Flux.jl/src/layers/basic.jl

"""
    Chain(layers...)

Chain multiple layers / functions together, so that they are called in sequence
on a given input.

```julia
m = Chain(x -> x^2, x -> x+1)
m(5) == 26

m = Chain(Dense(10, 5), Dense(5, 2))
x = rand(10)
m(x) == m[2](m[1](x))
```

`Chain` also supports indexing and slicing, e.g. `m[2]` or `m[1:end-1]`.
`m[1:3](x)` will calculate the output of the first three layers.
"""
struct Chain{T<:Tuple}
  layers::T
  Chain(xs...) = new{typeof(xs)}(xs)
end

@forward Chain.layers Base.getindex, Base.length, Base.first, Base.last,
  Base.iterate, Base.lastindex

children(c::Chain) = c.layers
mapchildren(f, c::Chain) = Chain(f.(c.layers)...)

applychain(::Tuple{}, x) = x
applychain(fs::Tuple, x) = applychain(tail(fs), first(fs)(x))

(c::Chain)(x) = applychain(c.layers, x)

Base.getindex(c::Chain, i::AbstractArray) = Chain(c.layers[i]...)

function Base.show(io::IO, c::Chain)
  print(io, "Chain(")
  join(io, c.layers, ", ")
  print(io, ")")
end

activations(c::Chain, x) = accumulate((x, m) -> m(x), c.layers, init = x)

"""
    Dense(in::Integer, out::Integer, σ = identity)

Creates a traditional `Dense` layer with parameters `W` and `b`.

    y = σ.(W * x .+ b)

The input `x` must be a vector of length `in`, or a batch of vectors represented
as an `in × N` matrix. The out `y` will be a vector or batch of length `out`.

```julia
julia> d = Dense(5, 2)
Dense(5, 2)

julia> d(rand(5))
Tracked 2-element Array{Float64,1}:
  0.00257447
  -0.00449443
```
"""
struct Dense{F,S,T}
  W::S
  b::T
  σ::F
end

Dense(W, b) = Dense(W, b, identity)

function Dense(in::Integer, out::Integer, σ = identity;
               initW = glorot_uniform, initb = zeros)
  return Dense(param(initW(out, in)), param(initb(out)), σ)
end

@treelike Dense

function (a::Dense)(x::AbstractArray)
  W, b, σ = a.W, a.b, a.σ
  σ.(W*x .+ b)
end

function Base.show(io::IO, l::Dense)
  print(io, "Dense(", size(l.W, 2), ", ", size(l.W, 1))
  l.σ == identity || print(io, ", ", l.σ)
  print(io, ")")
end

# Try to avoid hitting generic matmul in some simple cases
# Base's matmul is so slow that it's worth the extra conversion to hit BLAS
(a::Dense{<:Any,W})(x::AbstractArray{T}) where {T <: Union{Float32,Float64}, W <: AbstractArray{T}} =
  invoke(a, Tuple{AbstractArray}, x)

(a::Dense{<:Any,W})(x::AbstractArray{<:Real}) where {T <: Union{Float32,Float64}, W <: AbstractArray{T}} =
  a(T.(x))

"""
    Diagonal(in::Integer)

Creates an element-wise linear transformation layer with learnable
vectors `α` and `β`:

    y = α .* x .+ β

The input `x` must be a array where `size(x, 1) == in`.
"""
struct Diagonal{T}
  α::T
  β::T
end

Diagonal(in::Integer; initα = ones, initβ = zeros) =
  Diagonal(param(initα(in)), param(initβ(in)))

@treelike Diagonal

function (a::Diagonal)(x)
  α, β = a.α, a.β
  α.*x .+ β
end

function Base.show(io::IO, l::Diagonal)
  print(io, "Diagonal(", length(l.α), ")")
end


"""
    MaxOut(over)

`MaxOut` is a neural network layer, which has a number of internal layers,
which all have the same input, and the max out returns the elementwise maximium
of the internal layers' outputs.

Maxout over linear dense layers satisfies the univeral approximation theorem.

Reference:
Ian J. Goodfellow, David Warde-Farley, Mehdi Mirza, Aaron Courville, and Yoshua Bengio.
2013. Maxout networks.
In Proceedings of the 30th International Conference on International Conference on Machine Learning - Volume 28 (ICML'13),
Sanjoy Dasgupta and David McAllester (Eds.), Vol. 28. JMLR.org III-1319-III-1327.
https://arxiv.org/pdf/1302.4389.pdf
"""
struct MaxOut{FS<:Tuple}
    over::FS
end

"""
    MaxOut(f, n_alts, args...; kwargs...)

Constructs a MaxOut layer over `n_alts` instances of  the layer given  by `f`.
All other arguements (`args` & `kwargs`) are passed to the constructor `f`.

For example the followeExample usage
will construct a MaxOut layer over 4 dense linear layers,
each identical in structure (784 inputs, 128 outputs).
```julia
    insize = 784
    outsie = 128
    MaxOut(Dense, 4, insize, outsize)
```
"""
function MaxOut(f, n_alts, args...; kwargs...)
  over = Tuple(f(args...; kwargs...) for _ in 1:n_alts)
  return MaxOut(over)
end

function (mo::MaxOut)(input::AbstractArray)
    mapreduce(f -> f(input), (acc, out) -> max.(acc, out), mo.over)
end