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

# -*- coding: utf-8 -*-
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
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# 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

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

The :class:`.SPComposedDistribution` class is a concrete class
inheriting from :class:`.ComposedDistribution` which is an abstract one.
SP stands for `scipy <https://docs.scipy.org/doc/scipy/reference/
tutorial/stats.html>`_ which is the library it relies on.

This class inherits from :class:`.SPDistribution`.
It builds a composed probability distribution
related to given random variables from a list of :class:`.SPDistribution` objects
implementing the probability distributions of these variables
based on the SciPy 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 division, unicode_literals

from typing import TYPE_CHECKING, Callable, Iterable, Sequence

if TYPE_CHECKING:
    from gemseo.uncertainty.distributions.scipy.distribution import SPDistribution

from numpy import array, ndarray

from gemseo.uncertainty.distributions.composed import ComposedDistribution


[docs]class SPComposedDistribution(ComposedDistribution): """Scipy composed distribution.""" _COPULA = {ComposedDistribution._INDEPENDENT_COPULA: None} AVAILABLE_COPULA_MODELS = sorted(_COPULA.keys()) def __init__( self, distributions, # type: Sequence[SPDistribution] copula=ComposedDistribution._INDEPENDENT_COPULA, # type: str ): # type: (...) -> None # noqa: D205,D212,D415 """ Args: distributions (list(SPDistribution)): The distributions. copula (str, optional): A name of copula. """ super(SPComposedDistribution, self).__init__(distributions, copula) self.distribution = distributions self._mapping = {} index = 0 for marginal_index, marginal in enumerate(self.distribution): for submarginal_index in range(marginal.dimension): self._mapping[index] = (marginal_index, submarginal_index) index += 1 self._set_bounds(distributions)
[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] tmp.append(self.distribution[id1].marginals[id2].cdf(value)) return array(tmp)
[docs] def compute_inverse_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] tmp.append(self.distribution[id1].marginals[id2].ppf(value)) 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.distribution[id1].marginals[id2].pdf(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.distribution[id1].marginals[id2].cdf(level) return cdf