.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_par_coo.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_par_coo.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_par_coo.py:


Parallel coordinates graph as sensitivity tool
==============================================

.. GENERATED FROM PYTHON SOURCE LINES 6-28

The parallel coordinates 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.

.. GENERATED FROM PYTHON SOURCE LINES 30-36

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt

    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 37-38

Create data to visualize

.. GENERATED FROM PYTHON SOURCE LINES 38-63

.. code-block:: Python


    # 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, 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

 .. code-block:: none

    [-2.24595] [11.4925] [2.95502]




.. GENERATED FROM PYTHON SOURCE LINES 64-65

Example 1: value based scale to describe the Y range

.. GENERATED FROM PYTHON SOURCE LINES 65-74

.. code-block:: Python

    minValue = 3.35
    maxValue = 20.0
    quantileScale = False
    graphCobweb = ot.VisualTest.DrawParallelCoordinates(
        X, Y, minValue, maxValue, "red", quantileScale
    )
    graphCobweb.setLegendPosition("lower right")
    view = viewer.View(graphCobweb)




.. image-sg:: /auto_reliability_sensitivity/sensitivity_analysis/images/sphx_glr_plot_sensitivity_par_coo_001.png
   :alt: Parallel coordinates - [Y] vs [X1,X2]
   :srcset: /auto_reliability_sensitivity/sensitivity_analysis/images/sphx_glr_plot_sensitivity_par_coo_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 75-76

Example 2: rank based scale to describe the Y range

.. GENERATED FROM PYTHON SOURCE LINES 76-85

.. code-block:: Python

    minValue = 0.9
    maxValue = 1.0
    quantileScale = True
    graphCobweb = ot.VisualTest.DrawParallelCoordinates(
        X, Y, minValue, maxValue, "red", quantileScale
    )
    graphCobweb.setLegendPosition("lower right")
    view = viewer.View(graphCobweb)
    plt.show()



.. image-sg:: /auto_reliability_sensitivity/sensitivity_analysis/images/sphx_glr_plot_sensitivity_par_coo_002.png
   :alt: Parallel coordinates - [Y] vs [X1,X2]
   :srcset: /auto_reliability_sensitivity/sensitivity_analysis/images/sphx_glr_plot_sensitivity_par_coo_002.png
   :class: sphx-glr-single-img






.. _sphx_glr_download_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_par_coo.py:

.. only:: html

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

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

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

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

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