"""Probabilistic Numerical Methods."""
from abc import ABC, abstractmethod
from typing import Generic, Tuple, TypeVar
ProblemType = TypeVar("ProblemType")
BeliefType = TypeVar("BeliefType")
StateType = TypeVar("StateType")
class ProbabilisticNumericalMethod(ABC, Generic[ProblemType, BeliefType]):
"""Probabilistic numerical methods.
An abstract base class defining the implementation of a probabilistic numerical
method [1]_ [2]_. A PN method solves a numerical problem by treating it as a
probabilistic inference task.
Parameters
----------
prior :
Prior knowledge about quantities of interest for the numerical problem.
References
----------
.. [1] Hennig, P., Osborne, Mike A. and Girolami M., Probabilistic numerics and
uncertainty in computations. *Proceedings of the Royal Society of London A:
Mathematical, Physical and Engineering Sciences*, 471(2179), 2015.
.. [2] Cockayne, J., Oates, C., Sullivan Tim J. and Girolami M., Bayesian
probabilistic numerical methods. *SIAM Review*, 61(4):756–789, 2019
Notes
-----
All PN methods should subclass this base class. Typically convenience functions
(such as :meth:`~probnum.linalg.problinsolve`) will instantiate an object of a
derived subclass.
"""
def __init__(self, prior: BeliefType):
self.prior = prior
[docs] @abstractmethod
def solve(
self,
problem: ProblemType,
) -> Tuple[BeliefType, StateType]:
"""Solve the given numerical problem.
Parameters
----------
problem :
Numerical problem to be solved.
"""
raise NotImplementedError