# using LuxCore
using Random: AbstractRNG
using Lux

"""
# Fields
- `embed_dim`: Queue vector length. `q_len`
- `kvdim::Int`: Key vector and value vector length.
- `num_heads`: Number of heads.

# Calculation
```math
\\begin{aligned}
    Q &\\in \\mathbb{R}^{qdim} \\\\
    W^Q &\\in M_{embed \\times qdim}(\\mathbb{R}) \\\\
    K &\\in \\mathbb{R}^{kvdim} \\\\
    W^K &\\in M_{embed \\times kvdim}(\\mathbb{R}) \\\\
    V &\\in \\mathbb{R}^{kvdim} \\\\
    W^V &\\in M_{vembed \\times kvdim}(\\mathbb{R}) \\\\
    head_i &= \\operatorname{Attention}(W^Q_i Q, W^K_ K, W^V_i V) \\\\
    \\operatorname{Attention}(Q, K, V) &= V \\operatorname{softmax}\\left(\\frac{K^T Q}{\\sqrt{kvdim}} \\right) \\\\
    \\operatorname{MultiheadAttention}(Q, K, V) &= W^O \\operatorname{Concat}(head_1, \\ldots, head_h)
\\end{aligned}
```

So far, ``Q, K, V`` are inputs `x` for the layer,
``W^Q, W^K, W^V, W^O`` are parameters `ps`,
and the layer has no states `st`.
"""
struct MultiheadAttention{F} <: LuxCore.AbstractLuxLayer
    embed_dim::Int
    qdim::Int
    kvdim::Int
    v_embed_dim::Int
    num_heads::Int
    init_weight::F
end

"""
    MultiheadAttention(embed_dim::Int, num_heads::Int; init_weight=glorot_uniform, kw...)

Constructor.

# Arguments
  - `embed_dim::Int`
  - `num_heads::Int`

## Keyword Arguments
- `init_weight`: weight initialzer (rng generator)
- `qdim`: Default `embed_dim`
- `kvdim::Int`: Default: `embed_dim`
- `v_embed_dim`: Default: `embed_dim`

# Parameters and states

## Parameters
- `weight_q`
TODO
"""
function MultiheadAttention(
    embed_dim::Int,
    num_heads::Int;
    init_weight = glorot_uniform,
    kw...,
)
    MultiheadAttention{typeof(init_weight)}(
        embed_dim,
        haskey(kw, :qdim) ? kw[:qdim] : embed_dim,
        haskey(kw, :kvdim) ? kw[:kvdim] : embed_dim,
        haskey(kw, :v_embed_dim) ? kw[:v_embed_dim] : embed_dim,
        num_heads,
        init_weight,
    )
end

function LuxCore.initialparameters(rng::AbstractRNG, l::MultiheadAttention)
    # see the original paper for weight dimensions (note that q,k,v weights have `num_heads` of matrices)
    (
        weight_q = l.init_weight(rng, l.embed_dim * l.num_heads, l.qdim),
        weight_k = l.init_weight(rng, l.embed_dim * l.num_heads, l.kvdim),
        weight_v = l.init_weight(rng, l.v_embed_dim * l.num_heads, l.kvdim),
        weight_o = l.init_weight(rng, l.v_embed_dim, l.v_embed_dim * l.num_heads), # TODO: next here maybe finished?
    )
end

function LuxCore.initialstates(::AbstractRNG, ::MultiheadAttention)
    NamedTuple()
end

function (l::MultiheadAttention)(x::NamedTuple, ps, st::NamedTuple)
    if size(x.q, 1) != l.embed_dim
        ArgumentError(
            "Length of queue must match the layer's embed_dim: size(q)[1] = $(size(x.q, 1)), embed_dim = $(l.embed_dim)",
        ) |> throw
    end
    if size(x.k, 1) != l.kvdim
        ArgumentError(
            "Length of key must match the layer's kvdim: size(k)[1] = $(size(x.k, 1)), kvdim = $(l.kvdim)",
        ) |> throw
    end
    if size(x.v, 1) != l.kvdim
        ArgumentError(
            "Length of value must match the layer's kvdim: size(v)[1] = $(size(x.v, 1)), kvdim = $(l.kvdim)",
        ) |> throw
    end
    # TODO

    # qk_dim, v_dim is divisible by num_heads. qk_dim = embed_dim * num_heads
    # [q] = (qk_dim, q_len, batch_size...)
    q = ps.weight_q * x.q
    # [k] = (qk_dim, kv_len, batch_size...)
    k = ps.weight_k * x.k
    # [v] = (v_dim, kv_len, batch_size...)
    v = ps.weight_v * x.v
    # [y] = (v_dim, q_len, batch_size...)
    # [α] = (kv_len, q_len, nheads, batch_size...)
    y, α = dot_product_attention(q, k, v; nheads = l.num_heads)
    ps.weight_o * y
end

# struct TransformerEncoder <: LuxCore.AbstractLuxContainerLayer{}
# end
#