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comparison test/Grids/mapped_grid_test.jl @ 1835:a6f28a8b8f3f refactor/lazy_tensors/elementwise_ops

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Merge default
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 09 Jan 2025 12:40:49 +0100
parents 43c0bfc13de3
children 2b5f81e288f1 d91a9f47380f
comparison
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1789:48eaa973159a 1835:a6f28a8b8f3f
1 using Diffinitive.Grids
2 using Diffinitive.RegionIndices
3 using Test
4 using StaticArrays
5 using LinearAlgebra
6
7
8 _skew_mapping(a,b) = (ξ̄->ξ̄[1]*a + ξ̄[2]*b, ξ̄->[a b])
9
10 function _partially_curved_mapping()
11 x̄((ξ, η)) = @SVector[ξ, η*(1+ξ*(ξ-1))]
12 J((ξ, η)) = @SMatrix[
13 1 0;
14 η*(2ξ-1) 1+ξ*(ξ-1);
15 ]
16
17 return x̄, J
18 end
19
20 function _fully_curved_mapping()
21 x̄((ξ, η)) = @SVector[2ξ + η*(1-η), 3η+(1+η/2)*ξ^2]
22 J((ξ, η)) = @SMatrix[
23 2 1-2η;
24 (2+η)*ξ 3+1/2*ξ^2;
25 ]
26
27 return x̄, J
28 end
29
30 @testset "MappedGrid" begin
31 @testset "Constructor" begin
32 lg = equidistant_grid((0,0), (1,1), 11, 21)
33
34 x̄ = map(ξ̄ -> 2ξ̄, lg)
35 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
36 mg = MappedGrid(lg, x̄, J)
37
38 @test mg isa Grid{SVector{2, Float64},2}
39 @test jacobian(mg) isa Array{<:AbstractMatrix}
40 @test logical_grid(mg) isa Grid
41
42 @test collect(mg) == x̄
43 @test jacobian(mg) == J
44 @test logical_grid(mg) == lg
45
46
47 x̄ = map(ξ̄ -> @SVector[ξ̄[1],ξ̄[2], ξ̄[1] + ξ̄[2]], lg)
48 J = map(ξ̄ -> @SMatrix[1 0; 0 1; 1 1], lg)
49 mg = MappedGrid(lg, x̄, J)
50
51 @test mg isa Grid{SVector{3, Float64},2}
52 @test jacobian(mg) isa Array{<:AbstractMatrix}
53 @test logical_grid(mg) isa Grid
54
55 @test collect(mg) == x̄
56 @test jacobian(mg) == J
57 @test logical_grid(mg) == lg
58
59 sz1 = (10,11)
60 sz2 = (10,12)
61 @test_throws ArgumentError("Sizes must match") MappedGrid(
62 equidistant_grid((0,0), (1,1), sz2...),
63 rand(SVector{2},sz1...),
64 rand(SMatrix{2,2},sz1...),
65 )
66
67 @test_throws ArgumentError("Sizes must match") MappedGrid(
68 equidistant_grid((0,0), (1,1), sz1...),
69 rand(SVector{2},sz2...),
70 rand(SMatrix{2,2},sz1...),
71 )
72
73 @test_throws ArgumentError("Sizes must match") MappedGrid(
74 equidistant_grid((0,0), (1,1), sz1...),
75 rand(SVector{2},sz1...),
76 rand(SMatrix{2,2},sz2...),
77 )
78
79 err_str = "The size of the jacobian must match the dimensions of the grid and coordinates"
80 @test_throws ArgumentError(err_str) MappedGrid(
81 equidistant_grid((0,0), (1,1), 10, 11),
82 rand(SVector{3}, 10, 11),
83 rand(SMatrix{3,4}, 10, 11),
84 )
85
86 @test_throws ArgumentError(err_str) MappedGrid(
87 equidistant_grid((0,0), (1,1), 10, 11),
88 rand(SVector{3}, 10, 11),
89 rand(SMatrix{4,2}, 10, 11),
90 )
91 end
92
93 @testset "Indexing Interface" begin
94 lg = equidistant_grid((0,0), (1,1), 11, 21)
95 x̄ = map(ξ̄ -> 2ξ̄, lg)
96 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
97 mg = MappedGrid(lg, x̄, J)
98 @test mg[1,1] == [0.0, 0.0]
99 @test mg[4,2] == [0.6, 0.1]
100 @test mg[6,10] == [1., 0.9]
101
102 @test mg[begin, begin] == [0.0, 0.0]
103 @test mg[end,end] == [2.0, 2.0]
104 @test mg[begin,end] == [0., 2.]
105
106 @test axes(mg) == (1:11, 1:21)
107
108 @testset "cartesian indexing" begin
109 cases = [
110 (1,1) ,
111 (3,5) ,
112 (10,6),
113 (1,1) ,
114 (3,2) ,
115 ]
116
117 @testset "i = $is" for (lg, is) ∈ cases
118 @test mg[CartesianIndex(is...)] == mg[is...]
119 end
120 end
121
122 @testset "eachindex" begin
123 @test eachindex(mg) == CartesianIndices((11,21))
124 end
125
126 @testset "firstindex" begin
127 @test firstindex(mg, 1) == 1
128 @test firstindex(mg, 2) == 1
129 end
130
131 @testset "lastindex" begin
132 @test lastindex(mg, 1) == 11
133 @test lastindex(mg, 2) == 21
134 end
135 end
136
137 @testset "Iterator interface" begin
138 lg = equidistant_grid((0,0), (1,1), 11, 21)
139 x̄ = map(ξ̄ -> 2ξ̄, lg)
140 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
141
142 mg = MappedGrid(lg, x̄, J)
143
144 lg2 = equidistant_grid((0,0), (1,1), 15, 11)
145 sg = MappedGrid(
146 equidistant_grid((0,0), (1,1), 15, 11),
147 map(ξ̄ -> @SArray[ξ̄[1], ξ̄[2], -ξ̄[1]], lg2), rand(SMatrix{3,2,Float64},15,11)
148 )
149
150 @test eltype(mg) == SVector{2,Float64}
151 @test eltype(sg) == SVector{3,Float64}
152
153 @test eltype(typeof(mg)) == SVector{2,Float64}
154 @test eltype(typeof(sg)) == SVector{3,Float64}
155
156 @test size(mg) == (11,21)
157 @test size(sg) == (15,11)
158
159 @test size(mg,2) == 21
160 @test size(sg,2) == 11
161
162 @test length(mg) == 231
163 @test length(sg) == 165
164
165 @test Base.IteratorSize(mg) == Base.HasShape{2}()
166 @test Base.IteratorSize(typeof(mg)) == Base.HasShape{2}()
167
168 @test Base.IteratorSize(sg) == Base.HasShape{2}()
169 @test Base.IteratorSize(typeof(sg)) == Base.HasShape{2}()
170
171 element, state = iterate(mg)
172 @test element == lg[1,1].*2
173 element, _ = iterate(mg, state)
174 @test element == lg[2,1].*2
175
176 element, state = iterate(sg)
177 @test element == sg.physicalcoordinates[1,1]
178 element, _ = iterate(sg, state)
179 @test element == sg.physicalcoordinates[2,1]
180
181 @test collect(mg) == 2 .* lg
182 end
183
184 @testset "Base" begin
185 lg = equidistant_grid((0,0), (1,1), 11, 21)
186 x̄ = map(ξ̄ -> 2ξ̄, lg)
187 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
188 mg = MappedGrid(lg, x̄, J)
189
190 @test ndims(mg) == 2
191 end
192
193 @testset "==" begin
194 sz = (15,11)
195 lg = equidistant_grid((0,0), (1,1), sz...)
196 x = rand(SVector{3,Float64}, sz...)
197 J = rand(SMatrix{3,2,Float64}, sz...)
198
199 sg = MappedGrid(lg, x, J)
200
201 sg1 = MappedGrid(equidistant_grid((0,0), (1,1), sz...), copy(x), copy(J))
202
203 sz2 = (15,12)
204 lg2 = equidistant_grid((0,0), (1,1), sz2...)
205 x2 = rand(SVector{3,Float64}, sz2...)
206 J2 = rand(SMatrix{3,2,Float64}, sz2...)
207 sg2 = MappedGrid(lg2, x2, J2)
208
209 sg3 = MappedGrid(lg, rand(SVector{3,Float64}, sz...), J)
210 sg4 = MappedGrid(lg, x, rand(SMatrix{3,2,Float64}, sz...))
211
212 @test sg == sg1
213 @test sg != sg2 # Different size
214 @test sg != sg3 # Different coordinates
215 @test sg != sg4 # Different jacobian
216 end
217
218 @testset "boundary_identifiers" begin
219 lg = equidistant_grid((0,0), (1,1), 11, 15)
220 x̄ = map(ξ̄ -> 2ξ̄, lg)
221 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
222 mg = MappedGrid(lg, x̄, J)
223 @test boundary_identifiers(mg) == boundary_identifiers(lg)
224 end
225
226 @testset "boundary_indices" begin
227 lg = equidistant_grid((0,0), (1,1), 11, 15)
228 x̄ = map(ξ̄ -> 2ξ̄, lg)
229 J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
230 mg = MappedGrid(lg, x̄, J)
231
232 @test boundary_indices(mg, CartesianBoundary{1,LowerBoundary}()) == boundary_indices(lg,CartesianBoundary{1,LowerBoundary}())
233 @test boundary_indices(mg, CartesianBoundary{2,LowerBoundary}()) == boundary_indices(lg,CartesianBoundary{2,LowerBoundary}())
234 @test boundary_indices(mg, CartesianBoundary{1,UpperBoundary}()) == boundary_indices(lg,CartesianBoundary{1,UpperBoundary}())
235 end
236
237 @testset "boundary_grid" begin
238 x̄, J = _partially_curved_mapping()
239 mg = mapped_grid(x̄, J, 10, 11)
240 J1((ξ, η)) = @SMatrix[
241 1 ;
242 η*(2ξ-1);
243 ]
244 J2((ξ, η)) = @SMatrix[
245 0;
246 1+ξ*(ξ-1);
247 ]
248
249 function expected_bg(mg, bId, Jb)
250 lg = logical_grid(mg)
251 return MappedGrid(
252 boundary_grid(lg, bId),
253 map(x̄, boundary_grid(lg, bId)),
254 map(Jb, boundary_grid(lg, bId)),
255 )
256 end
257
258 let bid = TensorGridBoundary{1, LowerBoundary}()
259 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J2)
260 end
261
262 let bid = TensorGridBoundary{1, UpperBoundary}()
263 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J2)
264 end
265
266 let bid = TensorGridBoundary{2, LowerBoundary}()
267 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J1)
268 end
269
270 let bid = TensorGridBoundary{2, UpperBoundary}()
271 @test boundary_grid(mg, bid) == expected_bg(mg, bid, J1)
272 end
273 end
274 end
275
276 @testset "mapped_grid" begin
277 x̄, J = _partially_curved_mapping()
278 mg = mapped_grid(x̄, J, 10, 11)
279 @test mg isa MappedGrid{SVector{2,Float64}, 2}
280
281 lg = equidistant_grid((0,0), (1,1), 10, 11)
282 @test logical_grid(mg) == lg
283 @test collect(mg) == map(x̄, lg)
284
285 @test mapped_grid(lg, x̄, J) == mg
286 end
287
288 @testset "metric_tensor" begin
289 x̄((ξ, η)) = @SVector[ξ*η, ξ + η^2]
290 J((ξ, η)) = @SMatrix[
291 η ξ;
292 1 2η;
293 ]
294
295 g = mapped_grid(x̄, J, 10, 11)
296 G = map(logical_grid(g)) do (ξ,η)
297 @SMatrix[
298 1+η^2 ξ*η+2η;
299 ξ*η+2η ξ^2 + 4η^2;
300 ]
301 end
302 @test metric_tensor(g) ≈ G
303 end
304
305 @testset "min_spacing" begin
306 let g = mapped_grid(identity, x->@SMatrix[1], 11)
307 @test min_spacing(g) ≈ 0.1
308 end
309
310 let g = mapped_grid(x->x+x.^2/2, x->@SMatrix[1 .+ x], 11)
311 @test min_spacing(g) ≈ 0.105
312 end
313
314 let g = mapped_grid(x->x + x.*(1 .- x)/2, x->@SMatrix[1.5 .- x], 11)
315 @test min_spacing(g) ≈ 0.055
316 end
317
318 let g = mapped_grid(identity, x->@SMatrix[1 0; 0 1], 11,11)
319 @test min_spacing(g) ≈ 0.1
320 end
321
322 let g = mapped_grid(identity, x->@SMatrix[1 0; 0 1], 11,21)
323 @test min_spacing(g) ≈ 0.05
324 end
325
326
327 @testset let a = @SVector[1,0], b = @SVector[1,1]/√2
328 g = mapped_grid(_skew_mapping(a,b)...,11,11)
329
330 @test min_spacing(g) ≈ 0.1*norm(b-a)
331 end
332
333 @testset let a = @SVector[1,0], b = @SVector[-1,1]/√2
334 g = mapped_grid(_skew_mapping(a,b)...,11,11)
335
336 @test min_spacing(g) ≈ 0.1*norm(a+b)
337 end
338 end
339
340 @testset "normal" begin
341 g = mapped_grid(_partially_curved_mapping()...,10, 11)
342
343 @test normal(g, CartesianBoundary{1,LowerBoundary}()) == fill(@SVector[-1,0], 11)
344 @test normal(g, CartesianBoundary{1,UpperBoundary}()) == fill(@SVector[1,0], 11)
345 @test normal(g, CartesianBoundary{2,LowerBoundary}()) == fill(@SVector[0,-1], 10)
346 @test normal(g, CartesianBoundary{2,UpperBoundary}()) ≈ map(boundary_grid(g,CartesianBoundary{2,UpperBoundary}())|>logical_grid) do ξ̄
347 α = 1-2ξ̄[1]
348 @SVector[α,1]/√(α^2 + 1)
349 end
350
351 g = mapped_grid(_fully_curved_mapping()...,5,4)
352
353 unit(v) = v/norm(v)
354 @testset let bId = CartesianBoundary{1,LowerBoundary}()
355 lbg = boundary_grid(logical_grid(g), bId)
356 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
357 -unit(@SVector[1/2, η/3-1/6])
358 end
359 end
360
361 @testset let bId = CartesianBoundary{1,UpperBoundary}()
362 lbg = boundary_grid(logical_grid(g), bId)
363 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
364 unit(@SVector[7/2, 2η-1]/(5 + 3η + 2η^2))
365 end
366 end
367
368 @testset let bId = CartesianBoundary{2,LowerBoundary}()
369 lbg = boundary_grid(logical_grid(g), bId)
370 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
371 -unit(@SVector[-2ξ, 2]/(6 + ξ^2 - 2ξ))
372 end
373 end
374
375 @testset let bId = CartesianBoundary{2,UpperBoundary}()
376 lbg = boundary_grid(logical_grid(g), bId)
377 @test normal(g, bId) ≈ map(lbg) do (ξ, η)
378 unit(@SVector[-3ξ, 2]/(6 + ξ^2 + 3ξ))
379 end
380 end
381 end