.. 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 25-34 .. code-block:: Python from __future__ import annotations import pprint 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 .. GENERATED FROM PYTHON SOURCE LINES 35-47 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 47-51 .. code-block:: Python discipline = IshigamiDiscipline() uncertain_space = IshigamiSpace() .. GENERATED FROM PYTHON SOURCE LINES 52-54 Then, we run sensitivity analysis of type :class:`.CorrelationAnalysis`: .. GENERATED FROM PYTHON SOURCE LINES 54-58 .. 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 INFO - 16:22:30: *** Start CorrelationAnalysisSamplingPhase execution *** INFO - 16:22:30: CorrelationAnalysisSamplingPhase INFO - 16:22:30: Disciplines: IshigamiDiscipline INFO - 16:22:30: MDO formulation: MDF INFO - 16:22:30: Running the algorithm OT_MONTE_CARLO: INFO - 16:22:30: 1%| | 6/1000 [00:00<00:00, 1832.11 it/sec] INFO - 16:22:30: 1%| | 7/1000 [00:00<00:00, 1925.25 it/sec] INFO - 16:22:30: 1%| | 8/1000 [00:00<00:00, 2055.15 it/sec] INFO - 16:22:30: 1%| | 9/1000 [00:00<00:00, 2166.11 it/sec] INFO - 16:22:30: 1%| | 10/1000 [00:00<00:00, 2271.73 it/sec] INFO - 16:22:30: 1%| | 11/1000 [00:00<00:00, 2369.91 it/sec] INFO - 16:22:30: 1%| | 12/1000 [00:00<00:00, 2460.72 it/sec] INFO - 16:22:30: 1%|▏ | 13/1000 [00:00<00:00, 2534.79 it/sec] INFO - 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16:22:30: 100%|██████████| 1000/1000 [00:00<00:00, 4083.83 it/sec] INFO - 16:22:30: *** End CorrelationAnalysisSamplingPhase execution *** 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 59-68 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 68-70 .. 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 71-73 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 73-75 .. 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 76-77 We can also get the input parameters sorted by decreasing order of influence: .. GENERATED FROM PYTHON SOURCE LINES 77-79 .. 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 80-82 We can use the method :meth:`.CorrelationAnalysis.plot` to visualize the different correlation coefficients: .. GENERATED FROM PYTHON SOURCE LINES 82-84 .. 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 .. GENERATED FROM PYTHON SOURCE LINES 85-87 Lastly, the sensitivity indices can be exported to a :class:`.Dataset`: .. GENERATED FROM PYTHON SOURCE LINES 87-88 .. 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 0.749 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 `_