"""Module D: Three-phase HPI control flow (Algorithm 1) — NN edition.

Phase 1: Find admissible L0 with PD critic (NN-based).
Phase 2: Homotopy contraction L_i -> 0 with safety constraint.
Phase 3: Standard policy iteration on original system (L = 0).
"""

import copy

import numpy as np
import torch

from .data_collector import DataCollector
from .nn_models import check_lyapunov_decrease, check_positive_definite
from .nn_trainer import NNTrainer


class HPIController:
    """Implements the three-phase Homotopy-Based Policy Iteration algorithm
    using neural network function approximators."""

    def __init__(self, J=1.0, mgl=1.0, R=1.0, pe_amplitude=0.5,
                 lr=1e-3, epochs=500, lambda_weight=1e-6):
        """
        Args:
            J: Moment of inertia (default 1.0).
            mgl: Mass x gravity x length product (default 1.0).
            R: Control cost weight (default 1.0).
            pe_amplitude: PE signal amplitude scale (default 0.5).
            lr: Learning rate for Adam optimizer.
            epochs: Training epochs per HPI iteration.
            lambda_weight: L2 regularization coefficient.
        """
        self.J = float(J)
        self.mgl = float(mgl)
        self.R = float(R)
        self.lr = float(lr)
        self.epochs = int(epochs)
        self.lambda_weight = float(lambda_weight)
        self.pe_amplitude = float(pe_amplitude)
        self.collector = DataCollector(J=J, mgl=mgl)
        self.trainer = NNTrainer(R=R, lr=lr, epochs=epochs,
                                 lambda_weight=lambda_weight)
        # Override PE amplitude
        self.collector._scale = pe_amplitude / np.sum(
            np.abs(self.collector._a) + np.abs(self.collector._b)
        )

    # ═══════════════════════════════════════════════════════════════
    # Utility
    # ═══════════════════════════════════════════════════════════════

    def check_positive_definite(self, critic_nn=None, X_traj=None):
        """Check if critic NN corresponds to a PD value function.

        Checks both Hessian at origin and V(x) positivity on trajectory.
        """
        if critic_nn is None:
            critic_nn = self.trainer.critic_nn
        return check_positive_definite(critic_nn, X_traj=X_traj)

    def check_lyapunov_decrease(self, X, f_X):
        """Check if current critic satisfies Lyapunov decrease on trajectory."""
        return check_lyapunov_decrease(self.trainer.critic_nn, X, f_X)

    def _compute_f_X(self, X):
        """Drift dynamics f(x) = [x2, sin(x1)] on trajectory."""
        X = np.asarray(X)
        f_X = np.zeros_like(X)
        f_X[:, 0] = X[:, 1]
        f_X[:, 1] = np.sin(X[:, 0])
        return f_X

    def _hessian_info(self):
        """Return (h11, h22, det) of the critic Hessian at origin for logging."""
        x0 = torch.zeros(1, 2, requires_grad=True)
        V0 = self.trainer.critic_nn(x0)
        grad_V = torch.autograd.grad(V0.sum(), x0, create_graph=True)[0]
        h11 = torch.autograd.grad(grad_V[0, 0], x0, retain_graph=True)[0][0, 0].item()
        h22 = torch.autograd.grad(grad_V[0, 1], x0, retain_graph=True)[0][0, 1].item()
        h12 = torch.autograd.grad(grad_V[0, 0], x0, retain_graph=True)[0][0, 1].item()
        det = h11 * h22 - h12 ** 2
        return h11, h22, det

    # ═══════════════════════════════════════════════════════════════
    # Phase 1: Find L0 — scan ALL L values, pick best loss
    # ═══════════════════════════════════════════════════════════════

    def phase_one_find_L0(self, x0, T, dt, L_start=0.1, L_step=0.5, L_max=20.0,
                          verbose=False):
        """Find admissible L0 by scanning all L values and picking the best.

        Unlike the polynomial version which returns at the FIRST PD L,
        this scans ALL L values and chooses the one with lowest Bellman
        residual loss AND positive-definite critic. This ensures Phase 2
        starts from the best possible critic.

        Args:
            x0: Initial state (2,).
            T: Simulation duration.
            dt: Time step.
            L_start: Starting L value.
            L_step: Increment step.
            L_max: Maximum L value before failure.
            verbose: If True, print progress.

        Returns:
            tuple: (L0, critic_sd, actor_sd, results_dict).

        Raises:
            RuntimeError: If no admissible L is found below L_max.
        """
        L_values = []
        L = L_start
        while L <= L_max:
            L_values.append(L)
            L += L_step

        if not L_values:
            raise RuntimeError("No L values to try (L_start > L_max)")

        # Collect ONE shared trajectory with PE-only control (no actor)
        # for training at all L values.
        def u_func(t, x):
            return self.collector.pe_signal(t)

        t, X, U = self.collector.collect_trajectory(x0, T, dt, u_func)
        f_X = self._compute_f_X(X)

        best_L = None
        best_loss = float('inf')
        best_critic_sd = None
        best_actor_sd = None
        best_info = None

        for L in L_values:
            if verbose:
                print(f"    Phase 1: trying L={L:.2f}...", flush=True)

            # Fresh trainer for each L
            trainer = NNTrainer(R=self.R, lr=self.lr, epochs=self.epochs,
                                lambda_weight=self.lambda_weight)

            result = trainer.train_one_iteration(t, X, U, L, prev_actor=None, dt=dt)
            loss = result['loss_c']
            pd = check_positive_definite(trainer.critic_nn, X_traj=X)
            lyap = check_lyapunov_decrease(trainer.critic_nn, X, f_X)

            if verbose:
                h11, h22, det = self._hessian_info_via_trainer(trainer)
                print(f"      loss={loss:.4e} PD={pd} lyap={lyap:.3f} "
                      f"H=[{h11:.4f},{h22:.4f}] det={det:.4e}", flush=True)

            # Only consider PD critics; pick lowest loss
            if pd and loss < best_loss:
                best_L = L
                best_loss = loss
                best_critic_sd = {k: v.clone() for k, v in trainer.critic_nn.state_dict().items()}
                best_actor_sd = {k: v.clone() for k, v in trainer.actor_nn.state_dict().items()}
                best_info = {'loss': loss, 'lyap': lyap, 'mse': result['mse_c']}

        if best_L is None:
            raise RuntimeError(
                f"Phase 1 failed: no admissible L found up to L_max={L_max}. "
                f"Try increasing L_max or adjusting training parameters."
            )

        if verbose:
            print(f"    Phase 1: selected L0={best_L:.2f} (loss={best_loss:.4e})",
                  flush=True)

        # Load best weights into main trainer
        self.trainer.critic_nn.load_state_dict(best_critic_sd)
        self.trainer.actor_nn.load_state_dict(best_actor_sd)

        return best_L, best_critic_sd, best_actor_sd, best_info

    def _hessian_info_via_trainer(self, trainer):
        """Get Hessian info from a specific trainer instance."""
        x0 = torch.zeros(1, 2, requires_grad=True)
        V0 = trainer.critic_nn(x0)
        grad_V = torch.autograd.grad(V0.sum(), x0, create_graph=True)[0]
        h11 = torch.autograd.grad(grad_V[0, 0], x0, retain_graph=True)[0][0, 0].item()
        h22 = torch.autograd.grad(grad_V[0, 1], x0, retain_graph=True)[0][0, 1].item()
        h12 = torch.autograd.grad(grad_V[0, 0], x0, retain_graph=True)[0][0, 1].item()
        det = h11 * h22 - h12 ** 2
        return h11, h22, det

    # ═══════════════════════════════════════════════════════════════
    # Phase 2: Homotopy contraction
    # ═══════════════════════════════════════════════════════════════

    def _compute_safe_alpha(self, X, prev_actor, L, gamma=0.1):
        """Compute safe homotopy step alpha via inequality constraint."""
        x_tensor = torch.tensor(X, dtype=torch.float32, requires_grad=True)
        V = self.trainer.critic_nn(x_tensor)
        grad_V = torch.autograd.grad(V.sum(), x_tensor, create_graph=False)[0]
        dot_V = (grad_V * x_tensor).sum(dim=1).detach().numpy()  # (M,)

        Q = X[:, 0] ** 2 + X[:, 1] ** 2  # (M,)

        if prev_actor is not None:
            with torch.no_grad():
                u_old = prev_actor(torch.tensor(X, dtype=torch.float32)).numpy()
        else:
            u_old = np.zeros(len(X))

        with torch.no_grad():
            u_new = self.trainer.actor_nn(torch.tensor(X, dtype=torch.float32)).numpy()

        gamma_c = 1.0 - gamma
        rhs = gamma_c * (Q + self.R * u_new ** 2) + self.R * (u_old - u_new) ** 2
        lhs = gamma_c * Q

        eps = 1e-10
        lower_candidates = []
        upper_candidates = []

        for k in range(len(dot_V)):
            d = dot_V[k]
            if d > eps:
                lower_candidates.append(lhs[k] / d)
                upper_candidates.append(rhs[k] / d)

        if not lower_candidates or not upper_candidates:
            return None

        alpha_lo = max(lower_candidates)
        alpha_hi = min(upper_candidates)

        if alpha_lo <= alpha_hi and alpha_hi > 0:
            return min(alpha_hi, L)
        return None

    def phase_two_contraction(self, x0, T, dt, L0, actor_sd_init, critic_sd_init,
                              gamma=0.1, max_iter=50, verbose=False):
        """Contract homotopy parameter L to zero via safety-constrained steps.

        Returns:
            tuple: (actor_sd, critic_sd, history).
        """
        L = L0
        self.trainer.critic_nn.load_state_dict(critic_sd_init)
        self.trainer.actor_nn.load_state_dict(actor_sd_init)
        self.trainer.reset_optimizer()

        best_actor_sd = {k: v.clone() for k, v in actor_sd_init.items()}
        best_critic_sd = {k: v.clone() for k, v in critic_sd_init.items()}
        reject_streak = 0
        history = [(L, 0.0, True)]  # (L, loss, PD)

        for iteration in range(max_iter):
            if verbose:
                print(f"    Phase 2 iter {iteration}: L={L:.4f}", flush=True)

            prev_actor = self.trainer.copy_actor()

            def u_func(t, x):
                pe = self.collector.pe_signal(t)
                u_policy = self.trainer.compute_u_hat(x)
                return pe + u_policy

            t, X, U = self.collector.collect_trajectory(x0, T, dt, u_func)
            f_X = self._compute_f_X(X)

            # Fresh optimizer per iteration
            self.trainer.reset_optimizer()
            result = self.trainer.train_one_iteration(t, X, U, L, prev_actor, dt)

            pd_new = check_positive_definite(self.trainer.critic_nn, X_traj=X)
            alpha = self._compute_safe_alpha(X, prev_actor, L, gamma)

            if alpha is None:
                alpha = L * 0.2

            if pd_new:
                best_actor_sd = {k: v.clone() for k, v in self.trainer.actor_nn.state_dict().items()}
                best_critic_sd = {k: v.clone() for k, v in self.trainer.critic_nn.state_dict().items()}
                reject_streak = 0
                if verbose:
                    lyap = check_lyapunov_decrease(self.trainer.critic_nn, X, f_X)
                    print(f"      alpha={alpha:.4f} loss={result['loss_c']:.4e} "
                          f"lyap={lyap:.3f} PD", flush=True)
            else:
                self.trainer.actor_nn.load_state_dict(best_actor_sd)
                self.trainer.critic_nn.load_state_dict(best_critic_sd)
                reject_streak += 1
                if verbose:
                    print(f"      alpha={alpha:.4f} loss={result['loss_c']:.4e} "
                          f"not PD (reject streak={reject_streak})", flush=True)

            L = max(0.0, L - alpha)
            history.append((L, result['loss_c'], pd_new))

            if L < 1e-14:
                if verbose:
                    print("    L reached 0, Phase 2 complete", flush=True)
                break

            if reject_streak > 15:
                if verbose:
                    print("    >15 consecutive rejections, stopping Phase 2", flush=True)
                break

        return best_actor_sd, best_critic_sd, history

    # ═══════════════════════════════════════════════════════════════
    # Phase 3: Standard policy iteration
    # ═══════════════════════════════════════════════════════════════

    def phase_three_pi(self, x0, T, dt, actor_sd_init, critic_sd_init,
                       epsilon=1e-6, max_iter=30, verbose=False):
        """Standard policy iteration on the original system (L = 0).

        Returns:
            tuple: (actor_sd, critic_sd, converged, history).
        """
        self.trainer.actor_nn.load_state_dict(actor_sd_init)
        self.trainer.critic_nn.load_state_dict(critic_sd_init)
        self.trainer.reset_optimizer()

        prev_loss = float('inf')
        converged = False
        history = []

        for iteration in range(max_iter):
            if verbose:
                print(f"    Phase 3 iter {iteration}", flush=True)

            prev_actor = self.trainer.copy_actor()

            def u_func(t, x):
                pe = self.collector.pe_signal(t)
                u_policy = self.trainer.compute_u_hat(x)
                u_policy = np.clip(u_policy, -5.0, 5.0)
                return pe + u_policy

            t, X, U = self.collector.collect_trajectory(x0, T, dt, u_func)

            self.trainer.reset_optimizer()
            result = self.trainer.train_one_iteration(t, X, U, 0.0, prev_actor, dt)
            loss = result['loss_c']
            history.append(loss)

            pd = check_positive_definite(self.trainer.critic_nn, X_traj=X)

            if verbose:
                f_X = self._compute_f_X(X)
                lyap = check_lyapunov_decrease(self.trainer.critic_nn, X, f_X)
                print(f"      loss={loss:.4e} PD={pd} lyap={lyap:.3f}", flush=True)

            if abs(prev_loss - loss) < epsilon:
                converged = True
                break

            prev_loss = loss

            if loss > 1e6 or not np.isfinite(loss):
                break

        actor_sd = {k: v.clone() for k, v in self.trainer.actor_nn.state_dict().items()}
        critic_sd = {k: v.clone() for k, v in self.trainer.critic_nn.state_dict().items()}
        return actor_sd, critic_sd, converged, history

    # ═══════════════════════════════════════════════════════════════
    # Full pipeline
    # ═══════════════════════════════════════════════════════════════

    def run(self, x0=None, T=10.0, dt=0.01,
            L_start=0.1, L_step=0.5, L_max=20.0,
            gamma=0.1, epsilon=1e-6, verbose=True):
        """Run the full three-phase HPI algorithm.

        Returns:
            dict: Results containing:
                - phase1_L0, phase1_critic_sd, phase1_actor_sd, phase1_info
                - phase2_history, phase2_actor_sd, phase2_critic_sd
                - phase3_actor_sd, phase3_critic_sd, phase3_converged, phase3_history
        """
        if x0 is None:
            x0 = np.array([0.5, 0.0])

        results = {}

        # ── Phase 1: Find L0 ──
        L0, critic_sd1, actor_sd1, info1 = self.phase_one_find_L0(
            x0, T, dt, L_start, L_step, L_max, verbose=verbose)
        results["phase1_L0"] = L0
        results["phase1_critic_sd"] = critic_sd1
        results["phase1_actor_sd"] = actor_sd1
        results["phase1_info"] = info1

        # ── Phase 2: Homotopy contraction ──
        actor_sd2, critic_sd2, hist2 = self.phase_two_contraction(
            x0, T, dt, L0, actor_sd1, critic_sd1, gamma=gamma, verbose=verbose)
        results["phase2_actor_sd"] = actor_sd2
        results["phase2_critic_sd"] = critic_sd2
        results["phase2_history"] = hist2

        # ── Phase 3: Policy iteration ──
        actor_sd3, critic_sd3, converged, hist3 = self.phase_three_pi(
            x0, T, dt, actor_sd2, critic_sd2, epsilon, verbose=verbose)
        results["phase3_actor_sd"] = actor_sd3
        results["phase3_critic_sd"] = critic_sd3
        results["phase3_converged"] = converged
        results["phase3_history"] = hist3

        # Load final weights
        self.trainer.actor_nn.load_state_dict(actor_sd3)
        self.trainer.critic_nn.load_state_dict(critic_sd3)

        return results