annotate test/testSbpOperators.jl @ 572:64f1b269e9fc feature/boundary_ops

Implement apply_transpose for different regions and remove boundschecks to simplify
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 01 Dec 2020 16:02:44 +0100
parents a8fe91861116
children 4e2490f568aa
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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 using LinearAlgebra
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7
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8 @testset "SbpOperators" begin
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9
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10 # @testset "apply_quadrature" begin
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11 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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12 # h = 0.5
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13 #
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14 # @test apply_quadrature(op, h, 1.0, 10, 100) == h
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15 #
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16 # N = 10
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17 # qc = op.quadratureClosure
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18 # q = h.*(qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
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19 # @assert length(q) == N
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20 #
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21 # for i ∈ 1:N
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22 # @test apply_quadrature(op, h, 1.0, i, N) == q[i]
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23 # end
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24 #
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25 # v = [2.,3.,2.,4.,5.,4.,3.,4.,5.,4.5]
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26 # for i ∈ 1:N
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27 # @test apply_quadrature(op, h, v[i], i, N) == q[i]*v[i]
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28 # end
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29 # end
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31 @testset "SecondDerivative" begin
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32 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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33 L = 3.5
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34 g = EquidistantGrid(101, 0.0, L)
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35 Dₓₓ = SecondDerivative(g,op.innerStencil,op.closureStencils)
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36
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37 f0(x) = 1.
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38 f1(x) = x
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39 f2(x) = 1/2*x^2
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40 f3(x) = 1/6*x^3
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41 f4(x) = 1/24*x^4
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42 f5(x) = sin(x)
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43 f5ₓₓ(x) = -f5(x)
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45 v0 = evalOn(g,f0)
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46 v1 = evalOn(g,f1)
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47 v2 = evalOn(g,f2)
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48 v3 = evalOn(g,f3)
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49 v4 = evalOn(g,f4)
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50 v5 = evalOn(g,f5)
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51
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52 @test Dₓₓ isa TensorMapping{T,1,1} where T
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53 @test Dₓₓ' isa TensorMapping{T,1,1} where T
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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 v - monomial up to order 3.
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57 # Exact differentiation is measured point-wise. For other grid functions
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58 # the error is measured in the l2-norm.
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59 @test norm(Dₓₓ*v0) ≈ 0.0 atol=5e-10
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60 @test norm(Dₓₓ*v1) ≈ 0.0 atol=5e-10
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61 @test Dₓₓ*v2 ≈ v0 atol=5e-11
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62 @test Dₓₓ*v3 ≈ v1 atol=5e-11
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63
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64 h = spacing(g)[1];
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65 l2(v) = sqrt(h*sum(v.^2))
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66 @test Dₓₓ*v4 ≈ v2 atol=5e-4 norm=l2
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67 @test Dₓₓ*v5 ≈ -v5 atol=5e-4 norm=l2
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68 end
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69
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70
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71 @testset "Laplace2D" begin
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72 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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73 Lx = 1.5
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74 Ly = 3.2
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75 g = EquidistantGrid((102,131), (0.0, 0.0), (Lx,Ly))
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76 L = Laplace(g, op.innerStencil, op.closureStencils)
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77
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78
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79 f0(x,y) = 2.
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80 f1(x,y) = x+y
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81 f2(x,y) = 1/2*x^2 + 1/2*y^2
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82 f3(x,y) = 1/6*x^3 + 1/6*y^3
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83 f4(x,y) = 1/24*x^4 + 1/24*y^4
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84 f5(x,y) = sin(x) + cos(y)
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85 f5ₓₓ(x,y) = -f5(x,y)
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86
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87 v0 = evalOn(g,f0)
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88 v1 = evalOn(g,f1)
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89 v2 = evalOn(g,f2)
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90 v3 = evalOn(g,f3)
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91 v4 = evalOn(g,f4)
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92 v5 = evalOn(g,f5)
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93 v5ₓₓ = evalOn(g,f5ₓₓ)
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94
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95 @test L isa TensorMapping{T,2,2} where T
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96 @test L' isa TensorMapping{T,2,2} where T
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97
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98 # 4th order interior stencil, 2nd order boundary stencil,
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99 # implies that L*v should be exact for v - monomial up to order 3.
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100 # Exact differentiation is measured point-wise. For other grid functions
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101 # the error is measured in the H-norm.
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102 @test norm(L*v0) ≈ 0 atol=5e-10
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103 @test norm(L*v1) ≈ 0 atol=5e-10
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104 @test L*v2 ≈ v0 # Seems to be more accurate
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105 @test L*v3 ≈ v1 atol=5e-10
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106
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107 h = spacing(g)
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108 l2(v) = sqrt(prod(h)*sum(v.^2))
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109 @test L*v4 ≈ v2 atol=5e-4 norm=l2
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110 @test L*v5 ≈ v5ₓₓ atol=5e-4 norm=l2
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111 end
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112
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113 @testset "DiagonalInnerProduct" begin
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114 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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115 L = 2.3
388
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116 g = EquidistantGrid(77, 0.0, L)
356
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117 H = DiagonalInnerProduct(g,op.quadratureClosure)
328
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118 v = ones(Float64, size(g))
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119
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120 @test H isa TensorMapping{T,1,1} where T
328
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121 @test H' isa TensorMapping{T,1,1} where T
383
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122 @test sum(H*v) ≈ L
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123 @test H*v == H'*v
328
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124 end
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125
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126 @testset "Quadrature" begin
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127 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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128 Lx = 2.3
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129 Ly = 5.2
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130 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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131
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132 Q = Quadrature(g, op.quadratureClosure)
328
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133
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134 @test Q isa TensorMapping{T,2,2} where T
328
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135 @test Q' isa TensorMapping{T,2,2} where T
382
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136
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137 v = ones(Float64, size(g))
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138 @test sum(Q*v) ≈ Lx*Ly
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139
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140 v = 2*ones(Float64, size(g))
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141 @test_broken sum(Q*v) ≈ 2*Lx*Ly
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142
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143 @test Q*v == Q'*v
328
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144 end
329
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145
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146 @testset "InverseDiagonalInnerProduct" begin
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147 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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148 L = 2.3
388
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149 g = EquidistantGrid(77, 0.0, L)
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150 H = DiagonalInnerProduct(g, op.quadratureClosure)
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151 Hi = InverseDiagonalInnerProduct(g,op.quadratureClosure)
329
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152 v = evalOn(g, x->sin(x))
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153
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154 @test Hi isa TensorMapping{T,1,1} where T
329
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155 @test Hi' isa TensorMapping{T,1,1} where T
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156 @test Hi*H*v ≈ v
383
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157 @test Hi*v == Hi'*v
329
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158 end
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159
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160 @testset "InverseQuadrature" begin
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161 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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162 Lx = 7.3
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163 Ly = 8.2
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164 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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165
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166 Q = Quadrature(g, op.quadratureClosure)
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167 Qinv = InverseQuadrature(g, op.quadratureClosure)
329
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168 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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169
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170 @test Qinv isa TensorMapping{T,2,2} where T
329
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171 @test Qinv' isa TensorMapping{T,2,2} where T
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172 @test_broken Qinv*(Q*v) ≈ v
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173 @test Qinv*v == Qinv'*v
329
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174 end
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175
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176 @testset "BoundaryRestrictrion" begin
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177 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
568
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178 g_1D = EquidistantGrid(11, 0.0, 1.0)
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179 g_2D = EquidistantGrid((11,15), (0.0, 0.0), (1.0,1.0))
513
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180
565
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181 @testset "Constructors" begin
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182 # 1D
570
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183 e_l = BoundaryRestriction{Float64,Lower,4}(op.eClosure,size(g_1D)[1])
565
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184 @test e_l == BoundaryRestriction(g_1D,op.eClosure,Lower())
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diff changeset
185 @test e_l == boundary_restriction(g_1D,op.eClosure,CartesianBoundary{1,Lower}())
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186 @test e_l isa TensorMapping{T,0,1} where T
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187
570
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188 e_r = BoundaryRestriction{Float64,Upper,4}(op.eClosure,size(g_1D)[1])
565
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189 @test e_r == BoundaryRestriction(g_1D,op.eClosure,Upper())
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190 @test e_r == boundary_restriction(g_1D,op.eClosure,CartesianBoundary{1,Upper}())
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191 @test e_r isa TensorMapping{T,0,1} where T
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192
565
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193 # 2D
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194 e_w = boundary_restriction(g_2D,op.eClosure,CartesianBoundary{1,Upper}())
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195 @test e_w isa InflatedTensorMapping
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196 @test e_w isa TensorMapping{T,1,2} where T
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197 end
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198
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diff changeset
199 e_l = boundary_restriction(g_1D, op.eClosure, CartesianBoundary{1,Lower}())
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diff changeset
200 e_r = boundary_restriction(g_1D, op.eClosure, CartesianBoundary{1,Upper}())
513
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201
565
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202 e_w = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{1,Lower}())
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diff changeset
203 e_e = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{1,Upper}())
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diff changeset
204 e_s = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{2,Lower}())
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diff changeset
205 e_n = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{2,Upper}())
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diff changeset
206
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diff changeset
207 @testset "Sizes" begin
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diff changeset
208 # 1D
568
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209 @test domain_size(e_l) == (11,)
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diff changeset
210 @test domain_size(e_r) == (11,)
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diff changeset
211
565
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diff changeset
212 @test range_size(e_l) == ()
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diff changeset
213 @test range_size(e_r) == ()
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diff changeset
214
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diff changeset
215 # 2D
568
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diff changeset
216 @test domain_size(e_w) == (11,15)
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diff changeset
217 @test domain_size(e_e) == (11,15)
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diff changeset
218 @test domain_size(e_s) == (11,15)
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diff changeset
219 @test domain_size(e_n) == (11,15)
565
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diff changeset
220
568
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diff changeset
221 @test range_size(e_w) == (15,)
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diff changeset
222 @test range_size(e_e) == (15,)
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223 @test range_size(e_s) == (11,)
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224 @test range_size(e_n) == (11,)
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225 end
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226
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227
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228 @testset "Application" begin
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229 # 1D
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230 v = evalOn(g_1D,x->1+x^2)
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231 u = fill(3.124)
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232 @test (e_l*v)[] == v[1]
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233 @test (e_r*v)[] == v[end]
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234 @test (e_r*v)[1] == v[end]
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235 @test e_l'*u == [u[]; zeros(10)]
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236 @test e_r'*u == [zeros(10); u[]]
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237
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238 # 2D
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239 v = rand(11, 15)
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240
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241 @test e_w*v == v[1,:]
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242 @test e_e*v == v[end,:]
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243 @test e_s*v == v[:,1]
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244 @test e_n*v == v[:,end]
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245
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246
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247 g_x = rand(11)
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248 g_y = rand(15)
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249
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250 G_w = zeros(Float64, (11,15))
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251 G_w[1,:] = g_y
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252
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253 G_e = zeros(Float64, (11,15))
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254 G_e[end,:] = g_y
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255
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256 G_s = zeros(Float64, (11,15))
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257 G_s[:,1] = g_x
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258
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259 G_n = zeros(Float64, (11,15))
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260 G_n[:,end] = g_x
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261
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262 @test e_w'*g_y == G_w
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263 @test e_e'*g_y == G_e
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264 @test e_s'*g_x == G_s
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265 @test e_n'*g_x == G_n
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266 end
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267
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268 @testset "Inferred" begin
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269 # # 1D
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270 v = ones(Float64, 11)
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271 u = fill(1.)
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272 @inferred (e_l*v)[] == 1
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273 @inferred (e_r*v)[] == 1
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274 @inferred e_l'*u == [1.; zeros(10)]
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275 @inferred e_r'*u == [zeros(10); 1.]
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276
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277 # # 2D
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278 v = ones(Float64, 11, 15)
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279 @inferred e_w*v == ones(Float64, 15)
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280 @inferred e_e*v == ones(Float64, 15)
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281 @inferred e_s*v == ones(Float64, 11)
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282 @inferred e_n*v == ones(Float64, 11)
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283
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284 g_x = ones(Float64,11)
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285 g_y = ones(Float64,15)
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286
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287 G_w = zeros(Float64, (11,15))
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288 G_w[1,:] = g_y
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289
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290 G_e = zeros(Float64, (11,15))
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291 G_e[4,:] = g_y
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292
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293 G_s = zeros(Float64, (11,15))
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294 G_s[:,1] = g_x
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295
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296 G_n = zeros(Float64, (11,15))
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297 G_n[:,5] = g_x
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298
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299 @inferred e_w'*g_y == G_w
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300 @inferred e_e'*g_y == G_e
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301 @inferred e_s'*g_x == G_s
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302 @inferred e_n'*g_x == G_n
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303 end
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304
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305 end
314
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306 #
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307 # @testset "NormalDerivative" begin
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308 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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309 # g = EquidistantGrid((5,6), (0.0, 0.0), (4.0,5.0))
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310 #
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311 # d_w = NormalDerivative(op, g, CartesianBoundary{1,Lower}())
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312 # d_e = NormalDerivative(op, g, CartesianBoundary{1,Upper}())
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313 # d_s = NormalDerivative(op, g, CartesianBoundary{2,Lower}())
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314 # d_n = NormalDerivative(op, g, CartesianBoundary{2,Upper}())
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315 #
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316 #
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317 # v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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318 # v∂x = evalOn(g, (x,y)-> 2*x + y)
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319 # v∂y = evalOn(g, (x,y)-> 2*(y-1) + x)
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320 #
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321 # @test d_w isa TensorMapping{T,2,1} where T
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322 # @test d_w' isa TensorMapping{T,1,2} where T
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323 #
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324 # @test domain_size(d_w, (3,2)) == (2,)
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325 # @test domain_size(d_e, (3,2)) == (2,)
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326 # @test domain_size(d_s, (3,2)) == (3,)
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327 # @test domain_size(d_n, (3,2)) == (3,)
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328 #
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329 # @test size(d_w'*v) == (6,)
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330 # @test size(d_e'*v) == (6,)
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331 # @test size(d_s'*v) == (5,)
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332 # @test size(d_n'*v) == (5,)
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333 #
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334 # @test d_w'*v .≈ v∂x[1,:]
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335 # @test d_e'*v .≈ v∂x[5,:]
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336 # @test d_s'*v .≈ v∂y[:,1]
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337 # @test d_n'*v .≈ v∂y[:,6]
314
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338 #
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339 #
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340 # d_x_l = zeros(Float64, 5)
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341 # d_x_u = zeros(Float64, 5)
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342 # for i ∈ eachindex(d_x_l)
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343 # d_x_l[i] = op.dClosure[i-1]
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344 # d_x_u[i] = -op.dClosure[length(d_x_u)-i]
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345 # end
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346 #
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347 # d_y_l = zeros(Float64, 6)
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348 # d_y_u = zeros(Float64, 6)
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349 # for i ∈ eachindex(d_y_l)
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350 # d_y_l[i] = op.dClosure[i-1]
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351 # d_y_u[i] = -op.dClosure[length(d_y_u)-i]
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352 # end
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353 #
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354 # function prod_matrix(x,y)
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355 # G = zeros(Float64, length(x), length(y))
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356 # for I ∈ CartesianIndices(G)
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357 # G[I] = x[I[1]]*y[I[2]]
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358 # end
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359 #
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360 # return G
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361 # end
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362 #
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363 # g_x = [1,2,3,4.0,5]
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364 # g_y = [5,4,3,2,1.0,11]
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365 #
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366 # G_w = prod_matrix(d_x_l, g_y)
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367 # G_e = prod_matrix(d_x_u, g_y)
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368 # G_s = prod_matrix(g_x, d_y_l)
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369 # G_n = prod_matrix(g_x, d_y_u)
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370 #
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371 #
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372 # @test size(d_w*g_y) == (UnknownDim,6)
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373 # @test size(d_e*g_y) == (UnknownDim,6)
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374 # @test size(d_s*g_x) == (5,UnknownDim)
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375 # @test size(d_n*g_x) == (5,UnknownDim)
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376 #
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377 # # These tests should be moved to where they are possible (i.e we know what the grid should be)
387
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378 # @test_broken d_w*g_y .≈ G_w
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379 # @test_broken d_e*g_y .≈ G_e
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380 # @test_broken d_s*g_x .≈ G_s
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381 # @test_broken d_n*g_x .≈ G_n
314
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382 # end
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383 #
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384 # @testset "BoundaryQuadrature" begin
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385 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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386 # g = EquidistantGrid((10,11), (0.0, 0.0), (1.0,1.0))
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387 #
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388 # H_w = BoundaryQuadrature(op, g, CartesianBoundary{1,Lower}())
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389 # H_e = BoundaryQuadrature(op, g, CartesianBoundary{1,Upper}())
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390 # H_s = BoundaryQuadrature(op, g, CartesianBoundary{2,Lower}())
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391 # H_n = BoundaryQuadrature(op, g, CartesianBoundary{2,Upper}())
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392 #
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393 # v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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394 #
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395 # function get_quadrature(N)
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396 # qc = op.quadratureClosure
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397 # q = (qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
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398 # @assert length(q) == N
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399 # return q
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400 # end
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401 #
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402 # v_w = v[1,:]
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403 # v_e = v[10,:]
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404 # v_s = v[:,1]
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405 # v_n = v[:,11]
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406 #
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407 # q_x = spacing(g)[1].*get_quadrature(10)
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408 # q_y = spacing(g)[2].*get_quadrature(11)
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409 #
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410 # @test H_w isa TensorOperator{T,1} where T
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411 #
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412 # @test domain_size(H_w, (3,)) == (3,)
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413 # @test domain_size(H_n, (3,)) == (3,)
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414 #
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415 # @test range_size(H_w, (3,)) == (3,)
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416 # @test range_size(H_n, (3,)) == (3,)
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417 #
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418 # @test size(H_w*v_w) == (11,)
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419 # @test size(H_e*v_e) == (11,)
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420 # @test size(H_s*v_s) == (10,)
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421 # @test size(H_n*v_n) == (10,)
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422 #
387
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423 # @test H_w*v_w .≈ q_y.*v_w
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424 # @test H_e*v_e .≈ q_y.*v_e
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425 # @test H_s*v_s .≈ q_x.*v_s
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426 # @test H_n*v_n .≈ q_x.*v_n
314
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427 #
383
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428 # @test H_w'*v_w == H_w'*v_w
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429 # @test H_e'*v_e == H_e'*v_e
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430 # @test H_s'*v_s == H_s'*v_s
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431 # @test H_n'*v_n == H_n'*v_n
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432 # end
338
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433
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434 end