}. OpenTURNS returns the point \vect{x}^p such that +\Prob{ X_1 > x_1^p} = \dots = \Prob{ X_d > x_d^p}.

    +
    + +
    +
    +computeLogCharacteristicFunction(*args)
    +

    Compute the logarithm of the characteristic function.

    +
    +
    Parameters:
    +
    +
    tfloat

    Characteristic function input.

    +
    +
    +
    +
    Returns:
    +
    +
    phicomplex

    Logarithm of the characteristic function value at input t.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeCharacteristicFunction
    +
    +
    +

    Notes

    +

    OpenTURNS features a generic implementation of the characteristic function for +all its univariate distributions (both continuous and discrete). This default +implementation might be time consuming, especially as the modulus of t gets +high. Only some univariate distributions benefit from dedicated more efficient +implementations.

    +
    + +
    +
    +computeLogGeneratingFunction(*args)
    +

    Compute the logarithm of the probability-generating function.

    +
    +
    Parameters:
    +
    +
    zfloat or complex

    Probability-generating function input.

    +
    +
    +
    +
    Returns:
    +
    +
    lgfloat

    Logarithm of the probability-generating function value at input X.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    isDiscrete, computeGeneratingFunction
    +
    +
    +

    Notes

    +

    This function only exists for discrete distributions. OpenTURNS implements +this method for univariate distributions only.

    +
    + +
    +
    +computeLogPDF(*args)
    +

    Compute the logarithm of the probability density function.

    +
    +
    Parameters:
    +
    +
    Xsequence of float, 2-d sequence of float

    PDF input(s).

    +
    +
    +
    +
    Returns:
    +
    +
    ffloat, Point

    Logarithm of the PDF value(s) at input(s) X.

    +
    +
    +
    +
    +
    + +
    +
    +computeLogPDFGradient(*args)
    +

    Compute the gradient of the log probability density function.

    +
    +
    Parameters:
    +
    +
    Xsequence of float

    PDF input.

    +
    +
    +
    +
    Returns:
    +
    +
    dfdthetaPoint

    Partial derivatives of the logPDF with respect to the distribution +parameters at input X.

    +
    +
    +
    +
    +
    + +
    +
    +computeLowerExtremalDependenceMatrix()
    +

    Compute the lower extremal dependence coefficients.

    +

    We assume that the distribution is d-dimensional, with d \geq 2 and that +its copula is denoted by C. +The lower extremal dependence matrix is (\bar{\chi}_L^{ij})_{1 \leq i, j \leq d} where +\\bar{\chi}_L^{ij} is the lower extremal dependence coefficient of the bivariate distribution +(X_i, X_j). +It is defined by:

    +
    +

    \bar{\chi}_L^{ij} = \lim_{u \to 0} \bar{\chi}_L^{ij}(u)

    +

    where u \mapsto \bar{\chi}_L^{ij}(u) is the lower extremal dependence function +of the bivariate distribution (X_i, X_j) defined by:

    +
    +

    \bar{\chi}_L(u) = \frac{2 \log u}{\log C(u,u)} - 1, \forall u \in [0,1]

    +

    Refer to Tail dependence coefficients to get more details.

    +
    +
    Returns:
    +
    +
    depCorrelationMatrix

    The dependence matrix.

    +
    +
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> copula = ot.FrankCopula()
+>>> chiLb = copula.computeLowerExtremalDependenceMatrix()[1, 0]
+
    +
    +
    + +
    +
    +computeLowerTailDependenceMatrix()
    +

    Compute the lower tail dependence coefficients.

    +

    We assume that the distribution is d-dimensional, with d \geq 2 and that +its copula is denoted by C. +The lower tail dependence matrix is (\chi_L^{ij})_{1 \leq i, j \leq d} where +\chi_L^{ij} is the lower tail dependence coefficient of the bivariate distribution +(X_i, X_j). +It is defined by:

    +
    +

    \chi_L^{ij} = \lim_{u \to 0} \chi_L^{ij}(u)

    +

    where u \mapsto \chi_L^{ij}(u) is the lower tail dependence function of the bivariate +distribution (X_i, X_j) defined by:

    +
    +

    \chi_L(u) = \frac{\log (1 - C(u,u))}{\log (1-u)}, \forall u \in [0,1]

    +

    Refer to Tail dependence coefficients to get more details.

    +
    +
    Returns:
    +
    +
    depCorrelationMatrix

    The dependence matrix.

    +
    +
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> copula = ot.FrankCopula()
+>>> chiL = copula.computeLowerTailDependenceMatrix()[1, 0]
+
    +
    +
    + +
    +
    +computeMinimumVolumeInterval(prob)
    +

    Compute the confidence interval with minimum volume.

    +
    +
    Parameters:
    +
    +
    alphafloat, \alpha \in [0,1]

    The confidence level.

    +
    +
    +
    +
    Returns:
    +
    +
    confIntervalInterval

    The confidence interval of level \alpha.

    +
    +
    +
    +
    +

    Notes

    +

    We consider an absolutely continuous measure \mu with density function p.

    +

    The minimum volume confidence interval I^*_{\alpha} is the cartesian product I^*_{\alpha} = [a_1, b_1] \times \dots \times [a_d, b_d] where [a_i, b_i] = \argmin_{I \in \Rset \, | \, \mu_i(I) = \beta} \lambda_i(I) and \mu(I^*_{\alpha}) = \alpha with \lambda is the Lebesgue measure on \Rset^d.

    +

    This problem resorts to solving d univariate non linear equations: for a fixed value \beta, we find each intervals [a_i, b_i] such that:

    +
    +

    \begin{eqnarray*} +F_i(b_i) - F_i(a_i) & = & \beta \\ +p_i(b_i) & = & p_i(a_i) +\end{eqnarray*}

    +

    which consists of finding the bound a_i such that:

    +
    +

    p_i(a_i) = p_i(F_i^{-1}(\beta + F_i(a_i)))

    +

    To find \beta, we use the Brent algorithm: \mu([\vect{a}(\beta); \vect{b}(\beta)] = g(\beta) = \alpha with g a non linear function.

    +

    Examples

    +

    Create a sample from a Normal distribution:

    +
    >>> import openturns as ot
+>>> sample = ot.Normal().getSample(10)
+>>> ot.ResourceMap.SetAsUnsignedInteger('DistributionFactory-DefaultBootstrapSize', 100)
+
    +
    +

    Fit a Normal distribution and extract the asymptotic parameters distribution:

    +
    >>> fittedRes = ot.NormalFactory().buildEstimator(sample)
+>>> paramDist = fittedRes.getParameterDistribution()
+
    +
    +

    Determine the confidence interval of the native parameters at level 0.9 with minimum volume:

    +
    >>> ot.ResourceMap.SetAsUnsignedInteger('Distribution-MinimumVolumeLevelSetSamplingSize', 1000)
+>>> confInt = paramDist.computeMinimumVolumeInterval(0.9)
+>>> ot.ResourceMap.Reload()
+
    +
    +
    + +
    +
    +computeMinimumVolumeIntervalWithMarginalProbability(prob)
    +

    Compute the confidence interval with minimum volume.

    +

    Refer to computeMinimumVolumeInterval()

    +
    +
    Parameters:
    +
    +
    alphafloat, \alpha \in [0,1]

    The confidence level.

    +
    +
    +
    +
    Returns:
    +
    +
    confIntervalInterval

    The confidence interval of level \alpha.

    +
    +
    marginalProbfloat

    The value \beta which is the common marginal probability of each marginal interval.

    +
    +
    +
    +
    +

    Examples

    +

    Create a sample from a Normal distribution:

    +
    >>> import openturns as ot
+>>> sample = ot.Normal().getSample(10)
+>>> ot.ResourceMap.SetAsUnsignedInteger('DistributionFactory-DefaultBootstrapSize', 100)
+
    +
    +

    Fit a Normal distribution and extract the asymptotic parameters distribution:

    +
    >>> fittedRes = ot.NormalFactory().buildEstimator(sample)
+>>> paramDist = fittedRes.getParameterDistribution()
+
    +
    +

    Determine the confidence interval of the native parameters at level 0.9 with minimum volume:

    +
    >>> ot.ResourceMap.SetAsUnsignedInteger('Distribution-MinimumVolumeLevelSetSamplingSize', 1000)
+>>> confInt, marginalProb = paramDist.computeMinimumVolumeIntervalWithMarginalProbability(0.9)
+>>> ot.ResourceMap.Reload()
+
    +
    +
    + +
    +
    +computeMinimumVolumeLevelSet(prob)
    +

    Compute the confidence domain with minimum volume.

    +
    +
    Parameters:
    +
    +
    alphafloat, \alpha \in [0,1]

    The confidence level.

    +
    +
    +
    +
    Returns:
    +
    +
    levelSetLevelSet

    The minimum volume domain of measure \alpha.

    +
    +
    +
    +
    +

    Notes

    +

    We consider an absolutely continuous measure \mu with density function p.

    +

    The minimum volume confidence domain A^*_{\alpha} is the set of minimum volume and which measure is at least \alpha. It is defined by:

    +
    +

    A^*_{\alpha} = \argmin_{A \in \Rset^d\, | \, \mu(A) \geq \alpha} \lambda(A)

    +

    where \lambda is the Lebesgue measure on \Rset^d. Under some general conditions on \mu (for example, no flat regions), the set A^*_{\alpha} is unique and realises the minimum: \mu(A^*_{\alpha}) = \alpha. We show that A^*_{\alpha} writes:

    +
    +

    A^*_{\alpha} = \{ \vect{x} \in \Rset^d \, | \, p(\vect{x}) \geq p_{\alpha} \}

    +

    for a certain p_{\alpha} >0.

    +

    If we consider the random variable Y = p(\vect{X}), with cumulative distribution function F_Y, then p_{\alpha} is defined by:

    +
    +

    1-F_Y(p_{\alpha}) = \alpha

    +

    Thus the minimum volume domain of confidence \alpha is the interior of the domain which frontier is the 1-\alpha quantile of Y. It can be determined with simulations of Y.

    +

    Examples

    +

    Create a sample from a Normal distribution:

    +
    >>> import openturns as ot
+>>> sample = ot.Normal().getSample(10)
+>>> ot.ResourceMap.SetAsUnsignedInteger('DistributionFactory-DefaultBootstrapSize', 100)
+
    +
    +

    Fit a Normal distribution and extract the asymptotic parameters distribution:

    +
    >>> fittedRes = ot.NormalFactory().buildEstimator(sample)
+>>> paramDist = fittedRes.getParameterDistribution()
+
    +
    +

    Determine the confidence region of minimum volume of the native parameters at level 0.9:

    +
    >>> levelSet = paramDist.computeMinimumVolumeLevelSet(0.9)
+>>> ot.ResourceMap.Reload()
+
    +
    +
    + +
    +
    +computeMinimumVolumeLevelSetWithThreshold(prob)
    +

    Compute the confidence domain with minimum volume.

    +

    Refer to computeMinimumVolumeLevelSet()

    +
    +
    Parameters:
    +
    +
    alphafloat, \alpha \in [0,1]

    The confidence level.

    +
    +
    +
    +
    Returns:
    +
    +
    levelSetLevelSet

    The minimum volume domain of measure \alpha.

    +
    +
    levelfloat

    The value p_{\alpha} of the density function defining the frontier of the domain.

    +
    +
    +
    +
    +

    Examples

    +

    Create a sample from a Normal distribution:

    +
    >>> import openturns as ot
+>>> sample = ot.Normal().getSample(10)
+>>> ot.ResourceMap.SetAsUnsignedInteger('DistributionFactory-DefaultBootstrapSize', 100)
+
    +
    +

    Fit a Normal distribution and extract the asymptotic parameters distribution:

    +
    >>> fittedRes = ot.NormalFactory().buildEstimator(sample)
+>>> paramDist = fittedRes.getParameterDistribution()
+
    +
    +

    Determine the confidence region of minimum volume of the native parameters at level 0.9 with PDF threshold:

    +
    >>> levelSet, threshold = paramDist.computeMinimumVolumeLevelSetWithThreshold(0.9)
+
    +
    +
    + +
    +
    +computePDF(*args)
    +

    Compute the probability density function.

    +
    +
    Parameters:
    +
    +
    Xsequence of float, 2-d sequence of float

    PDF input(s).

    +
    +
    +
    +
    Returns:
    +
    +
    ffloat, Point

    PDF value(s) at input(s) X.

    +
    +
    +
    +
    +

    Notes

    +

    The probability density function is defined as follows:

    +
    +

    f_{\vect{X}}(\vect{x}) = \frac{\partial^n F_{\vect{X}}(\vect{x})} + {\prod_{i=1}^n \partial x_i}, + \quad \vect{x} \in \supp{\vect{X}}

    +
    + +
    +
    +computePDFGradient(*args)
    +

    Compute the gradient of the probability density function.

    +
    +
    Parameters:
    +
    +
    Xsequence of float

    PDF input.

    +
    +
    +
    +
    Returns:
    +
    +
    dfdthetaPoint

    Partial derivatives of the PDF with respect to the distribution +parameters at input X.

    +
    +
    +
    +
    +
    + +
    +
    +computeProbability(interval)
    +

    Compute the interval probability.

    +
    +
    Parameters:
    +
    +
    intervalInterval

    An interval, possibly multivariate.

    +
    +
    +
    +
    Returns:
    +
    +
    Pfloat

    Interval probability.

    +
    +
    +
    +
    +

    Notes

    +

    This computes the probability that the random vector \vect{X} lies in +the hyper-rectangular region formed by the vectors \vect{a} and +\vect{b}:

    +
    +

    \Prob{\bigcap\limits_{i=1}^n a_i < X_i \leq b_i} = + \sum\limits_{\vect{c}} (-1)^{n(\vect{c})} + F_{\vect{X}}\left(\vect{c}\right)

    +

    where the sum runs over the 2^n vectors such that +\vect{c} = \Tr{(c_i, i = 1, \ldots, n)} with c_i \in [a_i, b_i], +and n(\vect{c}) is the number of components in +\vect{c} such that c_i = a_i.

    +
    + +
    +
    +computeQuantile(*args)
    +

    Compute the quantile function.

    +
    +
    Parameters:
    +
    +
    pfloat (or sequence of float), 0 < p < 1

    Quantile function input (a probability).

    +
    +
    tailbool, optional (default=False)

    Whether p should be interpreted as the complementary probability.

    +
    +
    +
    +
    Returns:
    +
    +
    XPoint (or Sample)

    Quantile at probability level p.

    +
    +
    +
    +
    +

    Notes

    +

    The quantile function is also known as the inverse cumulative distribution +function:

    +
    +

    Q_{\vect{X}}(p) = F_{\vect{X}}^{-1}(p), + \quad p \in [0; 1]

    +
    + +
    +
    +computeRadialDistributionCDF(radius, tail=False)
    +

    Compute the cumulative distribution function of the squared radius.

    +

    For the underlying standard spherical distribution (for elliptical +distributions only).

    +
    +
    Parameters:
    +
    +
    r2float, 0 \leq r^2

    Squared radius.

    +
    +
    +
    +
    Returns:
    +
    +
    Ffloat

    CDF value at input r^2.

    +
    +
    +
    +
    +

    Notes

    +

    This is the CDF of the sum of the squared independent, standard, identically +distributed components:

    +
    +

    R^2 = \sqrt{\sum\limits_{i=1}^n U_i^2}

    +
    + +
    +
    +computeScalarQuantile(prob, tail=False)
    +

    Compute the quantile function for univariate distributions.

    +
    +
    Parameters:
    +
    +
    pfloat, 0 < p < 1

    Quantile function input (a probability).

    +
    +
    +
    +
    Returns:
    +
    +
    Xfloat

    Quantile at probability level p.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeQuantile
    +
    +
    +

    Notes

    +

    The quantile function is also known as the inverse cumulative distribution +function:

    +
    +

    Q_X(p) = F_X^{-1}(p), \quad p \in [0; 1]

    +
    + +
    +
    +computeSequentialConditionalCDF(x)
    +

    Compute the sequential conditional cumulative distribution functions.

    +
    +
    Parameters:
    +
    +
    Xsequence of float, with size d

    Values to be taken sequentially as argument and conditioning part of the CDF.

    +
    +
    +
    +
    Returns:
    +
    +
    Fsequence of float

    Conditional CDF values at input.

    +
    +
    +
    +
    +

    Notes

    +

    The sequential conditional cumulative distribution function is defined as follows:

    +
    +

    F^{seq}_{X_1,\ldots,X_d}(x_1,\ldots,x_d) = \left(\Prob{X_n \leq x_n \mid X_1=x_1, \ldots, X_{n-1}=x_{n-1}}\right)_{i=1,\ldots,d}

    +

    ie its n-th component is the conditional CDF of X_n at x_n given that X_1=x_1,\ldots,X_{n-1}=x_{n-1}. For n=1 it reduces to \Prob{X_1 \leq x_1}, ie the CDF of the first component at x_1.

    +
    + +
    +
    +computeSequentialConditionalDDF(x)
    +

    Compute the sequential conditional derivative density function.

    +
    +
    Parameters:
    +
    +
    Xsequence of float, with size d

    Values to be taken sequentially as argument and conditioning part of the DDF.

    +
    +
    +
    +
    Returns:
    +
    +
    ddfsequence of float

    Conditional DDF values at input.

    +
    +
    +
    +
    +

    Notes

    +

    The sequential conditional derivative density function is defined as follows:

    +
    +

    ddf^{seq}_{X_1,\ldots,X_d}(x_1,\ldots,x_d) = \left(\dfrac{d^2}{d\,x_n^2}\Prob{X_n \leq x_n \mid X_1=x_1, \ldots, +X_{n-1}=x_{n-1}}\right)_{i=1,\ldots,d}

    +

    ie its n-th component is the conditional DDF of X_n at x_n given that X_1=x_1, +\ldots,X_{n-1}=x_{n-1}. For n=1 it reduces to \dfrac{d^2}{d\,x_1^2}\Prob{X_1 \leq x_1}, ie the DDF of +the first component at x_1.

    +
    + +
    +
    +computeSequentialConditionalPDF(x)
    +

    Compute the sequential conditional probability density function.

    +
    +
    Parameters:
    +
    +
    Xsequence of float, with size d

    Values to be taken sequentially as argument and conditioning part of the PDF.

    +
    +
    +
    +
    Returns:
    +
    +
    pdfsequence of float

    Conditional PDF values at input.

    +
    +
    +
    +
    +

    Notes

    +

    The sequential conditional density function is defined as follows:

    +
    +

    pdf^{seq}_{X_1,\ldots,X_d}(x_1,\ldots,x_d) = \left(\dfrac{d}{d\,x_n}\Prob{X_n \leq x_n \mid X_1=x_1, \ldots, X_{n-1}=x_{n-1}}\right)_{i=1,\ldots,d}

    +

    ie its n-th component is the conditional PDF of X_n at x_n given that X_1=x_1,\ldots,X_{n-1}=x_{n-1}. For n=1 it reduces to \dfrac{d}{d\,x_1}\Prob{X_1 \leq x_1}, ie the PDF of the first component at x_1.

    +
    + +
    +
    +computeSequentialConditionalQuantile(q)
    +

    Compute the conditional quantile function of the last component.

    +
    +
    Parameters:
    +
    +
    qsequence of float in [0,1], with size d

    Values to be taken sequentially as the argument of the conditional quantile.

    +
    +
    +
    +
    Returns:
    +
    +
    Qsequence of float

    Conditional quantiles values at input.

    +
    +
    +
    +
    +

    Notes

    +

    The sequential conditional quantile function is defined as follows:

    +
    +

    Q^{seq}_{X_1,\ldots,X_d}(q_1,\ldots,q_d) = \left(F^{-1}(q_n|X_1=x_1,\ldots,X_{n-1}=x_{n_1}\right)_{i=1,\ldots,d}

    +

    where x_1,\ldots,x_{n-1} are defined recursively as x_1=F_1^{-1}(q_1) and given (x_i)_{i=1, +\ldots,n-1}, x_n=F^{-1}(q_n|X_1=x_1,\ldots,X_{n-1}=x_{n_1}): the conditioning part is the set of already +computed conditional quantiles.

    +
    + +
    +
    +computeSurvivalFunction(*args)
    +

    Compute the survival function.

    +
    +
    Parameters:
    +
    +
    xsequence of float, 2-d sequence of float

    Survival function input(s).

    +
    +
    +
    +
    Returns:
    +
    +
    Sfloat, Point

    Survival function value(s) at input(s) x.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeComplementaryCDF
    +
    +
    +

    Notes

    +

    The survival function of the random vector \vect{X} is defined as follows:

    +
    +

    S_{\vect{X}}(\vect{x}) = \Prob{\bigcap_{i=1}^d X_i > x_i} + \quad \forall \vect{x} \in \Rset^d

    +
    +

    Warning

    +

    This is not the complementary cumulative distribution function (except for +1-dimensional distributions).

    +
    +
    + +
    +
    +computeUnilateralConfidenceInterval(prob, tail=False)
    +

    Compute a unilateral confidence interval.

    +
    +
    Parameters:
    +
    +
    alphafloat, \alpha \in [0,1]

    The confidence level.

    +
    +
    tailboolean

    True indicates the interval is bounded by an lower value. +False indicates the interval is bounded by an upper value. +Default value is False.

    +
    +
    +
    +
    Returns:
    +
    +
    confIntervalInterval

    The unilateral confidence interval of level \alpha.

    +
    +
    +
    +
    +

    Notes

    +

    We consider an absolutely continuous measure \mu.

    +

    The left unilateral confidence interval I^*_{\alpha} is the cartesian product I^*_{\alpha} = ]-\infty, b_1] \times \dots \times ]-\infty, b_d] where b_i = F_i^{-1}(\beta) for all i and which verifies \mu(I^*_{\alpha}) = \alpha. +It means that \vect{b} is the quantile of level \alpha of the measure \mu, with iso-quantile components.

    +

    The right unilateral confidence interval I^*_{\alpha} is the cartesian product I^*_{\alpha} = ]a_1; +\infty[ \times \dots \times ]a_d; +\infty[ where a_i = F_i^{-1}(1-\beta) for all i and which verifies \mu(I^*_{\alpha}) = \alpha. +It means that S_{\mu}^{-1}(\vect{a}) = \alpha with iso-quantile components, where S_{\mu} is the survival function of the measure \mu.

    +

    Examples

    +

    Create a sample from a Normal distribution:

    +
    >>> import openturns as ot
+>>> sample = ot.Normal().getSample(10)
+>>> ot.ResourceMap.SetAsUnsignedInteger('DistributionFactory-DefaultBootstrapSize', 100)
+
    +
    +

    Fit a Normal distribution and extract the asymptotic parameters distribution:

    +
    >>> fittedRes = ot.NormalFactory().buildEstimator(sample)
+>>> paramDist = fittedRes.getParameterDistribution()
+
    +
    +

    Determine the right unilateral confidence interval at level 0.9:

    +
    >>> confInt = paramDist.computeUnilateralConfidenceInterval(0.9)
+
    +
    +

    Determine the left unilateral confidence interval at level 0.9:

    +
    >>> confInt = paramDist.computeUnilateralConfidenceInterval(0.9, True)
+
    +
    +
    + +
    +
    +computeUnilateralConfidenceIntervalWithMarginalProbability(prob, tail)
    +

    Compute a unilateral confidence interval.

    +

    Refer to computeUnilateralConfidenceInterval()

    +
    +
    Parameters:
    +
    +
    alphafloat, \alpha \in [0,1]

    The confidence level.

    +
    +
    tailboolean

    True indicates the interval is bounded by an lower value. +False indicates the interval is bounded by an upper value. +Default value is False.

    +
    +
    +
    +
    Returns:
    +
    +
    confIntervalInterval

    The unilateral confidence interval of level \alpha.

    +
    +
    marginalProbfloat

    The value \beta which is the common marginal probability of each marginal interval.

    +
    +
    +
    +
    +

    Examples

    +

    Create a sample from a Normal distribution:

    +
    >>> import openturns as ot
+>>> sample = ot.Normal().getSample(10)
+>>> ot.ResourceMap.SetAsUnsignedInteger('DistributionFactory-DefaultBootstrapSize', 100)
+
    +
    +

    Fit a Normal distribution and extract the asymptotic parameters distribution:

    +
    >>> fittedRes = ot.NormalFactory().buildEstimator(sample)
+>>> paramDist = fittedRes.getParameterDistribution()
+
    +
    +

    Determine the right unilateral confidence interval at level 0.9:

    +
    >>> confInt, marginalProb = paramDist.computeUnilateralConfidenceIntervalWithMarginalProbability(0.9, False)
+
    +
    +

    Determine the left unilateral confidence interval at level 0.9:

    +
    >>> confInt, marginalProb = paramDist.computeUnilateralConfidenceIntervalWithMarginalProbability(0.9, True)
+>>> ot.ResourceMap.Reload()
+
    +
    +
    + +
    +
    +computeUpperExtremalDependenceMatrix()
    +

    Compute the upper extremal dependence coefficients.

    +

    We assume that the distribution is d-dimensional, with d \geq 2 and that its copula is +denoted by C. +The upper extremal dependence matrix is (\bar{\chi}^{ij})_{1 \leq i, j \leq d} where +\bar{\chi}^{ij} is the upper extremal dependence coefficient of the bivariate distribution +(X_i, X_j). +It is defined by:

    +
    +

    \bar{\chi}^{ij} = \lim_{u \to 1} \bar{\chi}^{ij}(u)

    +

    where u \mapsto \bar{\chi}^{ij}(u) is the upper extremal dependence function of the bivariate +distribution (X_i, X_j) defined by:

    +
    +

    \bar{\chi}(u) = \frac{2 \log 1-u}{\log \bar{C}(u,u)} - 1, \forall u \in [0,1]

    +

    Refer to Tail dependence coefficients to get more details.

    +
    +
    Returns:
    +
    +
    depCorrelationMatrix

    The dependence matrix.

    +
    +
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> copula = ot.FrankCopula()
+>>> chib = copula.computeUpperExtremalDependenceMatrix()[1, 0]
+
    +
    +
    + +
    +
    +computeUpperTailDependenceMatrix()
    +

    Compute the upper tail dependence coefficients.

    +

    We assume that the distribution is d-dimensional, with d \geq 2 and that its copula is +denoted by C. +The upper tail dependence matrix is (\chi^{ij})_{1 \leq i, j \leq d} where \chi^{ij} is +the upper tail dependence coefficient of the bivariate distribution (X_i, X_j). +It is defined by:

    +
    +

    \chi^{ij} = \lim_{u \to 1} \chi^{ij}(u)

    +

    where u \mapsto \chi^{ij}(u) is the upper tail dependence function of the bivariate distribution +(X_i, X_j) defined by:

    +
    +

    \chi(u) = 2 - \frac{\log C(u,u)}{\log u}, \forall u \in [0,1]

    +

    Refer to Tail dependence coefficients to get more details.

    +
    +
    Returns:
    +
    +
    depCorrelationMatrix

    The dependence matrix.

    +
    +
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> copula = ot.FrankCopula()
+>>> chi = copula.computeUpperTailDependenceMatrix()[1, 0]
+
    +
    +
    + +
    +
    +cos()
    +

    Transform distribution by cosine function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +cosh()
    +

    Transform distribution by cosh function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +drawCDF(*args)
    +

    Draw the cumulative distribution function.

    +
    +
    Available constructors:

    drawCDF(x_min, x_max, pointNumber, logScale)

    +

    drawCDF(lowerCorner, upperCorner, pointNbrInd, logScaleX, logScaleY)

    +

    drawCDF(lowerCorner, upperCorner)

    +
    +
    +
    +
    Parameters:
    +
    +
    x_minfloat, optional

    The min-value of the mesh of the x-axis. +Defaults uses the quantile associated to the probability level +Distribution-QMin from the ResourceMap.

    +
    +
    x_maxfloat, optional, x_{\max} > x_{\min}

    The max-value of the mesh of the y-axis. +Defaults uses the quantile associated to the probability level +Distribution-QMax from the ResourceMap.

    +
    +
    pointNumberint

    The number of points that is used for meshing each axis. +Defaults uses DistributionImplementation-DefaultPointNumber from the +ResourceMap.

    +
    +
    logScalebool

    Flag to tell if the plot is done on a logarithmic scale. Default is False.

    +
    +
    lowerCornersequence of float, of dimension 2, optional

    The lower corner [x_{min}, y_{min}].

    +
    +
    upperCornersequence of float, of dimension 2, optional

    The upper corner [x_{max}, y_{max}].

    +
    +
    pointNbrIndIndices, of dimension 2

    Number of points that is used for meshing each axis.

    +
    +
    logScaleXbool

    Flag to tell if the plot is done on a logarithmic scale for X. Default is False.

    +
    +
    logScaleYbool

    Flag to tell if the plot is done on a logarithmic scale for Y. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the CDF.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeCDF, viewer.View, ResourceMap
    +
    +
    +

    Notes

    +

    Only valid for univariate and bivariate distributions.

    +

    Examples

    +

    View the CDF of a univariate distribution:

    +
    >>> import openturns as ot
+>>> dist = ot.Normal()
+>>> graph = dist.drawCDF()
+>>> graph.setLegends(['normal cdf'])
+
    +
    +

    View the iso-lines CDF of a bivariate distribution:

    +
    >>> import openturns as ot
+>>> dist = ot.Normal(2)
+>>> graph2 = dist.drawCDF()
+>>> graph2.setLegends(['iso- normal cdf'])
+>>> graph3 = dist.drawCDF([-10, -5],[5, 10], [511, 511])
+
    +
    +
    + +
    +
    +drawLogPDF(*args)
    +

    Draw the graph or of iso-lines of log-probability density function.

    +
    +
    Available constructors:

    drawLogPDF(x_min, x_max, pointNumber, logScale)

    +

    drawLogPDF(lowerCorner, upperCorner, pointNbrInd, logScaleX, logScaleY)

    +

    drawLogPDF(lowerCorner, upperCorner)

    +
    +
    +
    +
    Parameters:
    +
    +
    x_minfloat, optional

    The min-value of the mesh of the x-axis. +Defaults uses the quantile associated to the probability level +Distribution-QMin from the ResourceMap.

    +
    +
    x_maxfloat, optional, x_{\max} > x_{\min}

    The max-value of the mesh of the y-axis. +Defaults uses the quantile associated to the probability level +Distribution-QMax from the ResourceMap.

    +
    +
    pointNumberint

    The number of points that is used for meshing each axis. +Defaults uses DistributionImplementation-DefaultPointNumber from the +ResourceMap.

    +
    +
    logScalebool

    Flag to tell if the plot is done on a logarithmic scale. Default is False.

    +
    +
    lowerCornersequence of float, of dimension 2, optional

    The lower corner [x_{min}, y_{min}].

    +
    +
    upperCornersequence of float, of dimension 2, optional

    The upper corner [x_{max}, y_{max}].

    +
    +
    pointNbrIndIndices, of dimension 2

    Number of points that is used for meshing each axis.

    +
    +
    logScaleXbool

    Flag to tell if the plot is done on a logarithmic scale for X. Default is False.

    +
    +
    logScaleYbool

    Flag to tell if the plot is done on a logarithmic scale for Y. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the log-PDF or its iso_lines.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeLogPDF, viewer.View, ResourceMap
    +
    +
    +

    Notes

    +

    Only valid for univariate and bivariate distributions.

    +

    Examples

    +

    View the log-PDF of a univariate distribution:

    +
    >>> import openturns as ot
+>>> dist = ot.Normal()
+>>> graph = dist.drawLogPDF()
+>>> graph.setLegends(['normal log-pdf'])
+
    +
    +

    View the iso-lines log-PDF of a bivariate distribution:

    +
    >>> import openturns as ot
+>>> dist = ot.Normal(2)
+>>> graph2 = dist.drawLogPDF()
+>>> graph2.setLegends(['iso- normal pdf'])
+>>> graph3 = dist.drawLogPDF([-10, -5],[5, 10], [511, 511])
+
    +
    +
    + +
    +
    +drawLowerExtremalDependenceFunction()
    +

    Draw the lower extremal dependence function.

    +

    We assume that the distribution is bivariate and that its copula is denoted by C. +The lower extremal dependence function u \mapsto \bar{\chi}(u) is defined by:

    +
    +

    \bar{\chi}_L(u) = \frac{2 \log u}{\log C(u,u)} - 1, \forall u \in [0,1]

    +

    Refer to Tail dependence coefficients to get more details.

    +
    +
    Returns:
    +
    +
    graphGraph

    The graph of the function u \mapsto \bar{\chi}_L(u).

    +
    +
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> copula = ot.FrankCopula()
+>>> graph = copula.drawLowerExtremalDependenceFunction()
+
    +
    +
    + +
    +
    +drawLowerTailDependenceFunction()
    +

    Draw the lower tail dependence function.

    +

    We assume that the distribution is bivariate and that its copula is denoted by C. +The lower tail dependence function u \mapsto \chi_L(u) is defined by:

    +
    +

    \chi_L(u) = \frac{\log (1 - C(u,u))}{\log (1-u)}, \forall u \in [0,1]

    +

    Refer to Tail dependence coefficients to get more details.

    +
    +
    Returns:
    +
    +
    graphGraph

    Graph of the function u \mapsto \chi_L(u).

    +
    +
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> copula = ot.FrankCopula()
+>>> graph = copula.drawLowerTailDependenceFunction()
+
    +
    +
    + +
    +
    +drawMarginal1DCDF(marginalIndex, xMin, xMax, pointNumber, logScale=False)
    +

    Draw the cumulative distribution function of a margin.

    +
    +
    Parameters:
    +
    +
    iint, 1 \leq i \leq n

    The index of the margin of interest.

    +
    +
    x_minfloat

    The starting value that is used for meshing the x-axis.

    +
    +
    x_maxfloat, x_{\max} > x_{\min}

    The ending value that is used for meshing the x-axis.

    +
    +
    n_pointsint

    The number of points that is used for meshing the x-axis.

    +
    +
    logScalebool

    Flag to tell if the plot is done on a logarithmic scale. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the CDF of the requested margin.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeCDF, getMarginal, viewer.View, ResourceMap
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> from openturns.viewer import View
+>>> distribution = ot.Normal(10)
+>>> graph = distribution.drawMarginal1DCDF(2, -6.0, 6.0, 100)
+>>> view = View(graph)
+>>> view.show()
+
    +
    +
    + +
    +
    +drawMarginal1DLogPDF(marginalIndex, xMin, xMax, pointNumber, logScale=False)
    +

    Draw the log-probability density function of a margin.

    +
    +
    Parameters:
    +
    +
    iint, 1 \leq i \leq n

    The index of the margin of interest.

    +
    +
    x_minfloat

    The starting value that is used for meshing the x-axis.

    +
    +
    x_maxfloat, x_{\max} > x_{\min}

    The ending value that is used for meshing the x-axis.

    +
    +
    n_pointsint

    The number of points that is used for meshing the x-axis.

    +
    +
    logScalebool

    Flag to tell if the plot is done on a logarithmic scale. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the log-PDF of the requested margin.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeLogPDF, getMarginal, viewer.View, ResourceMap
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> from openturns.viewer import View
+>>> distribution = ot.Normal(10)
+>>> graph = distribution.drawMarginal1DLogPDF(2, -6.0, 6.0, 100)
+>>> view = View(graph)
+>>> view.show()
+
    +
    +
    + +
    +
    +drawMarginal1DPDF(marginalIndex, xMin, xMax, pointNumber, logScale=False)
    +

    Draw the probability density function of a margin.

    +
    +
    Parameters:
    +
    +
    iint, 1 \leq i \leq n

    The index of the margin of interest.

    +
    +
    x_minfloat

    The starting value that is used for meshing the x-axis.

    +
    +
    x_maxfloat, x_{\max} > x_{\min}

    The ending value that is used for meshing the x-axis.

    +
    +
    n_pointsint

    The number of points that is used for meshing the x-axis.

    +
    +
    logScalebool

    Flag to tell if the plot is done on a logarithmic scale. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the PDF of the requested margin.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computePDF, getMarginal, viewer.View, ResourceMap
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> from openturns.viewer import View
+>>> distribution = ot.Normal(10)
+>>> graph = distribution.drawMarginal1DPDF(2, -6.0, 6.0, 100)
+>>> view = View(graph)
+>>> view.show()
+
    +
    +
    + +
    +
    +drawMarginal1DSurvivalFunction(marginalIndex, xMin, xMax, pointNumber, logScale=False)
    +

    Draw the cumulative distribution function of a margin.

    +
    +
    Parameters:
    +
    +
    iint, 1 \leq i \leq n

    The index of the margin of interest.

    +
    +
    x_minfloat

    The starting value that is used for meshing the x-axis.

    +
    +
    x_maxfloat, x_{\max} > x_{\min}

    The ending value that is used for meshing the x-axis.

    +
    +
    n_pointsint

    The number of points that is used for meshing the x-axis.

    +
    +
    logScalebool

    Flag to tell if the plot is done on a logarithmic scale. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the SurvivalFunction of the requested margin.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeSurvivalFunction, getMarginal, viewer.View, ResourceMap
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> from openturns.viewer import View
+>>> distribution = ot.Normal(10)
+>>> graph = distribution.drawMarginal1DSurvivalFunction(2, -6.0, 6.0, 100)
+>>> view = View(graph)
+>>> view.show()
+
    +
    +
    + +
    +
    +drawMarginal2DCDF(firstMarginal, secondMarginal, xMin, xMax, pointNumber, logScaleX=False, logScaleY=False)
    +

    Draw the cumulative distribution function of a couple of margins.

    +
    +
    Parameters:
    +
    +
    iint, 1 \leq i \leq n

    The index of the first margin of interest.

    +
    +
    jint, 1 \leq i \neq j \leq n

    The index of the second margin of interest.

    +
    +
    x_minlist of 2 floats

    The starting values that are used for meshing the x- and y- axes.

    +
    +
    x_maxlist of 2 floats, x_{\max} > x_{\min}

    The ending values that are used for meshing the x- and y- axes.

    +
    +
    n_pointslist of 2 ints

    The number of points that are used for meshing the x- and y- axes.

    +
    +
    logScaleXbool

    Flag to tell if the plot is done on a logarithmic scale for X. Default is False.

    +
    +
    logScaleYbool

    Flag to tell if the plot is done on a logarithmic scale for Y. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the marginal CDF of the requested couple of +margins.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeCDF, getMarginal, viewer.View, ResourceMap
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> from openturns.viewer import View
+>>> distribution = ot.Normal(10)
+>>> graph = distribution.drawMarginal2DCDF(2, 3, [-6.0] * 2, [6.0] * 2, [100] * 2)
+>>> view = View(graph)
+>>> view.show()
+
    +
    +
    + +
    +
    +drawMarginal2DLogPDF(firstMarginal, secondMarginal, xMin, xMax, pointNumber, logScaleX=False, logScaleY=False)
    +

    Draw the log-probability density function of a couple of margins.

    +
    +
    Parameters:
    +
    +
    iint, 1 \leq i \leq n

    The index of the first margin of interest.

    +
    +
    jint, 1 \leq i \neq j \leq n

    The index of the second margin of interest.

    +
    +
    x_minlist of 2 floats

    The starting values that are used for meshing the x- and y- axes.

    +
    +
    x_maxlist of 2 floats, x_{\max} > x_{\min}

    The ending values that are used for meshing the x- and y- axes.

    +
    +
    n_pointslist of 2 ints

    The number of points that are used for meshing the x- and y- axes.

    +
    +
    logScaleXbool

    Flag to tell if the plot is done on a logarithmic scale for X. Default is False.

    +
    +
    logScaleYbool

    Flag to tell if the plot is done on a logarithmic scale for Y. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the marginal log-PDF of the requested couple of +margins.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeLogPDF, getMarginal, viewer.View, ResourceMap
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> from openturns.viewer import View
+>>> distribution = ot.Normal(10)
+>>> graph = distribution.drawMarginal2DLogPDF(2, 3, [-6.0] * 2, [6.0] * 2, [100] * 2)
+>>> view = View(graph)
+>>> view.show()
+
    +
    +
    + +
    +
    +drawMarginal2DPDF(firstMarginal, secondMarginal, xMin, xMax, pointNumber, logScaleX=False, logScaleY=False)
    +

    Draw the probability density function of a couple of margins.

    +
    +
    Parameters:
    +
    +
    iint, 1 \leq i \leq n

    The index of the first margin of interest.

    +
    +
    jint, 1 \leq i \neq j \leq n

    The index of the second margin of interest.

    +
    +
    x_minlist of 2 floats

    The starting values that are used for meshing the x- and y- axes.

    +
    +
    x_maxlist of 2 floats, x_{\max} > x_{\min}

    The ending values that are used for meshing the x- and y- axes.

    +
    +
    n_pointslist of 2 ints

    The number of points that are used for meshing the x- and y- axes.

    +
    +
    logScaleXbool

    Flag to tell if the plot is done on a logarithmic scale for X. Default is False.

    +
    +
    logScaleYbool

    Flag to tell if the plot is done on a logarithmic scale for Y. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the marginal PDF of the requested couple of +margins.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computePDF, getMarginal, viewer.View, ResourceMap
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> from openturns.viewer import View
+>>> distribution = ot.Normal(10)
+>>> graph = distribution.drawMarginal2DPDF(2, 3, [-6.0] * 2, [6.0] * 2, [100] * 2)
+>>> view = View(graph)
+>>> view.show()
+
    +
    +
    + +
    +
    +drawMarginal2DSurvivalFunction(firstMarginal, secondMarginal, xMin, xMax, pointNumber, logScaleX=False, logScaleY=False)
    +

    Draw the cumulative distribution function of a couple of margins.

    +
    +
    Parameters:
    +
    +
    iint, 1 \leq i \leq n

    The index of the first margin of interest.

    +
    +
    jint, 1 \leq i \neq j \leq n

    The index of the second margin of interest.

    +
    +
    x_minlist of 2 floats

    The starting values that are used for meshing the x- and y- axes.

    +
    +
    x_maxlist of 2 floats, x_{\max} > x_{\min}

    The ending values that are used for meshing the x- and y- axes.

    +
    +
    n_pointslist of 2 ints

    The number of points that are used for meshing the x- and y- axes.

    +
    +
    logScaleXbool

    Flag to tell if the plot is done on a logarithmic scale for X. Default is False.

    +
    +
    logScaleYbool

    Flag to tell if the plot is done on a logarithmic scale for Y. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the marginal SurvivalFunction of the requested couple of +margins.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeSurvivalFunction, getMarginal, viewer.View, ResourceMap
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> from openturns.viewer import View
+>>> distribution = ot.Normal(10)
+>>> graph = distribution.drawMarginal2DSurvivalFunction(2, 3, [-6.0] * 2, [6.0] * 2, [100] * 2)
+>>> view = View(graph)
+>>> view.show()
+
    +
    +
    + +
    +
    +drawPDF(*args)
    +

    Draw the graph or of iso-lines of probability density function.

    +
    +
    Available constructors:

    drawPDF(x_min, x_max, pointNumber, logScale)

    +

    drawPDF(lowerCorner, upperCorner, pointNbrInd, logScaleX, logScaleY)

    +

    drawPDF(lowerCorner, upperCorner)

    +
    +
    +
    +
    Parameters:
    +
    +
    x_minfloat, optional

    The min-value of the mesh of the x-axis. +Defaults uses the quantile associated to the probability level +Distribution-QMin from the ResourceMap.

    +
    +
    x_maxfloat, optional, x_{\max} > x_{\min}

    The max-value of the mesh of the y-axis. +Defaults uses the quantile associated to the probability level +Distribution-QMax from the ResourceMap.

    +
    +
    pointNumberint

    The number of points that is used for meshing each axis. +Defaults uses DistributionImplementation-DefaultPointNumber from the +ResourceMap.

    +
    +
    logScalebool

    Flag to tell if the plot is done on a logarithmic scale. Default is False.

    +
    +
    lowerCornersequence of float, of dimension 2, optional

    The lower corner [x_{min}, y_{min}].

    +
    +
    upperCornersequence of float, of dimension 2, optional

    The upper corner [x_{max}, y_{max}].

    +
    +
    pointNbrIndIndices, of dimension 2

    Number of points that is used for meshing each axis.

    +
    +
    logScaleXbool

    Flag to tell if the plot is done on a logarithmic scale for X. Default is False.

    +
    +
    logScaleYbool

    Flag to tell if the plot is done on a logarithmic scale for Y. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the PDF or its iso_lines.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computePDF, viewer.View, ResourceMap
    +
    +
    +

    Notes

    +

    Only valid for univariate and bivariate distributions.

    +

    Examples

    +

    View the PDF of a univariate distribution:

    +
    >>> import openturns as ot
+>>> dist = ot.Normal()
+>>> graph = dist.drawPDF()
+>>> graph.setLegends(['normal pdf'])
+
    +
    +

    View the iso-lines PDF of a bivariate distribution:

    +
    >>> import openturns as ot
+>>> dist = ot.Normal(2)
+>>> graph2 = dist.drawPDF()
+>>> graph2.setLegends(['iso- normal pdf'])
+>>> graph3 = dist.drawPDF([-10, -5],[5, 10], [511, 511])
+
    +
    +
    + +
    +
    +drawQuantile(*args)
    +

    Draw the quantile function.

    +
    +
    Parameters:
    +
    +
    q_minfloat, in [0,1]

    The min value of the mesh of the x-axis.

    +
    +
    q_maxfloat, in [0,1]

    The max value of the mesh of the x-axis.

    +
    +
    n_pointsint, optional

    The number of points that is used for meshing the quantile curve. +Defaults uses DistributionImplementation-DefaultPointNumber from the +ResourceMap.

    +
    +
    logScalebool

    Flag to tell if the plot is done on a logarithmic scale. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the quantile function.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeQuantile, viewer.View, ResourceMap
    +
    +
    +

    Notes

    +

    This is implemented for univariate and bivariate distributions only. +In the case of bivariate distributions, defined by its CDF F and its marginals (F_1, F_2), the quantile of order q is the point (F_1(u),F_2(u)) defined by

    +
    +

    F(F_1(u), F_2(u)) = q

    +

    Examples

    +
    >>> import openturns as ot
+>>> from openturns.viewer import View
+>>> distribution = ot.Normal()
+>>> graph = distribution.drawQuantile()
+>>> view = View(graph)
+>>> view.show()
+>>> distribution = ot.ComposedDistribution([ot.Normal(), ot.Exponential(1.0)], ot.ClaytonCopula(0.5))
+>>> graph = distribution.drawQuantile()
+>>> view = View(graph)
+>>> view.show()
+
    +
    +
    + +
    +
    +drawSurvivalFunction(*args)
    +

    Draw the cumulative distribution function.

    +
    +
    Available constructors:

    drawSurvivalFunction(x_min, x_max, pointNumber, logScale)

    +

    drawSurvivalFunction(lowerCorner, upperCorner, pointNbrInd, logScaleX, logScaleY)

    +

    drawSurvivalFunction(lowerCorner, upperCorner)

    +
    +
    +
    +
    Parameters:
    +
    +
    x_minfloat, optional

    The min-value of the mesh of the x-axis. +Defaults uses the quantile associated to the probability level +Distribution-QMin from the ResourceMap.

    +
    +
    x_maxfloat, optional, x_{\max} > x_{\min}

    The max-value of the mesh of the y-axis. +Defaults uses the quantile associated to the probability level +Distribution-QMax from the ResourceMap.

    +
    +
    pointNumberint

    The number of points that is used for meshing each axis. +Defaults uses DistributionImplementation-DefaultPointNumber from the +ResourceMap.

    +
    +
    logScalebool

    Flag to tell if the plot is done on a logarithmic scale. Default is False.

    +
    +
    lowerCornersequence of float, of dimension 2, optional

    The lower corner [x_{min}, y_{min}].

    +
    +
    upperCornersequence of float, of dimension 2, optional

    The upper corner [x_{max}, y_{max}].

    +
    +
    pointNbrIndIndices, of dimension 2

    Number of points that is used for meshing each axis.

    +
    +
    logScaleXbool

    Flag to tell if the plot is done on a logarithmic scale for X. Default is False.

    +
    +
    logScaleYbool

    Flag to tell if the plot is done on a logarithmic scale for Y. Default is False.

    +
    +
    +
    +
    Returns:
    +
    +
    graphGraph

    A graphical representation of the SurvivalFunction.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computeSurvivalFunction, viewer.View, ResourceMap
    +
    +
    +

    Notes

    +

    Only valid for univariate and bivariate distributions.

    +

    Examples

    +

    View the SurvivalFunction of a univariate distribution:

    +
    >>> import openturns as ot
+>>> dist = ot.Normal()
+>>> graph = dist.drawSurvivalFunction()
+>>> graph.setLegends(['normal cdf'])
+
    +
    +

    View the iso-lines SurvivalFunction of a bivariate distribution:

    +
    >>> import openturns as ot
+>>> dist = ot.Normal(2)
+>>> graph2 = dist.drawSurvivalFunction()
+>>> graph2.setLegends(['iso- normal cdf'])
+>>> graph3 = dist.drawSurvivalFunction([-10, -5],[5, 10], [511, 511])
+
    +
    +
    + +
    +
    +drawUpperExtremalDependenceFunction()
    +

    Draw the upper extremal dependence function.

    +

    We assume that the distribution is bivariate and that its copula is denoted by C. +The upper extremal dependence function u \mapsto \bar{\chi}(u) is defined by:

    +
    +

    \bar{\chi}(u) = \frac{2 \log 1-u}{\log \bar{C}(u,u)} - 1, \forall u \in [0,1]

    +

    Refer to Tail dependence coefficients to get more details.

    +
    +
    Returns:
    +
    +
    graphGraph

    Graph of the function u \mapsto \bar{\chi}(u).

    +
    +
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> copula = ot.FrankCopula()
+>>> graph = copula.drawUpperExtremalDependenceFunction()
+
    +
    +
    + +
    +
    +drawUpperTailDependenceFunction()
    +

    Draw the upper tail dependence function.

    +

    We assume that the distribution is bivariate and that its copula is denoted by C. +The upper tail dependence function u \mapsto \chi(u) is defined by:

    +
    +

    \chi(u) = 2 - \frac{\log C(u,u)}{\log u}, \forall u \in [0,1]

    +

    Refer to Tail dependence coefficients to get more details.

    +
    +
    Returns:
    +
    +
    graphGraph

    Graph of the function u \mapsto \chi(u).

    +
    +
    +
    +
    +

    Examples

    +
    >>> import openturns as ot
+>>> copula = ot.FrankCopula()
+>>> graph = copula.drawUpperTailDependenceFunction()
+
    +
    +
    + +
    +
    +exp()
    +

    Transform distribution by exponential function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +getCDFEpsilon()
    +

    Accessor to the CDF computation precision.

    +
    +
    Returns:
    +
    +
    CDFEpsilonfloat

    CDF computation precision.

    +
    +
    +
    +
    +
    + +
    +
    +getCentralMoment(n)
    +

    Accessor to the componentwise central moments.

    +
    +
    Parameters:
    +
    +
    kint

    The order of the central moment.

    +
    +
    +
    +
    Returns:
    +
    +
    mPoint

    Componentwise central moment of order k.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getMoment
    +
    +
    +

    Notes

    +

    Central moments are centered with respect to the first-order moment:

    +
    +

    \vect{m}^{(k)}_0 = \Tr{\left(\Expect{\left(X_i - \mu_i\right)^k}, + \quad i = 1, \ldots, n\right)}

    +
    + +
    +
    +getCholesky()
    +

    Accessor to the Cholesky factor of the covariance matrix.

    +
    +
    Returns:
    +
    +
    LSquareMatrix

    Cholesky factor of the covariance matrix.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getCovariance
    +
    +
    +
    + +
    +
    +getClassName()
    +

    Accessor to the object’s name.

    +
    +
    Returns:
    +
    +
    class_namestr

    The object class name (object.__class__.__name__).

    +
    +
    +
    +
    +
    + +
    +
    +getCopula()
    +

    Accessor to the copula of the distribution.

    +
    +
    Returns:
    +
    +
    CDistribution

    Copula of the distribution.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    ComposedDistribution
    +
    +
    +
    + +
    +
    +getCorrelation()
    +
    +

    Accessor to the correlation matrix.

    +
    +
    +
    Returns:
    +
    +
    RCorrelationMatrix

    The correlation matrix of the distribution.

    +
    +
    +
    +
    +

    Notes

    +
    +

    R_{ij} = \dfrac{C_{ij}}{\sigma_i\sigma_j}

    +

    where the (\sigma_i) are the margin standard deviations +and (C_{ij}) the covariance coefficients.

    +
    + +
    +
    +getCovariance()
    +

    Accessor to the covariance matrix.

    +
    +
    Returns:
    +
    +
    SigmaCovarianceMatrix

    Covariance matrix.

    +
    +
    +
    +
    +

    Notes

    +

    The covariance is the second-order central moment. It is defined as:

    +
    +

    \mat{\Sigma} & = \Cov{\vect{X}} \\ + & = \Expect{\left(\vect{X} - \vect{\mu}\right) + \Tr{\left(\vect{X} - \vect{\mu}\right)}}

    +
    + +
    +
    +getDescription()
    +

    Accessor to the componentwise description.

    +
    +
    Returns:
    +
    +
    descriptionDescription

    Description of the components of the distribution.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    setDescription
    +
    +
    +
    + +
    +
    +getDimension()
    +

    Accessor to the dimension of the distribution.

    +
    +
    Returns:
    +
    +
    nint

    The number of components in the distribution.

    +
    +
    +
    +
    +
    + +
    +
    +getDispersionIndicator()
    +

    Dispersion indicator accessor.

    +

    Defines a generic metric of the dispersion. When the standard deviation is not +defined it falls back to the interquartile. +Only available for 1-d distributions.

    +
    +
    Returns:
    +
    +
    dispersionfloat

    Standard deviation or interquartile.

    +
    +
    +
    +
    +
    + +
    +
    +getId()
    +

    Accessor to the object’s id.

    +
    +
    Returns:
    +
    +
    idint

    Internal unique identifier.

    +
    +
    +
    +
    +
    + +
    +
    +getIntegrationNodesNumber()
    +

    Accessor to the number of Gauss integration points.

    +
    +
    Returns:
    +
    +
    Nint

    Number of integration points.

    +
    +
    +
    +
    +
    + +
    +
    +getInverseCholesky()
    +

    Accessor to the inverse Cholesky factor of the covariance matrix.

    +
    +
    Returns:
    +
    +
    LinvSquareMatrix

    Inverse Cholesky factor of the covariance matrix.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getCholesky
    +
    +
    +
    + +
    +
    +getInverseIsoProbabilisticTransformation()
    +

    Accessor to the inverse iso-probabilistic transformation.

    +
    +
    Returns:
    +
    +
    TinvFunction

    Inverse iso-probabilistic transformation.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getIsoProbabilisticTransformation
    +
    +
    +

    Notes

    +

    The inverse iso-probabilistic transformation is defined as follows:

    +
    +

    T^{-1}: \left|\begin{array}{rcl} + \Rset^n & \rightarrow & \supp{\vect{X}} \\ + \vect{u} & \mapsto & \vect{x} + \end{array}\right.

    +
    + +
    +
    +getIsoProbabilisticTransformation()
    +

    Accessor to the iso-probabilistic transformation.

    +

    Refer to Isoprobabilistic transformations.

    +
    +
    Returns:
    +
    +
    TFunction

    Iso-probabilistic transformation.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getInverseIsoProbabilisticTransformation, isElliptical, hasEllipticalCopula
    +
    +
    +

    Notes

    +

    The iso-probabilistic transformation is defined as follows:

    +
    +

    T: \left|\begin{array}{rcl} + \supp{\vect{X}} & \rightarrow & \Rset^n \\ + \vect{x} & \mapsto & \vect{u} + \end{array}\right.

    +

    An iso-probabilistic transformation is a diffeomorphism [1] from +\supp{\vect{X}} to \Rset^d that maps realizations +\vect{x} of a random vector \vect{X} into realizations +\vect{y} of another random vector \vect{Y} while +preserving probabilities. It is hence defined so that it satisfies:

    +
    +

    \begin{eqnarray*} + \Prob{\bigcap_{i=1}^d X_i \leq x_i} + & = & \Prob{\bigcap_{i=1}^d Y_i \leq y_i} \\ + F_{\vect{X}}(\vect{x}) + & = & F_{\vect{Y}}(\vect{y}) +\end{eqnarray*}

    +

    The present implementation of the iso-probabilistic transformation maps +realizations \vect{x} into realizations \vect{u} of a +random vector \vect{U} with spherical distribution [2]. +To be more specific:

    +
    +
      +

    • if the distribution is elliptical, then the transformed distribution is +simply made spherical using the Nataf (linear) transformation.

      • +

    • if the distribution has an elliptical Copula, then the transformed +distribution is made spherical using the generalized Nataf +transformation.

      • +

    • otherwise, the transformed distribution is the standard multivariate +Normal distribution and is obtained by means of the Rosenblatt +transformation.

      • +
    +
    + +
    + +
    +
    +getKendallTau()
    +

    Accessor to the Kendall coefficients matrix.

    +
    +
    Returns:
    +
    +
    tau: SquareMatrix

    Kendall coefficients matrix.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getSpearmanCorrelation
    +
    +
    +

    Notes

    +

    The Kendall coefficients matrix is defined as:

    +
    +

    \mat{\tau} = \Big[& \Prob{X_i < x_i \cap X_j < x_j + \cup + X_i > x_i \cap X_j > x_j} \\ + & - \Prob{X_i < x_i \cap X_j > x_j + \cup + X_i > x_i \cap X_j < x_j}, + \quad i,j = 1, \ldots, n\Big]

    +
    + +
    +
    +getKurtosis()
    +

    Accessor to the componentwise kurtosis.

    +
    +
    Returns:
    +
    +
    kPoint

    Componentwise kurtosis.

    +
    +
    +
    +
    +

    Notes

    +

    The kurtosis is the fourth-order central moment standardized by the standard deviation:

    +
    +

    \vect{\kappa} = \Tr{\left(\Expect{\left(\frac{X_i - \mu_i} + {\sigma_i}\right)^4}, + \quad i = 1, \ldots, n\right)}

    +
    + +
    +
    +getMarginal(*args)
    +

    Accessor to marginal distributions.

    +
    +
    Parameters:
    +
    +
    iint or list of ints, 1 \leq i \leq n

    Component(s) indice(s).

    +
    +
    +
    +
    Returns:
    +
    +
    distributionDistribution

    The marginal distribution of the selected component(s).

    +
    +
    +
    +
    +
    + +
    +
    +getMean()
    +

    Accessor to the mean.

    +
    +
    Returns:
    +
    +
    kPoint

    Mean.

    +
    +
    +
    +
    +

    Notes

    +

    The mean is the first-order moment:

    +
    +

    \vect{\mu} = \Tr{\left(\Expect{X_i}, \quad i = 1, \ldots, n\right)}

    +
    + +
    +
    +getMesh()
    +

    Accessor to the distribution’s mesh.

    +
    +
    Returns:
    +
    +
    meshMesh

    Mesh.

    +
    +
    +
    +
    +
    + +
    +
    +getMoment(n)
    +

    Accessor to the componentwise moments.

    +
    +
    Parameters:
    +
    +
    kint

    The order of the moment.

    +
    +
    +
    +
    Returns:
    +
    +
    mPoint

    Componentwise moment of order k.

    +
    +
    +
    +
    +

    Notes

    +

    The componentwise moment of order k is defined as:

    +
    +

    \vect{m}^{(k)} = \Tr{\left(\Expect{X_i^k}, \quad i = 1, \ldots, n\right)}

    +
    + +
    +
    +getName()
    +

    Accessor to the object’s name.

    +
    +
    Returns:
    +
    +
    namestr

    The name of the object.

    +
    +
    +
    +
    +
    + +
    +
    +getPDFEpsilon()
    +

    Accessor to the PDF computation precision.

    +
    +
    Returns:
    +
    +
    PDFEpsilonfloat

    PDF computation precision.

    +
    +
    +
    +
    +
    + +
    +
    +getParameter()
    +

    Accessor to the parameter of the distribution.

    +
    +
    Returns:
    +
    +
    parameterPoint

    Parameter values.

    +
    +
    +
    +
    +
    + +
    +
    +getParameterDescription()
    +

    Accessor to the parameter description of the distribution.

    +
    +
    Returns:
    +
    +
    descriptionDescription

    Parameter names.

    +
    +
    +
    +
    +
    + +
    +
    +getParameterDimension()
    +

    Accessor to the number of parameters in the distribution.

    +
    +
    Returns:
    +
    +
    n_parametersint

    Number of parameters in the distribution.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getParametersCollection
    +
    +
    +
    + +
    +
    +getParametersCollection()
    +

    Accessor to the parameter of the distribution.

    +
    +
    Returns:
    +
    +
    parametersPointWithDescription

    Dictionary-like object with parameters names and values.

    +
    +
    +
    +
    +
    + +
    +
    +getPearsonCorrelation()
    +

    Accessor to the Pearson correlation matrix.

    +
    +
    Returns:
    +
    +
    RCorrelationMatrix

    Pearson’s correlation matrix.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getCovariance
    +
    +
    +

    Notes

    +

    Pearson’s correlation is defined as the normalized covariance matrix:

    +
    +

    \mat{\rho} & = \left[\frac{\Cov{X_i, X_j}}{\sqrt{\Var{X_i}\Var{X_j}}}, + \quad i,j = 1, \ldots, n\right] \\ + & = \left[\frac{\Sigma_{i,j}}{\sqrt{\Sigma_{i,i}\Sigma_{j,j}}}, + \quad i,j = 1, \ldots, n\right]

    +
    + +
    +
    +getPositionIndicator()
    +

    Position indicator accessor.

    +

    Defines a generic metric of the position. When the mean is not defined it falls +back to the median. +Available only for 1-d distributions.

    +
    +
    Returns:
    +
    +
    positionfloat

    Mean or median of the distribution.

    +
    +
    +
    +
    +
    + +
    +
    +getProbabilities()
    +

    Accessor to the discrete probability levels.

    +
    +
    Returns:
    +
    +
    probabilitiesPoint

    The probability levels of a discrete distribution.

    +
    +
    +
    +
    +
    + +
    +
    +getRange()
    +

    Accessor to the range of the distribution.

    +
    +
    Returns:
    +
    +
    rangeInterval

    Range of the distribution.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getSupport
    +
    +
    +

    Notes

    +

    The mathematical range is the smallest closed interval outside of which the +PDF is zero. The numerical range is the interval outside of which the PDF is +rounded to zero in double precision.

    +
    + +
    +
    +getRealization()
    +

    Accessor to a pseudo-random realization from the distribution.

    +

    Refer to Distribution realizations.

    +
    +
    Returns:
    +
    +
    pointPoint

    A pseudo-random realization of the distribution.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getSample, getSampleByInversion, getSampleByQMC, RandomGenerator
    +
    +
    +
    + +
    +
    +getRoughness()
    +

    Accessor to roughness of the distribution.

    +
    +
    Returns:
    +
    +
    rfloat

    Roughness of the distribution.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    computePDF
    +
    +
    +

    Notes

    +

    The roughness of the distribution is defined as the \cL^2-norm of its +PDF:

    +
    +

    r = \int_{\supp{\vect{X}}} f_{\vect{X}}(\vect{x})^2 \di{\vect{x}}

    +
    + +
    +
    +getSample(size)
    +

    Accessor to a pseudo-random sample from the distribution.

    +
    +
    Parameters:
    +
    +
    sizeint

    Sample size.

    +
    +
    +
    +
    Returns:
    +
    +
    sampleSample

    A pseudo-random sample of the distribution.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getRealization, RandomGenerator, getSampleByInversion, getSampleByQMC
    +
    +
    +
    + +
    +
    +getSampleByInversion(size)
    +

    Accessor to a pseudo-random sample from the distribution.

    +
    +
    Parameters:
    +
    +
    sizeint

    Sample size.

    +
    +
    +
    +
    Returns:
    +
    +
    sampleSample

    A pseudo-random sample of the distribution based on conditional quantiles.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getRealization, RandomGenerator, getSample, getSampleByQMC
    +
    +
    +
    + +
    +
    +getSampleByQMC(size)
    +

    Accessor to a low discrepancy sample from the distribution.

    +
    +
    Parameters:
    +
    +
    sizeint

    Sample size.

    +
    +
    +
    +
    Returns:
    +
    +
    sampleSample

    A low discrepancy sample of the distribution based on Sobol’s sequences +and conditional quantiles.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getRealization, RandomGenerator, getSample, getSampleByInversion
    +
    +
    +
    + +
    +
    +getShadowedId()
    +

    Accessor to the object’s shadowed id.

    +
    +
    Returns:
    +
    +
    idint

    Internal unique identifier.

    +
    +
    +
    +
    +
    + +
    +
    +getShapeMatrix()
    +

    Accessor to the shape matrix of the underlying copula if it is elliptical.

    +
    +
    Returns:
    +
    +
    shapeCorrelationMatrix

    Shape matrix of the elliptical copula of a distribution.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getPearsonCorrelation
    +
    +
    +

    Notes

    +

    This is not the Pearson correlation matrix.

    +
    + +
    +
    +getShiftedMoment(n, shift)
    +

    Accessor to the componentwise shifted moments.

    +
    +
    Parameters:
    +
    +
    kint

    The order of the shifted moment.

    +
    +
    shiftsequence of float

    The shift of the moment.

    +
    +
    +
    +
    Returns:
    +
    +
    mPoint

    Componentwise central moment of order k.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getMoment, getCentralMoment
    +
    +
    +

    Notes

    +

    The moments are centered with respect to the given shift \vect{s}:

    +
    +

    \vect{m}^{(k)}_0 = \Tr{\left(\Expect{\left(X_i - s_i\right)^k}, + \quad i = 1, \ldots, n\right)}

    +
    + +
    +
    +getSingularities()
    +

    Accessor to the singularities of the PDF function.

    +

    It is defined for univariate distributions only, and gives all the singularities (ie discontinuities of any order) strictly inside of the range of the distribution.

    +
    +
    Returns:
    +
    +
    singularitiesPoint

    The singularities of the PDF of an univariate distribution.

    +
    +
    +
    +
    +
    + +
    +
    +getSkewness()
    +

    Accessor to the componentwise skewness.

    +
    +
    Returns:
    +
    +
    dPoint

    Componentwise skewness.

    +
    +
    +
    +
    +

    Notes

    +

    The skewness is the third-order central moment standardized by the standard deviation:

    +
    +

    \vect{\delta} = \Tr{\left(\Expect{\left(\frac{X_i - \mu_i} + {\sigma_i}\right)^3}, + \quad i = 1, \ldots, n\right)}

    +
    + +
    +
    +getSpearmanCorrelation()
    +

    Accessor to the Spearman correlation matrix.

    +
    +
    Returns:
    +
    +
    RCorrelationMatrix

    Spearman’s correlation matrix.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getKendallTau
    +
    +
    +

    Notes

    +

    Spearman’s (rank) correlation is defined as the normalized covariance matrix +of the copula (ie that of the uniform margins):

    +
    +

    \mat{\rho_S} = \left[\frac{\Cov{F_{X_i}(X_i), F_{X_j}(X_j)}} + {\sqrt{\Var{F_{X_i}(X_i)} \Var{F_{X_j}(X_j)}}}, + \quad i,j = 1, \ldots, n\right]

    +
    + +
    +
    +getStandardDeviation()
    +

    Accessor to the componentwise standard deviation.

    +

    The standard deviation is the square root of the variance.

    +
    +
    Returns:
    +
    +
    sigmaPoint

    Componentwise standard deviation.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getCovariance
    +
    +
    +
    + +
    +
    +getStandardDistribution()
    +

    Accessor to the standard distribution.

    +
    +
    Returns:
    +
    +
    standard_distributionDistribution

    Standard distribution.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getIsoProbabilisticTransformation
    +
    +
    +

    Notes

    +

    The standard distribution is determined according to the distribution +properties. This is the target distribution achieved by the iso-probabilistic +transformation.

    +
    + +
    +
    +getStandardRepresentative()
    +

    Accessor to the standard representative distribution in the parametric family.

    +
    +
    Returns:
    +
    +
    std_repr_distDistribution

    Standard representative distribution.

    +
    +
    +
    +
    +

    Notes

    +

    The standard representative distribution is defined on a distribution by distribution basis, most of the time by scaling the distribution with bounded support to [0,1] or by standardizing (ie zero mean, unit variance) the distributions with unbounded support. It is the member of the family for which orthonormal polynomials will be built using generic algorithms of orthonormalization.

    +
    + +
    +
    +getSupport(*args)
    +

    Accessor to the support of the distribution.

    +
    +
    Parameters:
    +
    +
    intervalInterval

    An interval to intersect with the support of the discrete part of the distribution.

    +
    +
    +
    +
    Returns:
    +
    +
    supportInterval

    The intersection of the support of the discrete part of the distribution with the given interval.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    getRange
    +
    +
    +

    Notes

    +

    The mathematical support \supp{\vect{X}} of the discrete part of a distribution is the collection of points with nonzero probability.

    +

    This is yet implemented for discrete distributions only.

    +
    + +
    +
    +getVisibility()
    +

    Accessor to the object’s visibility state.

    +
    +
    Returns:
    +
    +
    visiblebool

    Visibility flag.

    +
    +
    +
    +
    +
    + +
    +
    +hasEllipticalCopula()
    +

    Test whether the copula of the distribution is elliptical or not.

    +
    +
    Returns:
    +
    +
    testbool

    Answer.

    +
    +
    +
    +
    +
    +

    See also

    +
    +
    isElliptical
    +
    +
    +
    + +
    +
    +hasIndependentCopula()
    +

    Test whether the copula of the distribution is the independent one.

    +
    +
    Returns:
    +
    +
    testbool

    Answer.

    +
    +
    +
    +
    +
    + +
    +
    +hasName()
    +

    Test if the object is named.

    +
    +
    Returns:
    +
    +
    hasNamebool

    True if the name is not empty.

    +
    +
    +
    +
    +
    + +
    +
    +hasVisibleName()
    +

    Test if the object has a distinguishable name.

    +
    +
    Returns:
    +
    +
    hasVisibleNamebool

    True if the name is not empty and not the default one.

    +
    +
    +
    +
    +
    + +
    +
    +inverse()
    +

    Transform distribution by inverse function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +isContinuous()
    +

    Test whether the distribution is continuous or not.

    +
    +
    Returns:
    +
    +
    testbool

    Answer.

    +
    +
    +
    +
    +
    + +
    +
    +isCopula()
    +

    Test whether the distribution is a copula or not.

    +
    +
    Returns:
    +
    +
    testbool

    Answer.

    +
    +
    +
    +
    +

    Notes

    +

    A copula is a distribution with uniform margins on [0; 1].

    +
    + +
    +
    +isDiscrete()
    +

    Test whether the distribution is discrete or not.

    +
    +
    Returns:
    +
    +
    testbool

    Answer.

    +
    +
    +
    +
    +
    + +
    +
    +isElliptical()
    +

    Test whether the distribution is elliptical or not.

    +
    +
    Returns:
    +
    +
    testbool

    Answer.

    +
    +
    +
    +
    +

    Notes

    +

    A multivariate distribution is said to be elliptical if its characteristic +function is of the form:

    +
    +

    \phi(\vect{t}) = \exp\left(i \Tr{\vect{t}} \vect{\mu}\right) + \Psi\left(\Tr{\vect{t}} \mat{\Sigma} \vect{t}\right), + \quad \vect{t} \in \Rset^n

    +

    for specified vector \vect{\mu} and positive-definite matrix +\mat{\Sigma}. The function \Psi is known as the +characteristic generator of the elliptical distribution.

    +
    + +
    +
    +isIntegral()
    +

    Test whether the distribution is integer-valued or not.

    +
    +
    Returns:
    +
    +
    testbool

    Answer.

    +
    +
    +
    +
    +
    + +
    +
    +ln()
    +

    Transform distribution by natural logarithm function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +log()
    +

    Transform distribution by natural logarithm function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +setDescription(description)
    +

    Accessor to the componentwise description.

    +
    +
    Parameters:
    +
    +
    descriptionsequence of str

    Description of the components of the distribution.

    +
    +
    +
    +
    +
    + +
    +
    +setIntegrationNodesNumber(integrationNodesNumber)
    +

    Accessor to the number of Gauss integration points.

    +
    +
    Parameters:
    +
    +
    Nint

    Number of integration points.

    +
    +
    +
    +
    +
    + +
    +
    +setMesh(mesh)
    +

    Accessor to the distribution’s mesh.

    +
    +
    Parameters:
    +
    +
    meshMesh

    Mesh.

    +
    +
    +
    +
    +
    + +
    +
    +setName(name)
    +

    Accessor to the object’s name.

    +
    +
    Parameters:
    +
    +
    namestr

    The name of the object.

    +
    +
    +
    +
    +
    + +
    +
    +setParameter(parameters)
    +

    Accessor to the parameter of the distribution.

    +
    +
    Parameters:
    +
    +
    parametersequence of float

    Parameter values.

    +
    +
    +
    +
    +
    + +
    +
    +setParametersCollection(*args)
    +

    Accessor to the parameter of the distribution.

    +
    +
    Parameters:
    +
    +
    parametersPointWithDescription

    Dictionary-like object with parameters names and values.

    +
    +
    +
    +
    +
    + +
    +
    +setShadowedId(id)
    +

    Accessor to the object’s shadowed id.

    +
    +
    Parameters:
    +
    +
    idint

    Internal unique identifier.

    +
    +
    +
    +
    +
    + +
    +
    +setVisibility(visible)
    +

    Accessor to the object’s visibility state.

    +
    +
    Parameters:
    +
    +
    visiblebool

    Visibility flag.

    +
    +
    +
    +
    +
    + +
    +
    +sin()
    +

    Transform distribution by sine function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +sinh()
    +

    Transform distribution by sinh function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +sqr()
    +

    Transform distribution by square function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +sqrt()
    +

    Transform distribution by square root function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +tan()
    +

    Transform distribution by tangent function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    +
    +tanh()
    +

    Transform distribution by tanh function.

    +
    +
    Returns:
    +
    +
    distDistribution

    The transformed distribution.

    +
    +
    +
    +
    +
    + +
    + +
    + + +
    +
    +
    +
    +
    +
    + + + + \ No newline at end of file diff --git a/openturns/master/user_manual/integration.html b/openturns/master/user_manual/integration.html index 99ed04a917e..548c43e0286 100644 --- a/openturns/master/user_manual/integration.html +++ b/openturns/master/user_manual/integration.html @@ -118,6 +118,9 @@

    Integration

    FilonQuadrature(*args)

    Tensorized integration algorithm of Gauss-Legendre.

    +

    experimental.SimplicialCubature(*args)

    +

    Integration over a simplex.

    + diff --git a/openturns/master/user_manual/probabilistic_modelling.html b/openturns/master/user_manual/probabilistic_modelling.html index 0c1ed7ae7e8..a7f7c60678e 100644 --- a/openturns/master/user_manual/probabilistic_modelling.html +++ b/openturns/master/user_manual/probabilistic_modelling.html @@ -274,22 +274,25 @@

    Probabilistic modelling

    - + + + + - + - + - + - + - +

    TruncatedNormal(*args)

    TruncatedNormal distribution.

    Uniform(*args)

    experimental.TruncatedOverMesh(*args)

    Truncated distribution over a mesh.

    Uniform(*args)

    Uniform distribution.

    experimental.UniformOverMesh(*args)

    experimental.UniformOverMesh(*args)

    UniformOverMesh distribution.

    VonMises(*args)

    VonMises(*args)

    Von Mises distribution.

    WeibullMin(*args)

    WeibullMin(*args)

    WeibullMin distribution.

    WeibullMax(*args)

    WeibullMax(*args)

    WeibullMax distribution.

    Wishart(*args)

    Wishart(*args)

    Wishart distribution.