using Test
using Sbplib.SbpOperators
using Sbplib.Grids
using Sbplib.RegionIndices
using Sbplib.LazyTensors

@testset "SbpOperators" begin

# @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)

    @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")
    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))

    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

    # 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 "DiagonalInnerProduct" begin
    op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
    L = 2.3
    g = EquidistantGrid((77,), (0.0,), (L,))
    h = spacing(g)
    H = DiagonalInnerProduct(h[1],op.quadratureClosure)
    v = ones(Float64, size(g))

    @test H isa TensorOperator{T,1} where T
    @test H' isa TensorMapping{T,1,1} where T
    @test sum(collect(H*v)) ≈ L
    @test collect(H*v) == collect(H'*v)
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 = spacing(g)
    Hx = DiagonalInnerProduct(h[1],op.quadratureClosure);
    Hy = DiagonalInnerProduct(h[2],op.quadratureClosure);
    Q = Quadrature((Hx,Hy))

    v = ones(Float64, size(g))

    @test Q isa TensorOperator{T,2} where T
    @test Q' isa TensorMapping{T,2,2} where T
    @test sum(collect(Q*v)) ≈ (Lx*Ly)
    @test collect(Q*v) == collect(Q'*v)
end

@testset "InverseDiagonalInnerProduct" begin
    op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
    L = 2.3
    g = EquidistantGrid((77,), (0.0,), (L,))
    h = spacing(g)
    H = DiagonalInnerProduct(h[1],op.quadratureClosure)

    h_i = inverse_spacing(g)
    Hi = InverseDiagonalInnerProduct(h_i[1],1 ./ op.quadratureClosure)
    v = evalOn(g, x->sin(x))

    @test Hi isa TensorOperator{T,1} where T
    @test Hi' isa TensorMapping{T,1,1} where T
    @test collect(Hi*H*v)  ≈ v
    @test collect(Hi*v) == collect(Hi'*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 = spacing(g)
    Hx = DiagonalInnerProduct(h[1], op.quadratureClosure);
    Hy = DiagonalInnerProduct(h[2], op.quadratureClosure);
    Q = Quadrature((Hx,Hy))

    hi = inverse_spacing(g)
    Hix = InverseDiagonalInnerProduct(hi[1], 1 ./ op.quadratureClosure);
    Hiy = InverseDiagonalInnerProduct(hi[2], 1 ./ op.quadratureClosure);
    Qinv = InverseQuadrature((Hix,Hiy))
    v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)

    @test Qinv isa TensorOperator{T,2} where T
    @test Qinv' isa TensorMapping{T,2,2} where T
    @test collect(Qinv*Q*v)  ≈ v
    @test collect(Qinv*v) == collect(Qinv'*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

end