From 50291487e5991e3b671f0a399406753919b203d2 Mon Sep 17 00:00:00 2001 From: islent Date: Mon, 18 Dec 2023 20:31:25 +0800 Subject: [PATCH] add test --- Project.toml | 2 + src/PhysicalFDM.jl | 49 +++++---- test/runtests.jl | 241 +++++++++++++++++++++++++++++++++++++++++++++ 3 files changed, 272 insertions(+), 20 deletions(-) create mode 100644 test/runtests.jl diff --git a/Project.toml b/Project.toml index 685a12d..c4ab2fe 100644 --- a/Project.toml +++ b/Project.toml @@ -5,9 +5,11 @@ version = "0.1.0" [deps] DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881" PaddedViews = "5432bcbf-9aad-5242-b902-cca2824c8663" PhysicalMeshes = "97d9904f-034f-4fb7-aeaa-03a173434233" PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" +Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" Tullio = "bc48ee85-29a4-5162-ae0b-a64e1601d4bc" diff --git a/src/PhysicalFDM.jl b/src/PhysicalFDM.jl index 8f86d2b..09598ab 100644 --- a/src/PhysicalFDM.jl +++ b/src/PhysicalFDM.jl @@ -1,7 +1,8 @@ module PhysicalFDM +using LinearAlgebra using DocStringExtensions -using PrecompieTools +using PrecompileTools using SparseArrays using OffsetArrays @@ -61,7 +62,7 @@ Generate differential matrix. - `lpoints`: Number of points at left to the target point, which differential is calculated by the fitted polynomial. - `rpoints`: Number of points at right to the target point. If `lpoints==rpoints`, then the differential is estimated as central finite difference. If `lpoints==0`, then it is normal forward finite difference. If `rpoints==0`, then it is backward finite difference. - `fitting_order`: The order of the fitted polynomial for estimating differential. -- `boundary`: Boundary condition. Can be `Dirichlet()`(boundary value is zero), `Periodic`(assume data is periodic), `:Extrapolation`(boundary value is extrapolated according to `boundary_points` and `boundary_order`), `:None`(not deal with boundary, will return non-square matrix). +- `boundary`: Boundary condition. Can be `:Dirichlet`(boundary value is zero), `:Periodic`(assume data is periodic), `:Extrapolation`(boundary value is extrapolated according to `boundary_points` and `boundary_order`), `:None`(not deal with boundary, will return non-square matrix). - `boundary_points`: Number of points for fitting polynomial to estimate differential at boundary. Normally it should not be much less than `points`, otherwise sometimes the current point may not be used to estimate the differential. - `boundary_order`: The order of the fitted polynomial for points determined by `boundary_points`. - `sparse`: If true, return sparse matrix instead of dense one. @@ -78,7 +79,7 @@ diff_mat(k,1;points=2,lpoints=0)*x #do the normal 1st order forward differential diff_mat(k,1;lpoints=1,rpoints=0)*x #do the 1st order backward differential (x[n-1]-x[n]). ``` """ -function diff_mat(n, order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, lpoints=div(points,2), rpoints=points-lpoints-1, fitting_order=lpoints+rpoints, boundary=Dirichlet(), boundary_points=lpoints+rpoints+1, boundary_order=boundary_points-1, sparse=false) +function diff_mat(n, order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, lpoints=div(points,2), rpoints=points-lpoints-1, fitting_order=lpoints+rpoints, boundary=:Dirichlet, boundary_points=lpoints+rpoints+1, boundary_order=boundary_points-1, sparse=false) nv[i]*ones(T,n-abs(x[i])) for i=1:length(x))...) + if boundary == :Dirichlet || boundary == :Vacuum # in the vacuum case, we manually compute solution on the boundaries + m=diagm1((x[i]=>v[i]*ones(T,n-abs(x[i])) for i=eachindex(x))...) elseif boundary isa Periodic m=zeros1(T,n,n) - for i=1:n, j=1:length(x) + for i=1:n, j=eachindex(x) jj=mod1(x[j]+i,n) m[i,jj]=v[j] end #elseif boundary==:None #TODO # nn=n-lpoints-rpoints - # m=diagm1(nn, n, (x[i]+lpoints=>v[i]*ones(T,nn) for i=1:length(x))...) + # m=diagm1(nn, n, (x[i]+lpoints=>v[i]*ones(T,nn) for i=eachindex(x))...) #elseif boundary==:Extrapolation #TODO # m=zeros1(T,n,n) # for i=1:n # if i<=lpoints # b=smooth_coef(T.(1-i:boundary_points-i),boundary_order,order)/dt - # m[i,1:length(b)]=b + # m[i,eachindex(b)]=b # elseif i>n-rpoints # b=smooth_coef(T.(n-i-boundary_points+1:n-i),boundary_order,order)/dt # m[i,n-length(b)+1:n]=b @@ -123,38 +124,38 @@ diff_vec(order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, lpoints=div(p #generate given order differential matrix for a vector which is expanded from row*col matrix -function diff_mat2_x(row,col,order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, boundary=Dirichlet(), sparse=false) +function diff_mat2_x(row,col,order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, boundary=:Dirichlet, sparse=false) t=diff_mat(col,order; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse) m=kron(t,I(row)) return m end -function diff_mat2_y(row,col,order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, boundary=Dirichlet(), sparse=false) +function diff_mat2_y(row,col,order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, boundary=:Dirichlet, sparse=false) t=diff_mat(row,order; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse) m=kron(I(col),t) return m end #2D Δ(Laplacian) operator -function delta_mat2(row,col; T=Float64, dt=one(T), points=3, boundary=Dirichlet(), sparse=false) +function delta_mat2(row,col; T=Float64, dt=one(T), points=3, boundary=:Dirichlet, sparse=false) return diff_mat2_x(row,col,2; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse)+diff_mat2_y(row,col,2; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse) end -function delta_mat2(row,col,Δx,Δy; T=Float64, dt=one(T), points=3, boundary=Dirichlet(), sparse=false) +function delta_mat2(row,col,Δx,Δy; T=Float64, dt=one(T), points=3, boundary=:Dirichlet, sparse=false) return diff_mat2_x(row,col,2; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse)/Δx^2+diff_mat2_y(row,col,2; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse)/Δy^2 end #generate given order differential matrix for a vector which is expanded from row*col*page tensor -function diff_mat3_x(row,col,page,order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, boundary=Dirichlet(), sparse=false) +function diff_mat3_x(row,col,page,order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, boundary=:Dirichlet, sparse=false) t=diff_mat(col,order; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse) m=kron(I(page),kron(t,I(row))) return m end -function diff_mat3_y(row,col,page,order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, boundary=Dirichlet(), sparse=false) +function diff_mat3_y(row,col,page,order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, boundary=:Dirichlet, sparse=false) t=diff_mat(row,order; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse) m=kron(I(col*page),t) #or: m=kron(I(page),kron(I(col),t)) return m end -function diff_mat3_z(row,col,page,order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, boundary=Dirichlet(), sparse=false) +function diff_mat3_z(row,col,page,order=1; T=Float64, dt=one(T), points=2*div(order+1,2)+1, boundary=:Dirichlet, sparse=false) t=diff_mat(page,order; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse) m=kron(t,I(row*col)) #or: m=kron(kron(t,I(row)),I(col)) return m @@ -162,29 +163,29 @@ end #3D Δ(Laplacian) operator -function delta_mat3(row,col,page; T=Float64, dt=one(T), points=3, boundary=Dirichlet(), sparse=false) +function delta_mat3(row,col,page; T=Float64, dt=one(T), points=3, boundary=:Dirichlet, sparse=false) return diff_mat3_x(row,col,page,2; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse)+diff_mat3_y(row,col,page,2; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse)+diff_mat3_z(row,col,page,2; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse) end -function delta_mat3(row,col,page,Δx,Δy,Δz; T=Float64, dt=one(T), points=3, boundary=Dirichlet(), sparse=false) +function delta_mat3(row,col,page,Δx,Δy,Δz; T=Float64, dt=one(T), points=3, boundary=:Dirichlet, sparse=false) return diff_mat3_x(row,col,page,2; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse)/Δx^2+diff_mat3_y(row,col,page,2; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse)/Δy^2+diff_mat3_z(row,col,page,2; T=T,dt=dt,points=points,boundary=boundary,sparse=sparse)/Δz^2 end -function conv(kernel::AbstractArray{T,1}, d::AbstractArray{T,1}, boundary=Dirichlet(); fill = zero(T)) where T +function conv(kernel::AbstractArray{T,1}, d::AbstractArray{T,1}, boundary=:Dirichlet; fill = zero(T)) where T h = div(length(kernel), 2) d1 = PaddedView(fill, d, (1-h:length(d)+h,)) @tullio out[x] := d1[x-i] * kernel[i] return out end -function conv(kernel::AbstractArray{T,2}, d::AbstractArray{T,2}, boundary=Dirichlet(); fill = zero(T)) where T +function conv(kernel::AbstractArray{T,2}, d::AbstractArray{T,2}, boundary=:Dirichlet; fill = zero(T)) where T h=div.(size(kernel),2) d1=PaddedView(fill,d,(1-h[1]:size(d,1)+h[1],1-h[2]:size(d,2)+h[2])) @tullio out[x,y]:=d1[x-i,y-j]*kernel[i,j] return parent(out) end -function conv(kernel::AbstractArray{T,3}, d::AbstractArray{T,3}, boundary=Dirichlet(); fill = zero(T)) where T +function conv(kernel::AbstractArray{T,3}, d::AbstractArray{T,3}, boundary=:Dirichlet; fill = zero(T)) where T h=div.(size(kernel),2) d1=PaddedView(fill,d,size(d).+h.+h,h.+1) @tullio out[x,y,z]:=d1[x-i,y-j,z-k]*kernel[i,j,k] @@ -304,4 +305,12 @@ end +### Precompile +@setup_workload begin + @compile_workload begin + diff_mat(3,1) + diff_mat(3,2) + end +end + end # module PhysicalFDM diff --git a/test/runtests.jl b/test/runtests.jl new file mode 100644 index 0000000..bc1a120 --- /dev/null +++ b/test/runtests.jl @@ -0,0 +1,241 @@ +using Test +using PhysicalFDM + +@testset "Diff Matrix" begin + @testset "1D" begin + @test diff_mat(3,1) == [0.0 0.5 0.0; -0.5 0.0 0.5; 0.0 -0.5 0.0] + @test diff_mat(3,2) ≈ [-2.0 1.0 0.0; 1.0 -2.0 1.0; 0.0 1.0 -2.0] + end + + @testset "2D" begin + @test diff_mat2_x(3,3,1) == [ + 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 + -0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 + 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.0 + 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.5 + 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 + ] + @test diff_mat2_y(3,3,1) == [ + 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + -0.5 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 -0.5 0.0 0.5 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.5 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 + ] + @test diff_mat2_x(3,3,2) ≈ [ + -2.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 + 0.0 -2.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 + 0.0 0.0 -2.0 0.0 0.0 1.0 0.0 0.0 0.0 + 1.0 0.0 0.0 -2.0 0.0 0.0 1.0 0.0 0.0 + 0.0 1.0 0.0 0.0 -2.0 0.0 0.0 1.0 0.0 + 0.0 0.0 1.0 0.0 0.0 -2.0 0.0 0.0 1.0 + 0.0 0.0 0.0 1.0 0.0 0.0 -2.0 0.0 0.0 + 0.0 0.0 0.0 0.0 1.0 0.0 0.0 -2.0 0.0 + 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 -2.0 + ] + @test diff_mat2_y(3,3,2) ≈ [ + -2.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 1.0 -2.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 -2.0 1.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 1.0 -2.0 1.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 1.0 -2.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 -2.0 1.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 1.0 -2.0 1.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 -2.0 + ] + end + + @testset "3D" begin + @test diff_mat3_x(3,3,3,1) == [ + 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + -0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.5 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 + ] + @test diff_mat3_y(3,3,3,1) == [ + 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + -0.5 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 -0.5 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 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0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.5 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.5 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 + ] + @test diff_mat3_z(3,3,3,1) == [ + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 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0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 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1.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 -2.0 0.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 -2.0 0.0 + 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 -2.0 + ] + @test diff_mat3_y(3,3,3,2) ≈ [ + -2.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 1.0 -2.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 -2.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 1.0 -2.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 + 0.0 0.0 0.0 0.0 1.0 -2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 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