Source code for gemseo_umdo.estimators.taylor_polynomial

# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
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# License version 3 as published by the Free Software Foundation.
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
# Lesser General Public License for more details.
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"""Estimators of statistic for U-MDO formulation based on Taylor polynomials."""
from __future__ import annotations

from typing import Any
from typing import TYPE_CHECKING

from gemseo.core.base_factory import BaseFactory
from numpy import array
from numpy import diag
from numpy import diagonal
from numpy.linalg import multi_dot

if TYPE_CHECKING:
    from gemseo_umdo.formulations.taylor_polynomial import TaylorPolynomial

from numpy import ndarray

from gemseo_umdo.estimators.estimator import BaseStatisticEstimator


[docs]class TaylorPolynomialEstimator(BaseStatisticEstimator): """Base statistic estimator for a U-MDO formulation using Taylor polynomials.""" def __init__(self, formulation: TaylorPolynomial) -> None: # noqa: D107 super().__init__(formulation)
[docs]class TaylorPolynomialEstimatorFactory(BaseFactory): """The factory of statistic estimators based on Taylor polynomials.""" _CLASS = TaylorPolynomialEstimator _MODULE_NAMES = ()
[docs]class Mean(TaylorPolynomialEstimator): """Estimator of the expectation, a.k.a. mean. """ def __call__( self, func: ndarray, jac: ndarray, hess: ndarray, **kwargs: Any ) -> float | ndarray: """ Args: func: The output value at the mean value of the uncertain variables. jac: The Jacobian value at the mean value of the uncertain variables. hess: The Hessian value at the mean value of the uncertain variables. """ # noqa: D205 D212 D415 if hess is None: return func std = self._formulation._uncertain_space.distribution.standard_deviation return func + 0.5 * array( [multi_dot([std, sub_hess, std]) for sub_hess in hess] )
[docs]class Variance(TaylorPolynomialEstimator): """Estimator of the variance.""" def __call__( self, func: ndarray, jac: ndarray, hess: ndarray, **kwargs: Any ) -> float | ndarray: """ Args: func: The output value at the mean value of the uncertain variables. jac: The Jacobian value at the mean value of the uncertain variables. hess: The Hessian value at the mean value of the uncertain variables. """ # noqa: D205 D212 D415 std = self._formulation._uncertain_space.distribution.standard_deviation return diagonal(multi_dot([jac, diag(std**2), jac.T]))
[docs]class StandardDeviation(Variance): """Estimator of the standard deviation.""" def __call__( self, func: ndarray, jac: ndarray, hess: ndarray, **kwargs: Any ) -> float | ndarray: """ Args: func: The output value at the mean value of the uncertain variables. jac: The Jacobian value at the mean value of the uncertain variables. hess: The Hessian value at the mean value of the uncertain variables. """ # noqa: D205 D212 D415 return super().__call__(func, jac, hess, **kwargs) ** 0.5
[docs]class Margin(TaylorPolynomialEstimator): """Estimator of a margin, i.e. mean + factor * deviation.""" def __init__(self, formulation: TaylorPolynomial) -> None: # noqa: D107 super().__init__(formulation) self.__mean = Mean(formulation) self.__standard_deviation = StandardDeviation(formulation) def __call__( self, func: ndarray, jac: ndarray, hess: ndarray, factor: float = 2.0, **kwargs: Any, ) -> float | ndarray: """# noqa: D205 D212 D415 Args: func: The output value at the mean value of the uncertain variables. jac: The Jacobian value at the mean value of the uncertain variables. hess: The Hessian value at the mean value of the uncertain variables. factor: The factor related to the standard deviation. """ return self.__mean( func, jac, hess, **kwargs ) + factor * self.__standard_deviation(func, jac, hess, **kwargs)