import math
from typing import Optional, Sequence, Tuple

import torch
import torch.nn as nn
import torch.nn.functional as F


# ============================================================
# Pair extraction (utility; not used by the losses below)
# ============================================================
def get_valid_pairs_and_dt(
    event_seqs: torch.Tensor,
    time_seqs: torch.Tensor,
    n_tech_tokens: int
) -> Optional[Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]]:
    """
    Extract valid event pairs (prev -> next) and compute dt in years.

    Args:
        event_seqs (torch.Tensor): Event sequences.
        time_seqs (torch.Tensor): Time sequences.
        n_tech_tokens (int): Number of technical tokens.

    Returns:
        Optional[Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]]:
        (dt, b_prev, t_prev, b_next, t_next) if valid pairs exist, else None.

    Notes:
        - Assumes strict right-padding.
        - Filters to next events that are disease tokens: token_id >= n_tech_tokens.
        - Filters to strictly positive dt.
    """
    real_mask = event_seqs >= 1
    idx = real_mask.nonzero(as_tuple=False)

    if idx.size(0) <= 1:
        return None

    same_batch = idx[1:, 0] == idx[:-1, 0]
    if not same_batch.any():
        return None

    prev_idx = idx[:-1][same_batch]
    next_idx = idx[1:][same_batch]

    b_next, t_next = next_idx[:, 0], next_idx[:, 1]
    valid_target = event_seqs[b_next, t_next] >= n_tech_tokens
    if not valid_target.any():
        return None

    prev_idx = prev_idx[valid_target]
    next_idx = next_idx[valid_target]

    b_prev, t_prev = prev_idx[:, 0], prev_idx[:, 1]
    b_next, t_next = next_idx[:, 0], next_idx[:, 1]

    dt = (time_seqs[b_next, t_next] -
          time_seqs[b_prev, t_prev]).to(torch.float32) / 365.25
    valid_dt = dt > 0
    if not valid_dt.any():
        return None

    dt = dt[valid_dt]
    b_prev = b_prev[valid_dt]
    t_prev = t_prev[valid_dt]
    b_next = b_next[valid_dt]
    t_next = t_next[valid_dt]

    return dt, b_prev, t_prev, b_next, t_next


# ============================================================
# Losses (clean interface): loss_fn(preds, target_events, dt) -> (nll, regularization)
# ============================================================
class ExponentialNLLLoss(nn.Module):
    """
    Competing risks exponential likelihood.

    The negative log-likelihood is given by:

    .. math::
        \\text{nll} = -\\log \\lambda_{k^*} + \\left(\\sum_k \\lambda_k\\right) \\cdot dt

    Args:
        eps (float): Small epsilon for numerical stability.
    """

    def __init__(
            self,
            lambda_reg: float = 0.0,
            eps: float = 1e-6,
    ):
        super().__init__()
        self.eps = eps
        self.lambda_reg = lambda_reg

    def forward(
        self,
        logits: torch.Tensor,
        target_events: torch.Tensor,
        dt: torch.Tensor,
        reduction: str = "mean",
    ) -> Tuple[torch.Tensor, torch.Tensor]:
        """
        Forward pass.

        Args:
            logits (torch.Tensor): (M, K) tensor of logits.
            target_events (torch.Tensor): (M,) int64 tensor of target events in [0, K).
            dt (torch.Tensor): (M,) float tensor of time intervals (years), strictly positive.
            reduction (str): 'mean', 'sum', or 'none'.

        Returns:
            Tuple[torch.Tensor, torch.Tensor]: (nll, regularization) where regularization is 0.
        """
        logits = logits.squeeze(-1) if logits.dim() == 3 else logits
        hazards = F.softplus(logits) + self.eps  # (M,K)
        hazard_event = hazards.gather(
            1, target_events.unsqueeze(1)).squeeze(1)  # (M,)
        total_hazard = hazards.sum(dim=1)  # (M,)
        log_hazards = torch.log(hazards)               # (M, K)
        nll = -torch.log(hazard_event) + total_hazard * dt

        if reduction == "mean":
            nll = nll.mean()
        elif reduction == "sum":
            nll = nll.sum()

        reg = F.cross_entropy(log_hazards, target_events,
                              reduction="mean") * self.lambda_reg
        return nll, reg


class PiecewiseExponentialLoss(nn.Module):
    """Piecewise-constant competing risks exponential likelihood.

    Uses B time bins defined by `bin_edges` (length B+1, strictly increasing, starting at 0).
    Within each bin b, hazards are constant and parameterized as:

        hazards = softplus(logits) + eps   with logits shape (M, K, B)

    For each sample i, dt is bucketized to bin b* and the NLL is:

        nll_i = -log(hazard_{k*}(b*)) + \int_0^{dt} sum_k hazard_k(u) du

    The integral is computed in closed form by summing full bins plus the partial bin b*.
    """

    def __init__(
        self,
        bin_edges: Sequence[float],
        eps: float = 1e-6,
        lambda_reg: float = 0.0,
    ):
        super().__init__()

        if len(bin_edges) < 2:
            raise ValueError("bin_edges must have length >= 2")
        if bin_edges[0] != 0:
            raise ValueError("bin_edges must start at 0")
        for i in range(1, len(bin_edges)):
            if not (bin_edges[i] > bin_edges[i - 1]):
                raise ValueError("bin_edges must be strictly increasing")

        self.eps = float(eps)
        self.lambda_reg = float(lambda_reg)

        edges = torch.tensor(list(bin_edges), dtype=torch.float32)
        self.register_buffer("bin_edges", edges, persistent=False)

    def forward(
        self,
        logits: torch.Tensor,
        target_events: torch.Tensor,
        dt: torch.Tensor,
        reduction: str = "mean",
    ) -> Tuple[torch.Tensor, torch.Tensor]:
        if logits.dim() != 3:
            raise ValueError("logits must have shape (M, K, B)")

        M, K, B = logits.shape
        if self.bin_edges.numel() != B + 1:
            raise ValueError(
                f"bin_edges length ({self.bin_edges.numel()}) must equal B+1 ({B+1})"
            )

        device = logits.device
        dt = dt.to(device=device)
        target_events = target_events.to(device=device)

        # Build a per-sample finite mask to avoid NaN/Inf propagation.
        logits_finite = torch.isfinite(logits).view(M, -1).all(dim=1)
        dt_finite = torch.isfinite(dt)
        target_finite = torch.isfinite(target_events)
        finite_mask = logits_finite & dt_finite & target_finite

        nll_full = logits.new_zeros((M,))

        if not finite_mask.any():
            nll_out = nll_full if reduction == "none" else logits.new_zeros(())
            reg_out = logits.new_zeros(())
            return nll_out, reg_out

        idx = finite_mask.nonzero(as_tuple=False).squeeze(1)
        logits_v = logits[idx]
        target_v = target_events[idx].to(torch.long)
        dt_v = dt[idx].to(torch.float32)

        # Clamp dt into [eps, max_edge) to keep bucket indices valid.
        eps = self.eps
        max_edge = self.bin_edges[-1].to(device=device, dtype=dt_v.dtype)
        dt_max = torch.nextafter(max_edge, max_edge.new_zeros(()))
        dt_v = torch.clamp(dt_v, min=eps, max=dt_max)

        hazards = F.softplus(logits_v) + eps  # (Mv, K, B)
        total_hazard = hazards.sum(dim=1)    # (Mv, B)

        edges = self.bin_edges.to(device=device, dtype=dt_v.dtype)
        widths = edges[1:] - edges[:-1]  # (B,)

        # Bin index b* in [0, B-1]. boundaries are edges[1:] (length B).
        b_star = torch.searchsorted(edges[1:], dt_v, right=False)  # (Mv,)
        b_star = torch.clamp(b_star, min=0, max=B - 1)

        ar = torch.arange(logits_v.size(0), device=device)
        hazard_event = hazards[ar, target_v, b_star]  # (Mv,)

        # Integral: sum_{b < b*} total_hazard[:,b]*width_b + total_hazard[:,b*]*(dt-edge_left)
        weighted = total_hazard * widths.unsqueeze(0)  # (Mv, B)
        cum = weighted.cumsum(dim=1)                   # (Mv, B)
        full_bins_int = torch.zeros_like(dt_v)
        has_full = b_star > 0
        if has_full.any():
            full_bins_int[has_full] = cum.gather(
                1, (b_star[has_full] - 1).unsqueeze(1)
            ).squeeze(1)

        edge_left = edges[b_star]  # (Mv,)
        partial = total_hazard.gather(
            1, b_star.unsqueeze(1)).squeeze(1) * (dt_v - edge_left)
        integral = full_bins_int + partial

        nll_v = -torch.log(hazard_event) + integral
        nll_full[idx] = nll_v

        if reduction == "none":
            nll_out = nll_full
        elif reduction == "sum":
            nll_out = nll_v.sum()
        elif reduction == "mean":
            nll_out = nll_v.mean() if nll_v.numel() > 0 else logits.new_zeros(())
        else:
            raise ValueError("reduction must be one of: 'mean', 'sum', 'none'")

        reg = logits.new_zeros(())

        if self.lambda_reg != 0.0:
            reg = reg + (self.lambda_reg * logits_v.pow(2).mean())

        return nll_out, reg


class WeibullNLLLoss(nn.Module):
    """
    Weibull hazard in t.

    .. math::
        \\Lambda_k(t) = \\text{scale}_k \\cdot t^{\\text{shape}_k}

        \\lambda_k(t) = \\text{shape}_k \\cdot \\text{scale}_k \\cdot t^{\\text{shape}_k-1}

    Args:
        eps (float): Small epsilon for numerical stability.
        lambda_reg (float): Regularization weight.
        use_interval_near_integer (bool): If True, use interval likelihood for near-integer-year samples.
        near_integer_eps_years (float): Near-integer threshold in years.
        interval_half_width_years (float): Half-width \u0394 for interval [t-\u0394, t+\u0394] in years.
        min_integer_year (float): Only apply near-integer logic when round(t) >= min_integer_year.
    """

    def __init__(
        self,
        eps: float = 1e-6,
        lambda_reg: float = 0.0,
    ):
        super().__init__()
        self.eps = eps
        self.lambda_reg = lambda_reg

    def forward(
        self,
        logits: torch.Tensor,
        target_events: torch.Tensor,
        dt: torch.Tensor,
        reduction: str = "mean",
    ) -> Tuple[torch.Tensor, torch.Tensor]:
        """
        Forward pass.

        Args:
            logits (torch.Tensor): (M, K, 2) tensor of logits.
            target_events (torch.Tensor): (M,) tensor of target events.
            dt (torch.Tensor): (M,) tensor of time intervals.
            reduction (str): 'mean', 'sum', or 'none'.

        Returns:
            Tuple[torch.Tensor, torch.Tensor]: (nll, regularization).
        """
        shapes = F.softplus(logits[..., 0]) + self.eps  # (M,K)
        scales = F.softplus(logits[..., 1]) + self.eps  # (M,K)
        eps = self.eps
        t = torch.clamp(dt, min=eps)

        t_mat = t.unsqueeze(1)  # (M,1)

        # cumulative hazard (M,K)
        cum_hazard = scales * t_mat.pow(shapes)

        # hazard (M,K)
        hazard = shapes * scales * t_mat.pow(shapes - 1.0)

        hazard_event = hazard.gather(1, target_events.unsqueeze(1)).squeeze(1)
        # Point-event likelihood: f_k(t) = \lambda_k(t) * exp(-\Lambda_total(t))
        # NLL_point = -log \lambda_{k*}(t) + \Lambda_total(t)
        nll = -torch.log(hazard_event + eps) + cum_hazard.sum(dim=1)

        if reduction == "mean":
            nll = nll.mean()
        elif reduction == "sum":
            nll = nll.sum()

        reg = shapes.new_zeros(())
        if self.lambda_reg > 0:
            reg = self.lambda_reg * (
                (torch.log(scales + eps) ** 2).mean() +
                (torch.log(shapes + eps) ** 2).mean()
            )
        return nll, reg