abstract type DiffOp end

function apply(D::DiffOp, v::AbstractVector, i::Int)
    error("not implemented")
end

function innerProduct(D::DiffOp, u::AbstractVector, v::AbstractVector)::Real
    error("not implemented")
end

function matrixRepresentation(D::DiffOp)
    error("not implemented")
end

function boundaryCondition(D::DiffOp,b::Grid.BoundaryId,type)::(Closure, Penalty)
    error("not implemented")
end

function interface(Du::DiffOp, Dv::DiffOp, b::Grid.BoundaryId; type)
    error("not implemented")
end

abstract type Closure end

function apply(c::Closure, v::AbstractVector, i::Int)
    error("not implemented")
end

abstract type Penalty end

function apply(c::Penalty, g, i::Int)
    error("not implemented")
end

# DiffOp must have a grid!!!
function apply!(D::DiffOp, u::AbstractVector, v::AbstractVector)
    li = LinearIndices(D.grid.numberOfPointsPerDim)

    Nx, Ny = D.grid.numberOfPointsPerDim

    h = Grid.spacings(D.grid)
    li = LinearIndices(D.grid.numberOfPointsPerDim)
    ci = CartesianIndices(D.grid.numberOfPointsPerDim)
    is = D.op.innerStencil
    for i ∈ view(li, 5:Nx-4, 5:Ny-4)
        I = ci[i]


        u[i] = zero(eltype(v))
        for j ∈ is.range[1]:is.range[2]
            u[i] += is[j]*v[(I[2]-1)*Nx - 1 + I[1]+j]/h[1]^2
        end

        for j ∈ is.range[1]:is.range[2]
            u[i] += is[j]*v[(I[2]-1)*Nx - 1 + I[1]+ j*Nx]/h[2]^2
        end
    end

    return nothing
end

function apply(D::DiffOp, v::AbstractVector)::AbstractVector
    u = zeros(eltype(v), size(v))
    apply!(D,v,u)
    return u
end

# Differential operator for a*d^2/dx^2
struct Laplace1D <: DiffOp
    grid::Grid.EquidistantGrid
    a::Real
    op::D2{Float64}
end

# u = L*v
function apply(L::Laplace1D, v::AbstractVector, i::Int)
    h = Grid.spacings(L.grid)[1]
    uᵢ = L.a * apply(L.op, h, v, i)
    return uᵢ
end


# Differential operator for a*d^2/dx^2 + a*d^2/dy^2
struct Laplace2D <: DiffOp
    grid::Grid.EquidistantGrid
    a::Real
    op::D2{Float64}
end

# u = L*v
function apply(L::Laplace2D, v::AbstractVector, i::Int)
    h = Grid.spacings(L.grid)

    li = LinearIndices(L.grid.numberOfPointsPerDim)
    ci = CartesianIndices(L.grid.numberOfPointsPerDim)
    I = ci[i]

    uᵢ  = apply(L.op.innerStencil, view(v, li[:,I[2]]), I[1])/h[1]^2
    uᵢ += apply(L.op.innerStencil, view(v, li[I[1],:]), I[2])/h[2]^2

    return uᵢ
end