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annotate test/testSbpOperators.jl @ 514:14e722e8607d feature/boundary_ops

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Clean up constructors
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 23 Nov 2020 21:19:08 +0100
parents 547639572208
children d55008f5e2f3
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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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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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
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116 g = EquidistantGrid(77, 0.0, L)
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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
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121 @test H' isa TensorMapping{T,1,1} where T
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122 @test sum(H*v) ≈ L
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123 @test H*v == H'*v
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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)
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133
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134 @test Q isa TensorMapping{T,2,2} where T
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135 @test Q' isa TensorMapping{T,2,2} where T
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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
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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
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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)
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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
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155 @test Hi' isa TensorMapping{T,1,1} where T
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156 @test Hi*H*v ≈ v
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157 @test Hi*v == Hi'*v
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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
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174 end
513
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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")
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178
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179 g = EquidistantGrid(4, 0.0, 1.0)
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180
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181 e_l = BoundaryRestriction(g,op.eClosure,Lower())
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182 e_r = BoundaryRestriction(g,op.eClosure,Upper())
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183
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184 v = evalOn(g,x->1+x^2)
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185 u = [3.124] #How to handle scalars having to be arrays? It's kind of ugly.
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186
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187 e_l*v isa LazyTensorMappingApplication
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188 @test (e_l*v)[Index{Lower}(1)] == v[1]
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189 @test (e_r*v)[Index{Upper}(4)] == v[end]
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190 @test e_l'*u == [u[1], 0, 0, 0]
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191 @test e_r'*u == [0, 0, 0, u[1]]
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192 @test_throws BoundsError (e_l*v)[Index{Lower}(3)]
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193 @test_throws BoundsError (e_r*v)[Index{Upper}(3)]
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194
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195 g = EquidistantGrid((4,5), (0.0, 0.0), (1.0,1.0))
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196
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197 e_w = boundary_restriction(g, op.eClosure, CartesianBoundary{1,Lower}())
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198 e_e = boundary_restriction(g, op.eClosure, CartesianBoundary{1,Upper}())
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199 e_s = boundary_restriction(g, op.eClosure, CartesianBoundary{2,Lower}())
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200 e_n = boundary_restriction(g, op.eClosure, CartesianBoundary{2,Upper}())
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201
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202 v = zeros(Float64, 4, 5)
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203 v[:,5] = [1, 2, 3,4]
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204 v[:,4] = [1, 2, 3,4]
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205 v[:,3] = [4, 5, 6, 7]
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206 v[:,2] = [7, 8, 9, 10]
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207 v[:,1] = [10, 11, 12, 13]
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208
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209 @test_broken e_w isa TensorMapping{T,1,2} where T
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210 @test_broken e_w' isa TensorMapping{T,2,1} where T
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211
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212
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213
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214 @test domain_size(e_w) == (4,5)
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215 @test domain_size(e_e) == (4,5)
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216 @test domain_size(e_s) == (4,5)
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217 @test domain_size(e_n) == (4,5)
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218
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219 @test range_size(e_w) == (1,5)
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220 @test range_size(e_e) == (1,5)
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221 @test range_size(e_s) == (4,1)
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222 @test range_size(e_n) == (4,1)
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223
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224 e_w*v isa LazyTensorMappingApplication
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225
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226 @test_broken e_w'*v == [10,7,4,1.0,1]
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227 @test_broken e_e'*v == [13,10,7,4,4.0]
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228 @test_broken e_s'*v == [10,11,12,13.0]
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229 @test_broken e_n'*v == [1,2,3,4.0]
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230
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231 g_x = [1,2,3,4.0]
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232 g_y = [5,4,3,2,1.0]
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233
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234 G_w = zeros(Float64, (4,5))
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235 G_w[1,:] = g_y
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236
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237 G_e = zeros(Float64, (4,5))
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238 G_e[4,:] = g_y
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239
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240 G_s = zeros(Float64, (4,5))
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241 G_s[:,1] = g_x
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242
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243 G_n = zeros(Float64, (4,5))
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244 G_n[:,5] = g_x
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245
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246 @test_broken size(e_w*g_y) == (UnknownDim,5)
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247 @test_broken size(e_e*g_y) == (UnknownDim,5)
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248 @test_broken size(e_s*g_x) == (4,UnknownDim)
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249 @test_broken size(e_n*g_x) == (4,UnknownDim)
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250
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251 # These tests should be moved to where they are possible (i.e we know what the grid should be)
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252 @test_broken e_w*g_y == G_w
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253 @test_broken e_e*g_y == G_e
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254 @test_broken e_s*g_x == G_s
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255 @test_broken e_n*g_x == G_n
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256 end
314
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257 #
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258 # @testset "NormalDerivative" begin
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259 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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260 # g = EquidistantGrid((5,6), (0.0, 0.0), (4.0,5.0))
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261 #
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262 # d_w = NormalDerivative(op, g, CartesianBoundary{1,Lower}())
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263 # d_e = NormalDerivative(op, g, CartesianBoundary{1,Upper}())
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264 # d_s = NormalDerivative(op, g, CartesianBoundary{2,Lower}())
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265 # d_n = NormalDerivative(op, g, CartesianBoundary{2,Upper}())
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266 #
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267 #
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268 # v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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269 # v∂x = evalOn(g, (x,y)-> 2*x + y)
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270 # v∂y = evalOn(g, (x,y)-> 2*(y-1) + x)
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271 #
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272 # @test d_w isa TensorMapping{T,2,1} where T
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273 # @test d_w' isa TensorMapping{T,1,2} where T
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274 #
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275 # @test domain_size(d_w, (3,2)) == (2,)
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276 # @test domain_size(d_e, (3,2)) == (2,)
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277 # @test domain_size(d_s, (3,2)) == (3,)
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278 # @test domain_size(d_n, (3,2)) == (3,)
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279 #
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280 # @test size(d_w'*v) == (6,)
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281 # @test size(d_e'*v) == (6,)
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282 # @test size(d_s'*v) == (5,)
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283 # @test size(d_n'*v) == (5,)
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284 #
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285 # @test d_w'*v .≈ v∂x[1,:]
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286 # @test d_e'*v .≈ v∂x[5,:]
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287 # @test d_s'*v .≈ v∂y[:,1]
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288 # @test d_n'*v .≈ v∂y[:,6]
314
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289 #
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290 #
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291 # d_x_l = zeros(Float64, 5)
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292 # d_x_u = zeros(Float64, 5)
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293 # for i ∈ eachindex(d_x_l)
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294 # d_x_l[i] = op.dClosure[i-1]
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295 # d_x_u[i] = -op.dClosure[length(d_x_u)-i]
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296 # end
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297 #
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298 # d_y_l = zeros(Float64, 6)
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299 # d_y_u = zeros(Float64, 6)
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300 # for i ∈ eachindex(d_y_l)
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301 # d_y_l[i] = op.dClosure[i-1]
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302 # d_y_u[i] = -op.dClosure[length(d_y_u)-i]
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303 # end
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304 #
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305 # function prod_matrix(x,y)
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306 # G = zeros(Float64, length(x), length(y))
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307 # for I ∈ CartesianIndices(G)
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308 # G[I] = x[I[1]]*y[I[2]]
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309 # end
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310 #
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311 # return G
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312 # end
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313 #
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314 # g_x = [1,2,3,4.0,5]
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315 # g_y = [5,4,3,2,1.0,11]
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316 #
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317 # G_w = prod_matrix(d_x_l, g_y)
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318 # G_e = prod_matrix(d_x_u, g_y)
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319 # G_s = prod_matrix(g_x, d_y_l)
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320 # G_n = prod_matrix(g_x, d_y_u)
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321 #
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322 #
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323 # @test size(d_w*g_y) == (UnknownDim,6)
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324 # @test size(d_e*g_y) == (UnknownDim,6)
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325 # @test size(d_s*g_x) == (5,UnknownDim)
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326 # @test size(d_n*g_x) == (5,UnknownDim)
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327 #
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328 # # These tests should be moved to where they are possible (i.e we know what the grid should be)
387
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329 # @test_broken d_w*g_y .≈ G_w
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330 # @test_broken d_e*g_y .≈ G_e
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331 # @test_broken d_s*g_x .≈ G_s
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332 # @test_broken d_n*g_x .≈ G_n
314
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333 # end
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334 #
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335 # @testset "BoundaryQuadrature" begin
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336 # op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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337 # g = EquidistantGrid((10,11), (0.0, 0.0), (1.0,1.0))
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338 #
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339 # H_w = BoundaryQuadrature(op, g, CartesianBoundary{1,Lower}())
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340 # H_e = BoundaryQuadrature(op, g, CartesianBoundary{1,Upper}())
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341 # H_s = BoundaryQuadrature(op, g, CartesianBoundary{2,Lower}())
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342 # H_n = BoundaryQuadrature(op, g, CartesianBoundary{2,Upper}())
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343 #
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344 # v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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345 #
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346 # function get_quadrature(N)
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347 # qc = op.quadratureClosure
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348 # q = (qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
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349 # @assert length(q) == N
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350 # return q
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351 # end
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352 #
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353 # v_w = v[1,:]
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354 # v_e = v[10,:]
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355 # v_s = v[:,1]
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356 # v_n = v[:,11]
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357 #
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358 # q_x = spacing(g)[1].*get_quadrature(10)
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359 # q_y = spacing(g)[2].*get_quadrature(11)
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360 #
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361 # @test H_w isa TensorOperator{T,1} where T
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362 #
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363 # @test domain_size(H_w, (3,)) == (3,)
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364 # @test domain_size(H_n, (3,)) == (3,)
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365 #
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366 # @test range_size(H_w, (3,)) == (3,)
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367 # @test range_size(H_n, (3,)) == (3,)
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368 #
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369 # @test size(H_w*v_w) == (11,)
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370 # @test size(H_e*v_e) == (11,)
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371 # @test size(H_s*v_s) == (10,)
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372 # @test size(H_n*v_n) == (10,)
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373 #
387
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374 # @test H_w*v_w .≈ q_y.*v_w
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375 # @test H_e*v_e .≈ q_y.*v_e
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376 # @test H_s*v_s .≈ q_x.*v_s
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377 # @test H_n*v_n .≈ q_x.*v_n
314
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378 #
383
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379 # @test H_w'*v_w == H_w'*v_w
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380 # @test H_e'*v_e == H_e'*v_e
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381 # @test H_s'*v_s == H_s'*v_s
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382 # @test H_n'*v_n == H_n'*v_n
314
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383 # end
338
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384
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385 end