Source code for gemseo.uncertainty.distributions.openturns.composed

# -*- 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

"""Class to create a joint probability distribution from the OpenTURNS library.

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.

This class inherits from :class:`.OTDistribution`.
It builds a composed probability distribution
related to given random variables 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 typing import TYPE_CHECKING, Callable, Iterable, Sequence

import openturns as ots

if TYPE_CHECKING:
    from gemseo.uncertainty.distributions.openturns.distribution import OTDistribution

from numpy import array, ndarray

from gemseo.uncertainty.distributions.composed import ComposedDistribution


[docs]class OTComposedDistribution(ComposedDistribution): """OpenTURNS composed distribution.""" _COPULA = {ComposedDistribution._INDEPENDENT_COPULA: ots.IndependentCopula} AVAILABLE_COPULA_MODELS = sorted(_COPULA.keys()) def __init__( self, distributions, # type: Sequence[OTDistribution] copula=ComposedDistribution._INDEPENDENT_COPULA, # type: str ): # type: (...) -> None # noqa: D205,D212,D415 """ Args: distributions: The distributions. copula: A name of copula. """ 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 distribution_index, distribution in enumerate(distributions): for marginal_index in range(distribution.dimension): self._mapping[index] = (distribution_index, marginal_index) index += 1 self._set_bounds(distributions)
[docs] def compute_samples( self, n_samples=1, # type: int ): # noqa: D102 # type: (...) -> ndarray sample = array(self.distribution.getSample(n_samples)) return sample
[docs] def compute_cdf( self, vector, # type: Iterable[float] ): # noqa: D102 # type: (...) -> ndarray 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 compute_inverse_cdf( self, vector, # type: ndarray ): # noqa: D102 # type: (...) -> Iterable[float] 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, # type: int ): # noqa: D102 # type: (...) -> Callable id1 = self._mapping[index][0] id2 = self._mapping[index][1] def pdf( point, # type: float ): # type: (...) -> float """Probability Density Function (PDF). Args: point: An evaluation point. Returns: The PDF value at the evaluation point. """ return self.marginals[id1].marginals[id2].computePDF(point) return pdf def _cdf( self, index, # type: int ): # noqa: D102 # type: (...) -> Callable id1 = self._mapping[index][0] id2 = self._mapping[index][1] def cdf( level, # type: float ): # type: (...) -> float """Cumulative Density Function (CDF). Args: level: A probability level. Returns: The CDF value for the probability level. """ return self.marginals[id1].marginals[id2].computeCDF(level) return cdf