├── .gitignore ├── Project.toml ├── exports ├── door.gif ├── crossroads.gif └── switching_positions.gif ├── CITATION.cff ├── LICENSE ├── README.md ├── switching_positions.jl └── crossroads.jl /.gitignore: -------------------------------------------------------------------------------- 1 | *.tikz 2 | *.pdf 3 | Manifest.toml -------------------------------------------------------------------------------- /Project.toml: -------------------------------------------------------------------------------- 1 | [deps] 2 | Pluto = "c3e4b0f8-55cb-11ea-2926-15256bba5781" 3 | -------------------------------------------------------------------------------- /exports/door.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/biaslab/MultiAgentTrajectoryPlanning/HEAD/exports/door.gif -------------------------------------------------------------------------------- /exports/crossroads.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/biaslab/MultiAgentTrajectoryPlanning/HEAD/exports/crossroads.gif -------------------------------------------------------------------------------- /exports/switching_positions.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/biaslab/MultiAgentTrajectoryPlanning/HEAD/exports/switching_positions.gif -------------------------------------------------------------------------------- /CITATION.cff: -------------------------------------------------------------------------------- 1 | cff-version: 1.2.0 2 | message: "Please cite this research as below." 3 | authors: 4 | - family-names: "van Erp" 5 | given-names: "Bart" 6 | orcid: "https://orcid.org/0000-0002-5619-7071" 7 | - family-names: "Bagaev" 8 | given-names: "Dmitry" 9 | - family-names: "Podusenko" 10 | given-names: "Albert" 11 | - family-names: "Senoz" 12 | given-names: "Ismail" 13 | - family-names: "de Vries" 14 | given-names: "Bert" 15 | title: "Multi-Agent Trajectory Planning with NUV Priors" 16 | url: "https://github.com/biaslab/MultiAgentTrajectoryPlanning" 17 | preferred-citation: 18 | authors: 19 | - family-names: "van Erp" 20 | given-names: "Bart" 21 | orcid: "https://orcid.org/0000-0002-5619-7071" 22 | - family-names: "Bagaev" 23 | given-names: "Dmitry" 24 | - family-names: "Podusenko" 25 | given-names: "Albert" 26 | - family-names: "Senoz" 27 | given-names: "Ismail" 28 | - family-names: "de Vries" 29 | given-names: "Bert" 30 | conference: 31 | name: "American Control Conference 2024" 32 | type: generic 33 | title: "Multi-Agent Trajectory Planning with NUV Priors" 34 | year: 2024 35 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2021-2023 BIASlab 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Multi-Agent Trajectory Planning with NUV Priors 2 | *By Bart van Erp, Dmitry Bagaev, Albert Podusenko Ismail Senoz and Bert de Vries* 3 | 4 | --- 5 | **Abstract** 6 | 7 | This paper presents a probabilistic model-based approach to centralized multi-agent trajectory planning. This approach allows for incorporating uncertainty of the state and dynamics of the agents directly in the model. Probabilistic inference is then efficiently automated using message passing. The recently introduced normal-with-unknown-variance (NUV) priors are used to prevent collisions between agents and obstacles. Furthermore, a new expectation-maximization inference scheme is presented for box and halfspace priors, which takes state uncertainty into account when avoiding collisions. 8 | 9 | 10 |
11 |
12 | 13 | --- 14 | This repository contains all experiments of the paper. 15 | 16 | ## Installation instructions 17 | 1. Install [Julia](https://julialang.org/) 18 | 19 | 2. activate environment (using `]` and backspace you can switch between the regular prompt and package manager) 20 | ```julia 21 | >> ] activate . 22 | ``` 23 | 24 | 3. instantiate environment (only required once) 25 | ```julia 26 | >> ] instantiate 27 | ``` 28 | 29 | 4. start Pluto 30 | ```julia 31 | >> using Pluto; Pluto.run() 32 | ``` 33 | 34 | # License 35 | 36 | [MIT License](LICENSE) Copyright (c) 2023 BIASlab 37 | -------------------------------------------------------------------------------- /switching_positions.jl: -------------------------------------------------------------------------------- 1 | ### A Pluto.jl notebook ### 2 | # v0.19.26 3 | 4 | using Markdown 5 | using InteractiveUtils 6 | 7 | # This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). 8 | macro bind(def, element) 9 | quote 10 | local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end 11 | local el = $(esc(element)) 12 | global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) 13 | el 14 | end 15 | end 16 | 17 | # ╔═╡ 248bf010-7d15-4886-82e5-7fbbd7e0f7ec 18 | using LinearAlgebra, RxInfer, Plots, PGFPlotsX, PlutoUI 19 | 20 | # ╔═╡ 90ef24e0-1fd9-11ee-2ed4-e947901d2a4c 21 | md""" 22 | # Switching positions 23 | """ 24 | 25 | # ╔═╡ e30f9fe4-2c6d-4dc5-bd9a-f3e4b1b79256 26 | md"Save figures $(@bind save_figures CheckBox(default=false))" 27 | 28 | # ╔═╡ 05110841-e078-4e36-9abf-1d8420b85f09 29 | if save_figures 30 | mkpath("exports") 31 | nothing 32 | end 33 | 34 | # ╔═╡ 5123688d-a83f-4e09-a0f1-e03a1f583264 35 | begin 36 | function draw_circle!(center, radius; kwargs...) 37 | θ = range(0, 2π, 100) 38 | plot!(center[1] .+ radius .* cos.(θ), center[2] .+ radius .* sin.(θ); kwargs...) 39 | end 40 | 41 | ReactiveMP.constrain_form(pmconstraint::RxInfer.PointMassFormConstraint, distribution::MultivariateNormalDistributionsFamily) = mean(distribution) 42 | 43 | ReactiveMP.prod(::ProdAnalytical, left::Distribution, right::PointMass{Float64}) = right 44 | end; 45 | 46 | # ╔═╡ f3b412ba-f0e6-4423-a44d-dcf04ad2b475 47 | md""" 48 | ## Problem sketch 49 | """ 50 | 51 | # ╔═╡ 156d54ec-126b-4de1-a483-990b503c4a94 52 | begin 53 | goals = hcat([ 54 | # agent 1: start at (0,0) with 0 velocity, end at (0, 50) with 0 velocity 55 | [ 56 | [0, 0, 0, 0], 57 | [0, 0, 50, 0] 58 | ], 59 | # agent 2: start at (0,50) with 0 velocity, end at (0, 0) with 0 velocity 60 | [ 61 | [0, 0, 50, 0], 62 | [0, 0, 0, 0] 63 | ] 64 | ]...) 65 | radius1 = 15 66 | radius2 = 15 67 | end; 68 | 69 | # ╔═╡ ef868b3a-0616-495e-9bd0-de2edf1089db 70 | begin 71 | plot(size = (600*0.8, 600)) 72 | 73 | scatter!([goals[2,1][1]], [goals[2,1][3]], color="red", label="", marker=:star5, markersize=10) 74 | scatter!([goals[2,2][1]], [goals[2,2][3]], color="blue", label="", marker=:star5, markersize=10) 75 | 76 | draw_circle!([goals[1,1][1], goals[1,1][3]], radius1; color="red", label="") 77 | draw_circle!([goals[1,2][1], goals[1,2][3]], radius2; color="blue", label="") 78 | 79 | xlims!(-40, 40) 80 | ylims!(-25, 75) 81 | 82 | end 83 | 84 | # ╔═╡ 452ea6ac-17ba-4bd5-8037-ef53b488e420 85 | md""" 86 | ## Halfspace prior implementation 87 | """ 88 | 89 | # ╔═╡ 60dd5591-cfd1-41c5-a6ed-4c485fa27bb2 90 | begin 91 | 92 | # node specification 93 | struct Halfspace end 94 | @node Halfspace Stochastic [out, a, σ2, γ] 95 | 96 | # rule specification 97 | @rule Halfspace(:out, Marginalisation) (q_a::PointMass, q_σ2::PointMass, q_γ::PointMass) = begin 98 | return NormalMeanVariance(mean(q_a) + mean(q_γ) * mean(q_σ2), mean(q_σ2)) 99 | end 100 | 101 | @rule Halfspace(:σ2, Marginalisation) (q_out::UnivariateNormalDistributionsFamily, q_a::PointMass, q_γ::PointMass, ) = begin 102 | return PointMass( 1 / mean(q_γ) * sqrt(abs2(mean(q_out) - mean(q_a)) + var(q_out))) 103 | end 104 | 105 | end 106 | 107 | # ╔═╡ 9638259f-f1bb-4b6e-849d-4455db3a3447 108 | md""" 109 | ## Model specification 110 | """ 111 | 112 | # ╔═╡ b1eec7ac-9ced-4aac-9647-a15322b30fb5 113 | function h(y1, y2; r1 = radius1, r2 = radius2) 114 | return norm(y1 - y2) - r1 - r2 115 | end; 116 | 117 | # ╔═╡ fe9df76f-9df5-46f7-8161-353ddbf94c09 118 | @model function switching_model(nr_steps; γ=1, ΔT=1) 119 | 120 | # controls 121 | u = randomvar(2, nr_steps) 122 | 123 | # hidden state 124 | x = randomvar(2, nr_steps + 1) 125 | 126 | # observations 127 | y = randomvar(2, nr_steps) 128 | goals = datavar(Vector{Int64}, (2, 2)) 129 | 130 | # distance variable 131 | d = randomvar(nr_steps) 132 | σ2 = randomvar(nr_steps) 133 | 134 | # transition model 135 | A = constvar([1 ΔT 0 0; 0 1 0 0; 0 0 1 ΔT; 0 0 0 1]) 136 | B = constvar([0 0; ΔT 0; 0 0; 0 ΔT]) 137 | C = constvar([1 0 0 0; 0 0 1 0]) 138 | 139 | # single agent models 140 | for k in 1:2 141 | 142 | # prior on state 143 | x[k,1] ~ MvNormalMeanCovariance(zeros(4), 1e2I) 144 | 145 | for t in 1:nr_steps 146 | 147 | # prior on controls 148 | u[k,t] ~ MvNormalMeanCovariance(zeros(2), 1e-2I) 149 | 150 | # state transition 151 | x[k,t+1] ~ A * x[k,t] + B * u[k,t] 152 | 153 | # observation model 154 | y[k,t] ~ C * x[k,t+1] 155 | 156 | end 157 | 158 | # goal priors (indexing reverse due to definition) 159 | goals[1,k] ~ MvNormalMeanCovariance(x[k,1], 1e-5I) 160 | goals[2,k] ~ MvNormalMeanCovariance(x[k,end], 1e-5I) 161 | 162 | end 163 | 164 | # multi-agent models 165 | for t = 1:nr_steps 166 | 167 | # observation constraint 168 | σ2[t] ~ GammaShapeRate(3/2, γ^2/2) 169 | d[t] ~ h(y[1,t], y[2,t]) 170 | d[t] ~ Halfspace(0, σ2[t], γ) 171 | 172 | end 173 | 174 | end; 175 | 176 | # ╔═╡ 6792be47-148c-414b-9f21-d7ae11807bd9 177 | md""" 178 | ## Constraint specification 179 | """ 180 | 181 | # ╔═╡ 1e2ba3eb-b073-40cc-8b56-633e18d041d9 182 | @constraints function switching_constraints() 183 | q(d, σ2) = q(d)q(σ2) 184 | end; 185 | 186 | # ╔═╡ e6d347ee-835b-4077-968b-0e7b11540056 187 | md""" 188 | ## Probabilistic inference 189 | """ 190 | 191 | # ╔═╡ daa54871-05cb-4987-a81c-16f7895da90f 192 | switching_meta = @meta begin 193 | h() -> Linearization() 194 | end; 195 | 196 | # ╔═╡ 12677bf1-5cae-405b-baf0-b3b741ed1770 197 | nr_steps = 50 198 | 199 | # ╔═╡ 5dba141f-a4ff-4439-91bc-c7d6d5a3f18e 200 | nr_iterations = 1000 201 | 202 | # ╔═╡ ead11ddb-2c4d-47a7-9cf5-483cb40598a0 203 | results = inference( 204 | model = switching_model(nr_steps), 205 | data = ( goals = goals, ), 206 | constraints = switching_constraints(), 207 | meta = switching_meta, 208 | iterations = nr_iterations, 209 | returnvars = KeepLast(), 210 | initmarginals = ( 211 | σ2 = repeat([PointMass(1)], nr_steps), 212 | u = repeat([PointMass(0)], nr_steps) 213 | ), 214 | initmessages = ( 215 | x = MvNormalMeanCovariance(randn(4), 100I), 216 | ) 217 | ) 218 | 219 | # ╔═╡ 8e994302-4316-4d23-87e2-020883800e65 220 | md""" 221 | ## Results 222 | """ 223 | 224 | # ╔═╡ 9512a92b-32df-4d9b-8e02-870ade5ef1ba 225 | begin 226 | 227 | if save_figures 228 | animation = @animate for t in 1:nr_steps 229 | plot(size = (600*0.8, 600), legend=false) 230 | 231 | plot!( 232 | map(x -> mean(x)[1], results.posteriors[:y][1,1:t]), 233 | map(x -> mean(x)[2], results.posteriors[:y][1,1:t]); 234 | color="red", linestyle=:dash 235 | ) 236 | plot!( 237 | map(x -> mean(x)[1], results.posteriors[:y][2,1:t]), 238 | map(x -> mean(x)[2], results.posteriors[:y][2,1:t]); 239 | color="blue", linestyle=:dash 240 | ) 241 | 242 | draw_circle!(mean(results.posteriors[:x][1,t])[[1,3]], radius1; color="red", label="") 243 | draw_circle!(mean(results.posteriors[:y][2,t]), radius2; color="blue", label="") 244 | 245 | 246 | scatter!([goals[2,1][1]], [goals[2,1][3]], color="red", label="", marker=:star5, markersize=10) 247 | scatter!([goals[2,2][1]], [goals[2,2][3]], color="blue", label="", marker=:star5, markersize=10) 248 | 249 | xlims!(-40, 40) 250 | ylims!(-25, 75) 251 | 252 | end 253 | gif(animation, "exports/switching_positions.gif", fps = 15) 254 | else 255 | animation = @gif for t in 1:nr_steps 256 | plot(size = (600*0.8, 600), legend=false) 257 | 258 | plot!( 259 | map(x -> mean(x)[1], results.posteriors[:y][1,1:t]), 260 | map(x -> mean(x)[2], results.posteriors[:y][1,1:t]); 261 | color="red", linestyle=:dash 262 | ) 263 | plot!( 264 | map(x -> mean(x)[1], results.posteriors[:y][2,1:t]), 265 | map(x -> mean(x)[2], results.posteriors[:y][2,1:t]); 266 | color="blue", linestyle=:dash 267 | ) 268 | 269 | draw_circle!(mean(results.posteriors[:x][1,t])[[1,3]], radius1; color="red", label="") 270 | draw_circle!(mean(results.posteriors[:y][2,t]), radius2; color="blue", label="") 271 | 272 | 273 | scatter!([goals[2,1][1]], [goals[2,1][3]], color="red", label="", marker=:star5, markersize=10) 274 | scatter!([goals[2,2][1]], [goals[2,2][3]], color="blue", label="", marker=:star5, markersize=10) 275 | 276 | xlims!(-40, 40) 277 | ylims!(-25, 75) 278 | 279 | end 280 | end 281 | end 282 | 283 | # ╔═╡ a7eebc8c-e3ec-4962-9088-af61b17af122 284 | begin 285 | θ = range(0, 2π, 100) 286 | 287 | fig = @pgf GroupPlot( 288 | 289 | # group plot options 290 | { 291 | group_style = { 292 | group_size = "10 by 1", 293 | vertical_sep = "0cm", 294 | horizontal_sep = "0cm" 295 | }, 296 | ticks = "none", 297 | ymin = -25, 298 | ymax = 75, 299 | xmin = -40, 300 | xmax = 40, 301 | width = "4cm", 302 | height = "5cm", 303 | grid = "major", 304 | scale_only_axis = true 305 | }, 306 | ) 307 | 308 | @pgf for k in 1:10 309 | push!( 310 | fig, 311 | {}, 312 | Plot( 313 | { 314 | "red", 315 | "dashed", 316 | line_width = 1.5 317 | }, 318 | Table( 319 | map(x -> mean(x)[1], results.posteriors[:y][1,1:Int(round(1 + (nr_steps-1) * (k-1) / 9))]), 320 | map(x -> mean(x)[2], results.posteriors[:y][1,1:Int(round(1 + (nr_steps-1) * (k-1) / 9))]), 321 | ) 322 | ), 323 | Plot( 324 | { 325 | "blue", 326 | "dashed", 327 | line_width = 1.5 328 | }, 329 | Table( 330 | map(x -> mean(x)[1], results.posteriors[:y][2,1:Int(round(1 + (nr_steps-1) * (k-1) / 9))]), 331 | map(x -> mean(x)[2], results.posteriors[:y][2,1:Int(round(1 + (nr_steps-1) * (k-1) / 9))]), 332 | ) 333 | ), 334 | Plot( 335 | { 336 | "red", 337 | line_width = 1.5 338 | }, 339 | Table( 340 | mean(results.posteriors[:y][1,Int(round(1 + (nr_steps-1) * (k-1) / 9))])[1] .+ radius1 .* cos.(θ), 341 | mean(results.posteriors[:y][1,Int(round(1 + (nr_steps-1) * (k-1) / 9))])[2] .+ radius1 .* sin.(θ) 342 | ) 343 | ), 344 | Plot( 345 | { 346 | "blue", 347 | line_width = 1.5 348 | }, 349 | Table( 350 | mean(results.posteriors[:y][2,Int(round(1 + (nr_steps-1) * (k-1) / 9))])[1] .+ radius2 .* cos.(θ), 351 | mean(results.posteriors[:y][2,Int(round(1 + (nr_steps-1) * (k-1) / 9))])[2] .+ radius2 .* sin.(θ) 352 | ) 353 | ), 354 | Plot( 355 | { 356 | "only marks", 357 | mark = "triangle*", 358 | mark_size = 5, 359 | "red", 360 | }, 361 | Table([goals[2,1][1]],[goals[2,1][3]]) 362 | ), 363 | Plot( 364 | { 365 | "only marks", 366 | mark = "triangle*", 367 | mark_size = 5, 368 | "blue", 369 | }, 370 | Table([goals[2,2][1]],[goals[2,2][3]]) 371 | ) 372 | ) 373 | end; 374 | 375 | if save_figures 376 | pgfsave("exports/switching_positions.pdf", fig) 377 | pgfsave("exports/switching_positions.tikz", fig) 378 | end 379 | 380 | fig 381 | 382 | end 383 | 384 | # ╔═╡ 00000000-0000-0000-0000-000000000001 385 | PLUTO_PROJECT_TOML_CONTENTS = """ 386 | [deps] 387 | LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" 388 | PGFPlotsX = "8314cec4-20b6-5062-9cdb-752b83310925" 389 | Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" 390 | PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" 391 | RxInfer = "86711068-29c9-4ff7-b620-ae75d7495b3d" 392 | 393 | [compat] 394 | PGFPlotsX = "~1.6.0" 395 | Plots = "~1.38.16" 396 | PlutoUI = "~0.7.51" 397 | RxInfer = "~2.11.1" 398 | """ 399 | 400 | # ╔═╡ 00000000-0000-0000-0000-000000000002 401 | PLUTO_MANIFEST_TOML_CONTENTS = """ 402 | # This file is machine-generated - editing it directly is not advised 403 | 404 | julia_version = "1.9.2" 405 | manifest_format = "2.0" 406 | project_hash = "72b0b20106651baae3b63bb818e09d155db6644a" 407 | 408 | [[deps.AbstractPlutoDingetjes]] 409 | deps = ["Pkg"] 410 | git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481" 411 | uuid = "6e696c72-6542-2067-7265-42206c756150" 412 | version = "1.1.4" 413 | 414 | [[deps.Adapt]] 415 | deps = ["LinearAlgebra", "Requires"] 416 | git-tree-sha1 = "76289dc51920fdc6e0013c872ba9551d54961c24" 417 | uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" 418 | version = "3.6.2" 419 | weakdeps = ["StaticArrays"] 420 | 421 | [deps.Adapt.extensions] 422 | AdaptStaticArraysExt = "StaticArrays" 423 | 424 | [[deps.ArgCheck]] 425 | git-tree-sha1 = "a3a402a35a2f7e0b87828ccabbd5ebfbebe356b4" 426 | uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197" 427 | version = "2.3.0" 428 | 429 | [[deps.ArgTools]] 430 | uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" 431 | version = "1.1.1" 432 | 433 | [[deps.ArrayInterface]] 434 | deps = ["Adapt", "LinearAlgebra", "Requires", "SparseArrays", "SuiteSparse"] 435 | git-tree-sha1 = "f83ec24f76d4c8f525099b2ac475fc098138ec31" 436 | uuid = 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1045 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1046 | git-tree-sha1 = "c7cb1f5d892775ba13767a87c7ada0b980ea0a71" 1047 | uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531" 1048 | version = "1.16.1+2" 1049 | 1050 | [[deps.Libmount_jll]] 1051 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1052 | git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73" 1053 | uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9" 1054 | version = "2.35.0+0" 1055 | 1056 | [[deps.Libtiff_jll]] 1057 | deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"] 1058 | git-tree-sha1 = "3eb79b0ca5764d4799c06699573fd8f533259713" 1059 | uuid = "89763e89-9b03-5906-acba-b20f662cd828" 1060 | version = "4.4.0+0" 1061 | 1062 | [[deps.Libuuid_jll]] 1063 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1064 | git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066" 1065 | uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700" 1066 | version = "2.36.0+0" 1067 | 1068 | 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1850 | uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e" 1851 | version = "0.3.9+1" 1852 | 1853 | [[deps.Xorg_xcb_util_wm_jll]] 1854 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] 1855 | git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67" 1856 | uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361" 1857 | version = "0.4.1+1" 1858 | 1859 | [[deps.Xorg_xkbcomp_jll]] 1860 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"] 1861 | git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb" 1862 | uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4" 1863 | version = "1.4.6+0" 1864 | 1865 | [[deps.Xorg_xkeyboard_config_jll]] 1866 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"] 1867 | git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3" 1868 | uuid = "33bec58e-1273-512f-9401-5d533626f822" 1869 | version = "2.39.0+0" 1870 | 1871 | [[deps.Xorg_xtrans_jll]] 1872 | deps = ["Artifacts", "JLLWrappers", "Libdl"] 1873 | git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77" 1874 | uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10" 1875 | version = "1.5.0+0" 1876 | 1877 | [[deps.Zlib_jll]] 1878 | deps = ["Libdl"] 1879 | uuid = "83775a58-1f1d-513f-b197-d71354ab007a" 1880 | version = "1.2.13+0" 1881 | 1882 | [[deps.Zstd_jll]] 1883 | deps = ["Artifacts", "JLLWrappers", "Libdl"] 1884 | git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c" 1885 | uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" 1886 | version = "1.5.5+0" 1887 | 1888 | [[deps.fzf_jll]] 1889 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1890 | git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56" 1891 | uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09" 1892 | version = "0.29.0+0" 1893 | 1894 | [[deps.libaom_jll]] 1895 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1896 | git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4" 1897 | uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b" 1898 | version = "3.4.0+0" 1899 | 1900 | [[deps.libass_jll]] 1901 | deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] 1902 | git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47" 1903 | uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" 1904 | version = "0.15.1+0" 1905 | 1906 | [[deps.libblastrampoline_jll]] 1907 | deps = ["Artifacts", "Libdl"] 1908 | uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" 1909 | version = "5.8.0+0" 1910 | 1911 | [[deps.libfdk_aac_jll]] 1912 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1913 | git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55" 1914 | uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" 1915 | version = "2.0.2+0" 1916 | 1917 | [[deps.libpng_jll]] 1918 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] 1919 | git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c" 1920 | uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" 1921 | version = "1.6.38+0" 1922 | 1923 | [[deps.libvorbis_jll]] 1924 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] 1925 | git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c" 1926 | uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" 1927 | version = "1.3.7+1" 1928 | 1929 | [[deps.nghttp2_jll]] 1930 | deps = ["Artifacts", "Libdl"] 1931 | uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" 1932 | version = "1.48.0+0" 1933 | 1934 | [[deps.p7zip_jll]] 1935 | deps = ["Artifacts", "Libdl"] 1936 | uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" 1937 | version = "17.4.0+0" 1938 | 1939 | [[deps.x264_jll]] 1940 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1941 | git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" 1942 | uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" 1943 | version = "2021.5.5+0" 1944 | 1945 | [[deps.x265_jll]] 1946 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1947 | git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" 1948 | uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" 1949 | version = "3.5.0+0" 1950 | 1951 | [[deps.xkbcommon_jll]] 1952 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] 1953 | git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a" 1954 | uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" 1955 | version = "1.4.1+0" 1956 | """ 1957 | 1958 | # ╔═╡ Cell order: 1959 | # ╟─90ef24e0-1fd9-11ee-2ed4-e947901d2a4c 1960 | # ╠═248bf010-7d15-4886-82e5-7fbbd7e0f7ec 1961 | # ╟─e30f9fe4-2c6d-4dc5-bd9a-f3e4b1b79256 1962 | # ╟─05110841-e078-4e36-9abf-1d8420b85f09 1963 | # ╟─5123688d-a83f-4e09-a0f1-e03a1f583264 1964 | # ╟─f3b412ba-f0e6-4423-a44d-dcf04ad2b475 1965 | # ╠═156d54ec-126b-4de1-a483-990b503c4a94 1966 | # ╟─ef868b3a-0616-495e-9bd0-de2edf1089db 1967 | # ╟─452ea6ac-17ba-4bd5-8037-ef53b488e420 1968 | # ╠═60dd5591-cfd1-41c5-a6ed-4c485fa27bb2 1969 | # ╟─9638259f-f1bb-4b6e-849d-4455db3a3447 1970 | # ╠═b1eec7ac-9ced-4aac-9647-a15322b30fb5 1971 | # ╠═fe9df76f-9df5-46f7-8161-353ddbf94c09 1972 | # ╟─6792be47-148c-414b-9f21-d7ae11807bd9 1973 | # ╠═1e2ba3eb-b073-40cc-8b56-633e18d041d9 1974 | # ╟─e6d347ee-835b-4077-968b-0e7b11540056 1975 | # ╠═daa54871-05cb-4987-a81c-16f7895da90f 1976 | # ╠═12677bf1-5cae-405b-baf0-b3b741ed1770 1977 | # ╠═5dba141f-a4ff-4439-91bc-c7d6d5a3f18e 1978 | # ╠═ead11ddb-2c4d-47a7-9cf5-483cb40598a0 1979 | # ╟─8e994302-4316-4d23-87e2-020883800e65 1980 | # ╟─9512a92b-32df-4d9b-8e02-870ade5ef1ba 1981 | # ╟─a7eebc8c-e3ec-4962-9088-af61b17af122 1982 | # ╟─00000000-0000-0000-0000-000000000001 1983 | # ╟─00000000-0000-0000-0000-000000000002 1984 | -------------------------------------------------------------------------------- /crossroads.jl: -------------------------------------------------------------------------------- 1 | ### A Pluto.jl notebook ### 2 | # v0.19.26 3 | 4 | using Markdown 5 | using InteractiveUtils 6 | 7 | # This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). 8 | macro bind(def, element) 9 | quote 10 | local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end 11 | local el = $(esc(element)) 12 | global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) 13 | el 14 | end 15 | end 16 | 17 | # ╔═╡ 248bf010-7d15-4886-82e5-7fbbd7e0f7ec 18 | using LinearAlgebra, RxInfer, Plots, PGFPlotsX, LogExpFunctions, PlutoUI 19 | 20 | # ╔═╡ 90ef24e0-1fd9-11ee-2ed4-e947901d2a4c 21 | md""" 22 | # Crossroads 23 | """ 24 | 25 | # ╔═╡ 5123688d-a83f-4e09-a0f1-e03a1f583264 26 | begin 27 | function draw_circle!(center, radius; kwargs...) 28 | θ = range(0, 2π, 100) 29 | plot!(center[1] .+ radius .* cos.(θ), center[2] .+ radius .* sin.(θ); kwargs...) 30 | end 31 | 32 | ReactiveMP.constrain_form(pmconstraint::RxInfer.PointMassFormConstraint, distribution::MultivariateNormalDistributionsFamily) = mean(distribution) 33 | 34 | ReactiveMP.prod(::ProdAnalytical, left::Distribution, right::PointMass{Float64}) = right 35 | 36 | softmin(x; l=10) = -logsumexp(-l .* x)/l 37 | 38 | end; 39 | 40 | # ╔═╡ fa3ebe3b-1ef9-4c1f-9849-72e1b4f3176c 41 | md"Save figures $(@bind save_figures CheckBox(default=false))" 42 | 43 | # ╔═╡ c4561368-15b9-49e4-a0ff-c5a85171a054 44 | if save_figures 45 | mkpath("exports") 46 | nothing 47 | end 48 | 49 | # ╔═╡ f3b412ba-f0e6-4423-a44d-dcf04ad2b475 50 | md""" 51 | ## Problem sketch 52 | """ 53 | 54 | # ╔═╡ 156d54ec-126b-4de1-a483-990b503c4a94 55 | begin 56 | goals = hcat([ 57 | # agent 1: start at (-15,5) with 0 velocity, end at (15,-5) with 0 velocity 58 | [ 59 | [-15, 0, 5, 0], 60 | [15, 0, -5, 0] 61 | ], 62 | # agent 2: start at (-15,-5) with 0 velocity, end at (15,5) with 0 velocity 63 | [ 64 | [-15, 0, -5, 0], 65 | [15, 0, 5, 0] 66 | ], 67 | # agent 3: start at (-5,15) with 0 velocity, end at (5,-15) with 0 velocity 68 | [ 69 | [-5, 0, 15, 0], 70 | [5, 0, -15, 0] 71 | ], 72 | # agent 4: start at (5,15) with 0 velocity, end at (-5,-15) with 0 velocity 73 | [ 74 | [5, 0, 15, 0], 75 | [-5, 0, -15, 0] 76 | ] 77 | ]...) 78 | radius1 = 2.5 79 | radius2 = 2.5 80 | radius3 = 2.5 81 | radius4 = 2.5 82 | end; 83 | 84 | # ╔═╡ ef868b3a-0616-495e-9bd0-de2edf1089db 85 | begin 86 | plot(size = (600, 600)) 87 | 88 | scatter!([goals[2,1][1]], [goals[2,1][3]], color="red", label="", marker=:star5, markersize=10) 89 | scatter!([goals[2,2][1]], [goals[2,2][3]], color="blue", label="", marker=:star5, markersize=10) 90 | scatter!([goals[2,3][1]], [goals[2,3][3]], color="orange", label="", marker=:star5, markersize=10) 91 | scatter!([goals[2,4][1]], [goals[2,4][3]], color="green", label="", marker=:star5, markersize=10) 92 | 93 | draw_circle!([goals[1,1][1], goals[1,1][3]], radius1; color="red", label="") 94 | draw_circle!([goals[1,2][1], goals[1,2][3]], radius2; color="blue", label="") 95 | draw_circle!([goals[1,3][1], goals[1,3][3]], radius3; color="orange", label="") 96 | draw_circle!([goals[1,4][1], goals[1,4][3]], radius4; color="green", label="") 97 | 98 | xlims!(-20, 20) 99 | ylims!(-20, 20) 100 | end 101 | 102 | # ╔═╡ 452ea6ac-17ba-4bd5-8037-ef53b488e420 103 | md""" 104 | ## Halfspace prior implementation 105 | """ 106 | 107 | # ╔═╡ 60dd5591-cfd1-41c5-a6ed-4c485fa27bb2 108 | begin 109 | 110 | # node specification 111 | struct Halfspace end 112 | @node Halfspace Stochastic [out, a, σ2, γ] 113 | 114 | # rule specification 115 | @rule Halfspace(:out, Marginalisation) (q_a::PointMass, q_σ2::PointMass, q_γ::PointMass) = begin 116 | return NormalMeanVariance(mean(q_a) + mean(q_γ) * mean(q_σ2), mean(q_σ2)) 117 | end 118 | 119 | @rule Halfspace(:σ2, Marginalisation) (q_out::UnivariateNormalDistributionsFamily, q_a::PointMass, q_γ::PointMass, ) = begin 120 | return PointMass( 1 / mean(q_γ) * sqrt(abs2(mean(q_out) - mean(q_a)) + var(q_out))) 121 | end 122 | 123 | end 124 | 125 | # ╔═╡ 9638259f-f1bb-4b6e-849d-4455db3a3447 126 | md""" 127 | ## Model specification 128 | """ 129 | 130 | # ╔═╡ b1eec7ac-9ced-4aac-9647-a15322b30fb5 131 | function h(y1, y2, y3, y4; r1 = radius1, r2 = radius2, r3 = radius3, r4 = radius4) 132 | return softmin([ 133 | norm(y1 - y2) - r1 - r2, 134 | norm(y1 - y3) - r1 - r3, 135 | norm(y1 - y4) - r1 - r4, 136 | norm(y2 - y3) - r2 - r3, 137 | norm(y2 - y4) - r2 - r4, 138 | norm(y3 - y4) - r3 - r4, 139 | ]) 140 | end; 141 | 142 | # ╔═╡ fe9df76f-9df5-46f7-8161-353ddbf94c09 143 | @model function crossroads_model(nr_steps; γ=10, ΔT=1) 144 | 145 | # controls 146 | u = randomvar(4, nr_steps) 147 | 148 | # hidden state 149 | x = randomvar(4, nr_steps + 1) 150 | 151 | # observations 152 | y = randomvar(4, nr_steps) 153 | goals = datavar(Vector{Int64}, (2, 4)) 154 | 155 | # distance variable 156 | d = randomvar(nr_steps) 157 | σ2 = randomvar(nr_steps) 158 | 159 | # transition model 160 | A = constvar([1 ΔT 0 0; 0 1 0 0; 0 0 1 ΔT; 0 0 0 1]) 161 | B = constvar([0 0; ΔT 0; 0 0; 0 ΔT]) 162 | C = constvar([1 0 0 0; 0 0 1 0]) 163 | 164 | # single agent models 165 | for k in 1:4 166 | 167 | # prior on state 168 | x[k,1] ~ MvNormalMeanCovariance(zeros(4), 1e2I) 169 | 170 | for t in 1:nr_steps 171 | 172 | # prior on controls 173 | u[k,t] ~ MvNormalMeanCovariance(zeros(2), 1e-2I) 174 | 175 | # state transition 176 | x[k,t+1] ~ A * x[k,t] + B * u[k,t] 177 | 178 | # observation model 179 | y[k,t] ~ C * x[k,t+1] 180 | 181 | end 182 | 183 | # goal priors (indexing reverse due to definition) 184 | goals[1,k] ~ MvNormalMeanCovariance(x[k,1], 1e-5I) 185 | goals[2,k] ~ MvNormalMeanCovariance(x[k,end], 1e-5I) 186 | 187 | end 188 | 189 | # multi-agent models 190 | for t = 1:nr_steps 191 | 192 | # observation constraint 193 | σ2[t] ~ GammaShapeRate(3/2, γ^2/2) 194 | d[t] ~ h(y[1,t], y[2,t], y[3,t], y[4,t]) 195 | d[t] ~ Halfspace(0, σ2[t], γ) 196 | 197 | end 198 | 199 | end; 200 | 201 | # ╔═╡ 6792be47-148c-414b-9f21-d7ae11807bd9 202 | md""" 203 | ## Constraint specification 204 | """ 205 | 206 | # ╔═╡ 1e2ba3eb-b073-40cc-8b56-633e18d041d9 207 | @constraints function crossroads_constraints() 208 | q(d, σ2) = q(d)q(σ2) 209 | end; 210 | 211 | # ╔═╡ e6d347ee-835b-4077-968b-0e7b11540056 212 | md""" 213 | ## Probabilistic inference 214 | """ 215 | 216 | # ╔═╡ daa54871-05cb-4987-a81c-16f7895da90f 217 | crossroads_meta = @meta begin 218 | h() -> Linearization() 219 | end; 220 | 221 | # ╔═╡ 12677bf1-5cae-405b-baf0-b3b741ed1770 222 | nr_steps = 50 223 | 224 | # ╔═╡ 5dba141f-a4ff-4439-91bc-c7d6d5a3f18e 225 | nr_iterations = 5000 226 | 227 | # ╔═╡ ead11ddb-2c4d-47a7-9cf5-483cb40598a0 228 | results = inference( 229 | model = crossroads_model(nr_steps), 230 | data = ( goals = goals, ), 231 | constraints = crossroads_constraints(), 232 | meta = crossroads_meta, 233 | iterations = nr_iterations, 234 | returnvars = KeepLast(), 235 | initmarginals = ( 236 | σ2 = repeat([PointMass(1)], nr_steps), 237 | u = repeat([PointMass(0)], nr_steps) 238 | ), 239 | initmessages = ( 240 | x = MvNormalMeanCovariance(randn(4), 100I), 241 | ), 242 | options = ( limit_stack_depth = 300, ) 243 | ) 244 | 245 | # ╔═╡ 8e994302-4316-4d23-87e2-020883800e65 246 | md""" 247 | ## Results 248 | """ 249 | 250 | # ╔═╡ 9512a92b-32df-4d9b-8e02-870ade5ef1ba 251 | begin 252 | if save_figures 253 | animation = @animate for t in 1:nr_steps 254 | plot(size = (600, 600), legend=false) 255 | 256 | plot!( 257 | map(x -> mean(x)[1], results.posteriors[:y][1,1:t]), 258 | map(x -> mean(x)[2], results.posteriors[:y][1,1:t]); 259 | color="red", linestyle=:dash 260 | ) 261 | plot!( 262 | map(x -> mean(x)[1], results.posteriors[:y][2,1:t]), 263 | map(x -> mean(x)[2], results.posteriors[:y][2,1:t]); 264 | color="blue", linestyle=:dash 265 | ) 266 | plot!( 267 | map(x -> mean(x)[1], results.posteriors[:y][3,1:t]), 268 | map(x -> mean(x)[2], results.posteriors[:y][3,1:t]); 269 | color="orange", linestyle=:dash 270 | ) 271 | plot!( 272 | map(x -> mean(x)[1], results.posteriors[:y][4,1:t]), 273 | map(x -> mean(x)[2], results.posteriors[:y][4,1:t]); 274 | color="green", linestyle=:dash 275 | ) 276 | 277 | draw_circle!(mean(results.posteriors[:x][1,t])[[1,3]], radius1; color="red", label="") 278 | draw_circle!(mean(results.posteriors[:y][2,t]), radius2; color="blue", label="") 279 | draw_circle!(mean(results.posteriors[:x][3,t])[[1,3]], radius3; color="orange", label="") 280 | draw_circle!(mean(results.posteriors[:y][4,t]), radius4; color="green", label="") 281 | 282 | scatter!([goals[2,1][1]], [goals[2,1][3]], color="red", label="", marker=:star5, markersize=10) 283 | scatter!([goals[2,2][1]], [goals[2,2][3]], color="blue", label="", marker=:star5, markersize=10) 284 | scatter!([goals[2,3][1]], [goals[2,3][3]], color="orange", label="", marker=:star5, markersize=10) 285 | scatter!([goals[2,4][1]], [goals[2,4][3]], color="green", label="", marker=:star5, markersize=10) 286 | 287 | xlims!(-20, 20) 288 | ylims!(-20, 20) 289 | 290 | end 291 | 292 | gif(animation, "exports/crossroads.gif", fps = 15) 293 | 294 | else 295 | 296 | @gif for t in 1:nr_steps 297 | plot(size = (600, 600), legend=false) 298 | 299 | plot!( 300 | map(x -> mean(x)[1], results.posteriors[:y][1,1:t]), 301 | map(x -> mean(x)[2], results.posteriors[:y][1,1:t]); 302 | color="red", linestyle=:dash 303 | ) 304 | plot!( 305 | map(x -> mean(x)[1], results.posteriors[:y][2,1:t]), 306 | map(x -> mean(x)[2], results.posteriors[:y][2,1:t]); 307 | color="blue", linestyle=:dash 308 | ) 309 | plot!( 310 | map(x -> mean(x)[1], results.posteriors[:y][3,1:t]), 311 | map(x -> mean(x)[2], results.posteriors[:y][3,1:t]); 312 | color="orange", linestyle=:dash 313 | ) 314 | plot!( 315 | map(x -> mean(x)[1], results.posteriors[:y][4,1:t]), 316 | map(x -> mean(x)[2], results.posteriors[:y][4,1:t]); 317 | color="green", linestyle=:dash 318 | ) 319 | 320 | draw_circle!(mean(results.posteriors[:x][1,t])[[1,3]], radius1; color="red", label="") 321 | draw_circle!(mean(results.posteriors[:y][2,t]), radius2; color="blue", label="") 322 | draw_circle!(mean(results.posteriors[:x][3,t])[[1,3]], radius3; color="orange", label="") 323 | draw_circle!(mean(results.posteriors[:y][4,t]), radius4; color="green", label="") 324 | 325 | scatter!([goals[2,1][1]], [goals[2,1][3]], color="red", label="", marker=:star5, markersize=10) 326 | scatter!([goals[2,2][1]], [goals[2,2][3]], color="blue", label="", marker=:star5, markersize=10) 327 | scatter!([goals[2,3][1]], [goals[2,3][3]], color="orange", label="", marker=:star5, markersize=10) 328 | scatter!([goals[2,4][1]], [goals[2,4][3]], color="green", label="", marker=:star5, markersize=10) 329 | 330 | xlims!(-20, 20) 331 | ylims!(-20, 20) 332 | 333 | end 334 | end 335 | end 336 | 337 | # ╔═╡ a7eebc8c-e3ec-4962-9088-af61b17af122 338 | begin 339 | θ = range(0, 2π, 100) 340 | 341 | fig = @pgf GroupPlot( 342 | 343 | # group plot options 344 | { 345 | group_style = { 346 | group_size = "8 by 1", 347 | vertical_sep = "0cm", 348 | horizontal_sep = "0cm" 349 | }, 350 | ticks = "none", 351 | ymin = -20, 352 | ymax = 20, 353 | xmin = -20, 354 | xmax = 20, 355 | width = "4cm", 356 | height = "4cm", 357 | grid = "major", 358 | scale_only_axis = true 359 | }, 360 | ) 361 | 362 | @pgf for k in 1:8 363 | push!( 364 | fig, 365 | {}, 366 | Plot( 367 | { 368 | "red", 369 | "dashed", 370 | line_width = 1.5 371 | }, 372 | Table( 373 | map(x -> mean(x)[1], results.posteriors[:y][1,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]), 374 | map(x -> mean(x)[2], results.posteriors[:y][1,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]), 375 | ) 376 | ), 377 | Plot( 378 | { 379 | "blue", 380 | "dashed", 381 | line_width = 1.5 382 | }, 383 | Table( 384 | map(x -> mean(x)[1], results.posteriors[:y][2,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]), 385 | map(x -> mean(x)[2], results.posteriors[:y][2,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]), 386 | ) 387 | ), 388 | Plot( 389 | { 390 | "orange", 391 | "dashed", 392 | line_width = 1.5 393 | }, 394 | Table( 395 | map(x -> mean(x)[1], results.posteriors[:y][3,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]), 396 | map(x -> mean(x)[2], results.posteriors[:y][3,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]), 397 | ) 398 | ), 399 | Plot( 400 | { 401 | "green", 402 | "dashed", 403 | line_width = 1.5 404 | }, 405 | Table( 406 | map(x -> mean(x)[1], results.posteriors[:y][4,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]), 407 | map(x -> mean(x)[2], results.posteriors[:y][4,1:Int(round(1 + (nr_steps-1) * (k-1) / 7))]), 408 | ) 409 | ), 410 | Plot( 411 | { 412 | "red", 413 | line_width = 1.5 414 | }, 415 | Table( 416 | mean(results.posteriors[:y][1,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[1] .+ radius1 .* cos.(θ), 417 | mean(results.posteriors[:y][1,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[2] .+ radius1 .* sin.(θ) 418 | ) 419 | ), 420 | Plot( 421 | { 422 | "blue", 423 | line_width = 1.5 424 | }, 425 | Table( 426 | mean(results.posteriors[:y][2,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[1] .+ radius2 .* cos.(θ), 427 | mean(results.posteriors[:y][2,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[2] .+ radius2 .* sin.(θ) 428 | ) 429 | ), 430 | Plot( 431 | { 432 | "orange", 433 | line_width = 1.5 434 | }, 435 | Table( 436 | mean(results.posteriors[:y][3,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[1] .+ radius1 .* cos.(θ), 437 | mean(results.posteriors[:y][3,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[2] .+ radius1 .* sin.(θ) 438 | ) 439 | ), 440 | Plot( 441 | { 442 | "green", 443 | line_width = 1.5 444 | }, 445 | Table( 446 | mean(results.posteriors[:y][4,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[1] .+ radius2 .* cos.(θ), 447 | mean(results.posteriors[:y][4,Int(round(1 + (nr_steps-1) * (k-1) / 7))])[2] .+ radius2 .* sin.(θ) 448 | ) 449 | ), 450 | Plot( 451 | { 452 | "only marks", 453 | mark = "triangle*", 454 | mark_size = 5, 455 | "red", 456 | }, 457 | Table([goals[2,1][1]],[goals[2,1][3]]) 458 | ), 459 | Plot( 460 | { 461 | "only marks", 462 | mark = "triangle*", 463 | mark_size = 5, 464 | "blue", 465 | }, 466 | Table([goals[2,2][1]],[goals[2,2][3]]) 467 | ), 468 | Plot( 469 | { 470 | "only marks", 471 | mark = "triangle*", 472 | mark_size = 5, 473 | "orange", 474 | }, 475 | Table([goals[2,3][1]],[goals[2,3][3]]) 476 | ), 477 | Plot( 478 | { 479 | "only marks", 480 | mark = "triangle*", 481 | mark_size = 5, 482 | "green", 483 | }, 484 | Table([goals[2,4][1]],[goals[2,4][3]]) 485 | ) 486 | ) 487 | end; 488 | if save_figures 489 | pgfsave("exports/crossroads.pdf", fig) 490 | pgfsave("exports/crossroads.tikz", fig) 491 | end 492 | fig 493 | 494 | end 495 | 496 | # ╔═╡ 00000000-0000-0000-0000-000000000001 497 | PLUTO_PROJECT_TOML_CONTENTS = """ 498 | [deps] 499 | LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" 500 | LogExpFunctions = "2ab3a3ac-af41-5b50-aa03-7779005ae688" 501 | PGFPlotsX = "8314cec4-20b6-5062-9cdb-752b83310925" 502 | Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" 503 | PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" 504 | RxInfer = "86711068-29c9-4ff7-b620-ae75d7495b3d" 505 | 506 | [compat] 507 | LogExpFunctions = "~0.3.24" 508 | PGFPlotsX = "~1.6.0" 509 | Plots = "~1.38.16" 510 | PlutoUI = "~0.7.51" 511 | RxInfer = "~2.11.1" 512 | """ 513 | 514 | # ╔═╡ 00000000-0000-0000-0000-000000000002 515 | PLUTO_MANIFEST_TOML_CONTENTS = """ 516 | # This file is machine-generated - editing it directly is not advised 517 | 518 | julia_version = "1.9.2" 519 | manifest_format = "2.0" 520 | project_hash = "991d5bf646c9d4f4c66050391af206eb114318fa" 521 | 522 | [[deps.AbstractPlutoDingetjes]] 523 | deps = ["Pkg"] 524 | git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481" 525 | uuid = "6e696c72-6542-2067-7265-42206c756150" 526 | version = "1.1.4" 527 | 528 | [[deps.Adapt]] 529 | deps = ["LinearAlgebra", "Requires"] 530 | git-tree-sha1 = "76289dc51920fdc6e0013c872ba9551d54961c24" 531 | uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" 532 | version = "3.6.2" 533 | weakdeps = ["StaticArrays"] 534 | 535 | [deps.Adapt.extensions] 536 | AdaptStaticArraysExt = "StaticArrays" 537 | 538 | [[deps.ArgCheck]] 539 | git-tree-sha1 = "a3a402a35a2f7e0b87828ccabbd5ebfbebe356b4" 540 | uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197" 541 | version = "2.3.0" 542 | 543 | [[deps.ArgTools]] 544 | uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" 545 | version = "1.1.1" 546 | 547 | [[deps.ArrayInterface]] 548 | deps = ["Adapt", "LinearAlgebra", "Requires", "SparseArrays", "SuiteSparse"] 549 | git-tree-sha1 = "f83ec24f76d4c8f525099b2ac475fc098138ec31" 550 | uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9" 551 | version = "7.4.11" 552 | 553 | [deps.ArrayInterface.extensions] 554 | ArrayInterfaceBandedMatricesExt = "BandedMatrices" 555 | ArrayInterfaceBlockBandedMatricesExt = "BlockBandedMatrices" 556 | ArrayInterfaceCUDAExt = "CUDA" 557 | ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore" 558 | ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore" 559 | ArrayInterfaceTrackerExt = "Tracker" 560 | 561 | [deps.ArrayInterface.weakdeps] 562 | BandedMatrices = "aae01518-5342-5314-be14-df237901396f" 563 | BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0" 564 | CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" 565 | GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527" 566 | StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c" 567 | Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c" 568 | 569 | [[deps.ArrayInterfaceCore]] 570 | deps = ["LinearAlgebra", "SnoopPrecompile", "SparseArrays", "SuiteSparse"] 571 | git-tree-sha1 = "e5f08b5689b1aad068e01751889f2f615c7db36d" 572 | uuid = "30b0a656-2188-435a-8636-2ec0e6a096e2" 573 | version = "0.1.29" 574 | 575 | [[deps.ArrayLayouts]] 576 | deps = ["FillArrays", "LinearAlgebra", "SparseArrays"] 577 | git-tree-sha1 = "4aff5fa660eb95c2e0deb6bcdabe4d9a96bc4667" 578 | uuid = "4c555306-a7a7-4459-81d9-ec55ddd5c99a" 579 | version = "0.8.18" 580 | 581 | [[deps.Artifacts]] 582 | uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" 583 | 584 | [[deps.Base64]] 585 | uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" 586 | 587 | [[deps.BitFlags]] 588 | git-tree-sha1 = "43b1a4a8f797c1cddadf60499a8a077d4af2cd2d" 589 | uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35" 590 | version = "0.1.7" 591 | 592 | [[deps.BitTwiddlingConvenienceFunctions]] 593 | deps = ["Static"] 594 | git-tree-sha1 = "0c5f81f47bbbcf4aea7b2959135713459170798b" 595 | uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b" 596 | version = "0.1.5" 597 | 598 | [[deps.Bzip2_jll]] 599 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 600 | git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2" 601 | uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0" 602 | version = "1.0.8+0" 603 | 604 | [[deps.CPUSummary]] 605 | deps = ["CpuId", "IfElse", "PrecompileTools", "Static"] 606 | git-tree-sha1 = "89e0654ed8c7aebad6d5ad235d6242c2d737a928" 607 | uuid = "2a0fbf3d-bb9c-48f3-b0a9-814d99fd7ab9" 608 | version = "0.2.3" 609 | 610 | [[deps.Cairo_jll]] 611 | deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] 612 | git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2" 613 | uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" 614 | version = "1.16.1+1" 615 | 616 | [[deps.Calculus]] 617 | deps = ["LinearAlgebra"] 618 | git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad" 619 | uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9" 620 | version = "0.5.1" 621 | 622 | [[deps.CloseOpenIntervals]] 623 | deps = ["Static", "StaticArrayInterface"] 624 | git-tree-sha1 = "70232f82ffaab9dc52585e0dd043b5e0c6b714f1" 625 | uuid = "fb6a15b2-703c-40df-9091-08a04967cfa9" 626 | version = "0.1.12" 627 | 628 | [[deps.CodecZlib]] 629 | deps = ["TranscodingStreams", "Zlib_jll"] 630 | git-tree-sha1 = "9c209fb7536406834aa938fb149964b985de6c83" 631 | uuid = "944b1d66-785c-5afd-91f1-9de20f533193" 632 | version = "0.7.1" 633 | 634 | [[deps.ColorSchemes]] 635 | deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"] 636 | git-tree-sha1 = "be6ab11021cd29f0344d5c4357b163af05a48cba" 637 | uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4" 638 | version = "3.21.0" 639 | 640 | [[deps.ColorTypes]] 641 | deps = ["FixedPointNumbers", "Random"] 642 | git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4" 643 | uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f" 644 | version = "0.11.4" 645 | 646 | [[deps.ColorVectorSpace]] 647 | deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"] 648 | git-tree-sha1 = "600cc5508d66b78aae350f7accdb58763ac18589" 649 | uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4" 650 | version = "0.9.10" 651 | 652 | [[deps.Colors]] 653 | deps = ["ColorTypes", "FixedPointNumbers", "Reexport"] 654 | git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a" 655 | uuid = "5ae59095-9a9b-59fe-a467-6f913c188581" 656 | version = "0.12.10" 657 | 658 | [[deps.Combinatorics]] 659 | git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860" 660 | uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa" 661 | version = "1.0.2" 662 | 663 | [[deps.CommonSubexpressions]] 664 | deps = ["MacroTools", "Test"] 665 | git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7" 666 | uuid = "bbf7d656-a473-5ed7-a52c-81e309532950" 667 | version = "0.3.0" 668 | 669 | [[deps.Compat]] 670 | deps = ["UUIDs"] 671 | git-tree-sha1 = "4e88377ae7ebeaf29a047aa1ee40826e0b708a5d" 672 | uuid = "34da2185-b29b-5c13-b0c7-acf172513d20" 673 | version = "4.7.0" 674 | weakdeps = ["Dates", "LinearAlgebra"] 675 | 676 | [deps.Compat.extensions] 677 | CompatLinearAlgebraExt = "LinearAlgebra" 678 | 679 | [[deps.CompilerSupportLibraries_jll]] 680 | deps = ["Artifacts", "Libdl"] 681 | uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" 682 | version = "1.0.5+0" 683 | 684 | [[deps.CompositeTypes]] 685 | git-tree-sha1 = "02d2316b7ffceff992f3096ae48c7829a8aa0638" 686 | uuid = "b152e2b5-7a66-4b01-a709-34e65c35f657" 687 | version = "0.1.3" 688 | 689 | [[deps.ConcurrentUtilities]] 690 | deps = ["Serialization", "Sockets"] 691 | git-tree-sha1 = "96d823b94ba8d187a6d8f0826e731195a74b90e9" 692 | uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb" 693 | version = "2.2.0" 694 | 695 | [[deps.ConstructionBase]] 696 | deps = ["LinearAlgebra"] 697 | git-tree-sha1 = "738fec4d684a9a6ee9598a8bfee305b26831f28c" 698 | uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9" 699 | version = "1.5.2" 700 | weakdeps = ["IntervalSets", "StaticArrays"] 701 | 702 | [deps.ConstructionBase.extensions] 703 | ConstructionBaseIntervalSetsExt = "IntervalSets" 704 | ConstructionBaseStaticArraysExt = "StaticArrays" 705 | 706 | [[deps.Contour]] 707 | git-tree-sha1 = "d05d9e7b7aedff4e5b51a029dced05cfb6125781" 708 | uuid = "d38c429a-6771-53c6-b99e-75d170b6e991" 709 | version = "0.6.2" 710 | 711 | [[deps.CpuId]] 712 | deps = ["Markdown"] 713 | git-tree-sha1 = "fcbb72b032692610bfbdb15018ac16a36cf2e406" 714 | uuid = "adafc99b-e345-5852-983c-f28acb93d879" 715 | version = "0.3.1" 716 | 717 | [[deps.DataAPI]] 718 | git-tree-sha1 = "8da84edb865b0b5b0100c0666a9bc9a0b71c553c" 719 | uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a" 720 | version = "1.15.0" 721 | 722 | [[deps.DataStructures]] 723 | deps = ["Compat", "InteractiveUtils", "OrderedCollections"] 724 | git-tree-sha1 = "cf25ccb972fec4e4817764d01c82386ae94f77b4" 725 | uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8" 726 | version = "0.18.14" 727 | 728 | [[deps.DataValueInterfaces]] 729 | git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6" 730 | uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464" 731 | version = "1.0.0" 732 | 733 | [[deps.Dates]] 734 | deps = ["Printf"] 735 | uuid = "ade2ca70-3891-5945-98fb-dc099432e06a" 736 | 737 | [[deps.DefaultApplication]] 738 | deps = ["InteractiveUtils"] 739 | git-tree-sha1 = "c0dfa5a35710a193d83f03124356eef3386688fc" 740 | uuid = "3f0dd361-4fe0-5fc6-8523-80b14ec94d85" 741 | version = "1.1.0" 742 | 743 | [[deps.DelimitedFiles]] 744 | deps = ["Mmap"] 745 | git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae" 746 | uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab" 747 | version = "1.9.1" 748 | 749 | [[deps.DiffResults]] 750 | deps = ["StaticArraysCore"] 751 | git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621" 752 | uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5" 753 | version = "1.1.0" 754 | 755 | [[deps.DiffRules]] 756 | deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"] 757 | git-tree-sha1 = "23163d55f885173722d1e4cf0f6110cdbaf7e272" 758 | uuid = "b552c78f-8df3-52c6-915a-8e097449b14b" 759 | version = "1.15.1" 760 | 761 | [[deps.Distributed]] 762 | deps = ["Random", "Serialization", "Sockets"] 763 | uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b" 764 | 765 | [[deps.Distributions]] 766 | deps = ["FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsAPI", "StatsBase", "StatsFuns", "Test"] 767 | git-tree-sha1 = "e76a3281de2719d7c81ed62c6ea7057380c87b1d" 768 | uuid = "31c24e10-a181-5473-b8eb-7969acd0382f" 769 | version = "0.25.98" 770 | 771 | [deps.Distributions.extensions] 772 | DistributionsChainRulesCoreExt = "ChainRulesCore" 773 | DistributionsDensityInterfaceExt = "DensityInterface" 774 | 775 | [deps.Distributions.weakdeps] 776 | ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" 777 | DensityInterface = "b429d917-457f-4dbc-8f4c-0cc954292b1d" 778 | 779 | [[deps.DocStringExtensions]] 780 | deps = ["LibGit2"] 781 | git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d" 782 | uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" 783 | version = "0.9.3" 784 | 785 | [[deps.DomainIntegrals]] 786 | deps = ["CompositeTypes", "DomainSets", "FastGaussQuadrature", "GaussQuadrature", "HCubature", "IntervalSets", "LinearAlgebra", "QuadGK", "StaticArrays"] 787 | git-tree-sha1 = "12b085bc1703d949539e333f823eaa875c60b03e" 788 | uuid = "cc6bae93-f070-4015-88fd-838f9505a86c" 789 | version = "0.4.4" 790 | 791 | [[deps.DomainSets]] 792 | deps = ["CompositeTypes", "IntervalSets", "LinearAlgebra", "Random", "StaticArrays", "Statistics"] 793 | git-tree-sha1 = "51b4b84d33ec5e0955b55ff4b748b99ce2c3faa9" 794 | uuid = "5b8099bc-c8ec-5219-889f-1d9e522a28bf" 795 | version = "0.6.7" 796 | 797 | [[deps.Downloads]] 798 | deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"] 799 | uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6" 800 | version = "1.6.0" 801 | 802 | [[deps.DualNumbers]] 803 | deps = ["Calculus", "NaNMath", "SpecialFunctions"] 804 | git-tree-sha1 = "5837a837389fccf076445fce071c8ddaea35a566" 805 | uuid = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74" 806 | version = "0.6.8" 807 | 808 | [[deps.ExceptionUnwrapping]] 809 | deps = ["Test"] 810 | git-tree-sha1 = "e90caa41f5a86296e014e148ee061bd6c3edec96" 811 | uuid = "460bff9d-24e4-43bc-9d9f-a8973cb893f4" 812 | version = "0.1.9" 813 | 814 | [[deps.Expat_jll]] 815 | deps = ["Artifacts", "JLLWrappers", "Libdl"] 816 | git-tree-sha1 = "4558ab818dcceaab612d1bb8c19cee87eda2b83c" 817 | uuid = "2e619515-83b5-522b-bb60-26c02a35a201" 818 | version = "2.5.0+0" 819 | 820 | [[deps.FFMPEG]] 821 | deps = ["FFMPEG_jll"] 822 | git-tree-sha1 = 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932 | deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"] 933 | git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046" 934 | uuid = "78b55507-aeef-58d4-861c-77aaff3498b1" 935 | version = "0.21.0+0" 936 | 937 | [[deps.Glib_jll]] 938 | deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Pkg", "Zlib_jll"] 939 | git-tree-sha1 = "d3b3624125c1474292d0d8ed0f65554ac37ddb23" 940 | uuid = "7746bdde-850d-59dc-9ae8-88ece973131d" 941 | version = "2.74.0+2" 942 | 943 | [[deps.GraphPPL]] 944 | deps = ["MacroTools", "TupleTools"] 945 | git-tree-sha1 = "36d1953626dcb87e87824488167a5a27e6046424" 946 | uuid = "b3f8163a-e979-4e85-b43e-1f63d8c8b42c" 947 | version = "3.1.0" 948 | 949 | [[deps.Graphite2_jll]] 950 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 951 | git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011" 952 | uuid = 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git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6" 1078 | uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac" 1079 | version = "2.10.1+0" 1080 | 1081 | [[deps.LaTeXStrings]] 1082 | git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996" 1083 | uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f" 1084 | version = "1.3.0" 1085 | 1086 | [[deps.Latexify]] 1087 | deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Printf", "Requires"] 1088 | git-tree-sha1 = "f428ae552340899a935973270b8d98e5a31c49fe" 1089 | uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316" 1090 | version = "0.16.1" 1091 | 1092 | [deps.Latexify.extensions] 1093 | DataFramesExt = "DataFrames" 1094 | SymEngineExt = "SymEngine" 1095 | 1096 | [deps.Latexify.weakdeps] 1097 | DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" 1098 | SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8" 1099 | 1100 | [[deps.LayoutPointers]] 1101 | deps = ["ArrayInterface", "LinearAlgebra", 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["MacroTools"] 1826 | git-tree-sha1 = "6cc9d682755680e0f0be87c56392b7651efc2c7b" 1827 | uuid = "9602ed7d-8fef-5bc8-8597-8f21381861e8" 1828 | version = "0.1.5" 1829 | 1830 | [[deps.Unzip]] 1831 | git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78" 1832 | uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d" 1833 | version = "0.2.0" 1834 | 1835 | [[deps.VectorizationBase]] 1836 | deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static", "StaticArrayInterface"] 1837 | git-tree-sha1 = "b182207d4af54ac64cbc71797765068fdeff475d" 1838 | uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f" 1839 | version = "0.21.64" 1840 | 1841 | [[deps.Wayland_jll]] 1842 | deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"] 1843 | git-tree-sha1 = "ed8d92d9774b077c53e1da50fd81a36af3744c1c" 1844 | uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89" 1845 | version = "1.21.0+0" 1846 | 1847 | [[deps.Wayland_protocols_jll]] 1848 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1849 | git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da" 1850 | uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91" 1851 | version = "1.25.0+0" 1852 | 1853 | [[deps.XML2_jll]] 1854 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"] 1855 | git-tree-sha1 = "93c41695bc1c08c46c5899f4fe06d6ead504bb73" 1856 | uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a" 1857 | version = "2.10.3+0" 1858 | 1859 | [[deps.XSLT_jll]] 1860 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"] 1861 | git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a" 1862 | uuid = "aed1982a-8fda-507f-9586-7b0439959a61" 1863 | version = "1.1.34+0" 1864 | 1865 | [[deps.Xorg_libX11_jll]] 1866 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"] 1867 | git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495" 1868 | uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc" 1869 | version = "1.8.6+0" 1870 | 1871 | [[deps.Xorg_libXau_jll]] 1872 | deps = ["Artifacts", "JLLWrappers", "Libdl"] 1873 | git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8" 1874 | uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec" 1875 | version = "1.0.11+0" 1876 | 1877 | [[deps.Xorg_libXcursor_jll]] 1878 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"] 1879 | git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd" 1880 | uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724" 1881 | version = "1.2.0+4" 1882 | 1883 | [[deps.Xorg_libXdmcp_jll]] 1884 | deps = ["Artifacts", "JLLWrappers", "Libdl"] 1885 | git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7" 1886 | uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05" 1887 | version = "1.1.4+0" 1888 | 1889 | [[deps.Xorg_libXext_jll]] 1890 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] 1891 | git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3" 1892 | uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3" 1893 | version = "1.3.4+4" 1894 | 1895 | [[deps.Xorg_libXfixes_jll]] 1896 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] 1897 | git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4" 1898 | uuid = "d091e8ba-531a-589c-9de9-94069b037ed8" 1899 | version = "5.0.3+4" 1900 | 1901 | [[deps.Xorg_libXi_jll]] 1902 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"] 1903 | git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246" 1904 | uuid = "a51aa0fd-4e3c-5386-b890-e753decda492" 1905 | version = "1.7.10+4" 1906 | 1907 | [[deps.Xorg_libXinerama_jll]] 1908 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"] 1909 | git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123" 1910 | uuid = "d1454406-59df-5ea1-beac-c340f2130bc3" 1911 | version = "1.1.4+4" 1912 | 1913 | [[deps.Xorg_libXrandr_jll]] 1914 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"] 1915 | git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631" 1916 | uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484" 1917 | version = "1.5.2+4" 1918 | 1919 | [[deps.Xorg_libXrender_jll]] 1920 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] 1921 | git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96" 1922 | uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa" 1923 | version = "0.9.10+4" 1924 | 1925 | [[deps.Xorg_libpthread_stubs_jll]] 1926 | deps = ["Artifacts", "JLLWrappers", "Libdl"] 1927 | git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9" 1928 | uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74" 1929 | version = "0.1.1+0" 1930 | 1931 | [[deps.Xorg_libxcb_jll]] 1932 | deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"] 1933 | git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d" 1934 | uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b" 1935 | version = "1.15.0+0" 1936 | 1937 | [[deps.Xorg_libxkbfile_jll]] 1938 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"] 1939 | git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4" 1940 | uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a" 1941 | version = "1.1.2+0" 1942 | 1943 | [[deps.Xorg_xcb_util_image_jll]] 1944 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] 1945 | git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97" 1946 | uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b" 1947 | version = "0.4.0+1" 1948 | 1949 | [[deps.Xorg_xcb_util_jll]] 1950 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"] 1951 | git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1" 1952 | uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5" 1953 | version = "0.4.0+1" 1954 | 1955 | [[deps.Xorg_xcb_util_keysyms_jll]] 1956 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] 1957 | git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00" 1958 | uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7" 1959 | version = "0.4.0+1" 1960 | 1961 | [[deps.Xorg_xcb_util_renderutil_jll]] 1962 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] 1963 | git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e" 1964 | uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e" 1965 | version = "0.3.9+1" 1966 | 1967 | [[deps.Xorg_xcb_util_wm_jll]] 1968 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] 1969 | git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67" 1970 | uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361" 1971 | version = "0.4.1+1" 1972 | 1973 | [[deps.Xorg_xkbcomp_jll]] 1974 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"] 1975 | git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb" 1976 | uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4" 1977 | version = "1.4.6+0" 1978 | 1979 | [[deps.Xorg_xkeyboard_config_jll]] 1980 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"] 1981 | git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3" 1982 | uuid = "33bec58e-1273-512f-9401-5d533626f822" 1983 | version = "2.39.0+0" 1984 | 1985 | [[deps.Xorg_xtrans_jll]] 1986 | deps = ["Artifacts", "JLLWrappers", "Libdl"] 1987 | git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77" 1988 | uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10" 1989 | version = "1.5.0+0" 1990 | 1991 | [[deps.Zlib_jll]] 1992 | deps = ["Libdl"] 1993 | uuid = "83775a58-1f1d-513f-b197-d71354ab007a" 1994 | version = "1.2.13+0" 1995 | 1996 | [[deps.Zstd_jll]] 1997 | deps = ["Artifacts", "JLLWrappers", "Libdl"] 1998 | git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c" 1999 | uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" 2000 | version = "1.5.5+0" 2001 | 2002 | [[deps.fzf_jll]] 2003 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 2004 | git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56" 2005 | uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09" 2006 | version = "0.29.0+0" 2007 | 2008 | [[deps.libaom_jll]] 2009 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 2010 | git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4" 2011 | uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b" 2012 | version = "3.4.0+0" 2013 | 2014 | [[deps.libass_jll]] 2015 | deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] 2016 | git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47" 2017 | uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" 2018 | version = "0.15.1+0" 2019 | 2020 | [[deps.libblastrampoline_jll]] 2021 | deps = ["Artifacts", "Libdl"] 2022 | uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" 2023 | version = "5.8.0+0" 2024 | 2025 | [[deps.libfdk_aac_jll]] 2026 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 2027 | git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55" 2028 | uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" 2029 | version = "2.0.2+0" 2030 | 2031 | [[deps.libpng_jll]] 2032 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] 2033 | git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c" 2034 | uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" 2035 | version = "1.6.38+0" 2036 | 2037 | [[deps.libvorbis_jll]] 2038 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] 2039 | git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c" 2040 | uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" 2041 | version = "1.3.7+1" 2042 | 2043 | [[deps.nghttp2_jll]] 2044 | deps = ["Artifacts", "Libdl"] 2045 | uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" 2046 | version = "1.48.0+0" 2047 | 2048 | [[deps.p7zip_jll]] 2049 | deps = ["Artifacts", "Libdl"] 2050 | uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" 2051 | version = "17.4.0+0" 2052 | 2053 | [[deps.x264_jll]] 2054 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 2055 | git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" 2056 | uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" 2057 | version = "2021.5.5+0" 2058 | 2059 | [[deps.x265_jll]] 2060 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 2061 | git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" 2062 | uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" 2063 | version = "3.5.0+0" 2064 | 2065 | [[deps.xkbcommon_jll]] 2066 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] 2067 | git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a" 2068 | uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" 2069 | version = "1.4.1+0" 2070 | """ 2071 | 2072 | # ╔═╡ Cell order: 2073 | # ╟─90ef24e0-1fd9-11ee-2ed4-e947901d2a4c 2074 | # ╠═248bf010-7d15-4886-82e5-7fbbd7e0f7ec 2075 | # ╟─5123688d-a83f-4e09-a0f1-e03a1f583264 2076 | # ╟─fa3ebe3b-1ef9-4c1f-9849-72e1b4f3176c 2077 | # ╟─c4561368-15b9-49e4-a0ff-c5a85171a054 2078 | # ╟─f3b412ba-f0e6-4423-a44d-dcf04ad2b475 2079 | # ╠═156d54ec-126b-4de1-a483-990b503c4a94 2080 | # ╟─ef868b3a-0616-495e-9bd0-de2edf1089db 2081 | # ╟─452ea6ac-17ba-4bd5-8037-ef53b488e420 2082 | # ╠═60dd5591-cfd1-41c5-a6ed-4c485fa27bb2 2083 | # ╟─9638259f-f1bb-4b6e-849d-4455db3a3447 2084 | # ╠═b1eec7ac-9ced-4aac-9647-a15322b30fb5 2085 | # ╠═fe9df76f-9df5-46f7-8161-353ddbf94c09 2086 | # ╟─6792be47-148c-414b-9f21-d7ae11807bd9 2087 | # ╠═1e2ba3eb-b073-40cc-8b56-633e18d041d9 2088 | # ╟─e6d347ee-835b-4077-968b-0e7b11540056 2089 | # ╠═daa54871-05cb-4987-a81c-16f7895da90f 2090 | # ╠═12677bf1-5cae-405b-baf0-b3b741ed1770 2091 | # ╠═5dba141f-a4ff-4439-91bc-c7d6d5a3f18e 2092 | # ╠═ead11ddb-2c4d-47a7-9cf5-483cb40598a0 2093 | # ╟─8e994302-4316-4d23-87e2-020883800e65 2094 | # ╟─9512a92b-32df-4d9b-8e02-870ade5ef1ba 2095 | # ╟─a7eebc8c-e3ec-4962-9088-af61b17af122 2096 | # ╟─00000000-0000-0000-0000-000000000001 2097 | # ╟─00000000-0000-0000-0000-000000000002 2098 | --------------------------------------------------------------------------------