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annotate test/testSbpOperators.jl @ 378:946516954c85

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Use concrete types in LazyTensorApplication
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 30 Sep 2020 21:25:50 +0200
parents 0844069ab5ff
children de4746d6d126
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1 using Test
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2 using Sbplib.SbpOperators
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3 using Sbplib.Grids
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4 using Sbplib.RegionIndices
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5 using Sbplib.LazyTensors
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6
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7 @testset "SbpOperators" begin
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8
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9 # @testset "apply_quadrature" begin
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10 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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11 # h = 0.5
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12 #
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13 # @test apply_quadrature(op, h, 1.0, 10, 100) == h
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14 #
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15 # N = 10
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16 # qc = op.quadratureClosure
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17 # q = h.*(qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
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18 # @assert length(q) == N
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19 #
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20 # for i ∈ 1:N
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21 # @test apply_quadrature(op, h, 1.0, i, N) == q[i]
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22 # end
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23 #
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24 # v = [2.,3.,2.,4.,5.,4.,3.,4.,5.,4.5]
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25 # for i ∈ 1:N
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26 # @test apply_quadrature(op, h, v[i], i, N) == q[i]*v[i]
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27 # end
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28 # end
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30 @testset "SecondDerivative" begin
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31 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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32 L = 3.5
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33 g = EquidistantGrid((101,), (0.0,), (L,))
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34 h_inv = inverse_spacing(g)
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35 h = 1/h_inv[1];
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36 Dₓₓ = SecondDerivative(g,op.innerStencil,op.closureStencils)
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38 f0(x::Float64) = 1.
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39 f1(x::Float64) = x
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40 f2(x::Float64) = 1/2*x^2
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41 f3(x::Float64) = 1/6*x^3
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42 f4(x::Float64) = 1/24*x^4
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43 f5(x::Float64) = sin(x)
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44 f5ₓₓ(x::Float64) = -f5(x)
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46 v0 = evalOn(g,f0)
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47 v1 = evalOn(g,f1)
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48 v2 = evalOn(g,f2)
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49 v3 = evalOn(g,f3)
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50 v4 = evalOn(g,f4)
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51 v5 = evalOn(g,f5)
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53 @test Dₓₓ isa TensorMapping{T,1,1} where T
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54 @test Dₓₓ' isa TensorMapping{T,1,1} where T
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55
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56 # TODO: Should perhaps set tolerance level for isapporx instead?
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57 # Are these tolerance levels resonable or should tests be constructed
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58 # differently?
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59 equalitytol = 0.5*1e-10
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60 accuracytol = 0.5*1e-3
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61 # 4th order interior stencil, 2nd order boundary stencil,
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62 # implies that L*v should be exact for v - monomial up to order 3.
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63 # Exact differentiation is measured point-wise. For other grid functions
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64 # the error is measured in the l2-norm.
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65 @test all(abs.(collect(Dₓₓ*v0)) .<= equalitytol)
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66 @test all(abs.(collect(Dₓₓ*v1)) .<= equalitytol)
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67 @test all(abs.((collect(Dₓₓ*v2) - v0)) .<= equalitytol)
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68 @test all(abs.((collect(Dₓₓ*v3) - v1)) .<= equalitytol)
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69 e4 = collect(Dₓₓ*v4) - v2
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70 e5 = collect(Dₓₓ*v5) + v5
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71 @test sqrt(h*sum(collect(e4.^2))) <= accuracytol
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72 @test sqrt(h*sum(collect(e5.^2))) <= accuracytol
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73 end
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74
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75 @testset "Laplace2D" begin
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76 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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77 Lx = 1.5
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78 Ly = 3.2
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79 g = EquidistantGrid((102,131), (0.0, 0.0), (Lx,Ly))
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80 L = Laplace(g, op.innerStencil, op.closureStencils)
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81
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82
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83 f0(x::Float64,y::Float64) = 2.
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84 f1(x::Float64,y::Float64) = x+y
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85 f2(x::Float64,y::Float64) = 1/2*x^2 + 1/2*y^2
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86 f3(x::Float64,y::Float64) = 1/6*x^3 + 1/6*y^3
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87 f4(x::Float64,y::Float64) = 1/24*x^4 + 1/24*y^4
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88 f5(x::Float64,y::Float64) = sin(x) + cos(y)
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89 f5ₓₓ(x::Float64,y::Float64) = -f5(x,y)
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90
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91 v0 = evalOn(g,f0)
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92 v1 = evalOn(g,f1)
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93 v2 = evalOn(g,f2)
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94 v3 = evalOn(g,f3)
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95 v4 = evalOn(g,f4)
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96 v5 = evalOn(g,f5)
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97 v5ₓₓ = evalOn(g,f5ₓₓ)
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98
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99 @test L isa TensorMapping{T,2,2} where T
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100 @test L' isa TensorMapping{T,2,2} where T
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101
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102 # TODO: Should perhaps set tolerance level for isapporx instead?
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103 # Are these tolerance levels resonable or should tests be constructed
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104 # differently?
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105 equalitytol = 0.5*1e-10
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106 accuracytol = 0.5*1e-3
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107 # 4th order interior stencil, 2nd order boundary stencil,
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108 # implies that L*v should be exact for v - monomial up to order 3.
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109 # Exact differentiation is measured point-wise. For other grid functions
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110 # the error is measured in the H-norm.
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111 @test all(abs.(collect(L*v0)) .<= equalitytol)
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112 @test all(abs.(collect(L*v1)) .<= equalitytol)
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113 @test all(collect(L*v2) .≈ v0) # Seems to be more accurate
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114 @test all(abs.((collect(L*v3) - v1)) .<= equalitytol)
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115 e4 = collect(L*v4) - v2
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116 e5 = collect(L*v5) - v5ₓₓ
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117
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118 h = spacing(g)
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119 @test sqrt(prod(h)*sum(collect(e4.^2))) <= accuracytol
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120 @test sqrt(prod(h)*sum(collect(e5.^2))) <= accuracytol
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121 end
328
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122
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123 @testset "DiagonalInnerProduct" begin
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124 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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125 L = 2.3
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126 g = EquidistantGrid((77,), (0.0,), (L,))
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127 H = DiagonalInnerProduct(g,op.quadratureClosure)
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128 v = ones(Float64, size(g))
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129
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130 @test H isa TensorMapping{T,1,1} where T
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131 @test H' isa TensorMapping{T,1,1} where T
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132 @test sum(collect(H*v)) ≈ L
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133 @test collect(H*v) == collect(H'*v)
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134 end
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135
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136 @testset "Quadrature" begin
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137 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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138 Lx = 2.3
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139 Ly = 5.2
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140 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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141
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142 Q = Quadrature(g, op.quadratureClosure)
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143
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144 v = ones(Float64, size(g))
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145
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146 @test Q isa TensorMapping{T,2,2} where T
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147 @test Q' isa TensorMapping{T,2,2} where T
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148 @test sum(collect(Q*v)) ≈ (Lx*Ly)
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149 @test collect(Q*v) == collect(Q'*v)
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150 end
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151
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152 @testset "InverseDiagonalInnerProduct" begin
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153 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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154 L = 2.3
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155 g = EquidistantGrid((77,), (0.0,), (L,))
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156 H = DiagonalInnerProduct(g, op.quadratureClosure)
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157 Hi = InverseDiagonalInnerProduct(g,op.quadratureClosure)
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158 v = evalOn(g, x->sin(x))
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159
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160 @test Hi isa TensorMapping{T,1,1} where T
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161 @test Hi' isa TensorMapping{T,1,1} where T
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162 @test collect(Hi*H*v) ≈ v
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163 @test collect(Hi*v) == collect(Hi'*v)
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164 end
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165
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166 @testset "InverseQuadrature" begin
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167 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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168 Lx = 7.3
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169 Ly = 8.2
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170 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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171
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172 Q = Quadrature(g, op.quadratureClosure)
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173 Qinv = InverseQuadrature(g, op.quadratureClosure)
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174 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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175
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176 @test Qinv isa TensorMapping{T,2,2} where T
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177 @test Qinv' isa TensorMapping{T,2,2} where T
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178 @test collect(Qinv*(Q*v)) ≈ v
329
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179 @test collect(Qinv*v) == collect(Qinv'*v)
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180 end
314
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181 #
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182 # @testset "BoundaryValue" begin
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183 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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184 # g = EquidistantGrid((4,5), (0.0, 0.0), (1.0,1.0))
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185 #
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186 # e_w = BoundaryValue(op, g, CartesianBoundary{1,Lower}())
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187 # e_e = BoundaryValue(op, g, CartesianBoundary{1,Upper}())
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188 # e_s = BoundaryValue(op, g, CartesianBoundary{2,Lower}())
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189 # e_n = BoundaryValue(op, g, CartesianBoundary{2,Upper}())
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190 #
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191 # v = zeros(Float64, 4, 5)
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192 # v[:,5] = [1, 2, 3,4]
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193 # v[:,4] = [1, 2, 3,4]
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194 # v[:,3] = [4, 5, 6, 7]
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195 # v[:,2] = [7, 8, 9, 10]
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196 # v[:,1] = [10, 11, 12, 13]
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197 #
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198 # @test e_w isa TensorMapping{T,2,1} where T
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199 # @test e_w' isa TensorMapping{T,1,2} where T
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200 #
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201 # @test domain_size(e_w, (3,2)) == (2,)
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202 # @test domain_size(e_e, (3,2)) == (2,)
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203 # @test domain_size(e_s, (3,2)) == (3,)
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204 # @test domain_size(e_n, (3,2)) == (3,)
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205 #
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206 # @test size(e_w'*v) == (5,)
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207 # @test size(e_e'*v) == (5,)
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208 # @test size(e_s'*v) == (4,)
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209 # @test size(e_n'*v) == (4,)
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210 #
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211 # @test collect(e_w'*v) == [10,7,4,1.0,1]
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212 # @test collect(e_e'*v) == [13,10,7,4,4.0]
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213 # @test collect(e_s'*v) == [10,11,12,13.0]
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214 # @test collect(e_n'*v) == [1,2,3,4.0]
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215 #
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216 # g_x = [1,2,3,4.0]
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217 # g_y = [5,4,3,2,1.0]
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218 #
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219 # G_w = zeros(Float64, (4,5))
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220 # G_w[1,:] = g_y
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221 #
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222 # G_e = zeros(Float64, (4,5))
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223 # G_e[4,:] = g_y
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224 #
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225 # G_s = zeros(Float64, (4,5))
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226 # G_s[:,1] = g_x
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227 #
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228 # G_n = zeros(Float64, (4,5))
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229 # G_n[:,5] = g_x
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230 #
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231 # @test size(e_w*g_y) == (UnknownDim,5)
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232 # @test size(e_e*g_y) == (UnknownDim,5)
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233 # @test size(e_s*g_x) == (4,UnknownDim)
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234 # @test size(e_n*g_x) == (4,UnknownDim)
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235 #
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236 # # These tests should be moved to where they are possible (i.e we know what the grid should be)
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237 # @test_broken collect(e_w*g_y) == G_w
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238 # @test_broken collect(e_e*g_y) == G_e
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239 # @test_broken collect(e_s*g_x) == G_s
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240 # @test_broken collect(e_n*g_x) == G_n
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241 # end
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242 #
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243 # @testset "NormalDerivative" begin
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244 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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245 # g = EquidistantGrid((5,6), (0.0, 0.0), (4.0,5.0))
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246 #
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247 # d_w = NormalDerivative(op, g, CartesianBoundary{1,Lower}())
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248 # d_e = NormalDerivative(op, g, CartesianBoundary{1,Upper}())
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249 # d_s = NormalDerivative(op, g, CartesianBoundary{2,Lower}())
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250 # d_n = NormalDerivative(op, g, CartesianBoundary{2,Upper}())
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251 #
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252 #
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253 # v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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254 # v∂x = evalOn(g, (x,y)-> 2*x + y)
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255 # v∂y = evalOn(g, (x,y)-> 2*(y-1) + x)
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256 #
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257 # @test d_w isa TensorMapping{T,2,1} where T
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258 # @test d_w' isa TensorMapping{T,1,2} where T
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259 #
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260 # @test domain_size(d_w, (3,2)) == (2,)
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261 # @test domain_size(d_e, (3,2)) == (2,)
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262 # @test domain_size(d_s, (3,2)) == (3,)
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263 # @test domain_size(d_n, (3,2)) == (3,)
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264 #
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265 # @test size(d_w'*v) == (6,)
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266 # @test size(d_e'*v) == (6,)
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267 # @test size(d_s'*v) == (5,)
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268 # @test size(d_n'*v) == (5,)
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269 #
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270 # @test collect(d_w'*v) ≈ v∂x[1,:]
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271 # @test collect(d_e'*v) ≈ v∂x[5,:]
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272 # @test collect(d_s'*v) ≈ v∂y[:,1]
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273 # @test collect(d_n'*v) ≈ v∂y[:,6]
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274 #
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275 #
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276 # d_x_l = zeros(Float64, 5)
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277 # d_x_u = zeros(Float64, 5)
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278 # for i ∈ eachindex(d_x_l)
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279 # d_x_l[i] = op.dClosure[i-1]
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280 # d_x_u[i] = -op.dClosure[length(d_x_u)-i]
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281 # end
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282 #
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283 # d_y_l = zeros(Float64, 6)
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284 # d_y_u = zeros(Float64, 6)
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285 # for i ∈ eachindex(d_y_l)
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286 # d_y_l[i] = op.dClosure[i-1]
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287 # d_y_u[i] = -op.dClosure[length(d_y_u)-i]
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288 # end
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289 #
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290 # function prod_matrix(x,y)
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291 # G = zeros(Float64, length(x), length(y))
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292 # for I ∈ CartesianIndices(G)
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293 # G[I] = x[I[1]]*y[I[2]]
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294 # end
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295 #
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296 # return G
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297 # end
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298 #
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299 # g_x = [1,2,3,4.0,5]
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300 # g_y = [5,4,3,2,1.0,11]
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301 #
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302 # G_w = prod_matrix(d_x_l, g_y)
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303 # G_e = prod_matrix(d_x_u, g_y)
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304 # G_s = prod_matrix(g_x, d_y_l)
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305 # G_n = prod_matrix(g_x, d_y_u)
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306 #
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307 #
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308 # @test size(d_w*g_y) == (UnknownDim,6)
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309 # @test size(d_e*g_y) == (UnknownDim,6)
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310 # @test size(d_s*g_x) == (5,UnknownDim)
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311 # @test size(d_n*g_x) == (5,UnknownDim)
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312 #
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313 # # These tests should be moved to where they are possible (i.e we know what the grid should be)
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314 # @test_broken collect(d_w*g_y) ≈ G_w
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315 # @test_broken collect(d_e*g_y) ≈ G_e
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316 # @test_broken collect(d_s*g_x) ≈ G_s
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317 # @test_broken collect(d_n*g_x) ≈ G_n
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318 # end
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319 #
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320 # @testset "BoundaryQuadrature" begin
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321 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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322 # g = EquidistantGrid((10,11), (0.0, 0.0), (1.0,1.0))
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323 #
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324 # H_w = BoundaryQuadrature(op, g, CartesianBoundary{1,Lower}())
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325 # H_e = BoundaryQuadrature(op, g, CartesianBoundary{1,Upper}())
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326 # H_s = BoundaryQuadrature(op, g, CartesianBoundary{2,Lower}())
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327 # H_n = BoundaryQuadrature(op, g, CartesianBoundary{2,Upper}())
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328 #
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329 # v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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330 #
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331 # function get_quadrature(N)
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332 # qc = op.quadratureClosure
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333 # q = (qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
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334 # @assert length(q) == N
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335 # return q
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336 # end
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337 #
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338 # v_w = v[1,:]
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339 # v_e = v[10,:]
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340 # v_s = v[:,1]
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341 # v_n = v[:,11]
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342 #
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343 # q_x = spacing(g)[1].*get_quadrature(10)
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344 # q_y = spacing(g)[2].*get_quadrature(11)
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345 #
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346 # @test H_w isa TensorOperator{T,1} where T
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347 #
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348 # @test domain_size(H_w, (3,)) == (3,)
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349 # @test domain_size(H_n, (3,)) == (3,)
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350 #
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351 # @test range_size(H_w, (3,)) == (3,)
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352 # @test range_size(H_n, (3,)) == (3,)
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353 #
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354 # @test size(H_w*v_w) == (11,)
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355 # @test size(H_e*v_e) == (11,)
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356 # @test size(H_s*v_s) == (10,)
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357 # @test size(H_n*v_n) == (10,)
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358 #
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359 # @test collect(H_w*v_w) ≈ q_y.*v_w
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360 # @test collect(H_e*v_e) ≈ q_y.*v_e
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361 # @test collect(H_s*v_s) ≈ q_x.*v_s
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362 # @test collect(H_n*v_n) ≈ q_x.*v_n
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363 #
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364 # @test collect(H_w'*v_w) == collect(H_w'*v_w)
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365 # @test collect(H_e'*v_e) == collect(H_e'*v_e)
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366 # @test collect(H_s'*v_s) == collect(H_s'*v_s)
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367 # @test collect(H_n'*v_n) == collect(H_n'*v_n)
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368 # end
338
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369
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370 end