import torch
from torch import nn, einsum

from einops import rearrange, repeat


def FeedForward(dim, mult=4):
    inner_dim = int(dim * mult)
    return nn.Sequential(
        nn.LayerNorm(dim),
        nn.Linear(dim, inner_dim, bias=False),
        nn.GELU(),
        nn.Linear(inner_dim, dim, bias=False),
    )


class PerceiverAttention(nn.Module):
    def __init__(self, *, dim, dim_head=64, heads=8):
        super().__init__()
        self.scale = dim_head**-0.5
        self.heads = heads
        inner_dim = dim_head * heads

        self.norm_media = nn.LayerNorm(dim)
        self.norm_latents = nn.LayerNorm(dim)

        self.to_q = nn.Linear(dim, inner_dim, bias=False)
        self.to_kv = nn.Linear(dim, inner_dim * 2, bias=False)
        self.to_out = nn.Linear(inner_dim, dim, bias=False)

    def forward(self, x, latents):
        """
        einstein notation
        b - batch
        t - time
        n - sequence
        d - dimension
        """
        x = self.norm_media(x)
        latents = self.norm_latents(latents)

        b, m, h = *x.shape[:2], self.heads

        q = self.to_q(latents)

        # the paper differs from Perceiver in which they also concat the key / values derived from the latents to be attended to
        kv_input = torch.cat((x, latents), dim=-2)
        k, v = self.to_kv(kv_input).chunk(2, dim=-1)

        q = rearrange(q, "b t n (h d) -> b h t n d", h=h)
        k = rearrange(k, "b t n (h d) -> b h t n d", h=h)
        v = rearrange(v, "b t n (h d) -> b h t n d", h=h)

        # attention
        q = q * self.scale
        sim = einsum("... i d, ... j d  -> ... i j", q, k)
        sim = sim - sim.amax(dim=-1, keepdim=True).detach()
        attn = sim.softmax(dim=-1)

        out = einsum("... i j, ... j d -> ... i d", attn, v)
        out = rearrange(out, "b h t n d -> b t n (h d)", h=h)
        return self.to_out(out)


class PerceiverResampler(nn.Module):
    def __init__(
        self,
        *,
        dim,
        depth,
        dim_head=64,
        heads=8,
        num_latents=64,
        num_media_embeds=4,
        ff_mult=4
    ):
        super().__init__()
        self.num_latents = num_latents
        self.latents = nn.Parameter(torch.randn(num_latents, dim))
        self.media_pos_emb = nn.Parameter(torch.randn(num_media_embeds, 1, dim))

        self.layers = nn.ModuleList([])
        for _ in range(depth):
            self.layers.append(
                nn.ModuleList(
                    [
                        PerceiverAttention(dim=dim, dim_head=dim_head, heads=heads),
                        FeedForward(dim=dim, mult=ff_mult),
                    ]
                )
            )

        self.norm = nn.LayerNorm(dim)

    def forward(self, x):
        if x.ndim == 3:
            x = rearrange(x, "b n d -> b 1 n d")

        times = x.shape[1]
        x = x + self.media_pos_emb[:times]

        latents = repeat(self.latents, "n d -> b m n d", b=x.shape[0], m=x.shape[1])
        for attn, ff in self.layers:
            latents = attn(x, latents) + latents
            latents = ff(latents) + latents
        return self.norm(latents)