"""
SBDenoiser — Anisotropic Schrödinger Bridge denoiser.

Training: Joint velocity + score matching with anisotropic bridge paths.
          v_θ target = x_T - x₀ (PF-ODE velocity, same as scDFM).
          s_θ target = -(x_t - μ_t) / var_t (conditional score).
          Minibatch anisotropic OT per step.

Inference: Euler-Maruyama SDE using drift = v_θ + (σ²/2)·s_θ.
           Or PF-ODE ablation: drift = v_θ.
"""

import math
import torch
import torch.nn as nn
import torchdiffeq

from ._scdfm_imports import make_lognorm_poisson_noise
from .model.model import SBModel
from .ot_anisotropic import AnisotropicOTSampler


def pairwise_sq_dists(X, Y):
    return torch.cdist(X, Y, p=2) ** 2


@torch.no_grad()
def median_sigmas(X, scales=(0.5, 1.0, 2.0, 4.0)):
    D2 = pairwise_sq_dists(X, X)
    tri = D2[~torch.eye(D2.size(0), dtype=bool, device=D2.device)]
    m = torch.median(tri).clamp_min(1e-12)
    s2 = torch.tensor(scales, device=X.device) * m
    return [float(s.item()) for s in torch.sqrt(s2)]


def mmd2_unbiased_multi_sigma(X, Y, sigmas):
    m, n = X.size(0), Y.size(0)
    Dxx = pairwise_sq_dists(X, X)
    Dyy = pairwise_sq_dists(Y, Y)
    Dxy = pairwise_sq_dists(X, Y)
    vals = []
    for sigma in sigmas:
        beta = 1.0 / (2.0 * (sigma ** 2) + 1e-12)
        Kxx = torch.exp(-beta * Dxx)
        Kyy = torch.exp(-beta * Dyy)
        Kxy = torch.exp(-beta * Dxy)
        term_xx = (Kxx.sum() - Kxx.diag().sum()) / (m * (m - 1) + 1e-12)
        term_yy = (Kyy.sum() - Kyy.diag().sum()) / (n * (n - 1) + 1e-12)
        term_xy = Kxy.mean()
        vals.append(term_xx + term_yy - 2.0 * term_xy)
    return torch.stack(vals).mean()


class SBDenoiser(nn.Module):
    """
    Anisotropic Schrödinger Bridge Denoiser.

    σ_g simultaneously controls:
    1. OT coupling cost (Mahalanobis weights)
    2. Bridge noise level (conditional bridge variance)
    3. SDE diffusion strength (Euler-Maruyama noise)
    """

    def __init__(
        self,
        model: SBModel,
        noise_type: str = "Gaussian",
        use_mmd_loss: bool = True,
        gamma: float = 0.5,
        poisson_alpha: float = 0.8,
        poisson_target_sum: float = 1e4,
        # Score training
        score_weight: float = 0.1,
        score_t_clip: float = 0.02,
        use_score: bool = True,
        # σ_g regularization
        sigma_base: float = 0.5,
        sigma_sparse_weight: float = 0.01,
        sigma_volume_weight: float = 0.01,
        # OT coupling
        ot_method: str = "sinkhorn",
        ot_reg: float = 0.05,
        ot_use_sigma: bool = True,
        sigma_min: float = 0.01,
        # Time sampling
        t_sample_mode: str = "logit_normal",
        t_mean: float = 0.0,
        t_std: float = 1.0,
        # SDE inference
        sde_steps: int = 50,
        use_sde_inference: bool = True,
        # Source-Anchored Bridge
        source_anchored: bool = False,
    ):
        super().__init__()
        self.model = model
        self.noise_type = noise_type
        self.use_mmd_loss = use_mmd_loss
        self.gamma = gamma
        self.poisson_alpha = poisson_alpha
        self.poisson_target_sum = poisson_target_sum
        self.score_weight = score_weight
        self.score_t_clip = score_t_clip
        self.use_score = use_score
        self.sigma_base = sigma_base
        self.sigma_sparse_weight = sigma_sparse_weight
        self.sigma_volume_weight = sigma_volume_weight
        self.ot_use_sigma = ot_use_sigma
        self.t_sample_mode = t_sample_mode
        self.t_mean = t_mean
        self.t_std = t_std
        self.sde_steps = sde_steps
        self.use_sde_inference = use_sde_inference
        self.source_anchored = source_anchored

        self.ot_sampler = AnisotropicOTSampler(
            method=ot_method, reg=ot_reg, sigma_min=sigma_min,
        )

    def _make_noise(self, source: torch.Tensor) -> torch.Tensor:
        if self.noise_type == "Gaussian":
            return torch.randn_like(source)
        elif self.noise_type == "Poisson":
            return make_lognorm_poisson_noise(
                target_log=source,
                alpha=self.poisson_alpha,
                per_cell_L=self.poisson_target_sum,
            )
        else:
            raise ValueError(f"Unknown noise_type: {self.noise_type}")

    def _sample_t(self, n: int, device: torch.device) -> torch.Tensor:
        if self.t_sample_mode == "logit_normal":
            t = torch.sigmoid(torch.randn(n, device=device) * self.t_std + self.t_mean)
        else:
            t = torch.rand(n, device=device)
        return t.clamp(self.score_t_clip, 1.0 - self.score_t_clip)

    def train_step(
        self,
        source: torch.Tensor,            # (B, G) control expression
        target: torch.Tensor,             # (B, G) perturbed expression
        perturbation_id: torch.Tensor,    # (B, n_pert)
        gene_input: torch.Tensor,         # (B, G) vocab-encoded gene IDs
    ) -> dict:
        """
        Single training step with anisotropic bridge + minibatch OT.
        """
        B = source.shape[0]
        device = source.device

        # 1. Sample time
        t = self._sample_t(B, device)                                    # (B,)
        t_col = t.unsqueeze(-1)                                          # (B, 1)

        # 2. Get σ_g from sigma_net (independent of backbone)
        #    Need gene_emb and pert_emb — compute them via the model's encoder
        with torch.no_grad():
            gene_emb = self.model.encoder(gene_input)                    # (B, G, d)
            pert_emb = self.model.get_perturbation_emb(
                perturbation_id, cell_1=source)                          # (B, d)
        # σ_g with gradient (for regularization loss)
        sigma_g = self.model.sigma_net(pert_emb, t, gene_emb)           # (B, G)
        sigma_g_det = sigma_g.detach()                                   # for bridge sampling

        # 3. Create x_0 and do minibatch anisotropic OT
        if self.source_anchored:
            x_0 = source                                                  # bridge from control
        else:
            x_0 = self._make_noise(source)                                # bridge from noise
        if self.ot_use_sigma:
            sigma_for_ot = sigma_g_det.mean(0)                            # (G,) batch mean
            x_0, target_matched = self.ot_sampler.sample_plan_fix_x0(
                x_0, target, sigma_for_ot)
        else:
            x_0, target_matched = self.ot_sampler.sample_plan_fix_x0(
                x_0, target, sigma_g=None)

        # 4. Anisotropic conditional bridge sampling
        mu_t = (1 - t_col) * x_0 + t_col * target_matched               # (B, G)
        var_t = (sigma_g_det ** 2 * (t_col * (1 - t_col))).clamp(min=1e-8)
        std_t = torch.sqrt(var_t)                                         # (B, G)
        eps = torch.randn_like(x_0)
        x_t = mu_t + std_t * eps                                          # (B, G)

        # 5. Targets
        v_target = target_matched - x_0                                    # source-anchored: Δ
        s_target = -eps / (std_t + 1e-8)                                   # conditional score

        # 6. Full model forward
        pred_v, pred_s, sigma_g_pred = self.model(
            gene_input, source, x_t, t, perturbation_id)

        # 7. Velocity loss
        loss_v = ((pred_v - v_target) ** 2).mean()

        # 8. Score loss (var_t-weighted DSM — equivalent to ε-prediction)
        #    var_t weighting cancels the 1/var_t in s_target, giving bounded loss ~O(1)
        loss_s = torch.tensor(0.0, device=device)
        if self.use_score and pred_s is not None:
            loss_s = (var_t * (pred_s - s_target) ** 2).mean()

        # 9. σ_g regularization
        #    Volume penalty anchors geometric mean at σ_base (global scale).
        #    L1 sparse penalty removed — it killed per-gene anisotropy by
        #    pulling every σ_g to σ_base.  Sigmoid [σ_min, σ_max] prevents
        #    collapse/explosion; volume penalty alone is sufficient.
        loss_sparse = (sigma_g_pred - self.sigma_base).abs().mean()  # monitor only
        loss_volume = (sigma_g_pred.log().mean() - math.log(self.sigma_base)) ** 2

        # 10. MMD loss (optional)
        loss_mmd = torch.tensor(0.0, device=device)
        if self.use_mmd_loss:
            x1_hat = x_t + pred_v * (1 - t_col)
            sigmas_mmd = median_sigmas(target_matched, scales=(0.5, 1.0, 2.0, 4.0))
            loss_mmd = mmd2_unbiased_multi_sigma(x1_hat, target_matched, sigmas_mmd)

        # 11. Total loss
        #    loss_sparse excluded — kept in return dict for monitoring
        loss = (
            loss_v
            + self.score_weight * loss_s
            + self.sigma_volume_weight * loss_volume
            + self.gamma * loss_mmd
        )

        return {
            "loss": loss,
            "loss_v": loss_v.detach(),
            "loss_s": loss_s.detach(),
            "loss_mmd": loss_mmd.detach(),
            "loss_sparse": loss_sparse.detach(),
            "loss_volume": loss_volume.detach(),
            "sigma_mean": sigma_g_pred.mean().detach(),
            "sigma_std": sigma_g_pred.std().detach(),
        }

    @torch.no_grad()
    def generate(
        self,
        source: torch.Tensor,            # (B, G)
        perturbation_id: torch.Tensor,    # (B, n_pert)
        gene_ids: torch.Tensor,           # (B, G) or (G,)
        steps: int = None,
        method: str = "sde",
    ) -> torch.Tensor:
        """
        Generate perturbed expression via SDE or PF-ODE.

        SDE:    dX = [v_θ + (σ²/2)·s_θ] dt + σ·dB  (Euler-Maruyama)
        PF-ODE: dx/dt = v_θ                          (torchdiffeq RK4)
        """
        B, G = source.shape
        device = source.device
        steps = steps or self.sde_steps

        if gene_ids.dim() == 1:
            gene_ids = gene_ids.unsqueeze(0).expand(B, -1)

        if self.source_anchored:
            x_0 = source.clone()                                          # start from control
        else:
            x_0 = self._make_noise(source)                                # start from noise

        use_sde = self.use_sde_inference and (method != "ode")

        if use_sde:
            # SDE: Euler-Maruyama (no high-order SDE solver available)
            x_t = x_0
            dt = 1.0 / steps
            for i in range(steps):
                t_val = i * dt
                t = torch.full((B,), t_val, device=device)
                pred_v, pred_s, sigma_g = self.model(
                    gene_ids, source, x_t, t, perturbation_id)
                if pred_s is not None:
                    drift = pred_v + 0.5 * sigma_g ** 2 * pred_s
                    diffusion_noise = sigma_g * math.sqrt(dt) * torch.randn_like(x_t)
                    x_t = x_t + drift * dt + diffusion_noise
                else:
                    x_t = x_t + pred_v * dt
        else:
            # PF-ODE: torchdiffeq RK4 (matches scDFM inference)
            def ode_func(t_scalar, x):
                t_batch = torch.full((B,), t_scalar.item(), device=device)
                pred_v, _, _ = self.model(
                    gene_ids, source, x, t_batch, perturbation_id)
                return pred_v

            t_span = torch.linspace(0, 1, steps, device=device)
            trajectory = torchdiffeq.odeint(
                ode_func, x_0, t_span,
                method="rk4", atol=1e-4, rtol=1e-4,
            )
            x_t = trajectory[-1]

        return torch.clamp(x_t, min=0)