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


# This is a temporary and naive implementation
# it might be replaced in the future for better performance
# see issue https://github.com/FluxML/Flux.jl/issues/702
# Johnny Chen -- @johnnychen94
"""
    activations(c::Chain, input)
Calculate the forward results of each layers in Chain `c` with `input` as model input.
"""
function activations(c::Chain, input)
  rst = []
  for l in c
    x = get(rst, length(rst), input)
    push!(rst, l(x))
  end
  return rst
end


"""
    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 maxout 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)

Constructs a Maxout layer over `n_alts` instances of  the layer given  by `f`.
The function takes no arguement and should return some callable layer.
Conventionally this is a linear dense layer.

For example the following example which
will construct a `Maxout` layer over 4 internal dense linear layers,
each identical in structure (784 inputs, 128 outputs).
```julia
    insize = 784
    outsize = 128
    Maxout(()->Dense(insize, outsize), 4)
```
"""
function Maxout(f, n_alts)
  over = Tuple(f() for _ in 1:n_alts)
  return Maxout(over)
end

@treelike Maxout

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

"""
    SkipConnection(layers...)

Creates a Skip Connection, which constitutes of a layer or Chain of consecutive layers
and a shortcut connection linking the input to the block to the
output through a user-supplied callable.

`SkipConnection` requires the output dimension to be the same as the input.

A 'ResNet'-type skip-connection with identity shortcut would simply be
```julia
    SkipConnection(layer, (a,b) -> a + b)
```
"""

struct SkipConnection
  layers
  connection  #user can pass arbitrary connections here, such as (a,b) -> a + b
end

@treelike SkipConnection

function (skip::SkipConnection)(input)
  #We apply the layers to the input and return the result of the application of the layers and the original input
  skip.connection(skip.layers(input), input)
end

function Base.show(io::IO, b::SkipConnection)
  print(io, "SkipConnection(")
  join(io, b.layers, ", ")
  print(io, ")")
end