Source code for gemseo.uncertainty.distributions.scipy.composed
# 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 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 annotations
from typing import Callable
from typing import Iterable
from typing import Sequence
from typing import TYPE_CHECKING
from gemseo.utils.base_enum import BaseEnum
from gemseo.utils.base_enum import get_names
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."""
[docs] class CopulaModel(BaseEnum):
"""A copula model."""
independent_copula = None
# TODO: API: remove this attribute in the next major release.
AVAILABLE_COPULA_MODELS = get_names(CopulaModel)
def __init__( # noqa: D107
self,
distributions: Sequence[SPDistribution],
copula: CopulaModel | str = CopulaModel.independent_copula,
variable: str = "",
) -> None:
super().__init__(distributions, copula=copula, variable=variable)
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( # noqa: D102
self,
vector: Iterable[float],
) -> 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( # noqa: D102
self,
vector: Iterable[float],
) -> 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( # noqa: D102
self,
index: int,
) -> Callable:
id1 = self._mapping[index][0]
id2 = self._mapping[index][1]
def pdf(
point: float,
) -> 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( # noqa: D102
self,
index: int,
) -> Callable:
id1 = self._mapping[index][0]
id2 = self._mapping[index][1]
def cdf(
level: float,
) -> 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