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annotate test/testSbpOperators.jl @ 584:4aa7fe13a984

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Add scale() and eltype() methods for stencils
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 02 Dec 2020 11:18:18 +0100
parents 3cecbfb3d623
children 8e4f86c4bf75
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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 "Stencil" begin
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11 s = SbpOperators.Stencil((-2,2), (1.,2.,2.,3.,4.))
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12 @test s isa SbpOperators.Stencil{Float64, 5}
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13
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14 @test eltype(s) == Float64
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15 @test SbpOperators.scale(s, 2) == SbpOperators.Stencil((-2,2), (2.,4.,4.,6.,8.))
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16 end
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17
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18 # @testset "apply_quadrature" begin
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19 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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20 # h = 0.5
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21 #
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22 # @test apply_quadrature(op, h, 1.0, 10, 100) == h
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23 #
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24 # N = 10
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25 # qc = op.quadratureClosure
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26 # q = h.*(qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
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27 # @assert length(q) == N
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28 #
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29 # for i ∈ 1:N
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30 # @test apply_quadrature(op, h, 1.0, i, N) == q[i]
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31 # end
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32 #
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33 # v = [2.,3.,2.,4.,5.,4.,3.,4.,5.,4.5]
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34 # for i ∈ 1:N
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35 # @test apply_quadrature(op, h, v[i], i, N) == q[i]*v[i]
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36 # end
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37 # end
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39 @testset "SecondDerivative" begin
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40 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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41 L = 3.5
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42 g = EquidistantGrid(101, 0.0, L)
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43 Dₓₓ = SecondDerivative(g,op.innerStencil,op.closureStencils)
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44
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45 f0(x) = 1.
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46 f1(x) = x
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47 f2(x) = 1/2*x^2
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48 f3(x) = 1/6*x^3
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49 f4(x) = 1/24*x^4
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50 f5(x) = sin(x)
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51 f5ₓₓ(x) = -f5(x)
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53 v0 = evalOn(g,f0)
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54 v1 = evalOn(g,f1)
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55 v2 = evalOn(g,f2)
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56 v3 = evalOn(g,f3)
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57 v4 = evalOn(g,f4)
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58 v5 = evalOn(g,f5)
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60 @test Dₓₓ isa TensorMapping{T,1,1} where T
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61 @test Dₓₓ' isa TensorMapping{T,1,1} where T
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62
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63 # 4th order interior stencil, 2nd order boundary stencil,
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64 # implies that L*v should be exact for v - monomial up to order 3.
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65 # Exact differentiation is measured point-wise. For other grid functions
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66 # the error is measured in the l2-norm.
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67 @test norm(Dₓₓ*v0) ≈ 0.0 atol=5e-10
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68 @test norm(Dₓₓ*v1) ≈ 0.0 atol=5e-10
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69 @test Dₓₓ*v2 ≈ v0 atol=5e-11
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70 @test Dₓₓ*v3 ≈ v1 atol=5e-11
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71
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72 h = spacing(g)[1];
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73 l2(v) = sqrt(h*sum(v.^2))
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74 @test Dₓₓ*v4 ≈ v2 atol=5e-4 norm=l2
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75 @test Dₓₓ*v5 ≈ -v5 atol=5e-4 norm=l2
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76 end
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77
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78
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79 @testset "Laplace2D" begin
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80 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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81 Lx = 1.5
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82 Ly = 3.2
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83 g = EquidistantGrid((102,131), (0.0, 0.0), (Lx,Ly))
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84 L = Laplace(g, op.innerStencil, op.closureStencils)
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85
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86
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87 f0(x,y) = 2.
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88 f1(x,y) = x+y
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89 f2(x,y) = 1/2*x^2 + 1/2*y^2
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90 f3(x,y) = 1/6*x^3 + 1/6*y^3
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91 f4(x,y) = 1/24*x^4 + 1/24*y^4
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92 f5(x,y) = sin(x) + cos(y)
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93 f5ₓₓ(x,y) = -f5(x,y)
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94
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95 v0 = evalOn(g,f0)
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96 v1 = evalOn(g,f1)
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97 v2 = evalOn(g,f2)
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98 v3 = evalOn(g,f3)
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99 v4 = evalOn(g,f4)
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100 v5 = evalOn(g,f5)
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101 v5ₓₓ = evalOn(g,f5ₓₓ)
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102
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103 @test L isa TensorMapping{T,2,2} where T
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104 @test L' isa TensorMapping{T,2,2} where T
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105
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106 # 4th order interior stencil, 2nd order boundary stencil,
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107 # implies that L*v should be exact for v - monomial up to order 3.
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108 # Exact differentiation is measured point-wise. For other grid functions
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109 # the error is measured in the H-norm.
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110 @test norm(L*v0) ≈ 0 atol=5e-10
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111 @test norm(L*v1) ≈ 0 atol=5e-10
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112 @test L*v2 ≈ v0 # Seems to be more accurate
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113 @test L*v3 ≈ v1 atol=5e-10
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114
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115 h = spacing(g)
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116 l2(v) = sqrt(prod(h)*sum(v.^2))
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117 @test L*v4 ≈ v2 atol=5e-4 norm=l2
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118 @test L*v5 ≈ v5ₓₓ atol=5e-4 norm=l2
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119 end
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120
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121 @testset "DiagonalInnerProduct" begin
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122 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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123 L = 2.3
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124 g = EquidistantGrid(77, 0.0, L)
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125 H = DiagonalInnerProduct(g,op.quadratureClosure)
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126 v = ones(Float64, size(g))
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127
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128 @test H isa TensorMapping{T,1,1} where T
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129 @test H' isa TensorMapping{T,1,1} where T
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130 @test sum(H*v) ≈ L
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131 @test H*v == H'*v
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132 end
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133
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134 @testset "Quadrature" begin
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135 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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136 Lx = 2.3
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137 Ly = 5.2
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138 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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139
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140 Q = Quadrature(g, op.quadratureClosure)
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141
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142 @test Q isa TensorMapping{T,2,2} where T
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143 @test Q' isa TensorMapping{T,2,2} where T
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144
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145 v = ones(Float64, size(g))
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146 @test sum(Q*v) ≈ Lx*Ly
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147
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148 v = 2*ones(Float64, size(g))
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149 @test_broken sum(Q*v) ≈ 2*Lx*Ly
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150
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151 @test Q*v == Q'*v
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152 end
329
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153
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154 @testset "InverseDiagonalInnerProduct" begin
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155 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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156 L = 2.3
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157 g = EquidistantGrid(77, 0.0, L)
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158 H = DiagonalInnerProduct(g, op.quadratureClosure)
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159 Hi = InverseDiagonalInnerProduct(g,op.quadratureClosure)
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160 v = evalOn(g, x->sin(x))
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161
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162 @test Hi isa TensorMapping{T,1,1} where T
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163 @test Hi' isa TensorMapping{T,1,1} where T
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164 @test Hi*H*v ≈ v
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165 @test Hi*v == Hi'*v
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166 end
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167
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168 @testset "InverseQuadrature" begin
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169 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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170 Lx = 7.3
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171 Ly = 8.2
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172 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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173
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174 Q = Quadrature(g, op.quadratureClosure)
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175 Qinv = InverseQuadrature(g, op.quadratureClosure)
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176 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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177
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178 @test Qinv isa TensorMapping{T,2,2} where T
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179 @test Qinv' isa TensorMapping{T,2,2} where T
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180 @test_broken Qinv*(Q*v) ≈ v
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181 @test Qinv*v == Qinv'*v
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182 end
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183 #
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184 # @testset "BoundaryValue" begin
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185 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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186 # g = EquidistantGrid((4,5), (0.0, 0.0), (1.0,1.0))
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187 #
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188 # e_w = BoundaryValue(op, g, CartesianBoundary{1,Lower}())
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189 # e_e = BoundaryValue(op, g, CartesianBoundary{1,Upper}())
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190 # e_s = BoundaryValue(op, g, CartesianBoundary{2,Lower}())
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191 # e_n = BoundaryValue(op, g, CartesianBoundary{2,Upper}())
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192 #
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193 # v = zeros(Float64, 4, 5)
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194 # v[:,5] = [1, 2, 3,4]
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195 # v[:,4] = [1, 2, 3,4]
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196 # v[:,3] = [4, 5, 6, 7]
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197 # v[:,2] = [7, 8, 9, 10]
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198 # v[:,1] = [10, 11, 12, 13]
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199 #
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200 # @test e_w isa TensorMapping{T,2,1} where T
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201 # @test e_w' isa TensorMapping{T,1,2} where T
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202 #
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203 # @test domain_size(e_w, (3,2)) == (2,)
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204 # @test domain_size(e_e, (3,2)) == (2,)
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205 # @test domain_size(e_s, (3,2)) == (3,)
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206 # @test domain_size(e_n, (3,2)) == (3,)
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207 #
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208 # @test size(e_w'*v) == (5,)
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209 # @test size(e_e'*v) == (5,)
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210 # @test size(e_s'*v) == (4,)
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211 # @test size(e_n'*v) == (4,)
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212 #
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213 # @test e_w'*v == [10,7,4,1.0,1]
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214 # @test e_e'*v == [13,10,7,4,4.0]
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215 # @test e_s'*v == [10,11,12,13.0]
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216 # @test e_n'*v == [1,2,3,4.0]
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217 #
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218 # g_x = [1,2,3,4.0]
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219 # g_y = [5,4,3,2,1.0]
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220 #
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221 # G_w = zeros(Float64, (4,5))
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222 # G_w[1,:] = g_y
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223 #
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224 # G_e = zeros(Float64, (4,5))
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225 # G_e[4,:] = g_y
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226 #
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227 # G_s = zeros(Float64, (4,5))
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228 # G_s[:,1] = g_x
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229 #
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230 # G_n = zeros(Float64, (4,5))
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231 # G_n[:,5] = g_x
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232 #
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233 # @test size(e_w*g_y) == (UnknownDim,5)
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234 # @test size(e_e*g_y) == (UnknownDim,5)
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235 # @test size(e_s*g_x) == (4,UnknownDim)
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236 # @test size(e_n*g_x) == (4,UnknownDim)
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237 #
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238 # # These tests should be moved to where they are possible (i.e we know what the grid should be)
383
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239 # @test_broken e_w*g_y == G_w
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240 # @test_broken e_e*g_y == G_e
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241 # @test_broken e_s*g_x == G_s
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242 # @test_broken e_n*g_x == G_n
314
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243 # end
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244 #
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245 # @testset "NormalDerivative" begin
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246 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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247 # g = EquidistantGrid((5,6), (0.0, 0.0), (4.0,5.0))
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248 #
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249 # d_w = NormalDerivative(op, g, CartesianBoundary{1,Lower}())
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250 # d_e = NormalDerivative(op, g, CartesianBoundary{1,Upper}())
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251 # d_s = NormalDerivative(op, g, CartesianBoundary{2,Lower}())
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252 # d_n = NormalDerivative(op, g, CartesianBoundary{2,Upper}())
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253 #
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254 #
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255 # v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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256 # v∂x = evalOn(g, (x,y)-> 2*x + y)
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257 # v∂y = evalOn(g, (x,y)-> 2*(y-1) + x)
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258 #
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259 # @test d_w isa TensorMapping{T,2,1} where T
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260 # @test d_w' isa TensorMapping{T,1,2} where T
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261 #
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262 # @test domain_size(d_w, (3,2)) == (2,)
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263 # @test domain_size(d_e, (3,2)) == (2,)
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264 # @test domain_size(d_s, (3,2)) == (3,)
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265 # @test domain_size(d_n, (3,2)) == (3,)
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266 #
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267 # @test size(d_w'*v) == (6,)
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268 # @test size(d_e'*v) == (6,)
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269 # @test size(d_s'*v) == (5,)
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270 # @test size(d_n'*v) == (5,)
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271 #
387
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272 # @test d_w'*v .≈ v∂x[1,:]
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273 # @test d_e'*v .≈ v∂x[5,:]
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274 # @test d_s'*v .≈ v∂y[:,1]
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275 # @test d_n'*v .≈ v∂y[:,6]
314
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276 #
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277 #
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278 # d_x_l = zeros(Float64, 5)
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279 # d_x_u = zeros(Float64, 5)
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280 # for i ∈ eachindex(d_x_l)
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281 # d_x_l[i] = op.dClosure[i-1]
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282 # d_x_u[i] = -op.dClosure[length(d_x_u)-i]
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283 # end
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284 #
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285 # d_y_l = zeros(Float64, 6)
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286 # d_y_u = zeros(Float64, 6)
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287 # for i ∈ eachindex(d_y_l)
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288 # d_y_l[i] = op.dClosure[i-1]
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289 # d_y_u[i] = -op.dClosure[length(d_y_u)-i]
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290 # end
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291 #
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292 # function prod_matrix(x,y)
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293 # G = zeros(Float64, length(x), length(y))
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294 # for I ∈ CartesianIndices(G)
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295 # G[I] = x[I[1]]*y[I[2]]
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296 # end
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297 #
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298 # return G
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299 # end
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300 #
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301 # g_x = [1,2,3,4.0,5]
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302 # g_y = [5,4,3,2,1.0,11]
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303 #
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304 # G_w = prod_matrix(d_x_l, g_y)
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305 # G_e = prod_matrix(d_x_u, g_y)
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306 # G_s = prod_matrix(g_x, d_y_l)
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307 # G_n = prod_matrix(g_x, d_y_u)
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308 #
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309 #
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310 # @test size(d_w*g_y) == (UnknownDim,6)
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311 # @test size(d_e*g_y) == (UnknownDim,6)
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312 # @test size(d_s*g_x) == (5,UnknownDim)
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313 # @test size(d_n*g_x) == (5,UnknownDim)
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314 #
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315 # # These tests should be moved to where they are possible (i.e we know what the grid should be)
387
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316 # @test_broken d_w*g_y .≈ G_w
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317 # @test_broken d_e*g_y .≈ G_e
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318 # @test_broken d_s*g_x .≈ G_s
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319 # @test_broken d_n*g_x .≈ G_n
314
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320 # end
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321 #
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322 # @testset "BoundaryQuadrature" begin
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323 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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324 # g = EquidistantGrid((10,11), (0.0, 0.0), (1.0,1.0))
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325 #
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326 # H_w = BoundaryQuadrature(op, g, CartesianBoundary{1,Lower}())
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327 # H_e = BoundaryQuadrature(op, g, CartesianBoundary{1,Upper}())
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328 # H_s = BoundaryQuadrature(op, g, CartesianBoundary{2,Lower}())
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329 # H_n = BoundaryQuadrature(op, g, CartesianBoundary{2,Upper}())
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330 #
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331 # v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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332 #
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333 # function get_quadrature(N)
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334 # qc = op.quadratureClosure
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335 # q = (qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
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336 # @assert length(q) == N
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337 # return q
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338 # end
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339 #
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340 # v_w = v[1,:]
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341 # v_e = v[10,:]
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342 # v_s = v[:,1]
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343 # v_n = v[:,11]
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344 #
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345 # q_x = spacing(g)[1].*get_quadrature(10)
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346 # q_y = spacing(g)[2].*get_quadrature(11)
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347 #
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348 # @test H_w isa TensorOperator{T,1} where T
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349 #
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350 # @test domain_size(H_w, (3,)) == (3,)
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351 # @test domain_size(H_n, (3,)) == (3,)
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352 #
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353 # @test range_size(H_w, (3,)) == (3,)
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354 # @test range_size(H_n, (3,)) == (3,)
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355 #
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356 # @test size(H_w*v_w) == (11,)
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357 # @test size(H_e*v_e) == (11,)
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358 # @test size(H_s*v_s) == (10,)
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359 # @test size(H_n*v_n) == (10,)
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360 #
387
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361 # @test H_w*v_w .≈ q_y.*v_w
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362 # @test H_e*v_e .≈ q_y.*v_e
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363 # @test H_s*v_s .≈ q_x.*v_s
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364 # @test H_n*v_n .≈ q_x.*v_n
314
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365 #
383
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366 # @test H_w'*v_w == H_w'*v_w
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367 # @test H_e'*v_e == H_e'*v_e
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368 # @test H_s'*v_s == H_s'*v_s
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369 # @test H_n'*v_n == H_n'*v_n
314
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370 # end
338
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371
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372 end