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annotate src/Grids/parameter_space.jl @ 2006:e48577b5e707 feature/grids/manifolds

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author Jonatan Werpers <jonatan@werpers.com>
date Thu, 01 May 2025 14:58:24 +0200
parents 889c18ad56bf
children
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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 @doc """
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22 in(x, S::ParameterSpace)
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23 ∈(x, S::ParameterSpace)
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24
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25 Test if the point `x` is in the parameter space `S`.
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26 """ Base.in(x,::ParameterSpace)
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28 """
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29 Interval{T} <: ParameterSpace{1}
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30
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31 A `ParameterSpace` representing an interval.
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32 """
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33 struct Interval{T} <: ParameterSpace{1}
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34 a::T
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35 b::T
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36 end
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38 """
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39 Interval(a,b)
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40
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41 An interval with limits `a` and `b`.
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42 """
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43 function Interval(a,b)
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44 a, b = promote(a, b)
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45 Interval{typeof(a)}(a,b)
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46 end
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48 """
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49 limits(i::Interval)
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50
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51 The limits of the interval.
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52 """
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53 limits(i::Interval) = (i.a, i.b)
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54
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55 boundary_identifiers(::Interval) = (LowerBoundary(), UpperBoundary())
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56
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57 Base.in(x, i::Interval) = i.a <= x <= i.b
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59 """
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60 unitinterval(T=Float64)
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61
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62 The interval ``(0,1)``.
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63 """
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64 unitinterval(T=Float64) = Interval(zero(T), one(T))
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67 """
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68 HyperBox{T,D} <: ParameterSpace{D}
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69
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70 A `ParameterSpace` representing a hyper box.
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71 """
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72 struct HyperBox{T,D} <: ParameterSpace{D}
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73 a::SVector{D,T}
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74 b::SVector{D,T}
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75 end
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77 """
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78 HyperBox(a,b)
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79
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80 A `HyperBox` with lower limits `a` and upper limits `b` for each dimension.
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81 """
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82 function HyperBox(a,b)
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83 ET = promote_type(eltype(a),eltype(b))
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84 T = SVector{length(a),ET}
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85 HyperBox(convert(T,a), convert(T,b))
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86 end
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87
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88 Rectangle{T} = HyperBox{T,2}
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89 Box{T} = HyperBox{T,3}
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91 """
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92 limits(box::HyperBox, d)
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93
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94 Limits of `box` along dimension `d`.
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95 """
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96 limits(box::HyperBox, d) = (box.a[d], box.b[d])
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97
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98 """
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99 limits(box::HyperBox)
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100
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101 The lower and upper limits of `box` as tuples.
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102 """
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103 limits(box::HyperBox) = (box.a, box.b)
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104
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105 function boundary_identifiers(box::HyperBox)
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106 mapreduce(vcat, 1:ndims(box)) do d
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107 [
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108 CartesianBoundary{d, LowerBoundary}(),
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109 CartesianBoundary{d, UpperBoundary}(),
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110 ]
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111 end
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112 end
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113
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114 function Base.in(x, box::HyperBox)
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115 return all(eachindex(x)) do i
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116 box.a[i] <= x[i] <= box.b[i]
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117 end
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118 end
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120 """
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121 unitsquare(T=Float64)
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122
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123 The square limited by 0 and 1 in each dimension.
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124 """
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125 unitsquare(T=Float64) = unithyperbox(T,2)
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126
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127 """
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128 unitcube(T=Float64)
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129
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130 The cube limited by 0 and 1 in each dimension.
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131 """
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132 unitcube(T=Float64) = unithyperbox(T,3)
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133
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134 """
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135 unithyperbox(T=Float64, D)
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136
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137 The hypercube limited by 0 and 1 in each dimension.
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138 """
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139 unithyperbox(T, D) = HyperBox((@SVector zeros(T,D)), (@SVector ones(T,D)))
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140 unithyperbox(D) = unithyperbox(Float64,D)
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141
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142
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143 """
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144 Simplex{T,D,NV} <: ParameterSpace{D}
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145
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146 A `ParameterSpace` representing a simplex.
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147 """
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148 struct Simplex{T,D,NV} <: ParameterSpace{D}
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149 verticies::NTuple{NV,SVector{D,T}}
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150
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151 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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152 Simplex(::Tuple{}) = throw(ArgumentError("Must provide at least one vertex."))
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153 end
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154
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155 """
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156 Simplex(verticies...)
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157
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158 A simplex with the given verticies.
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159 """
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160 function Simplex(verticies::Vararg{AbstractArray})
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161 ET = mapreduce(eltype,promote_type,verticies)
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162 T = SVector{length(verticies[1]),ET}
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163
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164 return Simplex(Tuple(convert(T,v) for v ∈ verticies))
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165 end
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166
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167 function Base.in(x, s::Simplex)
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168 v₁ = s.verticies[1]
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169 V = map(s.verticies) do v
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170 v - v₁
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171 end
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172
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173 A = hcat(V[2:end]...) # Matrix with edge vectors as columns
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174 λ = A \ (x - v₁)
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175
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176 λ_full = (1 - sum(λ), λ...) # Full barycentric coordinates
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177
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178 return all(λᵢ -> zero(λᵢ) ≤ λᵢ ≤ one(λᵢ), λ_full)
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179 end
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180
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181 """
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182 verticies(s::Simplex)
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183
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184 Verticies of `s`.
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185 """
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186 verticies(s::Simplex) = s.verticies
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187
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188 Triangle{T} = Simplex{T,2}
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189 Tetrahedron{T} = Simplex{T,3}
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190
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191 """
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192 unittriangle(T=Float64)
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193
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194 The simplex with verticies ``(0,0)``, ``(1,0)``, and ``(0,1)``.
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195 """
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196 unittriangle(T=Float64) = unitsimplex(T,2)
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197
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198 """
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199 unittetrahedron(T=Float64)
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200
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201 The simplex with verticies ``(0,0,0)``, ``(1,0,0)``, ``(0,1,0)``, and ``(0,0,1)``.
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202 """
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203 unittetrahedron(T=Float64) = unitsimplex(T,3)
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204
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205 """
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206 unitsimplex(T=Float64,D)
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207
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208 The unit simplex in dimension `D` with verticies ``(0,0,0,...)``, ``(1,0,0,...)``, ``(0,1,0,...)``, ``(0,0,1,...)``...
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209 """
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210 function unitsimplex(T,D)
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211 z = @SVector zeros(T,D)
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212 unitelement = one(eltype(z))
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213 verticies = ntuple(i->setindex(z, unitelement, i), D)
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214 return Simplex((z,verticies...))
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215 end
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216 unitsimplex(D) = unitsimplex(Float64, D)