--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/SbpOperators/quadrature/inverse_quadrature.jl	Sat Sep 26 15:22:13 2020 +0200
@@ -0,0 +1,34 @@
+export InverseQuadrature
+"""
+    InverseQuadrature{Dim,T<:Real,M,K} <: TensorMapping{T,Dim,Dim}
+
+Implements the inverse quadrature operator `Qi` of Dim dimension as a TensorOperator
+The multi-dimensional tensor operator consists of a tuple of 1D InverseDiagonalInnerProduct
+tensor operators.
+"""
+struct InverseQuadrature{Dim,T<:Real,M} <: TensorOperator{T,Dim}
+    Hi::NTuple{Dim,InverseDiagonalInnerProduct{T,M}}
+end
+
+LazyTensors.domain_size(Qi::InverseQuadrature{Dim}, range_size::NTuple{Dim,Integer}) where Dim = range_size
+
+function LazyTensors.apply(Qi::InverseQuadrature{Dim,T}, v::AbstractArray{T,Dim}, I::Vararg{Index,Dim}) where {T,Dim}
+    error("not implemented")
+end
+
+@inline function LazyTensors.apply(Qi::InverseQuadrature{1,T}, v::AbstractVector{T}, I::Index) where T
+    @inbounds q = apply(Qi.Hi[1], v , I)
+    return q
+end
+
+@inline function LazyTensors.apply(Qi::InverseQuadrature{2,T}, v::AbstractArray{T,2}, I::Index, J::Index) where T
+    # InverseQuadrature in x direction
+    @inbounds vx = view(v, :, Int(J))
+    @inbounds qx_inv = apply(Qi.Hi[1], vx , I)
+    # InverseQuadrature in y-direction
+    @inbounds vy = view(v, Int(I), :)
+    @inbounds qy_inv = apply(Qi.Hi[2], vy, J)
+    return qx_inv*qy_inv
+end
+
+LazyTensors.apply_transpose(Qi::InverseQuadrature{Dim,T}, v::AbstractArray{T,Dim}, I::Vararg{Index,Dim}) where {Dim,T} = LazyTensors.apply(Qi,v,I...)