Source code for gemseo.uncertainty.distributions.ot_cdist
# -*- coding: utf-8 -*-
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
# Contributors:
# INITIAL AUTHORS - initial API and implementation and/or initial
# documentation
# :author: Matthias De Lozzo
# OTHER AUTHORS - MACROSCOPIC CHANGES
"""
Composed distribution based on OpenTURNS
========================================
Overview
--------
The :class:`.OTComposedDistribution` class is a concrete class
inheriting from :class:`.ComposedDistribution` which is an abstract one.
OT stands for `OpenTURNS <http://www.openturns.org/>`_
which is the library it relies on.
Construction
------------
The :class:`.OTComposedDistribution` of a list of given uncertain variables
is built from a list of :class:`.OTDistribution` objects
implementing the probability distributions of these variables
based on the OpenTURNS library and from a copula name.
.. note::
A copula is a mathematical function used to define the dependence
between random variables from their cumulative density functions.
`See more <https://en.wikipedia.org/wiki/Copula_(probability_theory)>`__.
"""
from __future__ import absolute_import, division, unicode_literals
import openturns as ots
from future import standard_library
from numpy import array
from gemseo.uncertainty.distributions.distribution import ComposedDistribution
standard_library.install_aliases()
[docs]class OTComposedDistribution(ComposedDistribution):
""" OpenTURNS composed distribution. """
COPULA = {ComposedDistribution.INDEPENDENT_COPULA: ots.IndependentCopula}
def __init__(self, distributions, copula=ComposedDistribution.INDEPENDENT_COPULA):
"""Constructor.
:param list(OTDistribution) distributions: list of OT distributions.
:param str copula: copula name.
"""
super(OTComposedDistribution, self).__init__(distributions, copula)
marginals = [
marginal
for distribution in distributions
for marginal in distribution.marginals
]
ot_copula = self.COPULA[copula](len(marginals))
self.distribution = ots.ComposedDistribution(marginals, ot_copula)
self._mapping = {}
index = 0
for id_dist, distribution in enumerate(distributions):
for id_marg in range(distribution.dimension):
self._mapping[index] = (id_dist, id_marg)
index += 1
self._set_bounds(distributions)
[docs] def get_sample(self, n_samples=1):
"""Get sample.
:param n_samples: number of samples.
:type n_samples: int
:return: samples
:rtype: list(array)
"""
sample = array(self.distribution.getSample(n_samples))
return sample
[docs] def cdf(self, vector):
"""Evaluate the cumulative density functions of the marginals
of a random variable for a given instance.
:param array vector: instance of the random variable.
"""
tmp = []
for index, value in enumerate(vector):
id1 = self._mapping[index][0]
id2 = self._mapping[index][1]
value = ots.Point([value])
tmp.append(self.marginals[id1].marginals[id2].computeCDF(value))
return array(tmp)
[docs] def inverse_cdf(self, vector):
"""Evaluate the inverses of the cumulative density functions of the
marginals of a random variable for a given vector .
:param array vector: vector of values comprised between 0 and 1 with
same dimension as the random variable.
"""
tmp = []
for index, value in enumerate(vector):
id1 = self._mapping[index][0]
id2 = self._mapping[index][1]
tmp.append(self.marginals[id1].marginals[id2].computeQuantile(value)[0])
return array(tmp)
def _pdf(self, index):
id1 = self._mapping[index][0]
id2 = self._mapping[index][1]
def pdf(level):
return self.marginals[id1].marginals[id2].computePDF(level)
return pdf
def _cdf(self, index):
id1 = self._mapping[index][0]
id2 = self._mapping[index][1]
def cdf(level):
return self.marginals[id1].marginals[id2].computeCDF(level)
return cdf
