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comparison src/Grids/parameter_space.jl @ 1913:e97f4352b8d0 feature/grids/manifolds

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Merge feature/grids/parameter_spaces
author Jonatan Werpers <jonatan@werpers.com>
date Sat, 01 Feb 2025 23:20:31 +0100
parents 09c4fda8779d
children 15be190a40cd
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1903:04c251bccbd4 1913:e97f4352b8d0
1 """ 1 """
2 ParameterSpace{D} 2 ParameterSpace{D}
3 3
4 A space of parameters of dimension `D`. Used with `Chart` to indicate which 4 A space of parameters of dimension `D`.
5 parameters are valid for that chart.
6 5
7 Common parameter spaces are created using the functions unit sized spaces 6 Common parameter spaces are created using functions for unit sized spaces
8 * `unitinterval` 7 * [`unitinterval`](@ref)
9 * `unitrectangle` 8 * [`unitsquare`](@ref)
10 * `unitbox` 9 * [`unitcube`](@ref)
11 * `unittriangle` 10 * [`unithyperbox`](@ref)
12 * `unittetrahedron` 11 * [`unittriangle`](@ref)
13 * `unithyperbox` 12 * [`unittetrahedron`](@ref)
14 * `unitsimplex` 13 * [`unitsimplex`](@ref)
15 14
16 See also: [`Interval`](@ref), [`Rectangle`](@ref), [`Box`](@ref), 15 See also: [`Interval`](@ref), [`HyperBox`](@ref),
17 [`Triangle`](@ref), [`Tetrahedron`](@ref), [`HyperBox`](@ref), 16 [`Simplex`](@ref).
18 [`Simplex`](@ref),
19 """ 17 """
20 abstract type ParameterSpace{D} end 18 abstract type ParameterSpace{D} end
21 Base.ndims(::ParameterSpace{D}) where D = D 19 Base.ndims(::ParameterSpace{D}) where D = D
22 20
21 """
22 Interval{T} <: ParameterSpace{1}
23
24 A `ParameterSpace` representing an interval.
25 """
23 struct Interval{T} <: ParameterSpace{1} 26 struct Interval{T} <: ParameterSpace{1}
24 a::T 27 a::T
25 b::T 28 b::T
26
27 function Interval(a,b)
28 a, b = promote(a, b)
29 new{typeof(a)}(a,b)
30 end
31 end 29 end
32 30
31 """
32 Interval(a,b)
33
34 An interval with limits `a` and `b`.
35 """
36 function Interval(a,b)
37 a, b = promote(a, b)
38 Interval{typeof(a)}(a,b)
39 end
40
41 """
42 limits(i::Interval)
43
44 The limits of the interval.
45 """
33 limits(i::Interval) = (i.a, i.b) 46 limits(i::Interval) = (i.a, i.b)
34 47
48 """
49 unitinterval(T=Float64)
50
51 The interval ``(0,1)``.
52 """
35 unitinterval(T=Float64) = Interval(zero(T), one(T)) 53 unitinterval(T=Float64) = Interval(zero(T), one(T))
36 54
37 55
56 """
57 HyperBox{T,D} <: ParameterSpace{D}
58
59 A `ParameterSpace` representing a hyper box.
60 """
38 struct HyperBox{T,D} <: ParameterSpace{D} 61 struct HyperBox{T,D} <: ParameterSpace{D}
39 a::SVector{D,T} 62 a::SVector{D,T}
40 b::SVector{D,T} 63 b::SVector{D,T}
41 end 64 end
42 65
66 """
67 HyperBox(a,b)
68
69 A `HyperBox` with lower limits `a` and upper limits `b` for each dimension.
70 """
43 function HyperBox(a,b) 71 function HyperBox(a,b)
44 ET = promote_type(eltype(a),eltype(b)) 72 ET = promote_type(eltype(a),eltype(b))
45 T = SVector{length(a),ET} 73 T = SVector{length(a),ET}
46 HyperBox(convert(T,a), convert(T,b)) 74 HyperBox(convert(T,a), convert(T,b))
47 end 75 end
48 76
49 Rectangle{T} = HyperBox{T,2} 77 Rectangle{T} = HyperBox{T,2}
50 Box{T} = HyperBox{T,3} 78 Box{T} = HyperBox{T,3}
51 79
80 """
81 limits(box::HyperBox, d)
82
83 Limits of `box` along dimension `d`.
84 """
52 limits(box::HyperBox, d) = (box.a[d], box.b[d]) 85 limits(box::HyperBox, d) = (box.a[d], box.b[d])
86
87 """
88 limits(box::HyperBox)
89
90 The lower and upper limits of `box` as tuples.
91 """
53 limits(box::HyperBox) = (box.a, box.b) 92 limits(box::HyperBox) = (box.a, box.b)
54 93
94 """
95 unitsquare(T=Float64)
96
97 The square starting at ``(0,0)`` with side length 1.
98 """
55 unitsquare(T=Float64) = unithyperbox(T,2) 99 unitsquare(T=Float64) = unithyperbox(T,2)
100
101 """
102 unitcube(T=Float64)
103
104 The cube starting at ``(0,0,0)`` with side length 1.
105 """
56 unitcube(T=Float64) = unithyperbox(T,3) 106 unitcube(T=Float64) = unithyperbox(T,3)
107
108 """
109 unithyperbox(T=Float64, D)
110
111 The hypercube in dimension `D` starting at ``(0,0,0,...)`` with side length 1.
112 """
57 unithyperbox(T, D) = HyperBox((@SVector zeros(T,D)), (@SVector ones(T,D))) 113 unithyperbox(T, D) = HyperBox((@SVector zeros(T,D)), (@SVector ones(T,D)))
58 unithyperbox(D) = unithyperbox(Float64,D) 114 unithyperbox(D) = unithyperbox(Float64,D)
59 115
60 116
117 """
118 Simplex{T,D,NV} <: ParameterSpace{D}
119
120 A `ParameterSpace` representing a simplex.
121 """
61 struct Simplex{T,D,NV} <: ParameterSpace{D} 122 struct Simplex{T,D,NV} <: ParameterSpace{D}
62 verticies::NTuple{NV,SVector{D,T}} 123 verticies::NTuple{NV,SVector{D,T}}
63 124
64 Simplex(verticies::Tuple{SVector{D,T}, Vararg{SVector{D,T},N}}) where {T,D,N} = new{T,D,N+1}(verticies) 125 Simplex(verticies::Tuple{SVector{D,T}, Vararg{SVector{D,T},N}}) where {T,D,N} = new{T,D,N+1}(verticies)
65 Simplex(::Tuple{}) = throw(ArgumentError("Must provide at least one vertex.")) 126 Simplex(::Tuple{}) = throw(ArgumentError("Must provide at least one vertex."))
66 end 127 end
67 128
129 """
130 Simplex(verticies...)
131
132 A simplex with the given vierticies.
133 """
68 function Simplex(verticies::Vararg{AbstractArray}) 134 function Simplex(verticies::Vararg{AbstractArray})
69 ET = mapreduce(eltype,promote_type,verticies) 135 ET = mapreduce(eltype,promote_type,verticies)
70 T = SVector{length(verticies[1]),ET} 136 T = SVector{length(verticies[1]),ET}
71 137
72 return Simplex(Tuple(convert(T,v) for v ∈ verticies)) 138 return Simplex(Tuple(convert(T,v) for v ∈ verticies))
73 end 139 end
74 140
141 """
142 verticies(s::Simplex)
143
144 Verticies of `s`.
145 """
75 verticies(s::Simplex) = s.verticies 146 verticies(s::Simplex) = s.verticies
76 147
77 Triangle{T} = Simplex{T,2} 148 Triangle{T} = Simplex{T,2}
78 Tetrahedron{T} = Simplex{T,3} 149 Tetrahedron{T} = Simplex{T,3}
79 150
151 """
152 unittriangle(T=Float64)
153
154 The simplex with verticies ``(0,0)``, ``(1,0)``, and ``(0,1)``.
155 """
80 unittriangle(T=Float64) = unitsimplex(T,2) 156 unittriangle(T=Float64) = unitsimplex(T,2)
157
158 """
159 unittetrahedron(T=Float64)
160
161 The simplex with verticies ``(0,0,0)``, ``(1,0,0)``, ``(0,1,0)``, and ``(0,0,1)``.
162 """
81 unittetrahedron(T=Float64) = unitsimplex(T,3) 163 unittetrahedron(T=Float64) = unitsimplex(T,3)
164
165 """
166 unitsimplex(T=Float64,D)
167
168 The unit simplex in dimension `D` with verticies ``(0,0,0,...)``, ``(1,0,0,...)``, ``(0,1,0,...)``, ``(0,0,1,...)``...
169 """
82 function unitsimplex(T,D) 170 function unitsimplex(T,D)
83 z = @SVector zeros(T,D) 171 z = @SVector zeros(T,D)
84 unitelement = one(eltype(z)) 172 unitelement = one(eltype(z))
85 verticies = ntuple(i->setindex(z, unitelement, i), D) 173 verticies = ntuple(i->setindex(z, unitelement, i), D)
86 return Simplex((z,verticies...)) 174 return Simplex((z,verticies...))