[ot-users] [External] Re: Custom distribution in FORM

regis lebrun regis_anne.lebrun_dutfoy at yahoo.fr
Sat Nov 11 10:20:30 CET 2017


 Hi Phil,
Don't forget to cast your OpenTURNSPyhtonDistribution (a pure Python class able to be bind to a C++ class) into an OpenTURNS distribution (a pure C++ class)! If you write b=ot.Distribution(UniformNdPy()) it should work like a charm. I am not a specialist of this part, but it looks like an impossibility in Python to overload a method with different signatures in contrast with C++.
Cheers
Régis
    Le samedi 11 novembre 2017 à 09:43:59 UTC+1, Julien Schueller | Phimeca <schueller at phimeca.com> a écrit :  
 
 
Hi Phil,




We have A SciPyDistribution class for that purpose in OpenTURNS but unfortunately it is currently broken and will be fixed for the 1.10 version to be released soon.




Luckily it's pure Python, so here is a script that redefines SciPyDistribution with the fixed range computation used with the johnsonSU distribution.




j




De : users-bounces at openturns.org <users-bounces at openturns.org> de la part de Phil Fernandes <phil.fernandes at enbridge.com>
Envoyé : samedi 11 novembre 2017 00:30:54
À : regis lebrun; users at openturns.org
Objet : Re: [ot-users] [External] Re: Custom distribution in FORM I tried implementing via distribution algebra, but for some reason my program just hangs, so I decided to try implementing the distribution as a subclass of PythonDistribution as per the examplehttps://github.com/openturns/openturns/blob/master/python/test/t_Distribution_python.py. Unfortunately there seem to be inconsistencies in the argument types that are accepted by the methods of Distribution objects and the example PythonDistribution. What are the required object types for the outputs of computeXXX(), e.g., computeQuantile() in order for the distribution to work in FORM? Would it suffice to output a list?

For example
        a = ot.Normal()
        x = np.linspace(0,1,5)[:,None]
        a.computePDF(x)
returns 
        class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=5 dimension=1 data=[[0.398942],[0.386668],[0.352065],[0.301137],[0.241971]]

However 
        b=UniformNdPy()
        b.computePDF(x)
returns 1.0. 

Thank you.


-----Original Message-----
From: regis lebrun [mailto:regis_anne.lebrun_dutfoy at yahoo.fr]
Sent: Friday, November 10, 2017 12:12 PM
To: users at openturns.org; Phil Fernandes
Subject: [External] Re: [ot-users] Custom distribution in FORM



Hi,

You can easily implement this distribution using OpenTURNS unique feature regarding distribution algebra (seehttps://en.wikipedia.org/wiki/Johnson%27s_SU-distribution):

import openturns as ot
lamb = 1.5
xi = 1.1
delta = 2.0
gamma = 1.0
distJU = ((ot.Normal() - gamma) / delta).sinh() * lamb + xi print("distJU=", distJU)
ot.Show(distJU.drawPDF())

You will get:
distJU= RandomMixture(1.1 + 1.5 * CompositeDistribution=f(RandomMixture(Normal(mu = -0.5, sigma = 0.5))) with f=[x]->[sinh(x)])

and a graph similar to the one given on the wikipedia page.

Your script contains some bugs (computeQuantile, getMean, getStandardDeviation should return the result as a float sequence of size 1) and a missing method, namely getRange(). To get a running distribution you must implement getRange() and computeCDF(), all the other methods have a generic implementation, but these generic algorithms may be slow or inaccurate in difficult situations, so the more methods you provide the most efficient your distribution is.

The online documentation (http://secure-web.cisco.com/1_QlR51NTnci244KawP-NQBpuYV0mfhSTp4JXBwTpGJAqWfkDBxUY1JGCpr_XGFfQIZiEjVXqGphin3yoL6fV0Ro5q1JtmYip6xNs_iSbp14Iqwp3nL4GrrNfOhdGLYYpkwqSHmNCB0HmQ9TV4e4AAXGci3esSntXt8UjGeLuSqsWVIAgSfMQHC-yrAm6_JuU7HLDfmDuKjh0tAEtKH4Exm1PXrpvRwVwODuNBTOUej_7Q49C1pP-1sswRmGgOGm3NLSy3q3ZTJfNSogVMSuyZ4wcTzp0YH2CW-VW6edm4x21iG0omiNXB3pYDqQmrnNqz_uUj9AvsTr72Dh6iW8jGw/http%3A%2F%2Fopenturns.github.io%2Fopenturns%2Fmaster%2Fuser_manual%2F_generated%2Fopenturns.PythonDistribution.html%3Fhighlight%3Dpythondistribution) is very poor and will be updated. You can have a look at https://github.com/openturns/openturns/blob/master/python/test/t_Distribution_python.py for an example of a custom Python distribution.

You could also have used the SciPyDistribution wrapper of scipy distributions (see http://secure-web.cisco.com/1B_pKGvPkYtC86WGBDSnrF--4exrvoUqVoGHUYGIgi2rsg8OcFilo_WAXcF13h2kI6KqhmosBqsMMIjA_MZ9-V-t5GJ0wnk2hxZCqcogsNY4Q-1P7-gw4Jaj5Q1Y4l_n0WzDuI9V0YpSEvzmwpq65VeVL9VfSWO3Ec7QcmzW3i2NaK5oYsp4X5rrLp03MjlZiJscbJaKKstp9LrMGohAul3vBWC30HVxArmix5guZPggdaAavQcloR4ZVn0HF0ZGPR1LI6wJzM4LA4ZLfRh_EnO3yzEybS_kpyPYtyPUHVZY4xpUX8ojw-cDz54hEAWAx3a4pqsF5QN57pa9gdsppCw/http%3A%2F%2Fopenturns.github.io%2Fopenturns%2Fmaster%2Fuser_manual%2F_generated%2Fopenturns.SciPyDistribution.html and https://github.com/openturns/openturns/blob/master/python/test/t_Distribution_scipy.py):

import openturns as ot
import scipy.stats as st

lamb = 1.5
xi = 1.1
delta = 2.0
gamma = 1.0
distJU = ot.Distribution(ot.ScyPyDistribution(st.johnsonsu(gamma, delta, loc=xi, scale=lamb)))

but unfortunately this wrapper has a bug for unbounded distributions, resulting in a wrong range and a boggus computeQuantile() method.

Thanks for the question, it raised a lot of problems in OT!

Best regards,

Régis




Le vendredi 10 novembre 2017 à 18:42:19 UTC+1, Phil Fernandes <phil.fernandes at enbridge.com> a écrit :








Hello,

 

I am attempting to use a custom continuous probability distribution for a probability of failure calculation via FORM, but when I try to create a ComposedDistribution with my custom dist, the program fails with

NotImplementedError: Wrong number or type of arguments for overloaded function 'new_ComposedDistribution'.

 

The custom dist is defined as

 

class JohnsonSU(ot.PythonDistribution):

    def __init__(self, gamma=1, xi=0, delta=0.5, lam=1):

        super(JohnsonSU, self).__init__(1)

        if np.any(delta <= 0):

            raise ValueError('Delta must be >0.')

        if np.any(lam <= 0):

            raise ValueError('Lambda must be >0.')

 

        self.gamma = gamma  # shape 1

        self.xi = xi    # location

        self.delta = delta  # shape 2, >0

        self.lam = lam  # scale, >0

        self.scipy_dist = st.johnsonsu(self.gamma, self.delta, loc=self.xi, scale=self.lam)

 

    def computeCDF(self, x):

        return self.scipy_dist.cdf(x)

 

    def computePDF(self, x):

        return self.scipy_dist.pdf(x)

 

    def computeQuantile(self, p):

        return self.scipy_dist.ppf(p)

    

    def getMean(self):

        return self.scipy_dist.mean()

    

    def getStandardDeviation(self):

        return self.scipy_dist.std()

 

 

Are there additional functions that must be defined in order for the PythonDistribution to be compatible with existing OpenTurns Distributions? Or, is there a straightforward way that I could add arbitrary distributions to the OpenTurns source code?

 

Many thanks!

 

Phil Fernandes   P.Eng, MASc
Engineer, Reliability Assessment

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