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annotate test/Grids/mapped_grid_test.jl @ 1842:f2b32da29b73 feature/grids/manifolds

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Introduce mapped_grid for ParameterSpace and simplify implementation of equidistant_grid(::Chart)
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 22 Oct 2024 15:32:33 +0200
parents 2b5f81e288f1
children 81559cb7b11c
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1 using Diffinitive.Grids
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2 using Diffinitive.RegionIndices
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3 using Test
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4 using StaticArrays
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5 using LinearAlgebra
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6
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7
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8 _skew_mapping(a,b) = (ξ̄->ξ̄[1]*a + ξ̄[2]*b, ξ̄->[a b])
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9
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10 function _partially_curved_mapping()
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11 x̄((ξ, η)) = @SVector[ξ, η*(1+ξ*(ξ-1))]
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12 J((ξ, η)) = @SMatrix[
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13 1 0;
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14 η*(2ξ-1) 1+ξ*(ξ-1);
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15 ]
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16
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17 return x̄, J
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18 end
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19
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20 function _fully_curved_mapping()
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21 x̄((ξ, η)) = @SVector[2ξ + η*(1-η), 3η+(1+η/2)*ξ^2]
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22 J((ξ, η)) = @SMatrix[
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23 2 1-2η;
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24 (2+η)*ξ 3+1/2*ξ^2;
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25 ]
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26
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27 return x̄, J
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28 end
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29
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30 @testset "MappedGrid" begin
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31 @testset "Constructor" begin
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32 lg = equidistant_grid((0,0), (1,1), 11, 21)
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33
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34 x̄ = map(ξ̄ -> 2ξ̄, lg)
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35 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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36 mg = MappedGrid(lg, x̄, J)
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37
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38 @test mg isa Grid{SVector{2, Float64},2}
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39 @test jacobian(mg) isa Array{<:AbstractMatrix}
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40 @test logical_grid(mg) isa Grid
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41
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42 @test collect(mg) == x̄
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43 @test jacobian(mg) == J
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44 @test logical_grid(mg) == lg
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45
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46
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47 x̄ = map(ξ̄ -> @SVector[ξ̄[1],ξ̄[2], ξ̄[1] + ξ̄[2]], lg)
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48 J = map(ξ̄ -> @SMatrix[1 0; 0 1; 1 1], lg)
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49 mg = MappedGrid(lg, x̄, J)
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50
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51 @test mg isa Grid{SVector{3, Float64},2}
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52 @test jacobian(mg) isa Array{<:AbstractMatrix}
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53 @test logical_grid(mg) isa Grid
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54
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55 @test collect(mg) == x̄
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56 @test jacobian(mg) == J
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57 @test logical_grid(mg) == lg
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58
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59 sz1 = (10,11)
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60 sz2 = (10,12)
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61 @test_throws ArgumentError("Sizes must match") MappedGrid(
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62 equidistant_grid((0,0), (1,1), sz2...),
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63 rand(SVector{2},sz1...),
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64 rand(SMatrix{2,2},sz1...),
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65 )
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66
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67 @test_throws ArgumentError("Sizes must match") MappedGrid(
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68 equidistant_grid((0,0), (1,1), sz1...),
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69 rand(SVector{2},sz2...),
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70 rand(SMatrix{2,2},sz1...),
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71 )
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72
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73 @test_throws ArgumentError("Sizes must match") MappedGrid(
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74 equidistant_grid((0,0), (1,1), sz1...),
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75 rand(SVector{2},sz1...),
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76 rand(SMatrix{2,2},sz2...),
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77 )
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78
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79 err_str = "The size of the jacobian must match the dimensions of the grid and coordinates"
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80 @test_throws ArgumentError(err_str) MappedGrid(
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81 equidistant_grid((0,0), (1,1), 10, 11),
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82 rand(SVector{3}, 10, 11),
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83 rand(SMatrix{3,4}, 10, 11),
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84 )
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85
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86 @test_throws ArgumentError(err_str) MappedGrid(
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87 equidistant_grid((0,0), (1,1), 10, 11),
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88 rand(SVector{3}, 10, 11),
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89 rand(SMatrix{4,2}, 10, 11),
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90 )
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91 end
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92
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93 @testset "Indexing Interface" begin
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94 lg = equidistant_grid((0,0), (1,1), 11, 21)
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95 x̄ = map(ξ̄ -> 2ξ̄, lg)
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96 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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97 mg = MappedGrid(lg, x̄, J)
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98 @test mg[1,1] == [0.0, 0.0]
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99 @test mg[4,2] == [0.6, 0.1]
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100 @test mg[6,10] == [1., 0.9]
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101
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102 @test mg[begin, begin] == [0.0, 0.0]
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103 @test mg[end,end] == [2.0, 2.0]
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104 @test mg[begin,end] == [0., 2.]
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105
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106 @test axes(mg) == (1:11, 1:21)
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107
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108 @testset "cartesian indexing" begin
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109 cases = [
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110 (1,1) ,
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111 (3,5) ,
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112 (10,6),
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113 (1,1) ,
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114 (3,2) ,
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115 ]
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116
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117 @testset "i = $is" for (lg, is) ∈ cases
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118 @test mg[CartesianIndex(is...)] == mg[is...]
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119 end
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120 end
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121
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122 @testset "eachindex" begin
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123 @test eachindex(mg) == CartesianIndices((11,21))
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124 end
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125
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126 @testset "firstindex" begin
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127 @test firstindex(mg, 1) == 1
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128 @test firstindex(mg, 2) == 1
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129 end
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130
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131 @testset "lastindex" begin
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132 @test lastindex(mg, 1) == 11
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133 @test lastindex(mg, 2) == 21
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134 end
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135 end
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136
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137 @testset "Iterator interface" begin
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138 lg = equidistant_grid((0,0), (1,1), 11, 21)
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139 x̄ = map(ξ̄ -> 2ξ̄, lg)
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140 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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141
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142 mg = MappedGrid(lg, x̄, J)
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143
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144 lg2 = equidistant_grid((0,0), (1,1), 15, 11)
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145 sg = MappedGrid(
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146 equidistant_grid((0,0), (1,1), 15, 11),
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147 map(ξ̄ -> @SArray[ξ̄[1], ξ̄[2], -ξ̄[1]], lg2), rand(SMatrix{3,2,Float64},15,11)
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148 )
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149
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150 @test eltype(mg) == SVector{2,Float64}
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151 @test eltype(sg) == SVector{3,Float64}
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152
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153 @test eltype(typeof(mg)) == SVector{2,Float64}
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154 @test eltype(typeof(sg)) == SVector{3,Float64}
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155
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156 @test size(mg) == (11,21)
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157 @test size(sg) == (15,11)
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158
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159 @test size(mg,2) == 21
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160 @test size(sg,2) == 11
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161
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162 @test length(mg) == 231
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163 @test length(sg) == 165
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164
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165 @test Base.IteratorSize(mg) == Base.HasShape{2}()
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166 @test Base.IteratorSize(typeof(mg)) == Base.HasShape{2}()
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167
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168 @test Base.IteratorSize(sg) == Base.HasShape{2}()
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169 @test Base.IteratorSize(typeof(sg)) == Base.HasShape{2}()
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170
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171 element, state = iterate(mg)
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172 @test element == lg[1,1].*2
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173 element, _ = iterate(mg, state)
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174 @test element == lg[2,1].*2
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175
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176 element, state = iterate(sg)
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177 @test element == sg.physicalcoordinates[1,1]
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178 element, _ = iterate(sg, state)
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179 @test element == sg.physicalcoordinates[2,1]
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180
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181 @test collect(mg) == 2 .* lg
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182 end
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183
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184 @testset "Base" begin
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185 lg = equidistant_grid((0,0), (1,1), 11, 21)
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186 x̄ = map(ξ̄ -> 2ξ̄, lg)
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187 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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188 mg = MappedGrid(lg, x̄, J)
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189
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190 @test ndims(mg) == 2
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191 end
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192
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193 @testset "==" begin
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194 sz = (15,11)
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195 lg = equidistant_grid((0,0), (1,1), sz...)
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196 x = rand(SVector{3,Float64}, sz...)
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197 J = rand(SMatrix{3,2,Float64}, sz...)
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198
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199 sg = MappedGrid(lg, x, J)
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200
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201 sg1 = MappedGrid(equidistant_grid((0,0), (1,1), sz...), copy(x), copy(J))
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202
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203 sz2 = (15,12)
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204 lg2 = equidistant_grid((0,0), (1,1), sz2...)
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205 x2 = rand(SVector{3,Float64}, sz2...)
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206 J2 = rand(SMatrix{3,2,Float64}, sz2...)
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207 sg2 = MappedGrid(lg2, x2, J2)
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208
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209 sg3 = MappedGrid(lg, rand(SVector{3,Float64}, sz...), J)
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210 sg4 = MappedGrid(lg, x, rand(SMatrix{3,2,Float64}, sz...))
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211
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212 @test sg == sg1
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213 @test sg != sg2 # Different size
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214 @test sg != sg3 # Different coordinates
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215 @test sg != sg4 # Different jacobian
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216 end
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217
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218 @testset "boundary_identifiers" begin
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219 lg = equidistant_grid((0,0), (1,1), 11, 15)
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220 x̄ = map(ξ̄ -> 2ξ̄, lg)
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221 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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222 mg = MappedGrid(lg, x̄, J)
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223 @test boundary_identifiers(mg) == boundary_identifiers(lg)
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224 end
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225
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226 @testset "boundary_indices" begin
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227 lg = equidistant_grid((0,0), (1,1), 11, 15)
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228 x̄ = map(ξ̄ -> 2ξ̄, lg)
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229 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
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230 mg = MappedGrid(lg, x̄, J)
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231
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232 @test boundary_indices(mg, CartesianBoundary{1,LowerBoundary}()) == boundary_indices(lg,CartesianBoundary{1,LowerBoundary}())
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233 @test boundary_indices(mg, CartesianBoundary{2,LowerBoundary}()) == boundary_indices(lg,CartesianBoundary{2,LowerBoundary}())
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diff changeset
234 @test boundary_indices(mg, CartesianBoundary{1,UpperBoundary}()) == boundary_indices(lg,CartesianBoundary{1,UpperBoundary}())
1493
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235 end
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236
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237 @testset "boundary_grid" begin
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238 x̄, J = _partially_curved_mapping()
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diff changeset
239 mg = mapped_grid(x̄, J, 10, 11)
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diff changeset
240 J1((ξ, η)) = @SMatrix[
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241 1 ;
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242 η*(2ξ-1);
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243 ]
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244 J2((ξ, η)) = @SMatrix[
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245 0;
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246 1+ξ*(ξ-1);
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247 ]
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248
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249 function expected_bg(mg, bId, Jb)
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035af82f559a Rename logicalgrid to logical_grid
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250 lg = logical_grid(mg)
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251 return MappedGrid(
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252 boundary_grid(lg, bId),
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253 map(x̄, boundary_grid(lg, bId)),
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254 map(Jb, boundary_grid(lg, bId)),
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255 )
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256 end
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257
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258 let bid = TensorGridBoundary{1, LowerBoundary}()
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diff changeset
259 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J2)
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260 end
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261
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262 let bid = TensorGridBoundary{1, UpperBoundary}()
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263 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J2)
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264 end
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265
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266 let bid = TensorGridBoundary{2, LowerBoundary}()
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267 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J1)
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268 end
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269
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270 let bid = TensorGridBoundary{2, UpperBoundary}()
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271 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J1)
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272 end
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273 end
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274 end
1502
a2dc80396808 Add functions `curvilinear_grid`
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275
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276 @testset "mapped_grid" begin
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277 x̄, J = _partially_curved_mapping()
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278 mg = mapped_grid(x̄, J, 10, 11)
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279 @test mg isa MappedGrid{SVector{2,Float64}, 2}
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280
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281 lg = equidistant_grid(unitsquare(), 10, 11)
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282 @test logical_grid(mg) == lg
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283 @test collect(mg) == map(x̄, lg)
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284
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285 @test mapped_grid(lg, x̄, J) == mg
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286
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287 @test mapped_grid(x̄, J, unitsquare(), 10, 11) == mg
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288 end
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289
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290 @testset "metric_tensor" begin
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291 x̄((ξ, η)) = @SVector[ξ*η, ξ + η^2]
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292 J((ξ, η)) = @SMatrix[
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293 η ξ;
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294 1 2η;
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295 ]
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296
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297 g = mapped_grid(x̄, J, 10, 11)
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298 G = map(logical_grid(g)) do (ξ,η)
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299 @SMatrix[
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300 1+η^2 ξ*η+2η;
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301 ξ*η+2η ξ^2 + 4η^2;
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302 ]
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303 end
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304 @test metric_tensor(g) ≈ G
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305 end
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306
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307 @testset "min_spacing" begin
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308 let g = mapped_grid(identity, x->@SMatrix[1], 11)
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309 @test min_spacing(g) ≈ 0.1
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310 end
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311
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312 let g = mapped_grid(x->x+x.^2/2, x->@SMatrix[1 .+ x], 11)
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313 @test min_spacing(g) ≈ 0.105
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314 end
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315
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316 let g = mapped_grid(x->x + x.*(1 .- x)/2, x->@SMatrix[1.5 .- x], 11)
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317 @test min_spacing(g) ≈ 0.055
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318 end
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319
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320 let g = mapped_grid(identity, x->@SMatrix[1 0; 0 1], 11,11)
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321 @test min_spacing(g) ≈ 0.1
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322 end
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323
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324 let g = mapped_grid(identity, x->@SMatrix[1 0; 0 1], 11,21)
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325 @test min_spacing(g) ≈ 0.05
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326 end
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327
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328
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329 @testset let a = @SVector[1,0], b = @SVector[1,1]/√2
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330 g = mapped_grid(_skew_mapping(a,b)...,11,11)
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331
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332 @test min_spacing(g) ≈ 0.1*norm(b-a)
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333 end
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334
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335 @testset let a = @SVector[1,0], b = @SVector[-1,1]/√2
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336 g = mapped_grid(_skew_mapping(a,b)...,11,11)
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337
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338 @test min_spacing(g) ≈ 0.1*norm(a+b)
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339 end
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340 end
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341
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342 @testset "normal" begin
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343 g = mapped_grid(_partially_curved_mapping()...,10, 11)
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344
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345 @test normal(g, CartesianBoundary{1,LowerBoundary}()) == fill(@SVector[-1,0], 11)
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346 @test normal(g, CartesianBoundary{1,UpperBoundary}()) == fill(@SVector[1,0], 11)
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347 @test normal(g, CartesianBoundary{2,LowerBoundary}()) == fill(@SVector[0,-1], 10)
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348 @test normal(g, CartesianBoundary{2,UpperBoundary}()) ≈ map(boundary_grid(g,CartesianBoundary{2,UpperBoundary}())|>logical_grid) do ξ̄
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349 α = 1-2ξ̄[1]
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350 @SVector[α,1]/√(α^2 + 1)
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351 end
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352
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353 g = mapped_grid(_fully_curved_mapping()...,5,4)
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354
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355 unit(v) = v/norm(v)
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356 @testset let bId = CartesianBoundary{1,LowerBoundary}()
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357 lbg = boundary_grid(logical_grid(g), bId)
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358 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
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359 -unit(@SVector[1/2, η/3-1/6])
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360 end
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361 end
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362
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363 @testset let bId = CartesianBoundary{1,UpperBoundary}()
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364 lbg = boundary_grid(logical_grid(g), bId)
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365 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
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366 unit(@SVector[7/2, 2η-1]/(5 + 3η + 2η^2))
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367 end
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368 end
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369
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370 @testset let bId = CartesianBoundary{2,LowerBoundary}()
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371 lbg = boundary_grid(logical_grid(g), bId)
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372 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
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373 -unit(@SVector[-2ξ, 2]/(6 + ξ^2 - 2ξ))
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374 end
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375 end
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376
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377 @testset let bId = CartesianBoundary{2,UpperBoundary}()
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378 lbg = boundary_grid(logical_grid(g), bId)
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379 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
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380 unit(@SVector[-3ξ, 2]/(6 + ξ^2 + 3ξ))
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381 end
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382 end
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383 end