--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/SbpOperators/quadrature/quadrature.jl	Fri Sep 25 13:06:02 2020 +0200
@@ -0,0 +1,34 @@
+export Quadrature
+"""
+    Quadrature{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
+
+Implements the quadrature operator `Q` of Dim dimension as a TensorMapping
+The multi-dimensional tensor operator consists of a tuple of 1D DiagonalInnerProduct H
+tensor operators.
+"""
+struct Quadrature{Dim,T<:Real,M} <: TensorOperator{T,Dim}
+    H::NTuple{Dim,DiagonalInnerProduct{T,M}}
+end
+
+LazyTensors.domain_size(Q::Quadrature{Dim}, range_size::NTuple{Dim,Integer}) where {Dim} = range_size
+
+function LazyTensors.apply(Q::Quadrature{Dim,T}, v::AbstractArray{T,Dim}, I::Vararg{Index,Dim}) where {T,Dim}
+    error("not implemented")
+end
+
+function LazyTensors.apply(Q::Quadrature{1,T}, v::AbstractVector{T}, I::Index) where T
+    @inbounds q = apply(Q.H[1], v , I)
+    return q
+end
+
+function LazyTensors.apply(Q::Quadrature{2,T}, v::AbstractArray{T,2}, I::Index, J::Index) where T
+    # Quadrature in x direction
+    @inbounds vx = view(v, :, Int(J))
+    @inbounds qx = apply(Q.H[1], vx , I)
+    # Quadrature in y-direction
+    @inbounds vy = view(v, Int(I), :)
+    @inbounds qy = apply(Q.H[2], vy, J)
+    return qx*qy
+end
+
+LazyTensors.apply_transpose(Q::Quadrature{Dim,T}, v::AbstractArray{T,Dim}, I::Vararg{Index,Dim}) where {Dim,T} = LazyTensors.apply(Q,v,I...)