--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/Grids/mapped_grid_test.jl	Thu Jan 09 12:40:49 2025 +0100
@@ -0,0 +1,381 @@
+using Diffinitive.Grids
+using Diffinitive.RegionIndices
+using Test
+using StaticArrays
+using LinearAlgebra
+
+
+_skew_mapping(a,b) = (ξ̄->ξ̄[1]*a + ξ̄[2]*b, ξ̄->[a  b])
+
+function _partially_curved_mapping()
+    x̄((ξ, η)) = @SVector[ξ, η*(1+ξ*(ξ-1))]
+    J((ξ, η)) = @SMatrix[
+        1         0;
+        η*(2ξ-1)  1+ξ*(ξ-1);
+    ]
+
+    return x̄, J
+end
+
+function _fully_curved_mapping()
+    x̄((ξ, η)) = @SVector[2ξ + η*(1-η), 3η+(1+η/2)*ξ^2]
+    J((ξ, η)) = @SMatrix[
+        2       1-2η;
+        (2+η)*ξ 3+1/2*ξ^2;
+    ]
+
+    return x̄, J
+end
+
+@testset "MappedGrid" begin
+    @testset "Constructor" begin
+        lg = equidistant_grid((0,0), (1,1), 11, 21)
+
+        x̄ = map(ξ̄ -> 2ξ̄, lg)
+        J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
+        mg = MappedGrid(lg, x̄, J)
+
+        @test mg isa Grid{SVector{2, Float64},2}
+        @test jacobian(mg) isa Array{<:AbstractMatrix}
+        @test logical_grid(mg) isa Grid
+
+        @test collect(mg) == x̄
+        @test jacobian(mg) == J
+        @test logical_grid(mg) == lg
+
+
+        x̄ = map(ξ̄ -> @SVector[ξ̄[1],ξ̄[2], ξ̄[1] + ξ̄[2]], lg)
+        J = map(ξ̄ -> @SMatrix[1 0; 0 1; 1 1], lg)
+        mg = MappedGrid(lg, x̄, J)
+
+        @test mg isa Grid{SVector{3, Float64},2}
+        @test jacobian(mg) isa Array{<:AbstractMatrix}
+        @test logical_grid(mg) isa Grid
+
+        @test collect(mg) == x̄
+        @test jacobian(mg) == J
+        @test logical_grid(mg) == lg
+
+        sz1 = (10,11)
+        sz2 = (10,12)
+        @test_throws ArgumentError("Sizes must match") MappedGrid(
+            equidistant_grid((0,0), (1,1), sz2...),
+            rand(SVector{2},sz1...),
+            rand(SMatrix{2,2},sz1...),
+        )
+
+        @test_throws ArgumentError("Sizes must match") MappedGrid(
+            equidistant_grid((0,0), (1,1), sz1...),
+            rand(SVector{2},sz2...),
+            rand(SMatrix{2,2},sz1...),
+        )
+
+        @test_throws ArgumentError("Sizes must match") MappedGrid(
+            equidistant_grid((0,0), (1,1), sz1...),
+            rand(SVector{2},sz1...),
+            rand(SMatrix{2,2},sz2...),
+        )
+
+        err_str = "The size of the jacobian must match the dimensions of the grid and coordinates"
+        @test_throws ArgumentError(err_str) MappedGrid(
+            equidistant_grid((0,0), (1,1), 10, 11),
+            rand(SVector{3}, 10, 11),
+            rand(SMatrix{3,4}, 10, 11),
+        )
+
+        @test_throws ArgumentError(err_str) MappedGrid(
+            equidistant_grid((0,0), (1,1), 10, 11),
+            rand(SVector{3}, 10, 11),
+            rand(SMatrix{4,2}, 10, 11),
+        )
+    end
+
+    @testset "Indexing Interface" begin
+        lg = equidistant_grid((0,0), (1,1), 11, 21)
+        x̄ = map(ξ̄ -> 2ξ̄, lg)
+        J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
+        mg = MappedGrid(lg, x̄, J)
+        @test mg[1,1] == [0.0, 0.0]
+        @test mg[4,2] == [0.6, 0.1]
+        @test mg[6,10] == [1., 0.9]
+
+        @test mg[begin, begin] == [0.0, 0.0]
+        @test mg[end,end] == [2.0, 2.0]
+        @test mg[begin,end] == [0., 2.]
+
+        @test axes(mg) == (1:11, 1:21)
+
+        @testset "cartesian indexing" begin
+            cases = [
+                 (1,1) ,
+                 (3,5) ,
+                 (10,6),
+                 (1,1) ,
+                 (3,2) ,
+            ]
+
+            @testset "i = $is" for (lg, is) ∈ cases
+                @test mg[CartesianIndex(is...)] == mg[is...]
+            end
+        end
+
+        @testset "eachindex" begin
+            @test eachindex(mg) == CartesianIndices((11,21))
+        end
+
+        @testset "firstindex" begin
+            @test firstindex(mg, 1) == 1
+            @test firstindex(mg, 2) == 1
+        end
+
+        @testset "lastindex" begin
+            @test lastindex(mg, 1) == 11
+            @test lastindex(mg, 2) == 21
+        end
+    end
+
+    @testset "Iterator interface" begin
+        lg = equidistant_grid((0,0), (1,1), 11, 21)
+        x̄ = map(ξ̄ -> 2ξ̄, lg)
+        J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
+
+        mg = MappedGrid(lg, x̄, J)
+
+        lg2 = equidistant_grid((0,0), (1,1), 15, 11)
+        sg = MappedGrid(
+            equidistant_grid((0,0), (1,1), 15, 11),
+            map(ξ̄ -> @SArray[ξ̄[1], ξ̄[2], -ξ̄[1]], lg2), rand(SMatrix{3,2,Float64},15,11)
+        )
+
+        @test eltype(mg) == SVector{2,Float64}
+        @test eltype(sg) == SVector{3,Float64}
+
+        @test eltype(typeof(mg)) == SVector{2,Float64}
+        @test eltype(typeof(sg)) == SVector{3,Float64}
+
+        @test size(mg) == (11,21)
+        @test size(sg) == (15,11)
+
+        @test size(mg,2) == 21
+        @test size(sg,2) == 11
+
+        @test length(mg) == 231
+        @test length(sg) == 165
+
+        @test Base.IteratorSize(mg) == Base.HasShape{2}()
+        @test Base.IteratorSize(typeof(mg)) == Base.HasShape{2}()
+
+        @test Base.IteratorSize(sg) == Base.HasShape{2}()
+        @test Base.IteratorSize(typeof(sg)) == Base.HasShape{2}()
+
+        element, state = iterate(mg)
+        @test element == lg[1,1].*2
+        element, _ =  iterate(mg, state)
+        @test element == lg[2,1].*2
+
+        element, state = iterate(sg)
+        @test element == sg.physicalcoordinates[1,1]
+        element, _ = iterate(sg, state)
+        @test element == sg.physicalcoordinates[2,1]
+
+        @test collect(mg) == 2 .* lg
+    end
+
+    @testset "Base" begin
+        lg = equidistant_grid((0,0), (1,1), 11, 21)
+        x̄ = map(ξ̄ -> 2ξ̄, lg)
+        J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
+        mg = MappedGrid(lg, x̄, J)
+
+        @test ndims(mg) == 2
+    end
+
+    @testset "==" begin
+        sz = (15,11)
+        lg = equidistant_grid((0,0), (1,1), sz...)
+        x = rand(SVector{3,Float64}, sz...)
+        J = rand(SMatrix{3,2,Float64}, sz...)
+
+        sg = MappedGrid(lg, x, J)
+
+        sg1 = MappedGrid(equidistant_grid((0,0), (1,1), sz...), copy(x), copy(J))
+
+        sz2 = (15,12)
+        lg2 = equidistant_grid((0,0), (1,1), sz2...)
+        x2 = rand(SVector{3,Float64}, sz2...)
+        J2 = rand(SMatrix{3,2,Float64}, sz2...)
+        sg2 = MappedGrid(lg2, x2, J2)
+
+        sg3 = MappedGrid(lg, rand(SVector{3,Float64}, sz...), J)
+        sg4 = MappedGrid(lg, x, rand(SMatrix{3,2,Float64}, sz...))
+
+        @test sg == sg1
+        @test sg != sg2 # Different size
+        @test sg != sg3 # Different coordinates
+        @test sg != sg4 # Different jacobian
+    end
+
+    @testset "boundary_identifiers" begin
+        lg = equidistant_grid((0,0), (1,1), 11, 15)
+        x̄ = map(ξ̄ -> 2ξ̄, lg)
+        J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
+        mg = MappedGrid(lg, x̄, J)
+        @test boundary_identifiers(mg) == boundary_identifiers(lg)
+    end
+
+    @testset "boundary_indices" begin
+        lg = equidistant_grid((0,0), (1,1), 11, 15)
+        x̄ = map(ξ̄ -> 2ξ̄, lg)
+        J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
+        mg = MappedGrid(lg, x̄, J)
+
+        @test boundary_indices(mg, CartesianBoundary{1,LowerBoundary}()) == boundary_indices(lg,CartesianBoundary{1,LowerBoundary}())
+        @test boundary_indices(mg, CartesianBoundary{2,LowerBoundary}()) == boundary_indices(lg,CartesianBoundary{2,LowerBoundary}())
+        @test boundary_indices(mg, CartesianBoundary{1,UpperBoundary}()) == boundary_indices(lg,CartesianBoundary{1,UpperBoundary}())
+    end
+
+    @testset "boundary_grid" begin
+        x̄, J = _partially_curved_mapping()
+        mg = mapped_grid(x̄, J, 10, 11)
+        J1((ξ, η)) = @SMatrix[
+            1       ;
+            η*(2ξ-1);
+        ]
+        J2((ξ, η)) = @SMatrix[
+            0;
+            1+ξ*(ξ-1);
+        ]
+
+        function expected_bg(mg, bId, Jb)
+            lg = logical_grid(mg)
+            return MappedGrid(
+                boundary_grid(lg, bId),
+                map(x̄, boundary_grid(lg, bId)),
+                map(Jb, boundary_grid(lg, bId)),
+            )
+        end
+
+        let bid = TensorGridBoundary{1, LowerBoundary}()
+            @test boundary_grid(mg, bid) == expected_bg(mg, bid, J2)
+        end
+
+        let bid = TensorGridBoundary{1, UpperBoundary}()
+            @test boundary_grid(mg, bid) == expected_bg(mg, bid, J2)
+        end
+
+        let bid = TensorGridBoundary{2, LowerBoundary}()
+            @test boundary_grid(mg, bid) == expected_bg(mg, bid, J1)
+        end
+
+        let bid = TensorGridBoundary{2, UpperBoundary}()
+            @test boundary_grid(mg, bid) == expected_bg(mg, bid, J1)
+        end
+    end
+end
+
+@testset "mapped_grid" begin
+    x̄, J = _partially_curved_mapping()
+    mg = mapped_grid(x̄, J, 10, 11)
+    @test mg isa MappedGrid{SVector{2,Float64}, 2}
+
+    lg = equidistant_grid((0,0), (1,1), 10, 11)
+    @test logical_grid(mg) == lg
+    @test collect(mg) == map(x̄, lg)
+
+    @test mapped_grid(lg, x̄, J) == mg
+end
+
+@testset "metric_tensor" begin
+    x̄((ξ, η)) = @SVector[ξ*η, ξ + η^2]
+    J((ξ, η)) = @SMatrix[
+        η    ξ;
+        1   2η;
+    ]
+
+    g = mapped_grid(x̄, J, 10, 11)
+    G = map(logical_grid(g)) do (ξ,η)
+        @SMatrix[
+            1+η^2   ξ*η+2η;
+            ξ*η+2η  ξ^2 + 4η^2;
+        ]
+    end
+    @test metric_tensor(g) ≈ G
+end
+
+@testset "min_spacing" begin
+    let g = mapped_grid(identity, x->@SMatrix[1], 11)
+        @test min_spacing(g) ≈ 0.1
+    end
+
+    let g = mapped_grid(x->x+x.^2/2, x->@SMatrix[1 .+ x], 11)
+        @test min_spacing(g) ≈ 0.105
+    end
+
+    let g = mapped_grid(x->x + x.*(1 .- x)/2, x->@SMatrix[1.5 .- x], 11)
+        @test min_spacing(g) ≈ 0.055
+    end
+
+    let g = mapped_grid(identity, x->@SMatrix[1 0; 0 1], 11,11)
+        @test min_spacing(g) ≈ 0.1
+    end
+
+    let g = mapped_grid(identity, x->@SMatrix[1 0; 0 1], 11,21)
+        @test min_spacing(g) ≈ 0.05
+    end
+
+
+    @testset let a = @SVector[1,0], b = @SVector[1,1]/√2
+        g = mapped_grid(_skew_mapping(a,b)...,11,11)
+
+        @test min_spacing(g) ≈ 0.1*norm(b-a)
+    end
+
+    @testset let a = @SVector[1,0], b = @SVector[-1,1]/√2
+        g = mapped_grid(_skew_mapping(a,b)...,11,11)
+
+        @test min_spacing(g) ≈ 0.1*norm(a+b)
+    end
+end
+
+@testset "normal" begin
+    g = mapped_grid(_partially_curved_mapping()...,10, 11)
+
+    @test normal(g, CartesianBoundary{1,LowerBoundary}()) == fill(@SVector[-1,0], 11)
+    @test normal(g, CartesianBoundary{1,UpperBoundary}()) == fill(@SVector[1,0], 11)
+    @test normal(g, CartesianBoundary{2,LowerBoundary}()) == fill(@SVector[0,-1], 10)
+    @test normal(g, CartesianBoundary{2,UpperBoundary}()) ≈ map(boundary_grid(g,CartesianBoundary{2,UpperBoundary}())|>logical_grid) do ξ̄
+        α = 1-2ξ̄[1]
+        @SVector[α,1]/√(α^2 + 1)
+    end
+
+    g = mapped_grid(_fully_curved_mapping()...,5,4)
+
+    unit(v) = v/norm(v)
+    @testset let bId = CartesianBoundary{1,LowerBoundary}()
+        lbg = boundary_grid(logical_grid(g), bId)
+        @test normal(g, bId) ≈ map(lbg) do (ξ, η)
+            -unit(@SVector[1/2,  η/3-1/6])
+        end
+    end
+
+    @testset let bId = CartesianBoundary{1,UpperBoundary}()
+        lbg = boundary_grid(logical_grid(g), bId)
+        @test normal(g, bId) ≈ map(lbg) do (ξ, η)
+            unit(@SVector[7/2, 2η-1]/(5 + 3η + 2η^2))
+        end
+    end
+
+    @testset let bId = CartesianBoundary{2,LowerBoundary}()
+        lbg = boundary_grid(logical_grid(g), bId)
+        @test normal(g, bId) ≈ map(lbg) do (ξ, η)
+            -unit(@SVector[-2ξ, 2]/(6 + ξ^2 - 2ξ))
+        end
+    end
+
+    @testset let bId = CartesianBoundary{2,UpperBoundary}()
+        lbg = boundary_grid(logical_grid(g), bId)
+        @test normal(g, bId) ≈ map(lbg) do (ξ, η)
+            unit(@SVector[-3ξ, 2]/(6 + ξ^2 + 3ξ))
+        end
+    end
+end