.. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` 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 =================== This example will describe the main statistical functionalities on data through the Sample object. The Sample is an output variable of interest. .. code-block:: default from __future__ import print_function import openturns as ot ot.Log.Show(ot.Log.NONE) A typical example ----------------- 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 `IndependentCopula` to describe the link between the two marginals. .. code-block:: default # input parameters inputDist = ot.ComposedDistribution([ot.Normal()] * 2, ot.IndependentCopula(2)) inputDist.setDescription(['X1', 'X2']) We create a vector from the 2D-distribution created before : .. code-block:: default inputVector = ot.RandomVector(inputDist) 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 `SymbolicFunction` .. code-block:: default f = ot.SymbolicFunction(["x1", "x2"], ["x1^2+x2", "x2^2+x1"]) Our output vector is Y=f(X), the image of the inputVector by the model .. code-block:: default outputVector = ot.CompositeRandomVector(f, inputVector) We can now get a sample out of Y, that is realizations (here 1000) of the random outputVector .. code-block:: default size = 1000 sample = outputVector.getSample(size) The `sample` may be seen as a matrix of size :math:`1000 \times 2`. We print the 5 first samples (out of 1000) : .. code-block:: default sample[:5] .. raw:: html
y0y1
0-0.58150720.7240122
13.26726-0.5563772
2-0.3683326-0.08640049
3-1.1399521.854578
45.692328-1.219674


Basic operations on samples --------------------------- We have access to basic information about a sample such as - minimum and maximum per component .. code-block:: default sample.getMin(), sample.getMax() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none (class=Point name=Unnamed dimension=2 values=[-2.56587,-2.84726], class=Point name=Unnamed dimension=2 values=[9.93535,12.1777]) - the range per component (max-min) .. code-block:: default sample.computeRange() .. raw:: html

[12.5012,15.025]



More elaborate functionalities are also available : - get the median per component .. code-block:: default sample.computeMedian() .. raw:: html

[0.680688,0.874763]



- compute the covariance .. code-block:: default sample.computeCovariance() .. raw:: html

[[ 2.59234 -0.0758625 ]
[ -0.0758625 3.30636 ]]



- get the empirical 0.95 quantile per component .. code-block:: default sample.computeQuantilePerComponent(0.95) .. raw:: html

[3.67518,4.13131]



- get the value of the empirical CDF at a point .. code-block:: default point = [1.1, 2.2] sample.computeEmpiricalCDF(point) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none 0.518 Estimate the statistical moments -------------------------------- Oftentimes, we need to estimate the first moments of the output data. We can then estimate statistical moments from the output sample : - estimate the moment of order 1 : mean .. code-block:: default sample.computeMean() .. raw:: html

[0.903872,1.15217]



- estimate the standard deviation (returns the Cholesky factor) .. code-block:: default sample.computeStandardDeviation() .. raw:: html

[[ 1.61007 0 ]
[ -0.0471174 1.81773 ]]



- estimate the standard deviation for each component .. code-block:: default sample.computeStandardDeviationPerComponent() .. raw:: html

[1.61007,1.81834]



- estimate the moment of order 2 : variance .. code-block:: default sample.computeVariance() .. raw:: html

[2.59234,3.30636]



- estimate the moment of order 3 : skewness .. code-block:: default sample.computeSkewness() .. raw:: html

[1.28241,1.80582]



- estimate the moment of order 4 : kurtosis .. code-block:: default sample.computeKurtosis() .. raw:: html

[6.40216,9.59074]



Test the correlation -------------------- Some statistical test for correlation are available : - get the sample Pearson correlation matrix : .. code-block:: default sample.computePearsonCorrelation() .. raw:: html

[[ 1 -0.0259123 ]
[ -0.0259123 1 ]]



- get the sample Kendall correlation matrix : .. code-block:: default sample.computeKendallTau() .. raw:: html

[[ 1 0.0183584 ]
[ 0.0183584 1 ]]



- get the sample Spearman correlation matrix : .. code-block:: default sample.computeSpearmanCorrelation() .. raw:: html

[[ 1 0.0200394 ]
[ 0.0200394 1 ]]



.. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.008 seconds) .. _sphx_glr_download_auto_data_analysis_manage_data_and_samples_plot_sample_manipulation.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_sample_manipulation.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_sample_manipulation.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_