Implementing and using a new contrast with `pygosa`

The benefit ot the module is to make easy the definition a new contrast class (see for example New sensitivity analysis subordinated to a contrast

Implementing such contrast and apply it within the pygosa module relies on:

The definintion of a new class that inherites from ContrastSensitivityClass;
The definintion of the internal contrast method as function of y and t;
The definintion of the get_risk_value method as function that takes into account a data sample and returns the quantity of interest;

Of course, the underlying contrast should be associated to the quantity of interest defined in get_rist_value. As an example, we illustrate how to define the mean contrast class in less than 10 lines and applying the contrast to compute the sensitivity factors:



In [1]:

    
import openturns as ot
import numpy as np
import pygosa
%pylab inline









    



Populating the interactive namespace from numpy and matplotlib

We define Sobol use-case, which is very common in case of sensitivity analysis:



In [2]:

    
model = ot.SymbolicFunction(["x1","x2","x3"], ["sin(x1) + 7*sin(x2)^2 + 0.1*(x3^4)*sin(x1)"])
dist = ot.ComposedDistribution( 3 * [ot.Uniform(-np.pi, np.pi)] )

Design of experiment

We define the experiment design. The benefits of using a crude Monte-Carlo approach is the potential use of several contrasts.



In [3]:

    
mcsp = pygosa.SensitivityDesign(dist=dist, model=model, size=5000)

Moment of second order

Hereafter we define a new contrast class that helps evaluating sensitivities of $\mathbb{E}(Y^2)$. The contrast class should :

Inherits from ContrastSensitivityAnalysis
Define the contrast method with signature contrast(self, y,t, **kwargs). It should have kwargs as arguments even if not used
Define the get_risk_value method with signature get_risk_value(self, data, **kwargs). Same remark concerning kwargs



In [4]:

    
class Moment2SA(pygosa.ContrastSensitivityAnalysis):
    def __init__(self, design):
        super(Moment2SA, self).__init__(design)

    # contrast method
    def contrast(self, y,t, **kwargs):
        """
        Contrast for moment of second order
        """
        return (y*y-t)*(y*y-t)

    # Define risk function (second order moment)
    # moments2 = var + mean * mean
    def get_risk_value(self, data, **kwargs):
        mu = ot.Sample(data).computeMean()
        var =  ot.Sample(data).computeVariance()
        return np.array(mu) * np.array(mu) + np.array(var)

The previous class is a contrast similar to those provided by the module. We can thus easily apply it using the previous design:



In [5]:

    
sam = Moment2SA(mcsp)
factors_m = sam.compute_factors()
fig, ax = sam.boxplot()









    



/usr/lib/python2.7/dist-packages/matplotlib/figure.py:402: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
  "matplotlib is currently using a non-GUI backend, "



In [6]:

    
print(factors_m)









    



[[ 0.21166235  0.28014466  0.12583268]]

Implementing and using a new contrast with pygosa

Design of experiment

Moment of second order

Implementing and using a new contrast with `pygosa`