Source code for gemseo.uncertainty.distributions.sp_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.
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# 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 scipy
====================================
Overview
--------
The :class:`.SPComposedDistribution` class is a concrete class
inheriting from :class:`.ComposedDistribution` which is an abstract one.
Construction
------------
The :class:`.SPComposedDistribution` of a list of given uncertain variables
is built from a list of :class:`.SPDistribution` 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
from future import standard_library
from numpy import array
from gemseo.uncertainty.distributions.distribution import ComposedDistribution
standard_library.install_aliases()
[docs]class SPComposedDistribution(ComposedDistribution):
""" Scipy composed distribution. """
COPULA = {ComposedDistribution.INDEPENDENT_COPULA: None}
def __init__(self, distributions, copula=ComposedDistribution.INDEPENDENT_COPULA):
"""Constructor.
:param list(SPDistribution) distributions: list of OT distributions.
:param str copula: copula name.
"""
super(SPComposedDistribution, self).__init__(distributions, copula)
self.distribution = distributions
self._mapping = {}
index = 0
for id_marg, marginal in enumerate(self.distribution):
for id_submarg in range(marginal.dimension):
self._mapping[index] = (id_marg, id_submarg)
index += 1
self._set_bounds(distributions)
[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]
tmp.append(self.distribution[id1].marginals[id2].cdf(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.distribution[id1].marginals[id2].ppf(value))
return array(tmp)
def _pdf(self, index):
id1 = self._mapping[index][0]
id2 = self._mapping[index][1]
def pdf(level):
return self.distribution[id1].marginals[id2].pdf(level)
return pdf
def _cdf(self, index):
id1 = self._mapping[index][0]
id2 = self._mapping[index][1]
def cdf(level):
return self.distribution[id1].marginals[id2].cdf(level)
return cdf