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annotate src/Grids/parameter_space.jl @ 1956:b0fcb29e3620 feature/grids/multiblock_boundaries

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author Jonatan Werpers <jonatan@werpers.com>
date Tue, 11 Feb 2025 08:54:18 +0100
parents 449cce897da9
children 77ff0a2acbe5
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1 """
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2 ParameterSpace{D}
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3
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4 A space of parameters of dimension `D`.
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5
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6 Common parameter spaces are created using functions for unit sized spaces
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7 * [`unitinterval`](@ref)
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8 * [`unitsquare`](@ref)
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9 * [`unitcube`](@ref)
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10 * [`unithyperbox`](@ref)
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11 * [`unittriangle`](@ref)
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12 * [`unittetrahedron`](@ref)
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13 * [`unitsimplex`](@ref)
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14
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15 See also: [`Interval`](@ref), [`HyperBox`](@ref),
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16 [`Simplex`](@ref).
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17 """
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18 abstract type ParameterSpace{D} end
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19 Base.ndims(::ParameterSpace{D}) where D = D
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21 """
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22 Interval{T} <: ParameterSpace{1}
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23
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24 A `ParameterSpace` representing an interval.
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25 """
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26 struct Interval{T} <: ParameterSpace{1}
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27 a::T
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28 b::T
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29 end
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30
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31 """
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32 Interval(a,b)
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33
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34 An interval with limits `a` and `b`.
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35 """
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36 function Interval(a,b)
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37 a, b = promote(a, b)
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38 Interval{typeof(a)}(a,b)
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39 end
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41 """
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42 limits(i::Interval)
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43
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44 The limits of the interval.
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45 """
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46 limits(i::Interval) = (i.a, i.b)
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47
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48 boundary_identifiers(::Interval) = (LowerBoundary(), UpperBoundary())
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50 """
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51 unitinterval(T=Float64)
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52
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53 The interval ``(0,1)``.
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54 """
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55 unitinterval(T=Float64) = Interval(zero(T), one(T))
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58 """
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59 HyperBox{T,D} <: ParameterSpace{D}
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60
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61 A `ParameterSpace` representing a hyper box.
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62 """
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63 struct HyperBox{T,D} <: ParameterSpace{D}
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64 a::SVector{D,T}
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65 b::SVector{D,T}
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66 end
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67
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68 """
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69 HyperBox(a,b)
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70
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71 A `HyperBox` with lower limits `a` and upper limits `b` for each dimension.
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72 """
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73 function HyperBox(a,b)
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74 ET = promote_type(eltype(a),eltype(b))
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75 T = SVector{length(a),ET}
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76 HyperBox(convert(T,a), convert(T,b))
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77 end
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78
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79 Rectangle{T} = HyperBox{T,2}
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80 Box{T} = HyperBox{T,3}
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81
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82 """
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83 limits(box::HyperBox, d)
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84
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85 Limits of `box` along dimension `d`.
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86 """
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87 limits(box::HyperBox, d) = (box.a[d], box.b[d])
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88
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89 """
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90 limits(box::HyperBox)
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91
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92 The lower and upper limits of `box` as tuples.
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93 """
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94 limits(box::HyperBox) = (box.a, box.b)
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95
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96 function boundary_identifiers(box::HyperBox)
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97 mapreduce(vcat, 1:ndims(box)) do d
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98 [
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99 CartesianBoundary{d, LowerBoundary}(),
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100 CartesianBoundary{d, UpperBoundary}(),
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101 ]
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102 end
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103 end
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106 """
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107 unitsquare(T=Float64)
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108
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109 The square limited by 0 and 1 in each dimension.
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110 """
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111 unitsquare(T=Float64) = unithyperbox(T,2)
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112
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113 """
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114 unitcube(T=Float64)
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115
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116 The cube limited by 0 and 1 in each dimension.
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117 """
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118 unitcube(T=Float64) = unithyperbox(T,3)
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119
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120 """
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121 unithyperbox(T=Float64, D)
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122
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123 The hypercube limited by 0 and 1 in each dimension.
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124 """
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125 unithyperbox(T, D) = HyperBox((@SVector zeros(T,D)), (@SVector ones(T,D)))
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126 unithyperbox(D) = unithyperbox(Float64,D)
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127
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128
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129 """
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130 Simplex{T,D,NV} <: ParameterSpace{D}
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131
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132 A `ParameterSpace` representing a simplex.
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133 """
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134 struct Simplex{T,D,NV} <: ParameterSpace{D}
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135 verticies::NTuple{NV,SVector{D,T}}
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136
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137 Simplex(verticies::Tuple{SVector{D,T}, Vararg{SVector{D,T},N}}) where {T,D,N} = new{T,D,N+1}(verticies)
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138 Simplex(::Tuple{}) = throw(ArgumentError("Must provide at least one vertex."))
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139 end
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140
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141 """
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142 Simplex(verticies...)
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143
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144 A simplex with the given verticies.
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145 """
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146 function Simplex(verticies::Vararg{AbstractArray})
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147 ET = mapreduce(eltype,promote_type,verticies)
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148 T = SVector{length(verticies[1]),ET}
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149
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150 return Simplex(Tuple(convert(T,v) for v ∈ verticies))
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151 end
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152
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153 """
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154 verticies(s::Simplex)
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155
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156 Verticies of `s`.
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157 """
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158 verticies(s::Simplex) = s.verticies
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159
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160 Triangle{T} = Simplex{T,2}
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161 Tetrahedron{T} = Simplex{T,3}
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162
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163 """
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164 unittriangle(T=Float64)
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165
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166 The simplex with verticies ``(0,0)``, ``(1,0)``, and ``(0,1)``.
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167 """
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168 unittriangle(T=Float64) = unitsimplex(T,2)
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169
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170 """
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171 unittetrahedron(T=Float64)
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172
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173 The simplex with verticies ``(0,0,0)``, ``(1,0,0)``, ``(0,1,0)``, and ``(0,0,1)``.
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174 """
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175 unittetrahedron(T=Float64) = unitsimplex(T,3)
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176
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177 """
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178 unitsimplex(T=Float64,D)
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179
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180 The unit simplex in dimension `D` with verticies ``(0,0,0,...)``, ``(1,0,0,...)``, ``(0,1,0,...)``, ``(0,0,1,...)``...
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181 """
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182 function unitsimplex(T,D)
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183 z = @SVector zeros(T,D)
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184 unitelement = one(eltype(z))
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185 verticies = ntuple(i->setindex(z, unitelement, i), D)
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186 return Simplex((z,verticies...))
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187 end
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188 unitsimplex(D) = unitsimplex(Float64, D)