import math
from typing import Optional
import numpy as np
import torch
from torch import nn


class MultiHeadedAttention(nn.Module):
    """Multi-Head Attention layer

    :param int n_head: the number of head s
    :param int n_feat: the number of features
    :param float dropout_rate: dropout rate
    """

    def __init__(self, n_head: int, n_feat: int, dropout_rate: float):
        super(MultiHeadedAttention, self).__init__()
        assert n_feat % n_head == 0
        # We assume d_v always equals d_k
        self.d_k = n_feat // n_head
        self.h = n_head
        self.linear_q = nn.Linear(n_feat, n_feat)
        self.linear_k = nn.Linear(n_feat, n_feat)
        self.linear_v = nn.Linear(n_feat, n_feat)
        self.linear_out = nn.Linear(n_feat, n_feat)
        # self.attn: Optional[torch.Tensor] = None # torch.empty(0)
        # self.register_buffer("attn", torch.empty(0))
        self.dropout = nn.Dropout(p=dropout_rate)

    def forward(self, query: torch.Tensor, key: torch.Tensor, value: torch.Tensor, mask: Optional[torch.Tensor] = None) -> torch.Tensor:
        """Compute 'Scaled Dot Product Attention'

        :param torch.Tensor query: (batch, time1, size)
        :param torch.Tensor key: (batch, time2, size)
        :param torch.Tensor value: (batch, time2, size)
        :param torch.Tensor mask: (batch, time1, time2)
        :param torch.nn.Dropout dropout:
        :return torch.Tensor: attentined and transformed `value` (batch, time1, d_model)
             weighted by the query dot key attention (batch, head, time1, time2)
        """
        n_batch = query.size(0)
        q = self.linear_q(query).view(n_batch, -1, self.h, self.d_k)
        k = self.linear_k(key).view(n_batch, -1, self.h, self.d_k)
        v = self.linear_v(value).view(n_batch, -1, self.h, self.d_k)
        q = q.transpose(1, 2)  # (batch, head, time1, d_k)
        k = k.transpose(1, 2)  # (batch, head, time2, d_k)
        v = v.transpose(1, 2)  # (batch, head, time2, d_k)

        scores = torch.matmul(q, k.transpose(-2, -1)) / math.sqrt(self.d_k)  # (batch, head, time1, time2)
        if mask is not None:
            mask = mask.unsqueeze(1).eq(0)  # (batch, 1, time1, time2)
            #min_value: float = float(numpy.finfo(torch.tensor(0, dtype=scores.dtype).numpy().dtype).min)
            mask = mask.to(device=scores.device)
            scores = scores.masked_fill_(mask, -np.inf)
            attn = torch.softmax(scores, dim=-1).masked_fill(mask, 0.0)  # (batch, head, time1, time2)
        else:
            attn = torch.softmax(scores, dim=-1)  # (batch, head, time1, time2)

        p_attn = self.dropout(attn)
        x = torch.matmul(p_attn, v)  # (batch, head, time1, d_k)
        x = x.transpose(1, 2).contiguous().view(n_batch, -1, self.h * self.d_k)  # (batch, time1, d_model)
        return self.linear_out(x)  # (batch, time1, d_model)
