"""State of a probabilistic linear solver."""
import dataclasses
from typing import Any, List, Optional, Tuple
import numpy as np
import probnum # pylint:disable="unused-import"
from probnum import problems
[docs]@dataclasses.dataclass
class ProbabilisticLinearSolverState:
"""State of a probabilistic linear solver.
The solver state separates the state of a probabilistic linear solver from the algorithm itself, making the solver stateless. The state contains the problem to be solved, the current belief over the quantities of interest and any miscellaneous quantities computed during an iteration of a probabilistic linear solver. The solver state is passed between the different components of the solver and may be used internally to cache quantities which are used more than once.
Parameters
----------
problem
Linear system to be solved.
prior
Prior belief over the quantities of interest of the linear system.
rng
Random number generator.
"""
def __init__(
self,
problem: problems.LinearSystem,
prior: "probnum.linalg.solvers.beliefs.LinearSystemBelief",
rng: Optional[np.random.Generator] = None,
):
self.problem = problem
self.belief = prior
self.step = 0
self._actions: List[np.ndarray] = [None]
self._observations: List[Any] = [None]
self._residuals: List[np.ndarray] = [
self.problem.A @ self.belief.x.mean - self.problem.b,
None,
]
self.rng = rng
def __repr__(self) -> str:
return f"{self.__class__.__name__}(step={self.step})"
@property
def action(self) -> Optional[np.ndarray]:
"""Action of the solver for the current step.
Is ``None`` at the beginning of a step and will be set by the
policy.
"""
return self._actions[self.step]
@action.setter
def action(self, value: np.ndarray) -> None:
assert self._actions[self.step] is None
self._actions[self.step] = value
@property
def observation(self) -> Optional[Any]:
"""Observation of the solver for the current step.
Is ``None`` at the beginning of a step, will be set by the
observation model for a given action.
"""
return self._observations[self.step]
@observation.setter
def observation(self, value: Any) -> None:
assert self._observations[self.step] is None
self._observations[self.step] = value
@property
def actions(self) -> Tuple[np.ndarray, ...]:
"""Actions taken by the solver."""
return tuple(self._actions)
@property
def observations(self) -> Tuple[Any, ...]:
"""Observations of the problem by the solver."""
return tuple(self._observations)
@property
def residual(self) -> np.ndarray:
r"""Cached residual :math:`Ax_i-b` for the current solution estimate :math:`x_i`."""
if self._residuals[self.step] is None:
self._residuals[self.step] = (
self.problem.A @ self.belief.x.mean - self.problem.b
)
return self._residuals[self.step]
@property
def residuals(self) -> Tuple[np.ndarray, ...]:
r"""Residuals :math:`\{Ax_i - b\}_i`."""
return tuple(self._residuals)
[docs] def next_step(self) -> None:
"""Advance the solver state to the next solver step.
Called after a completed step / iteration of the probabilistic
linear solver.
"""
self._actions.append(None)
self._observations.append(None)
self._residuals.append(None)
self.step += 1