using Test

using Sbplib.SbpOperators
using Sbplib.Grids
using Sbplib.LazyTensors

@testset "Laplace" begin
    g_1D = EquidistantGrid(101, 0.0, 1.)
    g_3D = EquidistantGrid((51,101,52), (0.0, -1.0, 0.0), (1., 1., 1.))
    @testset "Constructors" begin
        stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=4)
        inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
        closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
        @testset "1D" begin
            L = laplace(g_1D, inner_stencil, closure_stencils)
            @test L == second_derivative(g_1D, inner_stencil, closure_stencils)
            @test L isa TensorMapping{T,1,1}  where T
        end
        @testset "3D" begin
            L = laplace(g_3D, inner_stencil, closure_stencils)
            @test L isa TensorMapping{T,3,3} where T
            Dxx = second_derivative(g_3D, inner_stencil, closure_stencils, 1)
            Dyy = second_derivative(g_3D, inner_stencil, closure_stencils, 2)
            Dzz = second_derivative(g_3D, inner_stencil, closure_stencils, 3)
            @test L == Dxx + Dyy + Dzz
        end
    end

    # Exact differentiation is measured point-wise. In other cases
    # the error is measured in the l2-norm.
    @testset "Accuracy" begin
        l2(v) = sqrt(prod(spacing(g_3D))*sum(v.^2));
        polynomials = ()
        maxOrder = 4;
        for i = 0:maxOrder-1
            f_i(x,y,z) = 1/factorial(i)*(y^i + x^i + z^i)
            polynomials = (polynomials...,evalOn(g_3D,f_i))
        end
        v = evalOn(g_3D, (x,y,z) -> sin(x) + cos(y) + exp(z))
        Δv = evalOn(g_3D,(x,y,z) -> -sin(x) - cos(y) + exp(z))

        # 2nd order interior stencil, 1st order boundary stencil,
        # implies that L*v should be exact for binomials up to order 2.
        @testset "2nd order" begin
            stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=2)
            inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
            closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
            L = laplace(g_3D, inner_stencil, closure_stencils)
            @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
            @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
            @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9
            @test L*v ≈ Δv rtol = 5e-2 norm = l2
        end

        # 4th order interior stencil, 2nd order boundary stencil,
        # implies that L*v should be exact for binomials up to order 3.
        @testset "4th order" begin
            stencil_set = read_stencil_set(sbp_operators_path()*"standard_diagonal.toml"; order=4)
            inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
            closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
            L = laplace(g_3D, inner_stencil, closure_stencils)
            # NOTE: high tolerances for checking the "exact" differentiation
            # due to accumulation of round-off errors/cancellation errors?
            @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
            @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
            @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9
            @test L*polynomials[4] ≈ polynomials[2] atol = 5e-9
            @test L*v ≈ Δv rtol = 5e-4 norm = l2
        end
    end
end