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annotate src/Grids/parameter_space.jl @ 1991:7ead7a87af18 feature/grids/parameter_spaces/in

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Add documentation stub
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 24 Apr 2025 09:05:30 +0200
parents 8cf1764ba124
children ca6d898d3a38
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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 @doc """
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23 in(x, S::ParameterSpace)
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24 ∈(x, S::ParameterSpace)
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25
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26 # TODO
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27 """ Base.in(x,::ParameterSpace)
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29 """
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30 Interval{T} <: ParameterSpace{1}
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31
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32 A `ParameterSpace` representing an interval.
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33 """
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34 struct Interval{T} <: ParameterSpace{1}
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35 a::T
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36 b::T
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37 end
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39 """
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40 Interval(a,b)
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41
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42 An interval with limits `a` and `b`.
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43 """
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44 function Interval(a,b)
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45 a, b = promote(a, b)
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46 Interval{typeof(a)}(a,b)
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47 end
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49 """
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50 limits(i::Interval)
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51
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52 The limits of the interval.
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53 """
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54 limits(i::Interval) = (i.a, i.b)
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55
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56 boundary_identifiers(::Interval) = (LowerBoundary(), UpperBoundary())
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57
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58 Base.in(x, i::Interval) = i.a <= x <= i.b
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60 """
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61 unitinterval(T=Float64)
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62
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63 The interval ``(0,1)``.
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64 """
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65 unitinterval(T=Float64) = Interval(zero(T), one(T))
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66
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68 """
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69 HyperBox{T,D} <: ParameterSpace{D}
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70
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71 A `ParameterSpace` representing a hyper box.
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72 """
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73 struct HyperBox{T,D} <: ParameterSpace{D}
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74 a::SVector{D,T}
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75 b::SVector{D,T}
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76 end
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78 """
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79 HyperBox(a,b)
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80
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81 A `HyperBox` with lower limits `a` and upper limits `b` for each dimension.
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82 """
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83 function HyperBox(a,b)
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84 ET = promote_type(eltype(a),eltype(b))
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85 T = SVector{length(a),ET}
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86 HyperBox(convert(T,a), convert(T,b))
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87 end
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88
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89 Rectangle{T} = HyperBox{T,2}
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90 Box{T} = HyperBox{T,3}
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91
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92 """
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93 limits(box::HyperBox, d)
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94
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95 Limits of `box` along dimension `d`.
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96 """
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97 limits(box::HyperBox, d) = (box.a[d], box.b[d])
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98
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99 """
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100 limits(box::HyperBox)
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101
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102 The lower and upper limits of `box` as tuples.
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103 """
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104 limits(box::HyperBox) = (box.a, box.b)
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105
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106 function boundary_identifiers(box::HyperBox)
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107 mapreduce(vcat, 1:ndims(box)) do d
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108 [
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109 CartesianBoundary{d, LowerBoundary}(),
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110 CartesianBoundary{d, UpperBoundary}(),
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111 ]
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112 end
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113 end
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114
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115 function Base.in(x, box::HyperBox)
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116 return all(eachindex(x)) do i
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117 box.a[i] <= x[i] <= box.b[i]
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118 end
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119 end
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121 """
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122 unitsquare(T=Float64)
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123
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124 The square limited by 0 and 1 in each dimension.
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125 """
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126 unitsquare(T=Float64) = unithyperbox(T,2)
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127
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128 """
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129 unitcube(T=Float64)
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130
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131 The cube limited by 0 and 1 in each dimension.
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132 """
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133 unitcube(T=Float64) = unithyperbox(T,3)
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134
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135 """
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136 unithyperbox(T=Float64, D)
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137
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138 The hypercube limited by 0 and 1 in each dimension.
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139 """
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140 unithyperbox(T, D) = HyperBox((@SVector zeros(T,D)), (@SVector ones(T,D)))
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141 unithyperbox(D) = unithyperbox(Float64,D)
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142
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143
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144 """
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145 Simplex{T,D,NV} <: ParameterSpace{D}
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146
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147 A `ParameterSpace` representing a simplex.
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148 """
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149 struct Simplex{T,D,NV} <: ParameterSpace{D}
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150 verticies::NTuple{NV,SVector{D,T}}
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151
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152 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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153 Simplex(::Tuple{}) = throw(ArgumentError("Must provide at least one vertex."))
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154 end
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155
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156 """
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157 Simplex(verticies...)
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158
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159 A simplex with the given verticies.
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160 """
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161 function Simplex(verticies::Vararg{AbstractArray})
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162 ET = mapreduce(eltype,promote_type,verticies)
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163 T = SVector{length(verticies[1]),ET}
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164
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165 return Simplex(Tuple(convert(T,v) for v ∈ verticies))
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166 end
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167
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168 """
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169 verticies(s::Simplex)
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170
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171 Verticies of `s`.
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172 """
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173 verticies(s::Simplex) = s.verticies
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174
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175 Triangle{T} = Simplex{T,2}
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176 Tetrahedron{T} = Simplex{T,3}
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177
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178 """
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179 unittriangle(T=Float64)
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180
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181 The simplex with verticies ``(0,0)``, ``(1,0)``, and ``(0,1)``.
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182 """
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183 unittriangle(T=Float64) = unitsimplex(T,2)
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184
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185 """
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186 unittetrahedron(T=Float64)
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187
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188 The simplex with verticies ``(0,0,0)``, ``(1,0,0)``, ``(0,1,0)``, and ``(0,0,1)``.
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189 """
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190 unittetrahedron(T=Float64) = unitsimplex(T,3)
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191
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192 """
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193 unitsimplex(T=Float64,D)
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194
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195 The unit simplex in dimension `D` with verticies ``(0,0,0,...)``, ``(1,0,0,...)``, ``(0,1,0,...)``, ``(0,0,1,...)``...
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196 """
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197 function unitsimplex(T,D)
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198 z = @SVector zeros(T,D)
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199 unitelement = one(eltype(z))
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200 verticies = ntuple(i->setindex(z, unitelement, i), D)
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201 return Simplex((z,verticies...))
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202 end
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203 unitsimplex(D) = unitsimplex(Float64, D)