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

.. only:: html

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

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

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

.. _sphx_glr_auto_data_analysis_manage_data_and_samples_plot_sample_manipulation.py:


Sample manipulation
===================

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This example will describe the main statistical functionalities on data through the :class:`~openturns.Sample` object. The Sample is an output variable of interest.

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.. code-block:: Python

    import openturns as ot









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A typical example
-----------------

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A recurring issue in uncertainty quantification is to perform analysis on an output variable of interest `Y` obtained through a model `f` and input parameters `X`.
Here we shall consider the input parameters as two independent standard Normal distributions :math:`X=(X_1, X_2)`.
We therefore use an :class:`~openturns.IndependentCopula` to describe the link between the two marginals.


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.. code-block:: Python


    # input parameters
    inputDist = ot.JointDistribution([ot.Normal()] * 2, ot.IndependentCopula(2))
    inputDist.setDescription(["X1", "X2"])








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We create a vector from the 2d-distribution created before :

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.. code-block:: Python

    inputVector = ot.RandomVector(inputDist)









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Suppose our model `f` is known and reads as :

.. math::
   f(x) = \begin{pmatrix}
            x_1^2 + x_2 \\
            x_1   + x_2^2
          \end{pmatrix}

We define our model `f` with a :class:`~openturns.SymbolicFunction`

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.. code-block:: Python

    f = ot.SymbolicFunction(["x1", "x2"], ["x1^2+x2", "x2^2+x1"])








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Our output vector is :math:`Y = f(X)`, the image of the inputVector by the model

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.. code-block:: Python

    outputVector = ot.CompositeRandomVector(f, inputVector)








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We can now get a sample out of `Y`, that is realizations (here 1000) of the random outputVector

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.. code-block:: Python

    size = 1000
    sample = outputVector.getSample(size)








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The sample may be seen as a matrix of size :math:`1000 \times 2`. We print the 5 first samples (out of 1000) :

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.. code-block:: Python

    sample[:5]







.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>y0</th><th>y1</th></tr>
      <tr><th>0</th><td>0.5519547</td><td>0.6413422</td></tr>
      <tr><th>1</th><td>2.069226</td><td>-1.048988</td></tr>
      <tr><th>2</th><td>-2.211924</td><td>5.340953</td></tr>
      <tr><th>3</th><td>0.7773735</td><td>1.66219</td></tr>
      <tr><th>4</th><td>4.325861</td><td>-1.994259</td></tr>
    </table>
    </div>
    <br />
    <br />

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Basic operations on samples
---------------------------
We have access to basic information about a sample such as

- minimum and maximum per component


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.. code-block:: Python

    sample.getMin(), sample.getMax()





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

 .. code-block:: none


    (class=Point name=Unnamed dimension=2 values=[-3.24513,-2.98342], class=Point name=Unnamed dimension=2 values=[10.6987,10.5037])



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- the range per component (max-min)


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.. code-block:: Python

    sample.computeRange()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[13.9438,13.4871]
    </div>
    <br />
    <br />

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More elaborate functionalities are also available :


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- get the median per component


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.. code-block:: Python

    sample.computeMedian()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[0.631033,0.715266]
    </div>
    <br />
    <br />

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- compute the covariance


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.. code-block:: Python

    sample.computeCovariance()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <p>[[ 2.77895   0.0913307 ]<br>
     [ 0.0913307 3.30989   ]]</p>
    </div>
    <br />
    <br />

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- get the empirical 0.95 quantile per component


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.. code-block:: Python

    sample.computeQuantilePerComponent(0.95)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[3.96521,4.45879]
    </div>
    <br />
    <br />

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- get the value of the empirical CDF at a point


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.. code-block:: Python

    point = [1.1, 2.2]
    sample.computeEmpiricalCDF(point)






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

 .. code-block:: none


    0.569



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Estimate the statistical moments
--------------------------------

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Oftentimes, we need to estimate the first moments of the output data. We can then estimate statistical moments from the output sample :

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- estimate the moment of order 1 : mean


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.. code-block:: Python

    sample.computeMean()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[0.928558,1.01799]
    </div>
    <br />
    <br />

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- estimate the standard deviation for each component


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.. code-block:: Python

    sample.computeStandardDeviation()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[1.66702,1.81931]
    </div>
    <br />
    <br />

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- estimate the moment of order 2 : variance


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.. code-block:: Python

    sample.computeVariance()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[2.77895,3.30989]
    </div>
    <br />
    <br />

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- estimate the moment of order 3 : skewness


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.. code-block:: Python

    sample.computeSkewness()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[1.40965,1.73437]
    </div>
    <br />
    <br />

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- estimate the moment of order 4 : kurtosis


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.. code-block:: Python

    sample.computeKurtosis()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[6.84373,7.96431]
    </div>
    <br />
    <br />

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Test the correlation
--------------------

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Some statistical test for correlation are available :

- get the sample linear correlation matrix :


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.. code-block:: Python

    sample.computeLinearCorrelation()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <p>[[ 1         0.0301141 ]<br>
     [ 0.0301141 1         ]]</p>
    </div>
    <br />
    <br />

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- get  the sample Kendall correlation matrix :


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.. code-block:: Python

    sample.computeKendallTau()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <p>[[  1        -0.010026 ]<br>
     [ -0.010026  1        ]]</p>
    </div>
    <br />
    <br />

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- get  the sample Spearman correlation matrix :


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.. code-block:: Python

    sample.computeSpearmanCorrelation()





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <p>[[ 1          0.00483728 ]<br>
     [ 0.00483728 1          ]]</p>
    </div>
    <br />
    <br />


.. _sphx_glr_download_auto_data_analysis_manage_data_and_samples_plot_sample_manipulation.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_sample_manipulation.zip <plot_sample_manipulation.zip>`