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annotate test/SbpOperators/volumeops/laplace/laplace_test.jl @ 1651:707fc9761c2b feature/sbp_operators/laplace_curvilinear

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Merge feature/grids/manifolds
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 26 Jun 2024 12:47:26 +0200
parents 0685d97ebcb0 b74e1a21265f
children a63278c25c40
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1 using Test
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2
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3 using Sbplib.SbpOperators
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4 using Sbplib.Grids
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5 using Sbplib.LazyTensors
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7 using StaticArrays
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8
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9 @testset "Laplace" begin
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10 # Default stencils (4th order)
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11 operator_path = sbp_operators_path()*"standard_diagonal.toml"
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12 stencil_set = read_stencil_set(operator_path; order=4)
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13 g_1D = equidistant_grid(0.0, 1., 101)
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14 g_3D = equidistant_grid((0.0, -1.0, 0.0), (1., 1., 1.), 51, 101, 52)
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16 @testset "Constructors" begin
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17 @testset "1D" begin
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18 @test Laplace(g_1D, stencil_set) == Laplace(laplace(g_1D, stencil_set), stencil_set)
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19 @test Laplace(g_1D, stencil_set) isa LazyTensor{Float64,1,1}
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20 end
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21 @testset "3D" begin
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22 @test Laplace(g_3D, stencil_set) == Laplace(laplace(g_3D, stencil_set),stencil_set)
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23 @test Laplace(g_3D, stencil_set) isa LazyTensor{Float64,3,3}
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24 end
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25 end
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27 # Exact differentiation is measured point-wise. In other cases
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28 # the error is measured in the l2-norm.
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29 @testset "Accuracy" begin
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30 l2(v) = sqrt(prod(spacing.(g_3D.grids))*sum(v.^2));
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31 polynomials = ()
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32 maxOrder = 4;
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33 for i = 0:maxOrder-1
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34 f_i(x,y,z) = 1/factorial(i)*(y^i + x^i + z^i)
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35 polynomials = (polynomials...,eval_on(g_3D,f_i))
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36 end
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37 # v = eval_on(g_3D, (x,y,z) -> sin(x) + cos(y) + exp(z))
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38 # Δv = eval_on(g_3D,(x,y,z) -> -sin(x) - cos(y) + exp(z))
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40 v = eval_on(g_3D, x̄ -> sin(x̄[1]) + cos(x̄[2]) + exp(x̄[3]))
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41 Δv = eval_on(g_3D, x̄ -> -sin(x̄[1]) - cos(x̄[2]) + exp(x̄[3]))
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42 @inferred v[1,2,3]
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44 # 2nd order interior stencil, 1st order boundary stencil,
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45 # implies that L*v should be exact for binomials up to order 2.
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46 @testset "2nd order" begin
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47 stencil_set = read_stencil_set(operator_path; order=2)
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48 Δ = Laplace(g_3D, stencil_set)
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49 @test Δ*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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50 @test Δ*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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51 @test Δ*polynomials[3] ≈ polynomials[1] atol = 5e-9
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52 @test Δ*v ≈ Δv rtol = 5e-2 norm = l2
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53 end
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54
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55 # 4th order interior stencil, 2nd order boundary stencil,
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56 # implies that L*v should be exact for binomials up to order 3.
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57 @testset "4th order" begin
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58 stencil_set = read_stencil_set(operator_path; order=4)
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59 Δ = Laplace(g_3D, stencil_set)
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60 # NOTE: high tolerances for checking the "exact" differentiation
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61 # due to accumulation of round-off errors/cancellation errors?
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62 @test Δ*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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63 @test Δ*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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64 @test Δ*polynomials[3] ≈ polynomials[1] atol = 5e-9
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65 @test Δ*polynomials[4] ≈ polynomials[2] atol = 5e-9
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66 @test Δ*v ≈ Δv rtol = 5e-4 norm = l2
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67 end
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68 end
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69 end
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70
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71 @testset "laplace" begin
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72 operator_path = sbp_operators_path()*"standard_diagonal.toml"
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73 stencil_set = read_stencil_set(operator_path; order=4)
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74 g_1D = equidistant_grid(0.0, 1., 101)
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75 g_3D = equidistant_grid((0.0, -1.0, 0.0), (1., 1., 1.), 51, 101, 52)
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76
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77 @testset "EquidistantGrid" begin
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78 Δ = laplace(g_1D, stencil_set)
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79 @test Δ == second_derivative(g_1D, stencil_set)
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80 @test Δ isa LazyTensor{Float64,1,1}
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81 end
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82 @testset "TensorGrid" begin
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83 Δ = laplace(g_3D, stencil_set)
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84 @test Δ isa LazyTensor{Float64,3,3}
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85 Dxx = second_derivative(g_3D, stencil_set, 1)
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86 Dyy = second_derivative(g_3D, stencil_set, 2)
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87 Dzz = second_derivative(g_3D, stencil_set, 3)
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88 @test Δ == Dxx + Dyy + Dzz
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89 @test Δ isa LazyTensor{Float64,3,3}
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90 end
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91
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92 @testset "MappedGrid" begin
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93 c = Chart(unitsquare()) do (ξ,η)
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94 @SVector[2ξ + η*(1-η), 3η+(1+η/2)*ξ^2]
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95 end
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96 Grids.jacobian(c::typeof(c), (ξ,η)) = @SMatrix[2 1-2η; (2+η)*ξ 3+ξ^2/2]
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97
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98 g = equidistant_grid(c, 30,30)
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99
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100 @test laplace(g, stencil_set) isa LazyTensor{<:Any,2,2}
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101
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102 f((x,y)) = sin(4(x + y))
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103 Δf((x,y)) = -16sin(4(x + y))
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104 gf = map(f,g)
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105
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106 Δ = laplace(g, stencil_set)
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107
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108 @test collect(Δ*gf) isa Array{<:Any,2}
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109 @test Δ*gf ≈ map(Δf, g)
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110 end
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111 end
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112
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113 @testset "sat_tensors" begin
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114 # TODO: The following tests should be implemented
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115 # 1. Symmetry D'H == H'D (test_broken below)
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116 # 2. Test eigenvalues of and/or solution to Poisson
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117 # 3. Test tuning of Dirichlet conditions
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118 #
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119 # These tests are likely easiest to implement once
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120 # we have support for generating matrices from tensors.
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121
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122 operator_path = sbp_operators_path()*"standard_diagonal.toml"
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123 orders = (2,4)
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124 tols = (5e-2,5e-4)
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125 sz = (201,401)
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126 g = equidistant_grid((0.,0.), (1.,1.), sz...)
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127
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128 # Verify implementation of sat_tensors by testing accuracy and symmetry (TODO)
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129 # of the operator D = Δ + SAT, where SAT is the tensor composition of the
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130 # operators from sat_tensor. Note that SAT*u should approximate 0 for the
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131 # conditions chosen.
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132
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133 @testset "Dirichlet" begin
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134 for (o, tol) ∈ zip(orders,tols)
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135 stencil_set = read_stencil_set(operator_path; order=o)
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136 Δ = Laplace(g, stencil_set)
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137 H = inner_product(g, stencil_set)
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138 u = collect(eval_on(g, (x,y) -> sin(π*x)sin(2*π*y)))
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139 Δu = collect(eval_on(g, (x,y) -> -5*π^2*sin(π*x)sin(2*π*y)))
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140 D = Δ
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141 for id ∈ boundary_identifiers(g)
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142 D = D + foldl(∘, sat_tensors(Δ, g, DirichletCondition(0., id)))
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143 end
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144 e = D*u .- Δu
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145 # Accuracy
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146 @test sqrt(sum(H*e.^2)) ≈ 0 atol = tol
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147 # Symmetry
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148 r = randn(size(u))
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149 @test_broken (D'∘H - H∘D)*r .≈ 0 atol = 1e-13 # TODO: Need to implement apply_transpose for D.
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150 end
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151 end
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152
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153 @testset "Neumann" begin
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154 @testset "Dirichlet" begin
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155 for (o, tol) ∈ zip(orders,tols)
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156 stencil_set = read_stencil_set(operator_path; order=o)
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157 Δ = Laplace(g, stencil_set)
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158 H = inner_product(g, stencil_set)
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159 u = collect(eval_on(g, (x,y) -> cos(π*x)cos(2*π*y)))
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160 Δu = collect(eval_on(g, (x,y) -> -5*π^2*cos(π*x)cos(2*π*y)))
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161 D = Δ
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162 for id ∈ boundary_identifiers(g)
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163 D = D + foldl(∘, sat_tensors(Δ, g, NeumannCondition(0., id)))
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164 end
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165 e = D*u .- Δu
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166 # Accuracy
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167 @test sqrt(sum(H*e.^2)) ≈ 0 atol = tol
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168 # Symmetry
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169 r = randn(size(u))
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170 @test_broken (D'∘H - H∘D)*r .≈ 0 atol = 1e-13 # TODO: Need to implement apply_transpose for D.
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171 end
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172 end
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173 end
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174 end
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175