.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_cobweb.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_cobweb.py:


Cobweb graph as sensitivity tool
================================

The Cobweb graph enables to visualize all the combinations of the input
variables which lead to a specific range of the output variable.

Let us consider a model :math:`f: \mathbb{R}^n \longrightarrow \mathbb{R}`, where :math:`f(\underline{X}) = Y`.

The graph requires to have an input sample :math:`X_s` and an output sample :math:`Y_s`.

The first figure draws such a graph: each column represents one component
:math:`X_i` of the input vector :math:`\underline{X}`.
The last column represents the scalar output variable :math:`Y`.
For each point :math:`\underline{X}^j`, each component :math:`X_i^j`
is noted on its respective axe and the last mark is the one which corresponds to
the associated :math:`Y^j`. A line joins all the marks. Thus, each point of the sample
corresponds to a particular line on the graph.

The scale of the axes are quantile based: each axe runs between 0 and 1 and each
value is represented by its quantile with respect to its marginal empirical distribution.

It is interesting to select, among those lines, the ones which correspond to a specific range of the output variable.
These particular lines are colored differently.
This specific range is defined in the quantile based scale of :math:`Y` or in its specific scale.
In that second case, the range is automatically converted into a quantile based scale range.


.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    ot.Log.Show(ot.Log.NONE)








Create data to visualize


.. code-block:: default


    # Create the model Y = x1^2 + x2
    model = ot.SymbolicFunction(["x1", "x2"], ["x1^2+x2"])

    # Create the input distribution and random vector X
    myCorMat = ot.CorrelationMatrix(2)
    myCorMat[0, 1] = -0.6
    inputDist = ot.Normal([0., 0.], myCorMat)
    inputDist.setDescription(['X1', 'X2'])

    inputVector = ot.RandomVector(inputDist)

    # Create the output random vector Y=model(X)
    output = ot.CompositeRandomVector(model, inputVector)

    # Generate the input sample
    N = 500
    X = inputVector.getSample(N)

    # Evaluate the associated output sample
    Y = model(X)
    Y.setDescription("Y")

    print(Y.getMin(), Y.getMax(), Y.computeQuantilePerComponent(0.9))





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [-2.65806] [11.6998] [2.98118]




Example 1: value based scale to describe the Y range


.. code-block:: default

    minValue = 3.35
    maxValue = 20.0
    quantileScale = False
    graphCobweb = ot.VisualTest.DrawCobWeb(X, Y, minValue, maxValue, 'red', quantileScale)
    graphCobweb.setLegendPosition('bottomright')
    view = viewer.View(graphCobweb)




.. image:: /auto_reliability_sensitivity/sensitivity_analysis/images/sphx_glr_plot_sensitivity_cobweb_001.png
    :alt: Cobweb graph - [Y] vs [X1,X2]
    :class: sphx-glr-single-img





Example 2: rank based scale to describe the Y range


.. code-block:: default

    minValue = 0.9
    maxValue = 1.0
    quantileScale = True
    graphCobweb = ot.VisualTest.DrawCobWeb(X, Y, minValue, maxValue, 'red', quantileScale)
    graphCobweb.setLegendPosition('bottomright')
    view = viewer.View(graphCobweb)
    plt.show()



.. image:: /auto_reliability_sensitivity/sensitivity_analysis/images/sphx_glr_plot_sensitivity_cobweb_002.png
    :alt: Cobweb graph - [Y] vs [X1,X2]
    :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.911 seconds)


.. _sphx_glr_download_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_cobweb.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: plot_sensitivity_cobweb.py <plot_sensitivity_cobweb.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: plot_sensitivity_cobweb.ipynb <plot_sensitivity_cobweb.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_