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annotate DiffOps/test/runtests.jl @ 284:0b8e041a1873 boundary_conditions

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Change how range_size and domain_size work with BoundaryValues and NormalDerivative Also add a whole bunch of questions and todos
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 18 Jun 2020 22:07:10 +0200
parents 12a12a5cd973
children e21dcda55163
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1 using Test
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2 using DiffOps
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3 using Grids
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4 using SbpOperators
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5 using RegionIndices
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6 using LazyTensors
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7
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8 @testset "Laplace2D" begin
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9 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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10 Lx = 3.5
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11 Ly = 7.2
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12 g = EquidistantGrid((42,41), (0.0, 0.0), (Lx,Ly))
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13 L = Laplace(g, 1., op)
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14 H = quadrature(L)
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16 f0(x::Float64,y::Float64) = 2.
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17 f1(x::Float64,y::Float64) = x+y
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18 f2(x::Float64,y::Float64) = 1/2*x^2 + 1/2*y^2
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19 f3(x::Float64,y::Float64) = 1/6*x^3 + 1/6*y^3
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20 f4(x::Float64,y::Float64) = 1/24*x^4 + 1/24*y^4
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21 f5(x::Float64,y::Float64) = sin(x) + cos(y)
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22 f5ₓₓ(x::Float64,y::Float64) = -f5(x,y)
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24 v0 = evalOn(g,f0)
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25 v1 = evalOn(g,f1)
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26 v2 = evalOn(g,f2)
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27 v3 = evalOn(g,f3)
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28 v4 = evalOn(g,f4)
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29 v5 = evalOn(g,f5)
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30 v5ₓₓ = evalOn(g,f5ₓₓ)
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31
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32 @test L isa TensorOperator{T,2} where T
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33 @test L' isa TensorMapping{T,2,2} where T
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34
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35 # TODO: Should perhaps set tolerance level for isapporx instead?
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36 # Are these tolerance levels resonable or should tests be constructed
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37 # differently?
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38 equalitytol = 0.5*1e-10
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39 accuracytol = 0.5*1e-3
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40 # 4th order interior stencil, 2nd order boundary stencil,
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41 # implies that L*v should be exact for v - monomial up to order 3.
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42 # Exact differentiation is measured point-wise. For other grid functions
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43 # the error is measured in the H-norm.
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44 @test all(abs.(collect(L*v0)) .<= equalitytol)
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45 @test all(abs.(collect(L*v1)) .<= equalitytol)
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46 @test all(collect(L*v2) .≈ v0) # Seems to be more accurate
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47 @test all(abs.((collect(L*v3) - v1)) .<= equalitytol)
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48 e4 = collect(L*v4) - v2
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49 e5 = collect(L*v5) - v5ₓₓ
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50 @test sum(collect(H*e4.^2)) <= accuracytol
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51 @test sum(collect(H*e5.^2)) <= accuracytol
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52 end
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53
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54 @testset "Quadrature" begin
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55 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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56 Lx = 2.3
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57 Ly = 5.2
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58 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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59 H = Quadrature(op,g)
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60 v = ones(Float64, size(g))
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61
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62 @test H isa TensorOperator{T,2} where T
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63 @test H' isa TensorMapping{T,2,2} where T
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64 @test sum(collect(H*v)) ≈ (Lx*Ly)
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65 @test collect(H*v) == collect(H'*v)
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66 end
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67
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68 @testset "InverseQuadrature" begin
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69 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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70 Lx = 7.3
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71 Ly = 8.2
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72 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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73 H = Quadrature(op,g)
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74 Hinv = InverseQuadrature(op,g)
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75 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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76
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77 @test Hinv isa TensorOperator{T,2} where T
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78 @test Hinv' isa TensorMapping{T,2,2} where T
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79 @test collect(Hinv*H*v) ≈ v
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80 @test collect(Hinv*v) == collect(Hinv'*v)
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81 end
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82
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83 @testset "BoundaryValue" begin
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84 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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85 g = EquidistantGrid((4,5), (0.0, 0.0), (1.0,1.0))
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86
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87 e_w = BoundaryValue(op, g, CartesianBoundary{1,Lower}())
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88 e_e = BoundaryValue(op, g, CartesianBoundary{1,Upper}())
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89 e_s = BoundaryValue(op, g, CartesianBoundary{2,Lower}())
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90 e_n = BoundaryValue(op, g, CartesianBoundary{2,Upper}())
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91
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92 v = zeros(Float64, 4, 5)
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93 v[:,5] = [1, 2, 3,4]
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94 v[:,4] = [1, 2, 3,4]
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95 v[:,3] = [4, 5, 6, 7]
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96 v[:,2] = [7, 8, 9, 10]
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97 v[:,1] = [10, 11, 12, 13]
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98
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99 @test e_w isa TensorMapping{T,2,1} where T
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100 @test e_w' isa TensorMapping{T,1,2} where T
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101
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102 @test domain_size(e_w, (3,2)) == (2,)
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103 @test domain_size(e_e, (3,2)) == (2,)
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104 @test domain_size(e_s, (3,2)) == (3,)
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105 @test domain_size(e_n, (3,2)) == (3,)
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106
239
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107 @test size(e_w'*v) == (5,)
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108 @test size(e_e'*v) == (5,)
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109 @test size(e_s'*v) == (4,)
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110 @test size(e_n'*v) == (4,)
235
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111
239
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112 @test collect(e_w'*v) == [10,7,4,1.0,1]
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113 @test collect(e_e'*v) == [13,10,7,4,4.0]
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114 @test collect(e_s'*v) == [10,11,12,13.0]
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115 @test collect(e_n'*v) == [1,2,3,4.0]
235
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116
242
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117 g_x = [1,2,3,4.0]
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118 g_y = [5,4,3,2,1.0]
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119
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120 G_w = zeros(Float64, (4,5))
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121 G_w[1,:] = g_y
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122
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123 G_e = zeros(Float64, (4,5))
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124 G_e[4,:] = g_y
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125
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126 G_s = zeros(Float64, (4,5))
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127 G_s[:,1] = g_x
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128
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129 G_n = zeros(Float64, (4,5))
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130 G_n[:,5] = g_x
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131
284
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132 @test size(e_w*g_y) === (missing,5)
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133 @test size(e_e*g_y) === (missing,5)
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134 @test size(e_s*g_x) === (4,missing)
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135 @test size(e_n*g_x) === (4,missing)
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136
284
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137 # These tests should be moved to where they are possible (i.e we know what the grid should be)
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138 @test_broken collect(e_w*g_y) == G_w
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139 @test_broken collect(e_e*g_y) == G_e
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140 @test_broken collect(e_s*g_x) == G_s
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141 @test_broken collect(e_n*g_x) == G_n
244
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142 end
242
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143
244
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144 @testset "NormalDerivative" begin
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145 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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146 g = EquidistantGrid((5,6), (0.0, 0.0), (4.0,5.0))
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147
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148 d_w = NormalDerivative(op, g, CartesianBoundary{1,Lower}())
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149 d_e = NormalDerivative(op, g, CartesianBoundary{1,Upper}())
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150 d_s = NormalDerivative(op, g, CartesianBoundary{2,Lower}())
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151 d_n = NormalDerivative(op, g, CartesianBoundary{2,Upper}())
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152
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153
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154 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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155 v∂x = evalOn(g, (x,y)-> 2*x + y)
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156 v∂y = evalOn(g, (x,y)-> 2*(y-1) + x)
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157
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158 @test d_w isa TensorMapping{T,2,1} where T
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159 @test d_w' isa TensorMapping{T,1,2} where T
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160
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161 @test domain_size(d_w, (3,2)) == (2,)
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162 @test domain_size(d_e, (3,2)) == (2,)
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163 @test domain_size(d_s, (3,2)) == (3,)
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164 @test domain_size(d_n, (3,2)) == (3,)
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165
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166 @test size(d_w'*v) == (6,)
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167 @test size(d_e'*v) == (6,)
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168 @test size(d_s'*v) == (5,)
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169 @test size(d_n'*v) == (5,)
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170
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171 @test collect(d_w'*v) ≈ v∂x[1,:]
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172 @test collect(d_e'*v) ≈ v∂x[5,:]
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173 @test collect(d_s'*v) ≈ v∂y[:,1]
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174 @test collect(d_n'*v) ≈ v∂y[:,6]
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175
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176
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177 d_x_l = zeros(Float64, 5)
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178 d_x_u = zeros(Float64, 5)
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179 for i ∈ eachindex(d_x_l)
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180 d_x_l[i] = op.dClosure[i-1]
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181 d_x_u[i] = -op.dClosure[length(d_x_u)-i]
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182 end
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183
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184 d_y_l = zeros(Float64, 6)
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185 d_y_u = zeros(Float64, 6)
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186 for i ∈ eachindex(d_y_l)
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187 d_y_l[i] = op.dClosure[i-1]
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188 d_y_u[i] = -op.dClosure[length(d_y_u)-i]
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189 end
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190
282
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191 function prod_matrix(x,y)
244
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192 G = zeros(Float64, length(x), length(y))
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193 for I ∈ CartesianIndices(G)
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194 G[I] = x[I[1]]*y[I[2]]
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195 end
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196
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197 return G
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198 end
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199
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200 g_x = [1,2,3,4.0,5]
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201 g_y = [5,4,3,2,1.0,11]
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202
282
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203 G_w = prod_matrix(d_x_l, g_y)
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204 G_e = prod_matrix(d_x_u, g_y)
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205 G_s = prod_matrix(g_x, d_y_l)
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206 G_n = prod_matrix(g_x, d_y_u)
244
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207
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208
284
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209 @test size(d_w*g_y) === (missing,6)
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210 @test size(d_e*g_y) === (missing,6)
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211 @test size(d_s*g_x) === (5,missing)
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212 @test size(d_n*g_x) === (5,missing)
244
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213
284
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214 # These tests should be moved to where they are possible (i.e we know what the grid should be)
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215 @test_broken collect(d_w*g_y) ≈ G_w
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216 @test_broken collect(d_e*g_y) ≈ G_e
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217 @test_broken collect(d_s*g_x) ≈ G_s
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218 @test_broken collect(d_n*g_x) ≈ G_n
235
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219 end
259
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220
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221 @testset "BoundaryQuadrature" begin
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222 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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223 g = EquidistantGrid((10,11), (0.0, 0.0), (1.0,1.0))
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224
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225 H_w = BoundaryQuadrature(op, g, CartesianBoundary{1,Lower}())
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226 H_e = BoundaryQuadrature(op, g, CartesianBoundary{1,Upper}())
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227 H_s = BoundaryQuadrature(op, g, CartesianBoundary{2,Lower}())
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228 H_n = BoundaryQuadrature(op, g, CartesianBoundary{2,Upper}())
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229
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230 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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231
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232 function get_quadrature(N)
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233 qc = op.quadratureClosure
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234 q = (qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
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235 @assert length(q) == N
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236 return q
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237 end
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238
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239 v_w = v[1,:]
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240 v_e = v[10,:]
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241 v_s = v[:,1]
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242 v_n = v[:,11]
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243
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244 q_x = spacing(g)[1].*get_quadrature(10)
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245 q_y = spacing(g)[2].*get_quadrature(11)
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246
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247 @test H_w isa TensorOperator{T,1} where T
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248
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249 @test domain_size(H_w, (3,)) == (3,)
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250 @test domain_size(H_n, (3,)) == (3,)
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251
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252 @test range_size(H_w, (3,)) == (3,)
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253 @test range_size(H_n, (3,)) == (3,)
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254
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255 @test size(H_w*v_w) == (11,)
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256 @test size(H_e*v_e) == (11,)
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257 @test size(H_s*v_s) == (10,)
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258 @test size(H_n*v_n) == (10,)
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259
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260 @test collect(H_w*v_w) ≈ q_y.*v_w
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261 @test collect(H_e*v_e) ≈ q_y.*v_e
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262 @test collect(H_s*v_s) ≈ q_x.*v_s
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263 @test collect(H_n*v_n) ≈ q_x.*v_n
262
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264
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265 @test collect(H_w'*v_w) == collect(H_w'*v_w)
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266 @test collect(H_e'*v_e) == collect(H_e'*v_e)
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267 @test collect(H_s'*v_s) == collect(H_s'*v_s)
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268 @test collect(H_n'*v_n) == collect(H_n'*v_n)
259
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269 end