"""Abstract base class and shared types for physical systems.

A physical system is responsible for three things and three things only:

1. Exposing **stable metadata** (id, tier, state-variable names, NL hint).
2. Generating a **noisy trajectory** for one episode given an RNG seed.
3. Reporting its **ground-truth equation** as a canonical SymPy expression
   for logging and verification.

Reward computation, simulation of the *agent's* hypotheses, residual analysis,
and natural-language mismatch summarisation all live in :mod:`physix.verifier`.
Systems do not import anything from the verifier; the dependency runs in one
direction.
"""

from __future__ import annotations

from abc import ABC, ABCMeta, abstractmethod
from enum import Enum

import numpy as np
from pydantic import BaseModel, ConfigDict, Field
from pydantic._internal._model_construction import ModelMetaclass
from scipy.integrate import odeint


class SystemTier(str, Enum):
    """Curriculum tier. Tier 3 is held out of training to enable a
    generalisation claim ("converges on systems it never trained on")."""

    TIER_1 = "tier1"
    TIER_2 = "tier2"
    TIER_3 = "tier3"


class TrajectoryData(BaseModel):
    """Numerical trajectory plus its initial conditions.

    ``initial_conditions`` is included so the verifier can re-simulate the
    agent's hypothesis from the *same* starting point, making residuals
    directly comparable.
    """

    model_config = ConfigDict(frozen=True, arbitrary_types_allowed=True)

    timestamps: np.ndarray
    states: dict[str, np.ndarray]
    initial_conditions: dict[str, float]
    state_variables: tuple[str, ...]

    def to_observation_samples(self, decimals: int = 5) -> list[dict[str, float]]:
        """Render as a JSON-friendly list of timestep dicts for the agent."""
        samples: list[dict[str, float]] = []
        for i, t in enumerate(self.timestamps):
            sample: dict[str, float] = {"t": round(float(t), decimals)}
            for var in self.state_variables:
                sample[var] = round(float(self.states[var][i]), decimals)
            samples.append(sample)
        return samples

    def stats(self) -> dict[str, float]:
        """Aggregate statistics for the agent's stats panel."""
        out: dict[str, float] = {
            "duration": float(self.timestamps[-1] - self.timestamps[0]),
            "n_timesteps": float(len(self.timestamps)),
            "dt": float(self.timestamps[1] - self.timestamps[0]) if len(self.timestamps) > 1 else 0.0,
        }
        for var in self.state_variables:
            arr = self.states[var]
            out[f"{var}_min"] = float(np.min(arr))
            out[f"{var}_max"] = float(np.max(arr))
            out[f"{var}_std"] = float(np.std(arr))
        return out


class _AbstractModelMeta(ModelMetaclass, ABCMeta):
    """Metaclass union so :class:`PhysicalSystem` is both a pydantic model and
    a true ABC (i.e. instantiating the base or a subclass that fails to
    implement an abstract method raises ``TypeError``)."""


class PhysicalSystem(BaseModel, ABC, metaclass=_AbstractModelMeta):
    """Abstract physical system.

    Concrete subclasses must:

    - Override :attr:`system_id`, :attr:`tier`, :attr:`state_variables`, and
      :attr:`hint_template`.
    - Implement :meth:`sample_parameters` to draw random episode parameters.
    - Implement :meth:`sample_initial_conditions` to draw random initial state.
    - Implement :meth:`rhs` returning the time derivatives.
    - Implement :meth:`ground_truth_equation` returning a canonical SymPy
      string of the system's equation of motion.

    The base class implements :meth:`simulate` once for all subclasses by
    delegating to ``scipy.integrate.odeint`` against :meth:`rhs`.
    """

    model_config = ConfigDict(arbitrary_types_allowed=True)

    system_id: str = ""
    tier: SystemTier = SystemTier.TIER_1
    state_variables: tuple[str, ...] = ()
    hint_template: str = ""

    duration: float = 10.0
    n_timesteps: int = 100
    #: Gaussian noise applied to each observed sample, expressed as a fraction
    #: of the per-variable *standard deviation* of the clean trajectory. Using
    #: std (rather than range) avoids the pathology where a system with a
    #: large total excursion (e.g. free fall) produces overwhelming noise.
    noise_std: float = 0.02

    parameters: dict[str, float] = Field(default_factory=dict)
    initial_conditions: dict[str, float] = Field(default_factory=dict)

    # ------------------------------------------------------------------ API

    @abstractmethod
    def sample_parameters(self, rng: np.random.Generator) -> dict[str, float]:
        """Draw a fresh set of physical parameters for one episode."""

    @abstractmethod
    def sample_initial_conditions(self, rng: np.random.Generator) -> dict[str, float]:
        """Draw fresh initial conditions for one episode."""

    @abstractmethod
    def rhs(
        self,
        t: float,
        state: np.ndarray,
        params: dict[str, float],
    ) -> np.ndarray:
        """Time derivatives at time ``t``.

        ``state`` is laid out in the order of :attr:`state_variables`. The
        return value must be a 1-D array of the same length.
        """

    @abstractmethod
    def ground_truth_equation(self) -> str:
        """Canonical SymPy-grammar string of the equation of motion.

        Used for logging only. Never surfaced to the agent during training
        or inference.
        """

    def hint(self, parameters: dict[str, float]) -> str:
        """Render the natural-language hint for the agent.

        Default behaviour formats :attr:`hint_template` against
        ``parameters``. Subclasses may override for more flexibility.
        """
        try:
            return self.hint_template.format(**parameters)
        except (KeyError, IndexError):
            return self.hint_template

    # -------------------------------------------------------------- behaviour

    def simulate(self, rng: np.random.Generator) -> TrajectoryData:
        """Generate one noisy trajectory for an episode."""
        params = self.sample_parameters(rng)
        ic = self.sample_initial_conditions(rng)

        timestamps = np.linspace(0.0, self.duration, self.n_timesteps)
        initial_state = np.array([ic[var] for var in self.state_variables], dtype=float)

        # scipy.integrate.odeint expects f(state, t, *args); we wrap to put
        # `t` second and pass params via closure.
        def _rhs_wrapper(state: np.ndarray, t: float) -> np.ndarray:
            return self.rhs(t, state, params)

        clean = odeint(_rhs_wrapper, initial_state, timestamps, full_output=False)

        states: dict[str, np.ndarray] = {}
        for col, var in enumerate(self.state_variables):
            clean_col = clean[:, col]
            scale = max(float(np.std(clean_col)), 1e-6)
            noise = rng.normal(0.0, self.noise_std * scale, size=clean_col.shape)
            states[var] = clean_col + noise

        # Cache for downstream access (parameters surfaced to the env).
        self.parameters = params
        self.initial_conditions = ic

        return TrajectoryData(
            timestamps=timestamps,
            states=states,
            initial_conditions=ic,
            state_variables=self.state_variables,
        )