.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/uncertainty/sensitivity/plot_correlation.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_uncertainty_sensitivity_plot_correlation.py: Correlation analysis ==================== .. GENERATED FROM PYTHON SOURCE LINES 25-37 .. code-block:: Python from __future__ import annotations import pprint from gemseo import configure_logger from gemseo.problems.uncertainty.ishigami.ishigami_discipline import IshigamiDiscipline from gemseo.problems.uncertainty.ishigami.ishigami_space import IshigamiSpace from gemseo.uncertainty.sensitivity.correlation_analysis import CorrelationAnalysis configure_logger() .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 38-50 In this example, we consider the Ishigami function :cite:`ishigami1990` .. math:: f(x_1,x_2,x_3)=\sin(x_1)+7\sin(x_2)^2+0.1x_3^4\sin(x_1) implemented as an :class:`.Discipline` by the :class:`.IshigamiDiscipline`. It is commonly used with the independent random variables :math:`X_1`, :math:`X_2` and :math:`X_3` uniformly distributed between :math:`-\pi` and :math:`\pi` and defined in the :class:`.IshigamiSpace`. .. GENERATED FROM PYTHON SOURCE LINES 50-54 .. code-block:: Python discipline = IshigamiDiscipline() uncertain_space = IshigamiSpace() .. GENERATED FROM PYTHON SOURCE LINES 55-57 Then, we run sensitivity analysis of type :class:`.CorrelationAnalysis`: .. GENERATED FROM PYTHON SOURCE LINES 57-61 .. code-block:: Python sensitivity_analysis = CorrelationAnalysis() sensitivity_analysis.compute_samples([discipline], uncertain_space, 1000) sensitivity_analysis.compute_indices() .. rst-class:: sphx-glr-script-out .. code-block:: none WARNING - 08:35:11: No coupling in MDA, switching chain_linearize to True. INFO - 08:35:11: INFO - 08:35:11: *** Start CorrelationAnalysisSamplingPhase execution *** INFO - 08:35:11: CorrelationAnalysisSamplingPhase INFO - 08:35:11: Disciplines: IshigamiDiscipline INFO - 08:35:11: MDO formulation: MDF INFO - 08:35:11: Running the algorithm OT_MONTE_CARLO: INFO - 08:35:11: 1%| | 6/1000 [00:00<00:00, 1166.60 it/sec] INFO - 08:35:11: 1%| | 7/1000 [00:00<00:00, 1221.25 it/sec] INFO - 08:35:11: 1%| | 8/1000 [00:00<00:00, 1267.64 it/sec] INFO - 08:35:11: 1%| | 9/1000 [00:00<00:00, 1307.50 it/sec] INFO - 08:35:11: 1%| | 10/1000 [00:00<00:00, 1342.18 it/sec] INFO - 08:35:11: 1%| | 11/1000 [00:00<00:00, 1371.79 it/sec] INFO - 08:35:11: 1%| | 12/1000 [00:00<00:00, 1398.26 it/sec] INFO - 08:35:11: 1%|▏ | 13/1000 [00:00<00:00, 1414.97 it/sec] INFO - 08:35:11: 1%|▏ | 14/1000 [00:00<00:00, 1433.64 it/sec] INFO - 08:35:11: 2%|▏ | 15/1000 [00:00<00:00, 1449.64 it/sec] INFO - 08:35:11: 2%|▏ | 16/1000 [00:00<00:00, 1465.52 it/sec] INFO - 08:35:11: 2%|▏ | 17/1000 [00:00<00:00, 1479.99 it/sec] INFO - 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08:35:12: *** End CorrelationAnalysisSamplingPhase execution (time: 0:00:00.932582) *** CorrelationAnalysis.SensitivityIndices(kendall={'y': [{'x1': array([0.31460661]), 'x2': array([0.02366366]), 'x3': array([0.0297978])}]}, pcc={'y': [{'x1': array([0.46282123]), 'x2': array([0.0306214]), 'x3': array([0.0512473])}]}, pearson={'y': [{'x1': array([0.46230446]), 'x2': array([0.02059071]), 'x3': array([0.04979026])}]}, prcc={'y': [{'x1': array([0.47248718]), 'x2': array([0.04368652]), 'x3': array([0.0419606])}]}, spearman={'y': [{'x1': array([0.47177886]), 'x2': array([0.03220921]), 'x3': array([0.04128518])}]}, src={'y': [{'x1': array([0.46220697]), 'x2': array([0.027121]), 'x3': array([0.04542585])}]}, srrc={'y': [{'x1': array([0.4718925]), 'x2': array([0.03849088]), 'x3': array([0.03696642])}]}, ssrc={'y': [{'x1': array([0.21363529]), 'x2': array([0.00073555]), 'x3': array([0.00206351])}]}) .. GENERATED FROM PYTHON SOURCE LINES 62-71 The resulting indices are - the Pearson correlation coefficients, - the Spearman correlation coefficients, - the Partial Correlation Coefficients (PCC), - the Partial Rank Correlation Coefficients (PRCC), - the Standard Regression Coefficients (SRC), - the Standard Rank Regression Coefficient (SRRC), - the Signed Standard Rank Regression Coefficient (SSRRC): .. GENERATED FROM PYTHON SOURCE LINES 71-73 .. code-block:: Python sensitivity_analysis.indices .. rst-class:: sphx-glr-script-out .. code-block:: none CorrelationAnalysis.SensitivityIndices(kendall={'y': [{'x1': array([0.31460661]), 'x2': array([0.02366366]), 'x3': array([0.0297978])}]}, pcc={'y': [{'x1': array([0.46282123]), 'x2': array([0.0306214]), 'x3': array([0.0512473])}]}, pearson={'y': [{'x1': array([0.46230446]), 'x2': array([0.02059071]), 'x3': array([0.04979026])}]}, prcc={'y': [{'x1': array([0.47248718]), 'x2': array([0.04368652]), 'x3': array([0.0419606])}]}, spearman={'y': [{'x1': array([0.47177886]), 'x2': array([0.03220921]), 'x3': array([0.04128518])}]}, src={'y': [{'x1': array([0.46220697]), 'x2': array([0.027121]), 'x3': array([0.04542585])}]}, srrc={'y': [{'x1': array([0.4718925]), 'x2': array([0.03849088]), 'x3': array([0.03696642])}]}, ssrc={'y': [{'x1': array([0.21363529]), 'x2': array([0.00073555]), 'x3': array([0.00206351])}]}) .. GENERATED FROM PYTHON SOURCE LINES 74-76 The main indices corresponds to the Spearman correlation indices (this main method can be changed with :attr:`.CorrelationAnalysis.main_method`): .. GENERATED FROM PYTHON SOURCE LINES 76-78 .. code-block:: Python pprint.pprint(sensitivity_analysis.main_indices) .. rst-class:: sphx-glr-script-out .. code-block:: none {'y': [{'x1': array([0.47177886]), 'x2': array([0.03220921]), 'x3': array([0.04128518])}]} .. GENERATED FROM PYTHON SOURCE LINES 79-80 We can also get the input parameters sorted by decreasing order of influence: .. GENERATED FROM PYTHON SOURCE LINES 80-82 .. code-block:: Python sensitivity_analysis.sort_input_variables("y") .. rst-class:: sphx-glr-script-out .. code-block:: none ['x1', 'x3', 'x2'] .. GENERATED FROM PYTHON SOURCE LINES 83-85 We can use the method :meth:`.CorrelationAnalysis.plot` to visualize the different correlation coefficients: .. GENERATED FROM PYTHON SOURCE LINES 85-87 .. code-block:: Python sensitivity_analysis.plot("y", save=False, show=True) .. image-sg:: /examples/uncertainty/sensitivity/images/sphx_glr_plot_correlation_001.png :alt: Correlation indices for the output y :srcset: /examples/uncertainty/sensitivity/images/sphx_glr_plot_correlation_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.0.0/lib/python3.9/site-packages/gemseo/post/dataset/plots/_matplotlib/plot.py:87: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect. figure.tight_layout() .. GENERATED FROM PYTHON SOURCE LINES 88-90 Lastly, the sensitivity indices can be exported to a :class:`.Dataset`: .. GENERATED FROM PYTHON SOURCE LINES 90-91 .. code-block:: Python sensitivity_analysis.to_dataset() .. raw:: html

GROUP	kendall	pcc	pearson	prcc	spearman	src	srrc	ssrc
VARIABLE	y	y	y	y	y	y	y	y
COMPONENT	0	0	0	0	0	0	0	0
x1	0.314607	0.462821	0.462304	0.472487	0.471779	0.462207	0.471893	0.213635
x2	0.023664	0.030621	0.020591	0.043687	0.032209	0.027121	0.038491	0.000736
x3	0.029798	0.051247	0.049790	0.041961	0.041285	0.045426	0.036966	0.002064

.. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.186 seconds) .. _sphx_glr_download_examples_uncertainty_sensitivity_plot_correlation.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_correlation.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_correlation.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_correlation.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_