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annotate src/Grids/parameter_space.jl @ 1990:8cf1764ba124 feature/grids/parameter_spaces/in

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Implement Base.in(x, ::HyperBox)
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 23 Apr 2025 15:42:38 +0200
parents 77ff0a2acbe5
children 7ead7a87af18
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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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20
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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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49
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50 Base.in(x, i::Interval) = i.a <= x <= i.b
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52 """
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53 unitinterval(T=Float64)
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54
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55 The interval ``(0,1)``.
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56 """
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57 unitinterval(T=Float64) = Interval(zero(T), one(T))
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60 """
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61 HyperBox{T,D} <: ParameterSpace{D}
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62
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63 A `ParameterSpace` representing a hyper box.
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64 """
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65 struct HyperBox{T,D} <: ParameterSpace{D}
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66 a::SVector{D,T}
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67 b::SVector{D,T}
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68 end
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70 """
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71 HyperBox(a,b)
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72
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73 A `HyperBox` with lower limits `a` and upper limits `b` for each dimension.
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74 """
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75 function HyperBox(a,b)
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76 ET = promote_type(eltype(a),eltype(b))
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77 T = SVector{length(a),ET}
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78 HyperBox(convert(T,a), convert(T,b))
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79 end
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80
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81 Rectangle{T} = HyperBox{T,2}
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82 Box{T} = HyperBox{T,3}
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83
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84 """
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85 limits(box::HyperBox, d)
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86
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87 Limits of `box` along dimension `d`.
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88 """
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89 limits(box::HyperBox, d) = (box.a[d], box.b[d])
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90
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91 """
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92 limits(box::HyperBox)
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93
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94 The lower and upper limits of `box` as tuples.
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95 """
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96 limits(box::HyperBox) = (box.a, box.b)
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97
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98 function boundary_identifiers(box::HyperBox)
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99 mapreduce(vcat, 1:ndims(box)) do d
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100 [
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101 CartesianBoundary{d, LowerBoundary}(),
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102 CartesianBoundary{d, UpperBoundary}(),
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103 ]
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104 end
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105 end
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106
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107 function Base.in(x, box::HyperBox)
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108 return all(eachindex(x)) do i
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109 box.a[i] <= x[i] <= box.b[i]
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110 end
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111 end
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113 """
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114 unitsquare(T=Float64)
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115
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116 The square limited by 0 and 1 in each dimension.
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117 """
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118 unitsquare(T=Float64) = unithyperbox(T,2)
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119
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120 """
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121 unitcube(T=Float64)
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122
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123 The cube limited by 0 and 1 in each dimension.
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124 """
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125 unitcube(T=Float64) = unithyperbox(T,3)
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126
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127 """
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128 unithyperbox(T=Float64, D)
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129
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130 The hypercube limited by 0 and 1 in each dimension.
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131 """
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132 unithyperbox(T, D) = HyperBox((@SVector zeros(T,D)), (@SVector ones(T,D)))
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133 unithyperbox(D) = unithyperbox(Float64,D)
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134
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135
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136 """
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137 Simplex{T,D,NV} <: ParameterSpace{D}
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138
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139 A `ParameterSpace` representing a simplex.
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140 """
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141 struct Simplex{T,D,NV} <: ParameterSpace{D}
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142 verticies::NTuple{NV,SVector{D,T}}
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143
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144 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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145 Simplex(::Tuple{}) = throw(ArgumentError("Must provide at least one vertex."))
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146 end
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147
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148 """
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149 Simplex(verticies...)
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150
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151 A simplex with the given verticies.
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152 """
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153 function Simplex(verticies::Vararg{AbstractArray})
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154 ET = mapreduce(eltype,promote_type,verticies)
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155 T = SVector{length(verticies[1]),ET}
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156
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157 return Simplex(Tuple(convert(T,v) for v ∈ verticies))
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158 end
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159
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160 """
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161 verticies(s::Simplex)
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162
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163 Verticies of `s`.
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164 """
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165 verticies(s::Simplex) = s.verticies
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166
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167 Triangle{T} = Simplex{T,2}
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168 Tetrahedron{T} = Simplex{T,3}
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169
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170 """
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171 unittriangle(T=Float64)
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172
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173 The simplex with verticies ``(0,0)``, ``(1,0)``, and ``(0,1)``.
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174 """
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175 unittriangle(T=Float64) = unitsimplex(T,2)
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176
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177 """
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178 unittetrahedron(T=Float64)
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179
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180 The simplex with verticies ``(0,0,0)``, ``(1,0,0)``, ``(0,1,0)``, and ``(0,0,1)``.
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181 """
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182 unittetrahedron(T=Float64) = unitsimplex(T,3)
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183
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184 """
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185 unitsimplex(T=Float64,D)
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186
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187 The unit simplex in dimension `D` with verticies ``(0,0,0,...)``, ``(1,0,0,...)``, ``(0,1,0,...)``, ``(0,0,1,...)``...
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188 """
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189 function unitsimplex(T,D)
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190 z = @SVector zeros(T,D)
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191 unitelement = one(eltype(z))
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192 verticies = ntuple(i->setindex(z, unitelement, i), D)
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193 return Simplex((z,verticies...))
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194 end
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195 unitsimplex(D) = unitsimplex(Float64, D)