"""Forward-simulate the agent's parsed hypothesis.

Responsibility:

- Given a :class:`ParsedEquation`, the system's state-variable layout, the
  agent's parameter dictionary, and a set of initial conditions and
  timestamps, run ``scipy.integrate.odeint`` to produce a predicted
  trajectory in the same shape as the system's observed data.

What this module does not do: parse text (see :mod:`physix.verifier.parser`),
score the trajectory (see :mod:`physix.verifier.metrics`), or compose rewards
(see :mod:`physix.verifier.reward`).
"""

from __future__ import annotations

from collections.abc import Iterable
from typing import Callable

import numpy as np
import sympy as sp
from scipy.integrate import odeint

from physix.verifier.parser import ParsedEquation


class SimulationError(RuntimeError):
    """Raised when the proposed system cannot be integrated numerically.

    Common causes: NaN/Inf produced by ``odeint``, mass-matrix singularity,
    or stiff dynamics that exhaust the integrator's step budget.
    """


def simulate_hypothesis(
    parsed: ParsedEquation,
    state_variables: Iterable[str],
    parameters: dict[str, float],
    initial_conditions: dict[str, float],
    timestamps: np.ndarray,
) -> dict[str, np.ndarray]:
    """Integrate the agent's hypothesis forward in time.

    Args:
        parsed: Parsed equations from :func:`physix.verifier.parser.parse_equation`.
        state_variables: Ordering of state variables in the underlying
            physical system. Used to derive the integration state vector.
        parameters: Numerical parameter substitutions supplied by the agent.
        initial_conditions: Initial state values keyed by variable name.
        timestamps: 1-D array of times at which to record state.

    Returns:
        A dict mapping each state variable to its predicted trajectory
        (1-D array of the same length as ``timestamps``).
    """
    state_vars = tuple(state_variables)
    int_layout = _build_integration_layout(parsed, state_vars)
    try:
        rhs_callable = _compile_rhs(parsed, int_layout, parameters)
    except Exception as exc:  # noqa: BLE001 — surfaced as SimulationError below
        raise SimulationError(f"failed to compile RHS: {exc}") from exc

    initial_state = _build_initial_state(int_layout, initial_conditions)

    try:
        result = odeint(
            rhs_callable,
            initial_state,
            timestamps,
            full_output=False,
            mxstep=2000,
            rtol=1e-6,
            atol=1e-9,
        )
    except Exception as exc:  # noqa: BLE001
        # ``odeint`` propagates whatever the user-supplied RHS callable
        # raises. The model can emit equations that lambdify into Python
        # code which then trips ``TypeError`` (e.g. ``np.sqrt`` on a
        # SymPy ``Add``), ``ZeroDivisionError``, ``OverflowError``, etc.
        # Any of those should be surfaced to the env as a clean
        # ``SimulationError`` (= ``r_match=0`` for the turn) rather than
        # crashing the route with a 500.
        raise SimulationError(f"odeint failed: {exc}") from exc

    if not np.all(np.isfinite(result)):
        raise SimulationError("Predicted trajectory contains NaN or Inf values.")

    return _project_back_to_state_vars(result, int_layout, state_vars)


_IntegrationLayout = tuple[tuple[str, ...], dict[str, int]]


def _build_integration_layout(
    parsed: ParsedEquation,
    state_vars: tuple[str, ...],
) -> _IntegrationLayout:
    """Return ``(integration_vars, index)`` for the integration state.

    For a system with second-order ODEs we need to integrate both ``var`` and
    ``dvar/dt``. We prefix-derive the names: e.g. ``y -> [y, vy]``, with the
    convention that ``v<name>`` is the first time derivative of ``<name>``
    (matching the conventions used in :mod:`physix.systems.tier1`).
    """
    integration_vars: list[str] = []

    eq_by_var = {eq.var: eq for eq in parsed.equations}

    for var in state_vars:
        # Skip variables that are themselves first derivatives of another
        # state variable (e.g. ``vy`` paired with ``y``); those will be added
        # as part of the higher-order companion.
        if _is_velocity_of(var, state_vars):
            continue

        eq = eq_by_var.get(var)
        if eq is not None and eq.order == 2:
            integration_vars.append(var)
            integration_vars.append(_velocity_name(var))
            continue
        if eq is not None and eq.order == 1:
            integration_vars.append(var)
            continue
        # No matching equation — accept anyway, treating as zero-derivative.
        integration_vars.append(var)

    # Now also append any equations whose var was not in state_vars (e.g.
    # the agent named a derivative directly). We log these but do not crash;
    # ``rhs_callable`` will simply not see them.
    declared = set(integration_vars)
    for eq in parsed.equations:
        if eq.var in declared:
            continue
        if eq.order == 2:
            integration_vars.append(eq.var)
            integration_vars.append(_velocity_name(eq.var))
        else:
            integration_vars.append(eq.var)

    index = {name: i for i, name in enumerate(integration_vars)}
    return tuple(integration_vars), index


def _is_velocity_of(var: str, state_vars: tuple[str, ...]) -> bool:
    """True if ``var`` looks like the first derivative of another state var."""
    if var.startswith("v"):
        return var[1:] in state_vars
    if var.startswith("d"):
        return var[1:] in state_vars
    return False


def _velocity_name(var: str) -> str:
    """Convention for naming a first time derivative."""
    if var.startswith("theta"):
        return "d" + var
    return "v" + var


def _compile_rhs(
    parsed: ParsedEquation,
    layout: _IntegrationLayout,
    parameters: dict[str, float],
) -> Callable[[np.ndarray, float], np.ndarray]:
    """Build a Python callable f(state, t) -> dstate/dt for ``odeint``."""
    integration_vars, index = layout
    eq_by_var = {eq.var: eq for eq in parsed.equations}

    # Lambdify each equation's RHS once. Symbols are bound to integration
    # variables (state) and to scalar parameters (substituted).
    state_symbols = sp.symbols(" ".join(integration_vars))
    if not isinstance(state_symbols, tuple):
        state_symbols = (state_symbols,)

    rhs_lambdas: dict[str, Callable[..., float]] = {}
    for var, eq in eq_by_var.items():
        rhs = eq.rhs.subs({sp.Symbol(k): v for k, v in parameters.items()})
        rhs_lambdas[var] = sp.lambdify(state_symbols, rhs, modules="numpy")

    def _rhs(state: np.ndarray, t: float) -> np.ndarray:
        derivs = np.zeros_like(state)
        for var, eq in eq_by_var.items():
            if eq.order == 1:
                idx = index[var]
                derivs[idx] = float(rhs_lambdas[var](*state))
            else:  # order == 2
                pos_idx = index[var]
                vel_name = _velocity_name(var)
                vel_idx = index[vel_name]
                derivs[pos_idx] = state[vel_idx]
                derivs[vel_idx] = float(rhs_lambdas[var](*state))
        return derivs

    return _rhs


def _build_initial_state(
    layout: _IntegrationLayout,
    initial_conditions: dict[str, float],
) -> np.ndarray:
    """Project the IC dict into the integration variable order."""
    integration_vars, _ = layout
    state = np.zeros(len(integration_vars), dtype=float)
    for i, var in enumerate(integration_vars):
        state[i] = float(initial_conditions.get(var, 0.0))
    return state


def _project_back_to_state_vars(
    result: np.ndarray,
    layout: _IntegrationLayout,
    state_vars: tuple[str, ...],
) -> dict[str, np.ndarray]:
    """Slice the integration output into per-system-variable trajectories."""
    _, index = layout
    out: dict[str, np.ndarray] = {}
    for var in state_vars:
        if var in index:
            out[var] = result[:, index[var]]
        else:
            # The agent never modelled this variable; predict the first
            # entry constant. This is rare and kept defensive.
            out[var] = np.full(result.shape[0], float(result[0, 0]))
    return out