.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/uncertainty/sensitivity/plot_sensitivity_comparison.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_uncertainty_sensitivity_plot_sensitivity_comparison.py: Comparing sensitivity indices ============================= .. GENERATED FROM PYTHON SOURCE LINES 25-34 .. code-block:: default from __future__ import annotations from gemseo.algos.parameter_space import ParameterSpace from gemseo.api import create_discipline from gemseo.uncertainty.sensitivity.correlation.analysis import CorrelationAnalysis from gemseo.uncertainty.sensitivity.morris.analysis import MorrisAnalysis from matplotlib import pyplot as plt from numpy import pi .. GENERATED FROM PYTHON SOURCE LINES 35-43 In this example, we consider the Ishigami function: .. math:: Y=\sin(X_1)+7\sin(X_2)^2+0.1*X_3^4\sin(X_1) which is well-known in the uncertainty domain: .. GENERATED FROM PYTHON SOURCE LINES 43-47 .. code-block:: default expressions = {"y": "sin(x1)+7*sin(x2)**2+0.1*x3**4*sin(x1)"} discipline = create_discipline( "AnalyticDiscipline", expressions=expressions, name="Ishigami" ) .. GENERATED FROM PYTHON SOURCE LINES 48-51 The different uncertain variables :math:`X_1` , :math:`X_2` and :math:`X_3` are independent and identically distributed according to an uniform distribution between :math:`-\pi` and :math:`\pi`: .. GENERATED FROM PYTHON SOURCE LINES 51-57 .. code-block:: default space = ParameterSpace() for variable in ["x1", "x2", "x3"]: space.add_random_variable( variable, "OTUniformDistribution", minimum=-pi, maximum=pi ) .. GENERATED FROM PYTHON SOURCE LINES 58-66 We would like to carry out two sensitivity analyses, e.g. a first one based on correlation coefficients and a second one based on the Morris methodology, and compare the results, Firstly, we create a :class:`.CorrelationAnalysis` and compute the sensitivity indices: .. GENERATED FROM PYTHON SOURCE LINES 66-69 .. code-block:: default correlation = CorrelationAnalysis([discipline], space, 10) correlation.compute_indices() .. rst-class:: sphx-glr-script-out .. code-block:: none {'pearson': {'y': [{'x1': array([0.685388]), 'x2': array([0.09681897]), 'x3': array([-0.23027298])}]}, 'spearman': {'y': [{'x1': array([0.74545455]), 'x2': array([0.04242424]), 'x3': array([-0.09090909])}]}, 'pcc': {'y': [{'x1': array([0.84696461]), 'x2': array([0.68814608]), 'x3': array([-0.29846394])}]}, 'prcc': {'y': [{'x1': array([0.90374102]), 'x2': array([0.76539572]), 'x3': array([-0.02232206])}]}, 'src': {'y': [{'x1': array([0.88362459]), 'x2': array([0.31079367]), 'x3': array([0.0261049])}]}, 'srrc': {'y': [{'x1': array([1.12896579]), 'x2': array([0.36201552]), 'x3': array([9.21486583e-05])}]}, 'ssrrc': {'y': [{'x1': array([0.94001308]), 'x2': array([0.55748872]), 'x3': array([-0.16157012])}]}} .. GENERATED FROM PYTHON SOURCE LINES 70-73 Then, we create a :class:`.MorrisAnalysis` and compute the sensitivity indices: .. GENERATED FROM PYTHON SOURCE LINES 73-76 .. code-block:: default morris = MorrisAnalysis([discipline], space, 10) morris.compute_indices() .. rst-class:: sphx-glr-script-out .. code-block:: none {'mu': {'y': [{'x1': array([-0.36000398]), 'x2': array([0.77781853]), 'x3': array([-0.70990541])}]}, 'mu_star': {'y': [{'x1': array([0.67947346]), 'x2': array([0.88906579]), 'x3': array([0.72694219])}]}, 'sigma': {'y': [{'x1': array([0.98724949]), 'x2': array([0.79064599]), 'x3': array([0.8074493])}]}, 'relative_sigma': {'y': [{'x1': array([1.45296254]), 'x2': array([0.88929976]), 'x3': array([1.11074761])}]}, 'min': {'y': [{'x1': array([0.0338188]), 'x2': array([0.11821721]), 'x3': array([8.72820113e-05])}]}, 'max': {'y': [{'x1': array([2.2360336]), 'x2': array([1.83987522]), 'x3': array([2.12052546])}]}} .. GENERATED FROM PYTHON SOURCE LINES 77-81 Lastly, we compare these analyses with the graphical method :meth:`.SensitivityAnalysis.plot_comparison`, either using a bar chart: .. GENERATED FROM PYTHON SOURCE LINES 81-83 .. code-block:: default morris.plot_comparison(correlation, "y", use_bar_plot=True, save=False, show=False) .. image-sg:: /examples/uncertainty/sensitivity/images/sphx_glr_plot_sensitivity_comparison_001.png :alt: plot sensitivity comparison :srcset: /examples/uncertainty/sensitivity/images/sphx_glr_plot_sensitivity_comparison_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 84-85 or a radar plot: .. GENERATED FROM PYTHON SOURCE LINES 85-88 .. code-block:: default morris.plot_comparison(correlation, "y", use_bar_plot=False, save=False, show=False) # Workaround for HTML rendering, instead of ``show=True`` plt.show() .. image-sg:: /examples/uncertainty/sensitivity/images/sphx_glr_plot_sensitivity_comparison_002.png :alt: plot sensitivity comparison :srcset: /examples/uncertainty/sensitivity/images/sphx_glr_plot_sensitivity_comparison_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.527 seconds) .. _sphx_glr_download_examples_uncertainty_sensitivity_plot_sensitivity_comparison.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_sensitivity_comparison.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_sensitivity_comparison.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_