Mercurial > repos > public > sbplib_julia
changeset 709:48a61e085e60 feature/selectable_tests
Add function for selecting tests
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Sat, 20 Feb 2021 20:31:08 +0100 |
| parents | 38f9894279cd |
| children | 44fa9a171557 |
| files | README.md test/Manifest.toml test/Project.toml test/SbpOperators/testSbpOperators.jl test/runtests.jl test/testSbpOperators.jl |
| diffstat | 6 files changed, 896 insertions(+), 836 deletions(-) [+] |
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diff -r 38f9894279cd -r 48a61e085e60 README.md --- a/README.md Mon Feb 15 11:13:12 2021 +0100 +++ b/README.md Sat Feb 20 20:31:08 2021 +0100 @@ -10,6 +10,17 @@ If you want to run tests from a specific file in `test/`, you can do ``` julia> using Pkg -julia> Pkg.test(test_args=["testLazyTensors"]) +julia> Pkg.test(test_args=["[glob pattern]"]) +``` +For example +``` +julia> Pkg.test(test_args=["SbpOperators/*"]) ``` +to run all test in the `SbpOperators` folder, or +``` +julia> Pkg.test(test_args=["*/readoperators.jl"]) +``` +to run only the tests in files named `readoperators.jl`. + + This works by using the `@includetests` macro from the [TestSetExtensions](https://github.com/ssfrr/TestSetExtensions.jl) package. For more information, see their documentation.
diff -r 38f9894279cd -r 48a61e085e60 test/Manifest.toml --- a/test/Manifest.toml Mon Feb 15 11:13:12 2021 +0100 +++ b/test/Manifest.toml Sat Feb 20 20:31:08 2021 +0100 @@ -34,6 +34,11 @@ deps = ["Random", "Serialization", "Sockets"] uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b" +[[Glob]] +git-tree-sha1 = "4df9f7e06108728ebf00a0a11edee4b29a482bb2" +uuid = "c27321d9-0574-5035-807b-f59d2c89b15c" +version = "1.3.0" + [[InteractiveUtils]] deps = ["Markdown"] uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
diff -r 38f9894279cd -r 48a61e085e60 test/Project.toml --- a/test/Project.toml Mon Feb 15 11:13:12 2021 +0100 +++ b/test/Project.toml Sat Feb 20 20:31:08 2021 +0100 @@ -1,4 +1,5 @@ [deps] +Glob = "c27321d9-0574-5035-807b-f59d2c89b15c" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" TOML = "fa267f1f-6049-4f14-aa54-33bafae1ed76" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff -r 38f9894279cd -r 48a61e085e60 test/SbpOperators/testSbpOperators.jl --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/test/SbpOperators/testSbpOperators.jl Sat Feb 20 20:31:08 2021 +0100 @@ -0,0 +1,832 @@ +using Test +using Sbplib.SbpOperators +using Sbplib.Grids +using Sbplib.RegionIndices +using Sbplib.LazyTensors +using LinearAlgebra +using TOML + +import Sbplib.SbpOperators.Stencil +import Sbplib.SbpOperators.VolumeOperator +import Sbplib.SbpOperators.volume_operator +import Sbplib.SbpOperators.BoundaryOperator +import Sbplib.SbpOperators.boundary_operator +import Sbplib.SbpOperators.even +import Sbplib.SbpOperators.odd + + +@testset "SbpOperators" begin + +@testset "Stencil" begin + s = Stencil((-2,2), (1.,2.,2.,3.,4.)) + @test s isa Stencil{Float64, 5} + + @test eltype(s) == Float64 + @test SbpOperators.scale(s, 2) == Stencil((-2,2), (2.,4.,4.,6.,8.)) + + @test Stencil(1,2,3,4; center=1) == Stencil((0, 3),(1,2,3,4)) + @test Stencil(1,2,3,4; center=2) == Stencil((-1, 2),(1,2,3,4)) + @test Stencil(1,2,3,4; center=4) == Stencil((-3, 0),(1,2,3,4)) + + @test CenteredStencil(1,2,3,4,5) == Stencil((-2, 2), (1,2,3,4,5)) + @test_throws ArgumentError CenteredStencil(1,2,3,4) +end + +@testset "parse_rational" begin + @test SbpOperators.parse_rational("1") isa Rational + @test SbpOperators.parse_rational("1") == 1//1 + @test SbpOperators.parse_rational("1/2") isa Rational + @test SbpOperators.parse_rational("1/2") == 1//2 + @test SbpOperators.parse_rational("37/13") isa Rational + @test SbpOperators.parse_rational("37/13") == 37//13 +end + +@testset "readoperator" begin + toml_str = """ + [meta] + type = "equidistant" + + [order2] + H.inner = ["1"] + + D1.inner_stencil = ["-1/2", "0", "1/2"] + D1.closure_stencils = [ + ["-1", "1"], + ] + + d1.closure = ["-3/2", "2", "-1/2"] + + [order4] + H.closure = ["17/48", "59/48", "43/48", "49/48"] + + D2.inner_stencil = ["-1/12","4/3","-5/2","4/3","-1/12"] + D2.closure_stencils = [ + [ "2", "-5", "4", "-1", "0", "0"], + [ "1", "-2", "1", "0", "0", "0"], + [ "-4/43", "59/43", "-110/43", "59/43", "-4/43", "0"], + [ "-1/49", "0", "59/49", "-118/49", "64/49", "-4/49"], + ] + """ + + parsed_toml = TOML.parse(toml_str) + @testset "get_stencil" begin + @test get_stencil(parsed_toml, "order2", "D1", "inner_stencil") == Stencil(-1/2, 0., 1/2, center=2) + @test get_stencil(parsed_toml, "order2", "D1", "inner_stencil", center=1) == Stencil(-1/2, 0., 1/2; center=1) + @test get_stencil(parsed_toml, "order2", "D1", "inner_stencil", center=3) == Stencil(-1/2, 0., 1/2; center=3) + + @test get_stencil(parsed_toml, "order2", "H", "inner") == Stencil(1.; center=1) + + @test_throws AssertionError get_stencil(parsed_toml, "meta", "type") + @test_throws AssertionError get_stencil(parsed_toml, "order2", "D1", "closure_stencils") + end + + @testset "get_stencils" begin + @test get_stencils(parsed_toml, "order2", "D1", "closure_stencils", centers=(1,)) == (Stencil(-1., 1., center=1),) + @test get_stencils(parsed_toml, "order2", "D1", "closure_stencils", centers=(2,)) == (Stencil(-1., 1., center=2),) + @test get_stencils(parsed_toml, "order2", "D1", "closure_stencils", centers=[2]) == (Stencil(-1., 1., center=2),) + + @test get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=[1,1,1,1]) == ( + Stencil( 2., -5., 4., -1., 0., 0., center=1), + Stencil( 1., -2., 1., 0., 0., 0., center=1), + Stencil( -4/43, 59/43, -110/43, 59/43, -4/43, 0., center=1), + Stencil( -1/49, 0., 59/49, -118/49, 64/49, -4/49, center=1), + ) + + @test get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=(4,2,3,1)) == ( + Stencil( 2., -5., 4., -1., 0., 0., center=4), + Stencil( 1., -2., 1., 0., 0., 0., center=2), + Stencil( -4/43, 59/43, -110/43, 59/43, -4/43, 0., center=3), + Stencil( -1/49, 0., 59/49, -118/49, 64/49, -4/49, center=1), + ) + + @test get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=1:4) == ( + Stencil( 2., -5., 4., -1., 0., 0., center=1), + Stencil( 1., -2., 1., 0., 0., 0., center=2), + Stencil( -4/43, 59/43, -110/43, 59/43, -4/43, 0., center=3), + Stencil( -1/49, 0., 59/49, -118/49, 64/49, -4/49, center=4), + ) + + @test_throws AssertionError get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=(1,2,3)) + @test_throws AssertionError get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=(1,2,3,5,4)) + @test_throws AssertionError get_stencils(parsed_toml, "order4", "D2", "inner_stencil",centers=(1,2)) + end + + @testset "get_tuple" begin + @test get_tuple(parsed_toml, "order2", "d1", "closure") == (-3/2, 2, -1/2) + + @test_throws AssertionError get_tuple(parsed_toml, "meta", "type") + end +end + +@testset "VolumeOperator" begin + inner_stencil = CenteredStencil(1/4, 2/4, 1/4) + closure_stencils = (Stencil(1/2, 1/2; center=1), Stencil(0.,1.; center=2)) + g_1D = EquidistantGrid(11,0.,1.) + g_2D = EquidistantGrid((11,12),(0.,0.),(1.,1.)) + g_3D = EquidistantGrid((11,12,10),(0.,0.,0.),(1.,1.,1.)) + @testset "Constructors" begin + @testset "1D" begin + op = VolumeOperator(inner_stencil,closure_stencils,(11,),even) + @test op == VolumeOperator(g_1D,inner_stencil,closure_stencils,even) + @test op == volume_operator(g_1D,inner_stencil,closure_stencils,even,1) + @test op isa TensorMapping{T,1,1} where T + end + @testset "2D" begin + op_x = volume_operator(g_2D,inner_stencil,closure_stencils,even,1) + op_y = volume_operator(g_2D,inner_stencil,closure_stencils,even,2) + Ix = IdentityMapping{Float64}((11,)) + Iy = IdentityMapping{Float64}((12,)) + @test op_x == VolumeOperator(inner_stencil,closure_stencils,(11,),even)⊗Iy + @test op_y == Ix⊗VolumeOperator(inner_stencil,closure_stencils,(12,),even) + @test op_x isa TensorMapping{T,2,2} where T + @test op_y isa TensorMapping{T,2,2} where T + end + @testset "3D" begin + op_x = volume_operator(g_3D,inner_stencil,closure_stencils,even,1) + op_y = volume_operator(g_3D,inner_stencil,closure_stencils,even,2) + op_z = volume_operator(g_3D,inner_stencil,closure_stencils,even,3) + Ix = IdentityMapping{Float64}((11,)) + Iy = IdentityMapping{Float64}((12,)) + Iz = IdentityMapping{Float64}((10,)) + @test op_x == VolumeOperator(inner_stencil,closure_stencils,(11,),even)⊗Iy⊗Iz + @test op_y == Ix⊗VolumeOperator(inner_stencil,closure_stencils,(12,),even)⊗Iz + @test op_z == Ix⊗Iy⊗VolumeOperator(inner_stencil,closure_stencils,(10,),even) + @test op_x isa TensorMapping{T,3,3} where T + @test op_y isa TensorMapping{T,3,3} where T + @test op_z isa TensorMapping{T,3,3} where T + end + end + + @testset "Sizes" begin + @testset "1D" begin + op = volume_operator(g_1D,inner_stencil,closure_stencils,even,1) + @test range_size(op) == domain_size(op) == size(g_1D) + end + + @testset "2D" begin + op_x = volume_operator(g_2D,inner_stencil,closure_stencils,even,1) + op_y = volume_operator(g_2D,inner_stencil,closure_stencils,even,2) + @test range_size(op_y) == domain_size(op_y) == + range_size(op_x) == domain_size(op_x) == size(g_2D) + end + @testset "3D" begin + op_x = volume_operator(g_3D,inner_stencil,closure_stencils,even,1) + op_y = volume_operator(g_3D,inner_stencil,closure_stencils,even,2) + op_z = volume_operator(g_3D,inner_stencil,closure_stencils,even,3) + @test range_size(op_z) == domain_size(op_z) == + range_size(op_y) == domain_size(op_y) == + range_size(op_x) == domain_size(op_x) == size(g_3D) + end + end + + op_x = volume_operator(g_2D,inner_stencil,closure_stencils,even,1) + op_y = volume_operator(g_2D,inner_stencil,closure_stencils,odd,2) + v = zeros(size(g_2D)) + Nx = size(g_2D)[1] + Ny = size(g_2D)[2] + for i = 1:Nx + v[i,:] .= i + end + rx = copy(v) + rx[1,:] .= 1.5 + rx[Nx,:] .= (2*Nx-1)/2 + ry = copy(v) + ry[:,Ny-1:Ny] = -v[:,Ny-1:Ny] + + @testset "Application" begin + @test op_x*v ≈ rx rtol = 1e-14 + @test op_y*v ≈ ry rtol = 1e-14 + end + + @testset "Regions" begin + @test (op_x*v)[Index(1,Lower),Index(3,Interior)] ≈ rx[1,3] rtol = 1e-14 + @test (op_x*v)[Index(2,Lower),Index(3,Interior)] ≈ rx[2,3] rtol = 1e-14 + @test (op_x*v)[Index(6,Interior),Index(3,Interior)] ≈ rx[6,3] rtol = 1e-14 + @test (op_x*v)[Index(10,Upper),Index(3,Interior)] ≈ rx[10,3] rtol = 1e-14 + @test (op_x*v)[Index(11,Upper),Index(3,Interior)] ≈ rx[11,3] rtol = 1e-14 + + @test_throws BoundsError (op_x*v)[Index(3,Lower),Index(3,Interior)] + @test_throws BoundsError (op_x*v)[Index(9,Upper),Index(3,Interior)] + + @test (op_y*v)[Index(3,Interior),Index(1,Lower)] ≈ ry[3,1] rtol = 1e-14 + @test (op_y*v)[Index(3,Interior),Index(2,Lower)] ≈ ry[3,2] rtol = 1e-14 + @test (op_y*v)[Index(3,Interior),Index(6,Interior)] ≈ ry[3,6] rtol = 1e-14 + @test (op_y*v)[Index(3,Interior),Index(11,Upper)] ≈ ry[3,11] rtol = 1e-14 + @test (op_y*v)[Index(3,Interior),Index(12,Upper)] ≈ ry[3,12] rtol = 1e-14 + + @test_throws BoundsError (op_y*v)[Index(3,Interior),Index(10,Upper)] + @test_throws BoundsError (op_y*v)[Index(3,Interior),Index(3,Lower)] + end + + @testset "Inferred" begin + @inferred apply(op_x, v,1,1) + @inferred apply(op_x, v, Index(1,Lower),Index(1,Lower)) + @inferred apply(op_x, v, Index(6,Interior),Index(1,Lower)) + @inferred apply(op_x, v, Index(11,Upper),Index(1,Lower)) + + @inferred apply(op_y, v,1,1) + @inferred apply(op_y, v, Index(1,Lower),Index(1,Lower)) + @inferred apply(op_y, v, Index(1,Lower),Index(6,Interior)) + @inferred apply(op_y, v, Index(1,Lower),Index(11,Upper)) + end + +end + +@testset "SecondDerivative" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + Lx = 3.5 + Ly = 3. + g_1D = EquidistantGrid(121, 0.0, Lx) + g_2D = EquidistantGrid((121,123), (0.0, 0.0), (Lx, Ly)) + + @testset "Constructors" begin + @testset "1D" begin + Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils) + @test Dₓₓ == second_derivative(g_1D,op.innerStencil,op.closureStencils,1) + @test Dₓₓ isa VolumeOperator + end + @testset "2D" begin + Dₓₓ = second_derivative(g_2D,op.innerStencil,op.closureStencils,1) + D2 = second_derivative(g_1D,op.innerStencil,op.closureStencils) + I = IdentityMapping{Float64}(size(g_2D)[2]) + @test Dₓₓ == D2⊗I + @test Dₓₓ isa TensorMapping{T,2,2} where T + end + end + + # Exact differentiation is measured point-wise. In other cases + # the error is measured in the l2-norm. + @testset "Accuracy" begin + @testset "1D" begin + l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2)); + monomials = () + maxOrder = 4; + for i = 0:maxOrder-1 + f_i(x) = 1/factorial(i)*x^i + monomials = (monomials...,evalOn(g_1D,f_i)) + end + v = evalOn(g_1D,x -> sin(x)) + vₓₓ = evalOn(g_1D,x -> -sin(x)) + + # 2nd order interior stencil, 1nd order boundary stencil, + # implies that L*v should be exact for monomials up to order 2. + @testset "2nd order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) + Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils) + @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10 + @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10 + @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10 + @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2 + end + + # 4th order interior stencil, 2nd order boundary stencil, + # implies that L*v should be exact for monomials up to order 3. + @testset "4th order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils) + # NOTE: high tolerances for checking the "exact" differentiation + # due to accumulation of round-off errors/cancellation errors? + @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10 + @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10 + @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10 + @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10 + @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2 + end + end + + @testset "2D" begin + l2(v) = sqrt(prod(spacing(g_2D))*sum(v.^2)); + binomials = () + maxOrder = 4; + for i = 0:maxOrder-1 + f_i(x,y) = 1/factorial(i)*y^i + x^i + binomials = (binomials...,evalOn(g_2D,f_i)) + end + v = evalOn(g_2D, (x,y) -> sin(x)+cos(y)) + v_yy = evalOn(g_2D,(x,y) -> -cos(y)) + + # 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 + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) + Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2) + @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 + @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 + @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9 + @test Dyy*v ≈ v_yy 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 + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2) + # NOTE: high tolerances for checking the "exact" differentiation + # due to accumulation of round-off errors/cancellation errors? + @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 + @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 + @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9 + @test Dyy*binomials[4] ≈ evalOn(g_2D,(x,y)->y) atol = 5e-9 + @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2 + end + end + end +end + +@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 + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + @testset "1D" begin + L = laplace(g_1D, op.innerStencil, op.closureStencils) + @test L == second_derivative(g_1D, op.innerStencil, op.closureStencils) + @test L isa TensorMapping{T,1,1} where T + end + @testset "3D" begin + L = laplace(g_3D, op.innerStencil, op.closureStencils) + @test L isa TensorMapping{T,3,3} where T + Dxx = second_derivative(g_3D, op.innerStencil, op.closureStencils,1) + Dyy = second_derivative(g_3D, op.innerStencil, op.closureStencils,2) + Dzz = second_derivative(g_3D, op.innerStencil, op.closureStencils,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 + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) + L = laplace(g_3D,op.innerStencil,op.closureStencils) + @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 + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + L = laplace(g_3D,op.innerStencil,op.closureStencils) + # 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 + +@testset "Diagonal-stencil inner_product" begin + Lx = π/2. + Ly = Float64(π) + Lz = 1. + g_1D = EquidistantGrid(77, 0.0, Lx) + g_2D = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly)) + g_3D = EquidistantGrid((10,10, 10), (0.0, 0.0, 0.0), (Lx,Ly,Lz)) + integral(H,v) = sum(H*v) + @testset "inner_product" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + @testset "0D" begin + H = inner_product(EquidistantGrid{Float64}(),op.quadratureClosure) + @test H == IdentityMapping{Float64}() + @test H isa TensorMapping{T,0,0} where T + end + @testset "1D" begin + H = inner_product(g_1D,op.quadratureClosure) + inner_stencil = CenteredStencil(1.) + @test H == inner_product(g_1D,op.quadratureClosure,inner_stencil) + @test H isa TensorMapping{T,1,1} where T + end + @testset "2D" begin + H = inner_product(g_2D,op.quadratureClosure) + H_x = inner_product(restrict(g_2D,1),op.quadratureClosure) + H_y = inner_product(restrict(g_2D,2),op.quadratureClosure) + @test H == H_x⊗H_y + @test H isa TensorMapping{T,2,2} where T + end + end + + @testset "Sizes" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + @testset "1D" begin + H = inner_product(g_1D,op.quadratureClosure) + @test domain_size(H) == size(g_1D) + @test range_size(H) == size(g_1D) + end + @testset "2D" begin + H = inner_product(g_2D,op.quadratureClosure) + @test domain_size(H) == size(g_2D) + @test range_size(H) == size(g_2D) + end + end + + @testset "Accuracy" begin + @testset "1D" begin + v = () + for i = 0:4 + f_i(x) = 1/factorial(i)*x^i + v = (v...,evalOn(g_1D,f_i)) + end + u = evalOn(g_1D,x->sin(x)) + + @testset "2nd order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) + H = inner_product(g_1D,op.quadratureClosure) + for i = 1:2 + @test integral(H,v[i]) ≈ v[i+1][end] - v[i+1][1] rtol = 1e-14 + end + @test integral(H,u) ≈ 1. rtol = 1e-4 + end + + @testset "4th order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + H = inner_product(g_1D,op.quadratureClosure) + for i = 1:4 + @test integral(H,v[i]) ≈ v[i+1][end] - v[i+1][1] rtol = 1e-14 + end + @test integral(H,u) ≈ 1. rtol = 1e-8 + end + end + + @testset "2D" begin + b = 2.1 + v = b*ones(Float64, size(g_2D)) + u = evalOn(g_2D,(x,y)->sin(x)+cos(y)) + @testset "2nd order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) + H = inner_product(g_2D,op.quadratureClosure) + @test integral(H,v) ≈ b*Lx*Ly rtol = 1e-13 + @test integral(H,u) ≈ π rtol = 1e-4 + end + @testset "4th order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + H = inner_product(g_2D,op.quadratureClosure) + @test integral(H,v) ≈ b*Lx*Ly rtol = 1e-13 + @test integral(H,u) ≈ π rtol = 1e-8 + end + end + end +end + +@testset "Diagonal-stencil inverse_inner_product" begin + Lx = π/2. + Ly = Float64(π) + g_1D = EquidistantGrid(77, 0.0, Lx) + g_2D = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly)) + @testset "inverse_inner_product" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + @testset "0D" begin + Hi = inverse_inner_product(EquidistantGrid{Float64}(),op.quadratureClosure) + @test Hi == IdentityMapping{Float64}() + @test Hi isa TensorMapping{T,0,0} where T + end + @testset "1D" begin + Hi = inverse_inner_product(g_1D, op.quadratureClosure); + inner_stencil = CenteredStencil(1.) + closures = () + for i = 1:length(op.quadratureClosure) + closures = (closures...,Stencil(op.quadratureClosure[i].range,1.0./op.quadratureClosure[i].weights)) + end + @test Hi == inverse_inner_product(g_1D,closures,inner_stencil) + @test Hi isa TensorMapping{T,1,1} where T + end + @testset "2D" begin + Hi = inverse_inner_product(g_2D,op.quadratureClosure) + Hi_x = inverse_inner_product(restrict(g_2D,1),op.quadratureClosure) + Hi_y = inverse_inner_product(restrict(g_2D,2),op.quadratureClosure) + @test Hi == Hi_x⊗Hi_y + @test Hi isa TensorMapping{T,2,2} where T + end + end + + @testset "Sizes" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + @testset "1D" begin + Hi = inverse_inner_product(g_1D,op.quadratureClosure) + @test domain_size(Hi) == size(g_1D) + @test range_size(Hi) == size(g_1D) + end + @testset "2D" begin + Hi = inverse_inner_product(g_2D,op.quadratureClosure) + @test domain_size(Hi) == size(g_2D) + @test range_size(Hi) == size(g_2D) + end + end + + @testset "Accuracy" begin + @testset "1D" begin + v = evalOn(g_1D,x->sin(x)) + u = evalOn(g_1D,x->x^3-x^2+1) + @testset "2nd order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) + H = inner_product(g_1D,op.quadratureClosure) + Hi = inverse_inner_product(g_1D,op.quadratureClosure) + @test Hi*H*v ≈ v rtol = 1e-15 + @test Hi*H*u ≈ u rtol = 1e-15 + end + @testset "4th order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + H = inner_product(g_1D,op.quadratureClosure) + Hi = inverse_inner_product(g_1D,op.quadratureClosure) + @test Hi*H*v ≈ v rtol = 1e-15 + @test Hi*H*u ≈ u rtol = 1e-15 + end + end + @testset "2D" begin + v = evalOn(g_2D,(x,y)->sin(x)+cos(y)) + u = evalOn(g_2D,(x,y)->x*y + x^5 - sqrt(y)) + @testset "2nd order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) + H = inner_product(g_2D,op.quadratureClosure) + Hi = inverse_inner_product(g_2D,op.quadratureClosure) + @test Hi*H*v ≈ v rtol = 1e-15 + @test Hi*H*u ≈ u rtol = 1e-15 + end + @testset "4th order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + H = inner_product(g_2D,op.quadratureClosure) + Hi = inverse_inner_product(g_2D,op.quadratureClosure) + @test Hi*H*v ≈ v rtol = 1e-15 + @test Hi*H*u ≈ u rtol = 1e-15 + end + end + end +end + +@testset "BoundaryOperator" begin + closure_stencil = Stencil((0,2), (2.,1.,3.)) + g_1D = EquidistantGrid(11, 0.0, 1.0) + g_2D = EquidistantGrid((11,15), (0.0, 0.0), (1.0,1.0)) + + @testset "Constructors" begin + @testset "1D" begin + op_l = BoundaryOperator{Lower}(closure_stencil,size(g_1D)[1]) + @test op_l == BoundaryOperator(g_1D,closure_stencil,Lower()) + @test op_l == boundary_operator(g_1D,closure_stencil,CartesianBoundary{1,Lower}()) + @test op_l isa TensorMapping{T,0,1} where T + + op_r = BoundaryOperator{Upper}(closure_stencil,size(g_1D)[1]) + @test op_r == BoundaryOperator(g_1D,closure_stencil,Upper()) + @test op_r == boundary_operator(g_1D,closure_stencil,CartesianBoundary{1,Upper}()) + @test op_r isa TensorMapping{T,0,1} where T + end + + @testset "2D" begin + e_w = boundary_operator(g_2D,closure_stencil,CartesianBoundary{1,Upper}()) + @test e_w isa InflatedTensorMapping + @test e_w isa TensorMapping{T,1,2} where T + end + end + + op_l = boundary_operator(g_1D, closure_stencil, CartesianBoundary{1,Lower}()) + op_r = boundary_operator(g_1D, closure_stencil, CartesianBoundary{1,Upper}()) + + op_w = boundary_operator(g_2D, closure_stencil, CartesianBoundary{1,Lower}()) + op_e = boundary_operator(g_2D, closure_stencil, CartesianBoundary{1,Upper}()) + op_s = boundary_operator(g_2D, closure_stencil, CartesianBoundary{2,Lower}()) + op_n = boundary_operator(g_2D, closure_stencil, CartesianBoundary{2,Upper}()) + + @testset "Sizes" begin + @testset "1D" begin + @test domain_size(op_l) == (11,) + @test domain_size(op_r) == (11,) + + @test range_size(op_l) == () + @test range_size(op_r) == () + end + + @testset "2D" begin + @test domain_size(op_w) == (11,15) + @test domain_size(op_e) == (11,15) + @test domain_size(op_s) == (11,15) + @test domain_size(op_n) == (11,15) + + @test range_size(op_w) == (15,) + @test range_size(op_e) == (15,) + @test range_size(op_s) == (11,) + @test range_size(op_n) == (11,) + end + end + + @testset "Application" begin + @testset "1D" begin + v = evalOn(g_1D,x->1+x^2) + u = fill(3.124) + @test (op_l*v)[] == 2*v[1] + v[2] + 3*v[3] + @test (op_r*v)[] == 2*v[end] + v[end-1] + 3*v[end-2] + @test (op_r*v)[1] == 2*v[end] + v[end-1] + 3*v[end-2] + @test op_l'*u == [2*u[]; u[]; 3*u[]; zeros(8)] + @test op_r'*u == [zeros(8); 3*u[]; u[]; 2*u[]] + end + + @testset "2D" begin + v = rand(size(g_2D)...) + u = fill(3.124) + @test op_w*v ≈ 2*v[1,:] + v[2,:] + 3*v[3,:] rtol = 1e-14 + @test op_e*v ≈ 2*v[end,:] + v[end-1,:] + 3*v[end-2,:] rtol = 1e-14 + @test op_s*v ≈ 2*v[:,1] + v[:,2] + 3*v[:,3] rtol = 1e-14 + @test op_n*v ≈ 2*v[:,end] + v[:,end-1] + 3*v[:,end-2] rtol = 1e-14 + + + g_x = rand(size(g_2D)[1]) + g_y = rand(size(g_2D)[2]) + + G_w = zeros(Float64, size(g_2D)...) + G_w[1,:] = 2*g_y + G_w[2,:] = g_y + G_w[3,:] = 3*g_y + + G_e = zeros(Float64, size(g_2D)...) + G_e[end,:] = 2*g_y + G_e[end-1,:] = g_y + G_e[end-2,:] = 3*g_y + + G_s = zeros(Float64, size(g_2D)...) + G_s[:,1] = 2*g_x + G_s[:,2] = g_x + G_s[:,3] = 3*g_x + + G_n = zeros(Float64, size(g_2D)...) + G_n[:,end] = 2*g_x + G_n[:,end-1] = g_x + G_n[:,end-2] = 3*g_x + + @test op_w'*g_y == G_w + @test op_e'*g_y == G_e + @test op_s'*g_x == G_s + @test op_n'*g_x == G_n + end + + @testset "Regions" begin + u = fill(3.124) + @test (op_l'*u)[Index(1,Lower)] == 2*u[] + @test (op_l'*u)[Index(2,Lower)] == u[] + @test (op_l'*u)[Index(6,Interior)] == 0 + @test (op_l'*u)[Index(10,Upper)] == 0 + @test (op_l'*u)[Index(11,Upper)] == 0 + + @test (op_r'*u)[Index(1,Lower)] == 0 + @test (op_r'*u)[Index(2,Lower)] == 0 + @test (op_r'*u)[Index(6,Interior)] == 0 + @test (op_r'*u)[Index(10,Upper)] == u[] + @test (op_r'*u)[Index(11,Upper)] == 2*u[] + end + end + + @testset "Inferred" begin + v = ones(Float64, 11) + u = fill(1.) + + @inferred apply(op_l, v) + @inferred apply(op_r, v) + + @inferred apply_transpose(op_l, u, 4) + @inferred apply_transpose(op_l, u, Index(1,Lower)) + @inferred apply_transpose(op_l, u, Index(2,Lower)) + @inferred apply_transpose(op_l, u, Index(6,Interior)) + @inferred apply_transpose(op_l, u, Index(10,Upper)) + @inferred apply_transpose(op_l, u, Index(11,Upper)) + + @inferred apply_transpose(op_r, u, 4) + @inferred apply_transpose(op_r, u, Index(1,Lower)) + @inferred apply_transpose(op_r, u, Index(2,Lower)) + @inferred apply_transpose(op_r, u, Index(6,Interior)) + @inferred apply_transpose(op_r, u, Index(10,Upper)) + @inferred apply_transpose(op_r, u, Index(11,Upper)) + end + +end + +@testset "boundary_restriction" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + g_1D = EquidistantGrid(11, 0.0, 1.0) + g_2D = EquidistantGrid((11,15), (0.0, 0.0), (1.0,1.0)) + + @testset "boundary_restriction" begin + @testset "1D" begin + e_l = boundary_restriction(g_1D,op.eClosure,Lower()) + @test e_l == boundary_restriction(g_1D,op.eClosure,CartesianBoundary{1,Lower}()) + @test e_l == BoundaryOperator(g_1D,op.eClosure,Lower()) + @test e_l isa BoundaryOperator{T,Lower} where T + @test e_l isa TensorMapping{T,0,1} where T + + e_r = boundary_restriction(g_1D,op.eClosure,Upper()) + @test e_r == boundary_restriction(g_1D,op.eClosure,CartesianBoundary{1,Upper}()) + @test e_r == BoundaryOperator(g_1D,op.eClosure,Upper()) + @test e_r isa BoundaryOperator{T,Upper} where T + @test e_r isa TensorMapping{T,0,1} where T + end + + @testset "2D" begin + e_w = boundary_restriction(g_2D,op.eClosure,CartesianBoundary{1,Upper}()) + @test e_w isa InflatedTensorMapping + @test e_w isa TensorMapping{T,1,2} where T + end + end + + @testset "Application" begin + @testset "1D" begin + e_l = boundary_restriction(g_1D, op.eClosure, CartesianBoundary{1,Lower}()) + e_r = boundary_restriction(g_1D, op.eClosure, CartesianBoundary{1,Upper}()) + + v = evalOn(g_1D,x->1+x^2) + u = fill(3.124) + + @test (e_l*v)[] == v[1] + @test (e_r*v)[] == v[end] + @test (e_r*v)[1] == v[end] + end + + @testset "2D" begin + e_w = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{1,Lower}()) + e_e = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{1,Upper}()) + e_s = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{2,Lower}()) + e_n = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{2,Upper}()) + + v = rand(11, 15) + u = fill(3.124) + + @test e_w*v == v[1,:] + @test e_e*v == v[end,:] + @test e_s*v == v[:,1] + @test e_n*v == v[:,end] + end + end +end + +@testset "normal_derivative" begin + g_1D = EquidistantGrid(11, 0.0, 1.0) + g_2D = EquidistantGrid((11,12), (0.0, 0.0), (1.0,1.0)) + @testset "normal_derivative" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + @testset "1D" begin + d_l = normal_derivative(g_1D, op.dClosure, Lower()) + @test d_l == normal_derivative(g_1D, op.dClosure, CartesianBoundary{1,Lower}()) + @test d_l isa BoundaryOperator{T,Lower} where T + @test d_l isa TensorMapping{T,0,1} where T + end + @testset "2D" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + d_w = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Lower}()) + d_n = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Upper}()) + Ix = IdentityMapping{Float64}((size(g_2D)[1],)) + Iy = IdentityMapping{Float64}((size(g_2D)[2],)) + d_l = normal_derivative(restrict(g_2D,1),op.dClosure,Lower()) + d_r = normal_derivative(restrict(g_2D,2),op.dClosure,Upper()) + @test d_w == d_l⊗Iy + @test d_n == Ix⊗d_r + @test d_w isa TensorMapping{T,1,2} where T + @test d_n isa TensorMapping{T,1,2} where T + end + end + @testset "Accuracy" begin + v = evalOn(g_2D, (x,y)-> x^2 + (y-1)^2 + x*y) + v∂x = evalOn(g_2D, (x,y)-> 2*x + y) + v∂y = evalOn(g_2D, (x,y)-> 2*(y-1) + x) + # TODO: Test for higher order polynomials? + @testset "2nd order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) + d_w = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Lower}()) + d_e = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Upper}()) + d_s = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Lower}()) + d_n = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Upper}()) + + @test d_w*v ≈ v∂x[1,:] atol = 1e-13 + @test d_e*v ≈ -v∂x[end,:] atol = 1e-13 + @test d_s*v ≈ v∂y[:,1] atol = 1e-13 + @test d_n*v ≈ -v∂y[:,end] atol = 1e-13 + end + + @testset "4th order" begin + op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) + d_w = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Lower}()) + d_e = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Upper}()) + d_s = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Lower}()) + d_n = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Upper}()) + + @test d_w*v ≈ v∂x[1,:] atol = 1e-13 + @test d_e*v ≈ -v∂x[end,:] atol = 1e-13 + @test d_s*v ≈ v∂y[:,1] atol = 1e-13 + @test d_n*v ≈ -v∂y[:,end] atol = 1e-13 + end + end +end + +end
diff -r 38f9894279cd -r 48a61e085e60 test/runtests.jl --- a/test/runtests.jl Mon Feb 15 11:13:12 2021 +0100 +++ b/test/runtests.jl Sat Feb 20 20:31:08 2021 +0100 @@ -1,6 +1,49 @@ using Test -using TestSetExtensions +using Glob + +""" + run_testfiles() + run_testfiles(path) + run_testfiles(path, glob) + +Find and run all files with filenames starting with "test". If `path` is omitted the test folder is assumed. +The argument `glob` can optionally be supplied to filter which test files are run. +""" +function run_testfiles(args) + if isempty(args) + glob = fn"./*" + else + glob = Glob.FilenameMatch("./"*args[1]) #TBD: Allow multiple filters? + end + + run_testfiles(".", glob) +end -@testset "All" begin - @includetests ARGS +# TODO change from prefix `test` to suffix `_test` for testfiles +function run_testfiles(path, glob) + for name ∈ readdir(path) + filepath = joinpath(path, name) + + if isdir(filepath) + @testset "$name" begin + run_testfiles(filepath, glob) + end + end + + if !endswith(name, ".jl") ## TODO combine this into test below when switching to suffix + continue + end + + if startswith(name, "test") && occursin(glob, filepath) + printstyled("Running "; bold=true, color=:green) + println(filepath) + include(filepath) + end + end end + +testsetname = isempty(ARGS) ? "Sbplib.jl" : ARGS[1] + +@testset "$testsetname" begin + run_testfiles(ARGS) +end
diff -r 38f9894279cd -r 48a61e085e60 test/testSbpOperators.jl --- a/test/testSbpOperators.jl Mon Feb 15 11:13:12 2021 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,832 +0,0 @@ -using Test -using Sbplib.SbpOperators -using Sbplib.Grids -using Sbplib.RegionIndices -using Sbplib.LazyTensors -using LinearAlgebra -using TOML - -import Sbplib.SbpOperators.Stencil -import Sbplib.SbpOperators.VolumeOperator -import Sbplib.SbpOperators.volume_operator -import Sbplib.SbpOperators.BoundaryOperator -import Sbplib.SbpOperators.boundary_operator -import Sbplib.SbpOperators.even -import Sbplib.SbpOperators.odd - - -@testset "SbpOperators" begin - -@testset "Stencil" begin - s = Stencil((-2,2), (1.,2.,2.,3.,4.)) - @test s isa Stencil{Float64, 5} - - @test eltype(s) == Float64 - @test SbpOperators.scale(s, 2) == Stencil((-2,2), (2.,4.,4.,6.,8.)) - - @test Stencil(1,2,3,4; center=1) == Stencil((0, 3),(1,2,3,4)) - @test Stencil(1,2,3,4; center=2) == Stencil((-1, 2),(1,2,3,4)) - @test Stencil(1,2,3,4; center=4) == Stencil((-3, 0),(1,2,3,4)) - - @test CenteredStencil(1,2,3,4,5) == Stencil((-2, 2), (1,2,3,4,5)) - @test_throws ArgumentError CenteredStencil(1,2,3,4) -end - -@testset "parse_rational" begin - @test SbpOperators.parse_rational("1") isa Rational - @test SbpOperators.parse_rational("1") == 1//1 - @test SbpOperators.parse_rational("1/2") isa Rational - @test SbpOperators.parse_rational("1/2") == 1//2 - @test SbpOperators.parse_rational("37/13") isa Rational - @test SbpOperators.parse_rational("37/13") == 37//13 -end - -@testset "readoperator" begin - toml_str = """ - [meta] - type = "equidistant" - - [order2] - H.inner = ["1"] - - D1.inner_stencil = ["-1/2", "0", "1/2"] - D1.closure_stencils = [ - ["-1", "1"], - ] - - d1.closure = ["-3/2", "2", "-1/2"] - - [order4] - H.closure = ["17/48", "59/48", "43/48", "49/48"] - - D2.inner_stencil = ["-1/12","4/3","-5/2","4/3","-1/12"] - D2.closure_stencils = [ - [ "2", "-5", "4", "-1", "0", "0"], - [ "1", "-2", "1", "0", "0", "0"], - [ "-4/43", "59/43", "-110/43", "59/43", "-4/43", "0"], - [ "-1/49", "0", "59/49", "-118/49", "64/49", "-4/49"], - ] - """ - - parsed_toml = TOML.parse(toml_str) - @testset "get_stencil" begin - @test get_stencil(parsed_toml, "order2", "D1", "inner_stencil") == Stencil(-1/2, 0., 1/2, center=2) - @test get_stencil(parsed_toml, "order2", "D1", "inner_stencil", center=1) == Stencil(-1/2, 0., 1/2; center=1) - @test get_stencil(parsed_toml, "order2", "D1", "inner_stencil", center=3) == Stencil(-1/2, 0., 1/2; center=3) - - @test get_stencil(parsed_toml, "order2", "H", "inner") == Stencil(1.; center=1) - - @test_throws AssertionError get_stencil(parsed_toml, "meta", "type") - @test_throws AssertionError get_stencil(parsed_toml, "order2", "D1", "closure_stencils") - end - - @testset "get_stencils" begin - @test get_stencils(parsed_toml, "order2", "D1", "closure_stencils", centers=(1,)) == (Stencil(-1., 1., center=1),) - @test get_stencils(parsed_toml, "order2", "D1", "closure_stencils", centers=(2,)) == (Stencil(-1., 1., center=2),) - @test get_stencils(parsed_toml, "order2", "D1", "closure_stencils", centers=[2]) == (Stencil(-1., 1., center=2),) - - @test get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=[1,1,1,1]) == ( - Stencil( 2., -5., 4., -1., 0., 0., center=1), - Stencil( 1., -2., 1., 0., 0., 0., center=1), - Stencil( -4/43, 59/43, -110/43, 59/43, -4/43, 0., center=1), - Stencil( -1/49, 0., 59/49, -118/49, 64/49, -4/49, center=1), - ) - - @test get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=(4,2,3,1)) == ( - Stencil( 2., -5., 4., -1., 0., 0., center=4), - Stencil( 1., -2., 1., 0., 0., 0., center=2), - Stencil( -4/43, 59/43, -110/43, 59/43, -4/43, 0., center=3), - Stencil( -1/49, 0., 59/49, -118/49, 64/49, -4/49, center=1), - ) - - @test get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=1:4) == ( - Stencil( 2., -5., 4., -1., 0., 0., center=1), - Stencil( 1., -2., 1., 0., 0., 0., center=2), - Stencil( -4/43, 59/43, -110/43, 59/43, -4/43, 0., center=3), - Stencil( -1/49, 0., 59/49, -118/49, 64/49, -4/49, center=4), - ) - - @test_throws AssertionError get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=(1,2,3)) - @test_throws AssertionError get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=(1,2,3,5,4)) - @test_throws AssertionError get_stencils(parsed_toml, "order4", "D2", "inner_stencil",centers=(1,2)) - end - - @testset "get_tuple" begin - @test get_tuple(parsed_toml, "order2", "d1", "closure") == (-3/2, 2, -1/2) - - @test_throws AssertionError get_tuple(parsed_toml, "meta", "type") - end -end - -@testset "VolumeOperator" begin - inner_stencil = CenteredStencil(1/4, 2/4, 1/4) - closure_stencils = (Stencil(1/2, 1/2; center=1), Stencil(0.,1.; center=2)) - g_1D = EquidistantGrid(11,0.,1.) - g_2D = EquidistantGrid((11,12),(0.,0.),(1.,1.)) - g_3D = EquidistantGrid((11,12,10),(0.,0.,0.),(1.,1.,1.)) - @testset "Constructors" begin - @testset "1D" begin - op = VolumeOperator(inner_stencil,closure_stencils,(11,),even) - @test op == VolumeOperator(g_1D,inner_stencil,closure_stencils,even) - @test op == volume_operator(g_1D,inner_stencil,closure_stencils,even,1) - @test op isa TensorMapping{T,1,1} where T - end - @testset "2D" begin - op_x = volume_operator(g_2D,inner_stencil,closure_stencils,even,1) - op_y = volume_operator(g_2D,inner_stencil,closure_stencils,even,2) - Ix = IdentityMapping{Float64}((11,)) - Iy = IdentityMapping{Float64}((12,)) - @test op_x == VolumeOperator(inner_stencil,closure_stencils,(11,),even)⊗Iy - @test op_y == Ix⊗VolumeOperator(inner_stencil,closure_stencils,(12,),even) - @test op_x isa TensorMapping{T,2,2} where T - @test op_y isa TensorMapping{T,2,2} where T - end - @testset "3D" begin - op_x = volume_operator(g_3D,inner_stencil,closure_stencils,even,1) - op_y = volume_operator(g_3D,inner_stencil,closure_stencils,even,2) - op_z = volume_operator(g_3D,inner_stencil,closure_stencils,even,3) - Ix = IdentityMapping{Float64}((11,)) - Iy = IdentityMapping{Float64}((12,)) - Iz = IdentityMapping{Float64}((10,)) - @test op_x == VolumeOperator(inner_stencil,closure_stencils,(11,),even)⊗Iy⊗Iz - @test op_y == Ix⊗VolumeOperator(inner_stencil,closure_stencils,(12,),even)⊗Iz - @test op_z == Ix⊗Iy⊗VolumeOperator(inner_stencil,closure_stencils,(10,),even) - @test op_x isa TensorMapping{T,3,3} where T - @test op_y isa TensorMapping{T,3,3} where T - @test op_z isa TensorMapping{T,3,3} where T - end - end - - @testset "Sizes" begin - @testset "1D" begin - op = volume_operator(g_1D,inner_stencil,closure_stencils,even,1) - @test range_size(op) == domain_size(op) == size(g_1D) - end - - @testset "2D" begin - op_x = volume_operator(g_2D,inner_stencil,closure_stencils,even,1) - op_y = volume_operator(g_2D,inner_stencil,closure_stencils,even,2) - @test range_size(op_y) == domain_size(op_y) == - range_size(op_x) == domain_size(op_x) == size(g_2D) - end - @testset "3D" begin - op_x = volume_operator(g_3D,inner_stencil,closure_stencils,even,1) - op_y = volume_operator(g_3D,inner_stencil,closure_stencils,even,2) - op_z = volume_operator(g_3D,inner_stencil,closure_stencils,even,3) - @test range_size(op_z) == domain_size(op_z) == - range_size(op_y) == domain_size(op_y) == - range_size(op_x) == domain_size(op_x) == size(g_3D) - end - end - - op_x = volume_operator(g_2D,inner_stencil,closure_stencils,even,1) - op_y = volume_operator(g_2D,inner_stencil,closure_stencils,odd,2) - v = zeros(size(g_2D)) - Nx = size(g_2D)[1] - Ny = size(g_2D)[2] - for i = 1:Nx - v[i,:] .= i - end - rx = copy(v) - rx[1,:] .= 1.5 - rx[Nx,:] .= (2*Nx-1)/2 - ry = copy(v) - ry[:,Ny-1:Ny] = -v[:,Ny-1:Ny] - - @testset "Application" begin - @test op_x*v ≈ rx rtol = 1e-14 - @test op_y*v ≈ ry rtol = 1e-14 - end - - @testset "Regions" begin - @test (op_x*v)[Index(1,Lower),Index(3,Interior)] ≈ rx[1,3] rtol = 1e-14 - @test (op_x*v)[Index(2,Lower),Index(3,Interior)] ≈ rx[2,3] rtol = 1e-14 - @test (op_x*v)[Index(6,Interior),Index(3,Interior)] ≈ rx[6,3] rtol = 1e-14 - @test (op_x*v)[Index(10,Upper),Index(3,Interior)] ≈ rx[10,3] rtol = 1e-14 - @test (op_x*v)[Index(11,Upper),Index(3,Interior)] ≈ rx[11,3] rtol = 1e-14 - - @test_throws BoundsError (op_x*v)[Index(3,Lower),Index(3,Interior)] - @test_throws BoundsError (op_x*v)[Index(9,Upper),Index(3,Interior)] - - @test (op_y*v)[Index(3,Interior),Index(1,Lower)] ≈ ry[3,1] rtol = 1e-14 - @test (op_y*v)[Index(3,Interior),Index(2,Lower)] ≈ ry[3,2] rtol = 1e-14 - @test (op_y*v)[Index(3,Interior),Index(6,Interior)] ≈ ry[3,6] rtol = 1e-14 - @test (op_y*v)[Index(3,Interior),Index(11,Upper)] ≈ ry[3,11] rtol = 1e-14 - @test (op_y*v)[Index(3,Interior),Index(12,Upper)] ≈ ry[3,12] rtol = 1e-14 - - @test_throws BoundsError (op_y*v)[Index(3,Interior),Index(10,Upper)] - @test_throws BoundsError (op_y*v)[Index(3,Interior),Index(3,Lower)] - end - - @testset "Inferred" begin - @inferred apply(op_x, v,1,1) - @inferred apply(op_x, v, Index(1,Lower),Index(1,Lower)) - @inferred apply(op_x, v, Index(6,Interior),Index(1,Lower)) - @inferred apply(op_x, v, Index(11,Upper),Index(1,Lower)) - - @inferred apply(op_y, v,1,1) - @inferred apply(op_y, v, Index(1,Lower),Index(1,Lower)) - @inferred apply(op_y, v, Index(1,Lower),Index(6,Interior)) - @inferred apply(op_y, v, Index(1,Lower),Index(11,Upper)) - end - -end - -@testset "SecondDerivative" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - Lx = 3.5 - Ly = 3. - g_1D = EquidistantGrid(121, 0.0, Lx) - g_2D = EquidistantGrid((121,123), (0.0, 0.0), (Lx, Ly)) - - @testset "Constructors" begin - @testset "1D" begin - Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils) - @test Dₓₓ == second_derivative(g_1D,op.innerStencil,op.closureStencils,1) - @test Dₓₓ isa VolumeOperator - end - @testset "2D" begin - Dₓₓ = second_derivative(g_2D,op.innerStencil,op.closureStencils,1) - D2 = second_derivative(g_1D,op.innerStencil,op.closureStencils) - I = IdentityMapping{Float64}(size(g_2D)[2]) - @test Dₓₓ == D2⊗I - @test Dₓₓ isa TensorMapping{T,2,2} where T - end - end - - # Exact differentiation is measured point-wise. In other cases - # the error is measured in the l2-norm. - @testset "Accuracy" begin - @testset "1D" begin - l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2)); - monomials = () - maxOrder = 4; - for i = 0:maxOrder-1 - f_i(x) = 1/factorial(i)*x^i - monomials = (monomials...,evalOn(g_1D,f_i)) - end - v = evalOn(g_1D,x -> sin(x)) - vₓₓ = evalOn(g_1D,x -> -sin(x)) - - # 2nd order interior stencil, 1nd order boundary stencil, - # implies that L*v should be exact for monomials up to order 2. - @testset "2nd order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) - Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils) - @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10 - @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10 - @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10 - @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2 - end - - # 4th order interior stencil, 2nd order boundary stencil, - # implies that L*v should be exact for monomials up to order 3. - @testset "4th order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils) - # NOTE: high tolerances for checking the "exact" differentiation - # due to accumulation of round-off errors/cancellation errors? - @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10 - @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10 - @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10 - @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10 - @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2 - end - end - - @testset "2D" begin - l2(v) = sqrt(prod(spacing(g_2D))*sum(v.^2)); - binomials = () - maxOrder = 4; - for i = 0:maxOrder-1 - f_i(x,y) = 1/factorial(i)*y^i + x^i - binomials = (binomials...,evalOn(g_2D,f_i)) - end - v = evalOn(g_2D, (x,y) -> sin(x)+cos(y)) - v_yy = evalOn(g_2D,(x,y) -> -cos(y)) - - # 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 - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) - Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2) - @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 - @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 - @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9 - @test Dyy*v ≈ v_yy 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 - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2) - # NOTE: high tolerances for checking the "exact" differentiation - # due to accumulation of round-off errors/cancellation errors? - @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 - @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9 - @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9 - @test Dyy*binomials[4] ≈ evalOn(g_2D,(x,y)->y) atol = 5e-9 - @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2 - end - end - end -end - -@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 - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - @testset "1D" begin - L = laplace(g_1D, op.innerStencil, op.closureStencils) - @test L == second_derivative(g_1D, op.innerStencil, op.closureStencils) - @test L isa TensorMapping{T,1,1} where T - end - @testset "3D" begin - L = laplace(g_3D, op.innerStencil, op.closureStencils) - @test L isa TensorMapping{T,3,3} where T - Dxx = second_derivative(g_3D, op.innerStencil, op.closureStencils,1) - Dyy = second_derivative(g_3D, op.innerStencil, op.closureStencils,2) - Dzz = second_derivative(g_3D, op.innerStencil, op.closureStencils,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 - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) - L = laplace(g_3D,op.innerStencil,op.closureStencils) - @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 - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - L = laplace(g_3D,op.innerStencil,op.closureStencils) - # 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 - -@testset "Diagonal-stencil inner_product" begin - Lx = π/2. - Ly = Float64(π) - Lz = 1. - g_1D = EquidistantGrid(77, 0.0, Lx) - g_2D = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly)) - g_3D = EquidistantGrid((10,10, 10), (0.0, 0.0, 0.0), (Lx,Ly,Lz)) - integral(H,v) = sum(H*v) - @testset "inner_product" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - @testset "0D" begin - H = inner_product(EquidistantGrid{Float64}(),op.quadratureClosure) - @test H == IdentityMapping{Float64}() - @test H isa TensorMapping{T,0,0} where T - end - @testset "1D" begin - H = inner_product(g_1D,op.quadratureClosure) - inner_stencil = CenteredStencil(1.) - @test H == inner_product(g_1D,op.quadratureClosure,inner_stencil) - @test H isa TensorMapping{T,1,1} where T - end - @testset "2D" begin - H = inner_product(g_2D,op.quadratureClosure) - H_x = inner_product(restrict(g_2D,1),op.quadratureClosure) - H_y = inner_product(restrict(g_2D,2),op.quadratureClosure) - @test H == H_x⊗H_y - @test H isa TensorMapping{T,2,2} where T - end - end - - @testset "Sizes" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - @testset "1D" begin - H = inner_product(g_1D,op.quadratureClosure) - @test domain_size(H) == size(g_1D) - @test range_size(H) == size(g_1D) - end - @testset "2D" begin - H = inner_product(g_2D,op.quadratureClosure) - @test domain_size(H) == size(g_2D) - @test range_size(H) == size(g_2D) - end - end - - @testset "Accuracy" begin - @testset "1D" begin - v = () - for i = 0:4 - f_i(x) = 1/factorial(i)*x^i - v = (v...,evalOn(g_1D,f_i)) - end - u = evalOn(g_1D,x->sin(x)) - - @testset "2nd order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) - H = inner_product(g_1D,op.quadratureClosure) - for i = 1:2 - @test integral(H,v[i]) ≈ v[i+1][end] - v[i+1][1] rtol = 1e-14 - end - @test integral(H,u) ≈ 1. rtol = 1e-4 - end - - @testset "4th order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - H = inner_product(g_1D,op.quadratureClosure) - for i = 1:4 - @test integral(H,v[i]) ≈ v[i+1][end] - v[i+1][1] rtol = 1e-14 - end - @test integral(H,u) ≈ 1. rtol = 1e-8 - end - end - - @testset "2D" begin - b = 2.1 - v = b*ones(Float64, size(g_2D)) - u = evalOn(g_2D,(x,y)->sin(x)+cos(y)) - @testset "2nd order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) - H = inner_product(g_2D,op.quadratureClosure) - @test integral(H,v) ≈ b*Lx*Ly rtol = 1e-13 - @test integral(H,u) ≈ π rtol = 1e-4 - end - @testset "4th order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - H = inner_product(g_2D,op.quadratureClosure) - @test integral(H,v) ≈ b*Lx*Ly rtol = 1e-13 - @test integral(H,u) ≈ π rtol = 1e-8 - end - end - end -end - -@testset "Diagonal-stencil inverse_inner_product" begin - Lx = π/2. - Ly = Float64(π) - g_1D = EquidistantGrid(77, 0.0, Lx) - g_2D = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly)) - @testset "inverse_inner_product" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - @testset "0D" begin - Hi = inverse_inner_product(EquidistantGrid{Float64}(),op.quadratureClosure) - @test Hi == IdentityMapping{Float64}() - @test Hi isa TensorMapping{T,0,0} where T - end - @testset "1D" begin - Hi = inverse_inner_product(g_1D, op.quadratureClosure); - inner_stencil = CenteredStencil(1.) - closures = () - for i = 1:length(op.quadratureClosure) - closures = (closures...,Stencil(op.quadratureClosure[i].range,1.0./op.quadratureClosure[i].weights)) - end - @test Hi == inverse_inner_product(g_1D,closures,inner_stencil) - @test Hi isa TensorMapping{T,1,1} where T - end - @testset "2D" begin - Hi = inverse_inner_product(g_2D,op.quadratureClosure) - Hi_x = inverse_inner_product(restrict(g_2D,1),op.quadratureClosure) - Hi_y = inverse_inner_product(restrict(g_2D,2),op.quadratureClosure) - @test Hi == Hi_x⊗Hi_y - @test Hi isa TensorMapping{T,2,2} where T - end - end - - @testset "Sizes" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - @testset "1D" begin - Hi = inverse_inner_product(g_1D,op.quadratureClosure) - @test domain_size(Hi) == size(g_1D) - @test range_size(Hi) == size(g_1D) - end - @testset "2D" begin - Hi = inverse_inner_product(g_2D,op.quadratureClosure) - @test domain_size(Hi) == size(g_2D) - @test range_size(Hi) == size(g_2D) - end - end - - @testset "Accuracy" begin - @testset "1D" begin - v = evalOn(g_1D,x->sin(x)) - u = evalOn(g_1D,x->x^3-x^2+1) - @testset "2nd order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) - H = inner_product(g_1D,op.quadratureClosure) - Hi = inverse_inner_product(g_1D,op.quadratureClosure) - @test Hi*H*v ≈ v rtol = 1e-15 - @test Hi*H*u ≈ u rtol = 1e-15 - end - @testset "4th order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - H = inner_product(g_1D,op.quadratureClosure) - Hi = inverse_inner_product(g_1D,op.quadratureClosure) - @test Hi*H*v ≈ v rtol = 1e-15 - @test Hi*H*u ≈ u rtol = 1e-15 - end - end - @testset "2D" begin - v = evalOn(g_2D,(x,y)->sin(x)+cos(y)) - u = evalOn(g_2D,(x,y)->x*y + x^5 - sqrt(y)) - @testset "2nd order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) - H = inner_product(g_2D,op.quadratureClosure) - Hi = inverse_inner_product(g_2D,op.quadratureClosure) - @test Hi*H*v ≈ v rtol = 1e-15 - @test Hi*H*u ≈ u rtol = 1e-15 - end - @testset "4th order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - H = inner_product(g_2D,op.quadratureClosure) - Hi = inverse_inner_product(g_2D,op.quadratureClosure) - @test Hi*H*v ≈ v rtol = 1e-15 - @test Hi*H*u ≈ u rtol = 1e-15 - end - end - end -end - -@testset "BoundaryOperator" begin - closure_stencil = Stencil((0,2), (2.,1.,3.)) - g_1D = EquidistantGrid(11, 0.0, 1.0) - g_2D = EquidistantGrid((11,15), (0.0, 0.0), (1.0,1.0)) - - @testset "Constructors" begin - @testset "1D" begin - op_l = BoundaryOperator{Lower}(closure_stencil,size(g_1D)[1]) - @test op_l == BoundaryOperator(g_1D,closure_stencil,Lower()) - @test op_l == boundary_operator(g_1D,closure_stencil,CartesianBoundary{1,Lower}()) - @test op_l isa TensorMapping{T,0,1} where T - - op_r = BoundaryOperator{Upper}(closure_stencil,size(g_1D)[1]) - @test op_r == BoundaryOperator(g_1D,closure_stencil,Upper()) - @test op_r == boundary_operator(g_1D,closure_stencil,CartesianBoundary{1,Upper}()) - @test op_r isa TensorMapping{T,0,1} where T - end - - @testset "2D" begin - e_w = boundary_operator(g_2D,closure_stencil,CartesianBoundary{1,Upper}()) - @test e_w isa InflatedTensorMapping - @test e_w isa TensorMapping{T,1,2} where T - end - end - - op_l = boundary_operator(g_1D, closure_stencil, CartesianBoundary{1,Lower}()) - op_r = boundary_operator(g_1D, closure_stencil, CartesianBoundary{1,Upper}()) - - op_w = boundary_operator(g_2D, closure_stencil, CartesianBoundary{1,Lower}()) - op_e = boundary_operator(g_2D, closure_stencil, CartesianBoundary{1,Upper}()) - op_s = boundary_operator(g_2D, closure_stencil, CartesianBoundary{2,Lower}()) - op_n = boundary_operator(g_2D, closure_stencil, CartesianBoundary{2,Upper}()) - - @testset "Sizes" begin - @testset "1D" begin - @test domain_size(op_l) == (11,) - @test domain_size(op_r) == (11,) - - @test range_size(op_l) == () - @test range_size(op_r) == () - end - - @testset "2D" begin - @test domain_size(op_w) == (11,15) - @test domain_size(op_e) == (11,15) - @test domain_size(op_s) == (11,15) - @test domain_size(op_n) == (11,15) - - @test range_size(op_w) == (15,) - @test range_size(op_e) == (15,) - @test range_size(op_s) == (11,) - @test range_size(op_n) == (11,) - end - end - - @testset "Application" begin - @testset "1D" begin - v = evalOn(g_1D,x->1+x^2) - u = fill(3.124) - @test (op_l*v)[] == 2*v[1] + v[2] + 3*v[3] - @test (op_r*v)[] == 2*v[end] + v[end-1] + 3*v[end-2] - @test (op_r*v)[1] == 2*v[end] + v[end-1] + 3*v[end-2] - @test op_l'*u == [2*u[]; u[]; 3*u[]; zeros(8)] - @test op_r'*u == [zeros(8); 3*u[]; u[]; 2*u[]] - end - - @testset "2D" begin - v = rand(size(g_2D)...) - u = fill(3.124) - @test op_w*v ≈ 2*v[1,:] + v[2,:] + 3*v[3,:] rtol = 1e-14 - @test op_e*v ≈ 2*v[end,:] + v[end-1,:] + 3*v[end-2,:] rtol = 1e-14 - @test op_s*v ≈ 2*v[:,1] + v[:,2] + 3*v[:,3] rtol = 1e-14 - @test op_n*v ≈ 2*v[:,end] + v[:,end-1] + 3*v[:,end-2] rtol = 1e-14 - - - g_x = rand(size(g_2D)[1]) - g_y = rand(size(g_2D)[2]) - - G_w = zeros(Float64, size(g_2D)...) - G_w[1,:] = 2*g_y - G_w[2,:] = g_y - G_w[3,:] = 3*g_y - - G_e = zeros(Float64, size(g_2D)...) - G_e[end,:] = 2*g_y - G_e[end-1,:] = g_y - G_e[end-2,:] = 3*g_y - - G_s = zeros(Float64, size(g_2D)...) - G_s[:,1] = 2*g_x - G_s[:,2] = g_x - G_s[:,3] = 3*g_x - - G_n = zeros(Float64, size(g_2D)...) - G_n[:,end] = 2*g_x - G_n[:,end-1] = g_x - G_n[:,end-2] = 3*g_x - - @test op_w'*g_y == G_w - @test op_e'*g_y == G_e - @test op_s'*g_x == G_s - @test op_n'*g_x == G_n - end - - @testset "Regions" begin - u = fill(3.124) - @test (op_l'*u)[Index(1,Lower)] == 2*u[] - @test (op_l'*u)[Index(2,Lower)] == u[] - @test (op_l'*u)[Index(6,Interior)] == 0 - @test (op_l'*u)[Index(10,Upper)] == 0 - @test (op_l'*u)[Index(11,Upper)] == 0 - - @test (op_r'*u)[Index(1,Lower)] == 0 - @test (op_r'*u)[Index(2,Lower)] == 0 - @test (op_r'*u)[Index(6,Interior)] == 0 - @test (op_r'*u)[Index(10,Upper)] == u[] - @test (op_r'*u)[Index(11,Upper)] == 2*u[] - end - end - - @testset "Inferred" begin - v = ones(Float64, 11) - u = fill(1.) - - @inferred apply(op_l, v) - @inferred apply(op_r, v) - - @inferred apply_transpose(op_l, u, 4) - @inferred apply_transpose(op_l, u, Index(1,Lower)) - @inferred apply_transpose(op_l, u, Index(2,Lower)) - @inferred apply_transpose(op_l, u, Index(6,Interior)) - @inferred apply_transpose(op_l, u, Index(10,Upper)) - @inferred apply_transpose(op_l, u, Index(11,Upper)) - - @inferred apply_transpose(op_r, u, 4) - @inferred apply_transpose(op_r, u, Index(1,Lower)) - @inferred apply_transpose(op_r, u, Index(2,Lower)) - @inferred apply_transpose(op_r, u, Index(6,Interior)) - @inferred apply_transpose(op_r, u, Index(10,Upper)) - @inferred apply_transpose(op_r, u, Index(11,Upper)) - end - -end - -@testset "boundary_restriction" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - g_1D = EquidistantGrid(11, 0.0, 1.0) - g_2D = EquidistantGrid((11,15), (0.0, 0.0), (1.0,1.0)) - - @testset "boundary_restriction" begin - @testset "1D" begin - e_l = boundary_restriction(g_1D,op.eClosure,Lower()) - @test e_l == boundary_restriction(g_1D,op.eClosure,CartesianBoundary{1,Lower}()) - @test e_l == BoundaryOperator(g_1D,op.eClosure,Lower()) - @test e_l isa BoundaryOperator{T,Lower} where T - @test e_l isa TensorMapping{T,0,1} where T - - e_r = boundary_restriction(g_1D,op.eClosure,Upper()) - @test e_r == boundary_restriction(g_1D,op.eClosure,CartesianBoundary{1,Upper}()) - @test e_r == BoundaryOperator(g_1D,op.eClosure,Upper()) - @test e_r isa BoundaryOperator{T,Upper} where T - @test e_r isa TensorMapping{T,0,1} where T - end - - @testset "2D" begin - e_w = boundary_restriction(g_2D,op.eClosure,CartesianBoundary{1,Upper}()) - @test e_w isa InflatedTensorMapping - @test e_w isa TensorMapping{T,1,2} where T - end - end - - @testset "Application" begin - @testset "1D" begin - e_l = boundary_restriction(g_1D, op.eClosure, CartesianBoundary{1,Lower}()) - e_r = boundary_restriction(g_1D, op.eClosure, CartesianBoundary{1,Upper}()) - - v = evalOn(g_1D,x->1+x^2) - u = fill(3.124) - - @test (e_l*v)[] == v[1] - @test (e_r*v)[] == v[end] - @test (e_r*v)[1] == v[end] - end - - @testset "2D" begin - e_w = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{1,Lower}()) - e_e = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{1,Upper}()) - e_s = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{2,Lower}()) - e_n = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{2,Upper}()) - - v = rand(11, 15) - u = fill(3.124) - - @test e_w*v == v[1,:] - @test e_e*v == v[end,:] - @test e_s*v == v[:,1] - @test e_n*v == v[:,end] - end - end -end - -@testset "normal_derivative" begin - g_1D = EquidistantGrid(11, 0.0, 1.0) - g_2D = EquidistantGrid((11,12), (0.0, 0.0), (1.0,1.0)) - @testset "normal_derivative" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - @testset "1D" begin - d_l = normal_derivative(g_1D, op.dClosure, Lower()) - @test d_l == normal_derivative(g_1D, op.dClosure, CartesianBoundary{1,Lower}()) - @test d_l isa BoundaryOperator{T,Lower} where T - @test d_l isa TensorMapping{T,0,1} where T - end - @testset "2D" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - d_w = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Lower}()) - d_n = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Upper}()) - Ix = IdentityMapping{Float64}((size(g_2D)[1],)) - Iy = IdentityMapping{Float64}((size(g_2D)[2],)) - d_l = normal_derivative(restrict(g_2D,1),op.dClosure,Lower()) - d_r = normal_derivative(restrict(g_2D,2),op.dClosure,Upper()) - @test d_w == d_l⊗Iy - @test d_n == Ix⊗d_r - @test d_w isa TensorMapping{T,1,2} where T - @test d_n isa TensorMapping{T,1,2} where T - end - end - @testset "Accuracy" begin - v = evalOn(g_2D, (x,y)-> x^2 + (y-1)^2 + x*y) - v∂x = evalOn(g_2D, (x,y)-> 2*x + y) - v∂y = evalOn(g_2D, (x,y)-> 2*(y-1) + x) - # TODO: Test for higher order polynomials? - @testset "2nd order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2) - d_w = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Lower}()) - d_e = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Upper}()) - d_s = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Lower}()) - d_n = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Upper}()) - - @test d_w*v ≈ v∂x[1,:] atol = 1e-13 - @test d_e*v ≈ -v∂x[end,:] atol = 1e-13 - @test d_s*v ≈ v∂y[:,1] atol = 1e-13 - @test d_n*v ≈ -v∂y[:,end] atol = 1e-13 - end - - @testset "4th order" begin - op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4) - d_w = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Lower}()) - d_e = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Upper}()) - d_s = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Lower}()) - d_n = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Upper}()) - - @test d_w*v ≈ v∂x[1,:] atol = 1e-13 - @test d_e*v ≈ -v∂x[end,:] atol = 1e-13 - @test d_s*v ≈ v∂y[:,1] atol = 1e-13 - @test d_n*v ≈ -v∂y[:,end] atol = 1e-13 - end - end -end - -end