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.
#
# 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