--- a/SbpOperators/test/runtests.jl	Wed Sep 09 21:20:25 2020 +0200
+++ b/SbpOperators/test/runtests.jl	Wed Sep 09 21:21:35 2020 +0200
@@ -1,23 +1,338 @@
+using Test
 using SbpOperators
-using Test
+using Grids
+using RegionIndices
+using LazyTensors
+
+# @testset "apply_quadrature" begin
+#     op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
+#     h = 0.5
+#
+#     @test apply_quadrature(op, h, 1.0, 10, 100) == h
+#
+#     N = 10
+#     qc = op.quadratureClosure
+#     q = h.*(qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
+#     @assert length(q) == N
+#
+#     for i ∈ 1:N
+#         @test apply_quadrature(op, h, 1.0, i, N) == q[i]
+#     end
+#
+#     v = [2.,3.,2.,4.,5.,4.,3.,4.,5.,4.5]
+#     for i ∈ 1:N
+#         @test apply_quadrature(op, h, v[i], i, N) == q[i]*v[i]
+#     end
+# end
+
+@testset "SecondDerivative" begin
+    op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
+    L = 3.5
+    g = EquidistantGrid((101,), (0.0,), (L,))
+    h_inv = inverse_spacing(g)
+    h = 1/h_inv[1];
+    Dₓₓ = SecondDerivative(h_inv[1],op.innerStencil,op.closureStencils,op.parity)
+
+    f0(x::Float64) = 1.
+    f1(x::Float64) = x
+    f2(x::Float64) = 1/2*x^2
+    f3(x::Float64) = 1/6*x^3
+    f4(x::Float64) = 1/24*x^4
+    f5(x::Float64) = sin(x)
+    f5ₓₓ(x::Float64) = -f5(x)
+
+    v0 = evalOn(g,f0)
+    v1 = evalOn(g,f1)
+    v2 = evalOn(g,f2)
+    v3 = evalOn(g,f3)
+    v4 = evalOn(g,f4)
+    v5 = evalOn(g,f5)
 
-@testset "apply_quadrature" begin
+    @test Dₓₓ isa TensorOperator{T,1} where T
+    @test Dₓₓ' isa TensorMapping{T,1,1} where T
+
+    # TODO: Should perhaps set tolerance level for isapporx instead?
+    #       Are these tolerance levels resonable or should tests be constructed
+    #       differently?
+    equalitytol = 0.5*1e-10
+    accuracytol = 0.5*1e-3
+    # 4th order interior stencil, 2nd order boundary stencil,
+    # implies that L*v should be exact for v - monomial up to order 3.
+    # Exact differentiation is measured point-wise. For other grid functions
+    # the error is measured in the l2-norm.
+    @test all(abs.(collect(Dₓₓ*v0)) .<= equalitytol)
+    @test all(abs.(collect(Dₓₓ*v1)) .<= equalitytol)
+    @test all(abs.((collect(Dₓₓ*v2) - v0)) .<= equalitytol)
+    @test all(abs.((collect(Dₓₓ*v3) - v1)) .<= equalitytol)
+    e4 = collect(Dₓₓ*v4) - v2
+    e5 = collect(Dₓₓ*v5) + v5
+    @test sqrt(h*sum(collect(e4.^2))) <= accuracytol
+    @test sqrt(h*sum(collect(e5.^2))) <= accuracytol
+end
+
+@testset "Laplace2D" begin
     op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
-    h = 0.5
+    Lx = 1.5
+    Ly = 3.2
+    g = EquidistantGrid((102,131), (0.0, 0.0), (Lx,Ly))
+
+    h_inv = inverse_spacing(g)
+    h = spacing(g)
+    D_xx = SecondDerivative(h_inv[1],op.innerStencil,op.closureStencils,op.parity)
+    D_yy = SecondDerivative(h_inv[2],op.innerStencil,op.closureStencils,op.parity)
+    L = Laplace((D_xx,D_yy))
 
-    @test apply_quadrature(op, h, 1.0, 10, 100) == h
+    f0(x::Float64,y::Float64) = 2.
+    f1(x::Float64,y::Float64) = x+y
+    f2(x::Float64,y::Float64) = 1/2*x^2 + 1/2*y^2
+    f3(x::Float64,y::Float64) = 1/6*x^3 + 1/6*y^3
+    f4(x::Float64,y::Float64) = 1/24*x^4 + 1/24*y^4
+    f5(x::Float64,y::Float64) = sin(x) + cos(y)
+    f5ₓₓ(x::Float64,y::Float64) = -f5(x,y)
+
+    v0 = evalOn(g,f0)
+    v1 = evalOn(g,f1)
+    v2 = evalOn(g,f2)
+    v3 = evalOn(g,f3)
+    v4 = evalOn(g,f4)
+    v5 = evalOn(g,f5)
+    v5ₓₓ = evalOn(g,f5ₓₓ)
+
+    @test L isa TensorOperator{T,2} where T
+    @test L' isa TensorMapping{T,2,2} where T
 
-    N = 10
-    qc = op.quadratureClosure
-    q = h.*(qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
-    @assert length(q) == N
-
-    for i ∈ 1:N
-        @test apply_quadrature(op, h, 1.0, i, N) == q[i]
-    end
-
-    v = [2.,3.,2.,4.,5.,4.,3.,4.,5.,4.5]
-    for i ∈ 1:N
-        @test apply_quadrature(op, h, v[i], i, N) == q[i]*v[i]
-    end
+    # TODO: Should perhaps set tolerance level for isapporx instead?
+    #       Are these tolerance levels resonable or should tests be constructed
+    #       differently?
+    equalitytol = 0.5*1e-10
+    accuracytol = 0.5*1e-3
+    # 4th order interior stencil, 2nd order boundary stencil,
+    # implies that L*v should be exact for v - monomial up to order 3.
+    # Exact differentiation is measured point-wise. For other grid functions
+    # the error is measured in the H-norm.
+    @test all(abs.(collect(L*v0)) .<= equalitytol)
+    @test all(abs.(collect(L*v1)) .<= equalitytol)
+    @test all(collect(L*v2) .≈ v0) # Seems to be more accurate
+    @test all(abs.((collect(L*v3) - v1)) .<= equalitytol)
+    e4 = collect(L*v4) - v2
+    e5 = collect(L*v5) - v5ₓₓ
+    @test sqrt(prod(h)*sum(collect(e4.^2))) <= accuracytol
+    @test sqrt(prod(h)*sum(collect(e5.^2))) <= accuracytol
 end
+#
+# @testset "Quadrature" begin
+#     op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
+#     Lx = 2.3
+#     Ly = 5.2
+#     g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
+#     H = Quadrature(op,g)
+#     v = ones(Float64, size(g))
+#
+#     @test H isa TensorOperator{T,2} where T
+#     @test H' isa TensorMapping{T,2,2} where T
+#     @test sum(collect(H*v)) ≈ (Lx*Ly)
+#     @test collect(H*v) == collect(H'*v)
+# end
+#
+# @testset "InverseQuadrature" begin
+#     op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
+#     Lx = 7.3
+#     Ly = 8.2
+#     g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
+#     H = Quadrature(op,g)
+#     Hinv = InverseQuadrature(op,g)
+#     v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
+#
+#     @test Hinv isa TensorOperator{T,2} where T
+#     @test Hinv' isa TensorMapping{T,2,2} where T
+#     @test collect(Hinv*H*v)  ≈ v
+#     @test collect(Hinv*v) == collect(Hinv'*v)
+# end
+#
+# @testset "BoundaryValue" begin
+#     op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
+#     g = EquidistantGrid((4,5), (0.0, 0.0), (1.0,1.0))
+#
+#     e_w = BoundaryValue(op, g, CartesianBoundary{1,Lower}())
+#     e_e = BoundaryValue(op, g, CartesianBoundary{1,Upper}())
+#     e_s = BoundaryValue(op, g, CartesianBoundary{2,Lower}())
+#     e_n = BoundaryValue(op, g, CartesianBoundary{2,Upper}())
+#
+#     v = zeros(Float64, 4, 5)
+#     v[:,5] = [1, 2, 3,4]
+#     v[:,4] = [1, 2, 3,4]
+#     v[:,3] = [4, 5, 6, 7]
+#     v[:,2] = [7, 8, 9, 10]
+#     v[:,1] = [10, 11, 12, 13]
+#
+#     @test e_w  isa TensorMapping{T,2,1} where T
+#     @test e_w' isa TensorMapping{T,1,2} where T
+#
+#     @test domain_size(e_w, (3,2)) == (2,)
+#     @test domain_size(e_e, (3,2)) == (2,)
+#     @test domain_size(e_s, (3,2)) == (3,)
+#     @test domain_size(e_n, (3,2)) == (3,)
+#
+#     @test size(e_w'*v) == (5,)
+#     @test size(e_e'*v) == (5,)
+#     @test size(e_s'*v) == (4,)
+#     @test size(e_n'*v) == (4,)
+#
+#     @test collect(e_w'*v) == [10,7,4,1.0,1]
+#     @test collect(e_e'*v) == [13,10,7,4,4.0]
+#     @test collect(e_s'*v) == [10,11,12,13.0]
+#     @test collect(e_n'*v) == [1,2,3,4.0]
+#
+#     g_x = [1,2,3,4.0]
+#     g_y = [5,4,3,2,1.0]
+#
+#     G_w = zeros(Float64, (4,5))
+#     G_w[1,:] = g_y
+#
+#     G_e = zeros(Float64, (4,5))
+#     G_e[4,:] = g_y
+#
+#     G_s = zeros(Float64, (4,5))
+#     G_s[:,1] = g_x
+#
+#     G_n = zeros(Float64, (4,5))
+#     G_n[:,5] = g_x
+#
+#     @test size(e_w*g_y) == (UnknownDim,5)
+#     @test size(e_e*g_y) == (UnknownDim,5)
+#     @test size(e_s*g_x) == (4,UnknownDim)
+#     @test size(e_n*g_x) == (4,UnknownDim)
+#
+#     # These tests should be moved to where they are possible (i.e we know what the grid should be)
+#     @test_broken collect(e_w*g_y) == G_w
+#     @test_broken collect(e_e*g_y) == G_e
+#     @test_broken collect(e_s*g_x) == G_s
+#     @test_broken collect(e_n*g_x) == G_n
+# end
+#
+# @testset "NormalDerivative" begin
+#     op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
+#     g = EquidistantGrid((5,6), (0.0, 0.0), (4.0,5.0))
+#
+#     d_w = NormalDerivative(op, g, CartesianBoundary{1,Lower}())
+#     d_e = NormalDerivative(op, g, CartesianBoundary{1,Upper}())
+#     d_s = NormalDerivative(op, g, CartesianBoundary{2,Lower}())
+#     d_n = NormalDerivative(op, g, CartesianBoundary{2,Upper}())
+#
+#
+#     v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
+#     v∂x = evalOn(g, (x,y)-> 2*x + y)
+#     v∂y = evalOn(g, (x,y)-> 2*(y-1) + x)
+#
+#     @test d_w  isa TensorMapping{T,2,1} where T
+#     @test d_w' isa TensorMapping{T,1,2} where T
+#
+#     @test domain_size(d_w, (3,2)) == (2,)
+#     @test domain_size(d_e, (3,2)) == (2,)
+#     @test domain_size(d_s, (3,2)) == (3,)
+#     @test domain_size(d_n, (3,2)) == (3,)
+#
+#     @test size(d_w'*v) == (6,)
+#     @test size(d_e'*v) == (6,)
+#     @test size(d_s'*v) == (5,)
+#     @test size(d_n'*v) == (5,)
+#
+#     @test collect(d_w'*v) ≈ v∂x[1,:]
+#     @test collect(d_e'*v) ≈ v∂x[5,:]
+#     @test collect(d_s'*v) ≈ v∂y[:,1]
+#     @test collect(d_n'*v) ≈ v∂y[:,6]
+#
+#
+#     d_x_l = zeros(Float64, 5)
+#     d_x_u = zeros(Float64, 5)
+#     for i ∈ eachindex(d_x_l)
+#         d_x_l[i] = op.dClosure[i-1]
+#         d_x_u[i] = -op.dClosure[length(d_x_u)-i]
+#     end
+#
+#     d_y_l = zeros(Float64, 6)
+#     d_y_u = zeros(Float64, 6)
+#     for i ∈ eachindex(d_y_l)
+#         d_y_l[i] = op.dClosure[i-1]
+#         d_y_u[i] = -op.dClosure[length(d_y_u)-i]
+#     end
+#
+#     function prod_matrix(x,y)
+#         G = zeros(Float64, length(x), length(y))
+#         for I ∈ CartesianIndices(G)
+#             G[I] = x[I[1]]*y[I[2]]
+#         end
+#
+#         return G
+#     end
+#
+#     g_x = [1,2,3,4.0,5]
+#     g_y = [5,4,3,2,1.0,11]
+#
+#     G_w = prod_matrix(d_x_l, g_y)
+#     G_e = prod_matrix(d_x_u, g_y)
+#     G_s = prod_matrix(g_x, d_y_l)
+#     G_n = prod_matrix(g_x, d_y_u)
+#
+#
+#     @test size(d_w*g_y) == (UnknownDim,6)
+#     @test size(d_e*g_y) == (UnknownDim,6)
+#     @test size(d_s*g_x) == (5,UnknownDim)
+#     @test size(d_n*g_x) == (5,UnknownDim)
+#
+#     # These tests should be moved to where they are possible (i.e we know what the grid should be)
+#     @test_broken collect(d_w*g_y) ≈ G_w
+#     @test_broken collect(d_e*g_y) ≈ G_e
+#     @test_broken collect(d_s*g_x) ≈ G_s
+#     @test_broken collect(d_n*g_x) ≈ G_n
+# end
+#
+# @testset "BoundaryQuadrature" begin
+#     op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
+#     g = EquidistantGrid((10,11), (0.0, 0.0), (1.0,1.0))
+#
+#     H_w = BoundaryQuadrature(op, g, CartesianBoundary{1,Lower}())
+#     H_e = BoundaryQuadrature(op, g, CartesianBoundary{1,Upper}())
+#     H_s = BoundaryQuadrature(op, g, CartesianBoundary{2,Lower}())
+#     H_n = BoundaryQuadrature(op, g, CartesianBoundary{2,Upper}())
+#
+#     v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
+#
+#     function get_quadrature(N)
+#         qc = op.quadratureClosure
+#         q = (qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
+#         @assert length(q) == N
+#         return q
+#     end
+#
+#     v_w = v[1,:]
+#     v_e = v[10,:]
+#     v_s = v[:,1]
+#     v_n = v[:,11]
+#
+#     q_x = spacing(g)[1].*get_quadrature(10)
+#     q_y = spacing(g)[2].*get_quadrature(11)
+#
+#     @test H_w isa TensorOperator{T,1} where T
+#
+#     @test domain_size(H_w, (3,)) == (3,)
+#     @test domain_size(H_n, (3,)) == (3,)
+#
+#     @test range_size(H_w, (3,)) == (3,)
+#     @test range_size(H_n, (3,)) == (3,)
+#
+#     @test size(H_w*v_w) == (11,)
+#     @test size(H_e*v_e) == (11,)
+#     @test size(H_s*v_s) == (10,)
+#     @test size(H_n*v_n) == (10,)
+#
+#     @test collect(H_w*v_w) ≈ q_y.*v_w
+#     @test collect(H_e*v_e) ≈ q_y.*v_e
+#     @test collect(H_s*v_s) ≈ q_x.*v_s
+#     @test collect(H_n*v_n) ≈ q_x.*v_n
+#
+#     @test collect(H_w'*v_w) == collect(H_w'*v_w)
+#     @test collect(H_e'*v_e) == collect(H_e'*v_e)
+#     @test collect(H_s'*v_s) == collect(H_s'*v_s)
+#     @test collect(H_n'*v_n) == collect(H_n'*v_n)
+# end