Merge pull request #128 from JuliaDiffEq/nnlib_convolutions

mul! implemented for 2d and 3d multiplication with NNlib

Author: ChrisRackauckas

Project.toml

@@ -11,6 +11,8 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SuiteSparse = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
 BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
+
 
 [compat]
 julia = "1"

src/DiffEqOperators.jl

@@ -4,7 +4,7 @@ import Base: +, -, *, /, \, size, getindex, setindex!, Matrix, convert
 using DiffEqBase, StaticArrays, LinearAlgebra
 import LinearAlgebra: mul!, ldiv!, lmul!, rmul!, axpy!, opnorm, factorize, I
 import DiffEqBase: AbstractDiffEqLinearOperator, update_coefficients!, is_constant
-using SparseArrays, ForwardDiff, BandedMatrices
+using SparseArrays, ForwardDiff, BandedMatrices, NNlib
 
 abstract type AbstractDerivativeOperator{T} <: AbstractDiffEqLinearOperator{T} end
 abstract type AbstractDiffEqCompositeOperator{T} <: AbstractDiffEqLinearOperator{T} end

src/derivative_operators/derivative_operator_functions.jl

@@ -1,9 +1,11 @@
 function LinearAlgebra.mul!(x_temp::AbstractArray{T}, A::DerivativeOperator{T,N}, M::AbstractArray{T}) where {T<:Real,N}
 
+    # Check that x_temp has correct dimensions
     v = zeros(ndims(x_temp))
     v[N] = 2
     @assert [size(x_temp)...]+v == [size(M)...]
 
+    # Check that axis of differentiation is in the dimensions of M and x_temp
     ndimsM = ndims(M)
     @assert N <= ndimsM
 
@@ -23,6 +25,69 @@ function LinearAlgebra.mul!(x_temp::AbstractArray{T}, A::DerivativeOperator{T,N}
     end
 end
 
+for MT in [2,3]
+    @eval begin
+        function LinearAlgebra.mul!(x_temp::AbstractArray{T,$MT}, A::DerivativeOperator{T,N,Wind,T2,S1}, M::AbstractArray{T,$MT}) where {T<:Real,N,Wind,T2,SL,S1<:SArray{Tuple{SL},T,1,SL}}
+
+            # Check that x_temp has correct dimensions
+            v = zeros(ndims(x_temp))
+            v[N] = 2
+            @assert [size(x_temp)...]+v == [size(M)...]
+
+            # Check that axis of differentiation is in the dimensions of M and x_temp
+            ndimsM = ndims(M)
+            @assert N <= ndimsM
+
+            # Respahe x_temp for NNlib.conv!
+            new_size = Any[size(x_temp)...]
+            bpc = A.boundary_point_count
+            setindex!(new_size, new_size[N]- 2*bpc, N)
+            new_shape = []
+            for i in 1:ndimsM
+                if i != N
+                    push!(new_shape,:)
+                else
+                    push!(new_shape,bpc+1:new_size[N]+bpc)
+                end
+             end
+             _x_temp = reshape(view(x_temp, new_shape...), (new_size...,1,1))
+
+            # Reshape M for NNlib.conv!
+            _M = reshape(M, (size(M)...,1,1))
+            s = A.stencil_coefs
+            sl = A.stencil_length
+
+            # Setup W, the kernel for NNlib.conv!
+            Wdims = ones(Int64, ndims(_x_temp))
+            Wdims[N] = sl
+            W = zeros(Wdims...)
+            Widx = Any[Wdims...]
+            setindex!(Widx,:,N)
+            W[Widx...] = s ./ A.dx^A.derivative_order # this will change later 
+            cv = DenseConvDims(_M, W)
+
+            conv!(_x_temp, _M, W, cv)
+
+            # Now deal with boundaries
+            dimsM = [axes(M)...]
+            alldims = [1:ndims(M);]
+            otherdims = setdiff(alldims, N)
+
+            idx = Any[first(ind) for ind in axes(M)]
+            itershape = tuple(dimsM[otherdims]...)
+            nidx = length(otherdims)
+            indices = Iterators.drop(CartesianIndices(itershape), 0)
+
+            setindex!(idx, :, N)
+            for I in indices
+                Base.replace_tuples!(nidx, idx, idx, otherdims, I)
+                convolve_BC_left!(view(x_temp, idx...), view(M, idx...), A)
+                convolve_BC_right!(view(x_temp, idx...), view(M, idx...), A)
+            end
+        end
+    end
+end
+
 function *(A::DerivativeOperator{T,N},M::AbstractArray{T}) where {T<:Real,N}
     size_x_temp = [size(M)...]
     size_x_temp[N] -= 2