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annotate DiffOps/test/runtests.jl @ 282:ce6a2f3f732a boundary_conditions

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Make Laplace a TensorOperator and add tests. NOTE: Two of the tests for Laplace2D are currently failing.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 09 Jan 2020 10:54:24 +0100
parents f1e90a92ad74
children 12a12a5cd973
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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((21,42), (0.0, 0.0), (Lx,Ly))
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13 L = Laplace(g, 1., op)
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14
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15 f0(x::Float64,y::Float64) = 2.
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16 f1(x::Float64,y::Float64) = x+y
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17 f2(x::Float64,y::Float64) = 1/2*x^2 + 1/2*y^2
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18 f3(x::Float64,y::Float64) = 1/6*x^3 + 1/6*y^3
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19 f4(x::Float64,y::Float64) = 1/24*x^4 + 1/24*y^4
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20 f5(x::Float64,y::Float64) = x^5 + 2*y^3 + 3/2*x^2 + y + 7
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21 f5ₓₓ(x::Float64,y::Float64) = 20*x^3 + 12*y + 3
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22
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23 v0 = evalOn(g,f0)
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24 v1 = evalOn(g,f1)
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25 v2 = evalOn(g,f2)
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26 v3 = evalOn(g,f3)
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27 v4 = evalOn(g,f4)
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28 v5 = evalOn(g,f5)
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29 v5ₓₓ = evalOn(g,f5ₓₓ)
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31 @test L isa TensorOperator{T,2} where T
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32 @test L' isa TensorMapping{T,2,2} where T
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33 # TODO: Should perhaps set tolerance level for isapporx instead?
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34 equalitytol = 0.5*1e-11
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35 accuracytol = 1e-4
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36 @test all(collect(L*v0) .<= equalitytol)
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37 @test all(collect(L*v1) .<= equalitytol)
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38 @test all(collect(L*v2) .≈ v0) # Seems to be more accurate
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39 @test all((collect(L*v3) - v1) .<= equalitytol)
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40 @show maximum(abs.(collect(L*v4) - v2))
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41 @show maximum(abs.(collect(L*v5) - v5ₓₓ))
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42 @test_broken all((collect(L*v4) - v2) .<= accuracytol) #TODO: Should be equality?
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43 @test_broken all((collect(L*v5) - v5ₓₓ) .<= accuracytol) #TODO: This is just wrong
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44 end
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46 @testset "Quadrature" begin
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47 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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48 Lx = 2.3
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49 Ly = 5.2
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50 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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51 H = Quadrature(op,g)
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52 v = ones(Float64, size(g))
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53
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54 @test H isa TensorOperator{T,2} where T
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55 @test H' isa TensorMapping{T,2,2} where T
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56 @test sum(collect(H*v)) ≈ (Lx*Ly)
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57 @test collect(H*v) == collect(H'*v)
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58 end
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59
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60 @testset "InverseQuadrature" begin
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61 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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62 Lx = 7.3
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63 Ly = 8.2
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64 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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65 H = Quadrature(op,g)
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66 Hinv = InverseQuadrature(op,g)
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67 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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69 @test Hinv isa TensorOperator{T,2} where T
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70 @test Hinv' isa TensorMapping{T,2,2} where T
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71 @test collect(Hinv*H*v) ≈ v
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72 @test collect(Hinv*v) == collect(Hinv'*v)
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73 end
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74
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75 @testset "BoundaryValue" 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 g = EquidistantGrid((4,5), (0.0, 0.0), (1.0,1.0))
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78
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79 e_w = BoundaryValue(op, g, CartesianBoundary{1,Lower}())
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80 e_e = BoundaryValue(op, g, CartesianBoundary{1,Upper}())
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81 e_s = BoundaryValue(op, g, CartesianBoundary{2,Lower}())
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82 e_n = BoundaryValue(op, g, CartesianBoundary{2,Upper}())
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83
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84 v = zeros(Float64, 4, 5)
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85 v[:,5] = [1, 2, 3,4]
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86 v[:,4] = [1, 2, 3,4]
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87 v[:,3] = [4, 5, 6, 7]
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88 v[:,2] = [7, 8, 9, 10]
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89 v[:,1] = [10, 11, 12, 13]
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90
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91 @test e_w isa TensorMapping{T,2,1} where T
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92 @test e_w' isa TensorMapping{T,1,2} where T
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93
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94 @test domain_size(e_w, (3,2)) == (2,)
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95 @test domain_size(e_e, (3,2)) == (2,)
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96 @test domain_size(e_s, (3,2)) == (3,)
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97 @test domain_size(e_n, (3,2)) == (3,)
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98
239
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99 @test size(e_w'*v) == (5,)
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100 @test size(e_e'*v) == (5,)
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101 @test size(e_s'*v) == (4,)
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102 @test size(e_n'*v) == (4,)
235
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103
239
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104 @test collect(e_w'*v) == [10,7,4,1.0,1]
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105 @test collect(e_e'*v) == [13,10,7,4,4.0]
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106 @test collect(e_s'*v) == [10,11,12,13.0]
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107 @test collect(e_n'*v) == [1,2,3,4.0]
235
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108
242
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109 g_x = [1,2,3,4.0]
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110 g_y = [5,4,3,2,1.0]
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111
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112 G_w = zeros(Float64, (4,5))
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113 G_w[1,:] = g_y
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114
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115 G_e = zeros(Float64, (4,5))
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116 G_e[4,:] = g_y
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117
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118 G_s = zeros(Float64, (4,5))
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119 G_s[:,1] = g_x
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120
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121 G_n = zeros(Float64, (4,5))
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122 G_n[:,5] = g_x
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123
244
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124 @test size(e_w*g_y) == (4,5)
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125 @test size(e_e*g_y) == (4,5)
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126 @test size(e_s*g_x) == (4,5)
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127 @test size(e_n*g_x) == (4,5)
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128
242
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129 @test collect(e_w*g_y) == G_w
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130 @test collect(e_e*g_y) == G_e
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131 @test collect(e_s*g_x) == G_s
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132 @test collect(e_n*g_x) == G_n
244
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133 end
242
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134
244
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135 @testset "NormalDerivative" begin
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136 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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137 g = EquidistantGrid((5,6), (0.0, 0.0), (4.0,5.0))
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138
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139 d_w = NormalDerivative(op, g, CartesianBoundary{1,Lower}())
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140 d_e = NormalDerivative(op, g, CartesianBoundary{1,Upper}())
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141 d_s = NormalDerivative(op, g, CartesianBoundary{2,Lower}())
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142 d_n = NormalDerivative(op, g, CartesianBoundary{2,Upper}())
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143
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144
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145 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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146 v∂x = evalOn(g, (x,y)-> 2*x + y)
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147 v∂y = evalOn(g, (x,y)-> 2*(y-1) + x)
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148
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149 @test d_w isa TensorMapping{T,2,1} where T
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150 @test d_w' isa TensorMapping{T,1,2} where T
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151
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152 @test domain_size(d_w, (3,2)) == (2,)
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153 @test domain_size(d_e, (3,2)) == (2,)
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154 @test domain_size(d_s, (3,2)) == (3,)
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155 @test domain_size(d_n, (3,2)) == (3,)
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156
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157 @test size(d_w'*v) == (6,)
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158 @test size(d_e'*v) == (6,)
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159 @test size(d_s'*v) == (5,)
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160 @test size(d_n'*v) == (5,)
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161
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162 @test collect(d_w'*v) ≈ v∂x[1,:]
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163 @test collect(d_e'*v) ≈ v∂x[5,:]
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164 @test collect(d_s'*v) ≈ v∂y[:,1]
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165 @test collect(d_n'*v) ≈ v∂y[:,6]
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166
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167
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168 d_x_l = zeros(Float64, 5)
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169 d_x_u = zeros(Float64, 5)
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170 for i ∈ eachindex(d_x_l)
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171 d_x_l[i] = op.dClosure[i-1]
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172 d_x_u[i] = -op.dClosure[length(d_x_u)-i]
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173 end
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174
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175 d_y_l = zeros(Float64, 6)
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176 d_y_u = zeros(Float64, 6)
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177 for i ∈ eachindex(d_y_l)
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178 d_y_l[i] = op.dClosure[i-1]
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179 d_y_u[i] = -op.dClosure[length(d_y_u)-i]
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180 end
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181
282
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182 function prod_matrix(x,y)
244
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183 G = zeros(Float64, length(x), length(y))
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184 for I ∈ CartesianIndices(G)
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185 G[I] = x[I[1]]*y[I[2]]
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186 end
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187
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188 return G
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189 end
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190
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191 g_x = [1,2,3,4.0,5]
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192 g_y = [5,4,3,2,1.0,11]
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193
282
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194 G_w = prod_matrix(d_x_l, g_y)
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195 G_e = prod_matrix(d_x_u, g_y)
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196 G_s = prod_matrix(g_x, d_y_l)
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197 G_n = prod_matrix(g_x, d_y_u)
244
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198
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199
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200 @test size(d_w*g_y) == (5,6)
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201 @test size(d_e*g_y) == (5,6)
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202 @test size(d_s*g_x) == (5,6)
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203 @test size(d_n*g_x) == (5,6)
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204
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205 @test collect(d_w*g_y) ≈ G_w
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206 @test collect(d_e*g_y) ≈ G_e
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207 @test collect(d_s*g_x) ≈ G_s
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208 @test collect(d_n*g_x) ≈ G_n
235
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209 end
259
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210
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211 @testset "BoundaryQuadrature" begin
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212 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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213 g = EquidistantGrid((10,11), (0.0, 0.0), (1.0,1.0))
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214
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215 H_w = BoundaryQuadrature(op, g, CartesianBoundary{1,Lower}())
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216 H_e = BoundaryQuadrature(op, g, CartesianBoundary{1,Upper}())
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217 H_s = BoundaryQuadrature(op, g, CartesianBoundary{2,Lower}())
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218 H_n = BoundaryQuadrature(op, g, CartesianBoundary{2,Upper}())
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219
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220 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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221
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222 function get_quadrature(N)
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223 qc = op.quadratureClosure
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224 q = (qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
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225 @assert length(q) == N
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226 return q
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227 end
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228
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229 v_w = v[1,:]
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230 v_e = v[10,:]
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231 v_s = v[:,1]
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232 v_n = v[:,11]
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233
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234 q_x = spacing(g)[1].*get_quadrature(10)
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235 q_y = spacing(g)[2].*get_quadrature(11)
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236
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237 @test H_w isa TensorOperator{T,1} where T
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238
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239 @test domain_size(H_w, (3,)) == (3,)
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240 @test domain_size(H_n, (3,)) == (3,)
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241
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242 @test range_size(H_w, (3,)) == (3,)
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243 @test range_size(H_n, (3,)) == (3,)
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244
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245 @test size(H_w*v_w) == (11,)
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246 @test size(H_e*v_e) == (11,)
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247 @test size(H_s*v_s) == (10,)
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248 @test size(H_n*v_n) == (10,)
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249
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250 @test collect(H_w*v_w) ≈ q_y.*v_w
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251 @test collect(H_e*v_e) ≈ q_y.*v_e
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252 @test collect(H_s*v_s) ≈ q_x.*v_s
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253 @test collect(H_n*v_n) ≈ q_x.*v_n
262
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254
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255 @test collect(H_w'*v_w) == collect(H_w'*v_w)
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256 @test collect(H_e'*v_e) == collect(H_e'*v_e)
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257 @test collect(H_s'*v_s) == collect(H_s'*v_s)
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258 @test collect(H_n'*v_n) == collect(H_n'*v_n)
259
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259 end