├── .gitignore ├── README.md ├── autodiff ├── README.md ├── coolad.jl └── coolad.pdf ├── copilot └── README.md ├── error-float ├── error_estimate.ipynb └── figs │ ├── complex_rule.png │ ├── conditional_number.png │ └── flIEEE.png ├── franklin └── README.md ├── helpdesk ├── README.md └── README.org ├── julia-packages ├── .gitignore ├── Manifest.toml ├── Project.toml ├── README.md ├── cuda.jl ├── makie.jl └── optim.jl ├── julia ├── 1.julia-setup.md ├── 2.first-package.md ├── 3.basic-grammar.md └── linear-algebra.md ├── mpi ├── .gitignore ├── LocalPreferences.toml ├── Manifest.toml ├── Project.toml ├── README.md ├── julia-helloworld-lsf.job ├── julia-helloworld-slurm.slurm └── mpi.jl ├── prompt └── prompt.pdf └── simulated-annealing ├── README.md ├── example.txt ├── notebook.jl ├── notebook.pdf └── programs ├── example.txt ├── fsa.f90 ├── problem.f90 ├── sa.py └── testsa.py /.gitignore: -------------------------------------------------------------------------------- 1 | *.pyc 2 | *.so 3 | *.mod 4 | .vscode 5 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # CodingClub Materials 2 | The coding club material is usually in the form of `.pdf`, `.md` or notebooks. 3 | 4 | ## Table of contents 5 | 1. [20221105-The Julia programming language - Jinguo Liu](julia) 6 | 2. [20221112-Create a static website with Franklin.jl - Jinguo Liu](franklin) 7 | 3. [20230218-An introduction to Zulip - Yusheng Zhao]() 8 | 4. [20230225-Automatic differentiation - Jinguo Liu](autodiff) 9 | 5. [20230303-Adapt latex template to personal use - Tong Yuan]() 10 | 6. [20230318-The Evolution of NLP: From Language Modeling to ChatGPT's Success with Prompt - Yijie Xu](prompt) 11 | 7. [20230325-Essential Julia packages - Jinguo Liu](julia-packages) 12 | 8. [20230401-Help Desk: Linux and Git - Yusheng Zhao](helpdesk) 13 | 9. [20230408-Simulated annealing for solving the spin-glass problem - Jinguo Liu](simulated-annealing) 14 | 11. [20230408-Message Passing Interfaces (MPI) - Jinguo Liu](mpi) 15 | 12. [20230527-Error in Floating Point System - Xuanzhao Gao](error-float) 16 | 17 | 18 | ## To join our coding club 19 | If you haven't joined the [HKUST-GZ Zulip workspace](http://zulip.hkust-gz.edu.cn/), please check the following invitation link to join our Zulip workspace and subscribe `#coding-club` stream. 20 | https://zulip.hkust-gz.edu.cn/join/uqe4q76jbpowflb42ydaav5b/ 21 | 22 | If you are already a member of the [HKUST-GZ Zulip workspace](http://zulip.hkust-gz.edu.cn/), you may subscript the updates directly by navigating to the `#coding-club` stream. 23 | -------------------------------------------------------------------------------- /autodiff/README.md: -------------------------------------------------------------------------------- 1 | # Cool examples about automatic differentiation 2 | 3 | 1. install Julia from here https://julialang.org/downloads/ 4 | 2. open a julia REPL and install related packages 5 | ```julia 6 | julia>] add Pluto Optim NiLang Zygote PlutoUI Compose Viznet Plots ChainRules StochasticOptimizers TupleTools TropicalNumbers ForwardDiff 7 | ``` 8 | 3. open the `coolad.jl` by 9 | ```julia 10 | julia> using Pluto 11 | 12 | julia> Pluto.run(1234) 13 | ``` 14 | Then open this file by typing the path to `coolad.jl` in input field. 15 | 16 | If you have any problem opening it, please file an issue: https://github.com/Happy-Diode/LunchTalks/issues/new 17 | -------------------------------------------------------------------------------- /autodiff/coolad.jl: -------------------------------------------------------------------------------- 1 | ### A Pluto.jl notebook ### 2 | # v0.12.21 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 el = $(esc(element)) 11 | global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing 12 | el 13 | end 14 | end 15 | 16 | # ╔═╡ b9a9214e-8830-11eb-1751-9d9161202c76 17 | using PlutoUI, Viznet, Compose, Plots 18 | 19 | # ╔═╡ bd3a4ece-8b09-11eb-2fcb-0710286e9892 20 | using ForwardDiff: Dual 21 | 22 | # ╔═╡ 0f22e7d6-88c5-11eb-0600-ff9b80f2113e 23 | using NiLang, Random 24 | 25 | # ╔═╡ 95b2f940-8a4c-11eb-1813-7b28745b5050 26 | using Optim 27 | 28 | # ╔═╡ 2b36cfd2-8d77-11eb-0b32-afc6294b5f50 29 | using Statistics: mean 30 | 31 | # ╔═╡ 5dfb2158-8c4a-11eb-33e6-f96facaf76fa 32 | using ChainRules 33 | 34 | # ╔═╡ f5e3b3de-8b61-11eb-2875-7594a13c1897 35 | using LinearAlgebra 36 | 37 | # ╔═╡ 270fef44-8c49-11eb-01af-43bd6e72da09 38 | using Zygote 39 | 40 | # ╔═╡ c239e57a-8b62-11eb-1f10-87cda664a87c 41 | using StochasticOptimizers 42 | 43 | # ╔═╡ b01b19b6-8bc8-11eb-1a02-bf79f074bad3 44 | begin 45 | using TupleTools, TropicalNumbers 46 | using NiLang.AD: GVar 47 | 48 | @i function bond_tensor(res::Matrix{T}) where T 49 | x ← zero(T) 50 | SWAP(res[2, 2], x) 51 | x → one(T) 52 | end 53 | 54 | @i function vertex_tensor(res::Array{T}, n::Int, val::T) where T 55 | for i=2:length(res)-1 56 | x ← zero(T) 57 | SWAP(res[i], x) 58 | x → one(T) 59 | end 60 | x ← one(T) 61 | res[1] *= x 62 | res[end] *= val 63 | end 64 | 65 | @i @inline function :(*=)(+)(z::Tropical, x::Tropical, y::Tropical) 66 | if x.n > y.n 67 | z.n += x.n 68 | else 69 | z.n += y.n 70 | end 71 | end 72 | 73 | @i @inline function (:*=(identity))(x::Tropical, y::Tropical) 74 | x.n += y.n 75 | end 76 | 77 | @i @inline function (:*=(*))(out!::Tropical, x::Tropical, y::Tropical) 78 | out!.n += x.n + y.n 79 | end 80 | 81 | """ 82 | i_einsum!(ixs, xs, iy, y::AbstractArray{T}) 83 | 84 | A naive reversible implementation of `i_einsum` function for tropical numbers. 85 | * `ixs`: input tensor indices, 86 | * `xs`: input tensors, 87 | * `iy`: output tensor indices, 88 | * `y`: accumulated tensor, notice it is initialized to 0 as output! 89 | 90 | # NOTE: this function is general purposed and slow! 91 | """ 92 | @i function i_einsum!(ixs, xs, iy, y::AbstractArray{T}) where {T<:Tropical} 93 | @routine begin 94 | # outer legs and inner legs 95 | outer_indices ← unique(iy) 96 | inner_indices ← setdiff(TupleTools.vcat(ixs...), outer_indices) 97 | 98 | # find size for each leg 99 | all_indices ← TupleTools.vcat(ixs..., iy) 100 | all_sizes ← TupleTools.vcat(size.(xs)..., size(y)) 101 | outer_sizes ← [map(i->all_sizes[i], indexin(outer_indices, [all_indices...]))...] 102 | inner_sizes ← [map(i->all_sizes[i], indexin(inner_indices, [all_indices...]))...] 103 | 104 | # cartesian indices for outer and inner legs 105 | outer_ci ← CartesianIndices((outer_sizes...,)) 106 | inner_ci ← CartesianIndices((inner_sizes...,)) 107 | 108 | # for indexing tensors (leg binding) 109 | indices ← (outer_indices..., inner_indices...) 110 | locs_xs ← map(ix->map(i->findfirst(isequal(i), indices), ix), ixs) 111 | locs_y ← map(i->findfirst(isequal(i), outer_indices), iy) 112 | end 113 | i_loop!(locs_xs, xs, locs_y, y, outer_ci, inner_ci) 114 | ~@routine 115 | end 116 | 117 | """take an index subset from `ind`""" 118 | index_map(ind::CartesianIndex, locs::Tuple) = CartesianIndex(TupleTools.getindices(Tuple(ind), locs)) 119 | 120 | """ 121 | loop and accumulate products to y, the GPU version, the CPU version. 122 | """ 123 | @i function i_loop!(locs_xs::NTuple{N,Any}, xs::NTuple{N, AbstractArray}, locs_y, y::AbstractArray{T}, outer_ci::CartesianIndices, inner_ci::CartesianIndices) where {N, T<:Tropical} 124 | @invcheckoff @inbounds for i in outer_ci 125 | @routine begin 126 | el ← zero(T) 127 | ind_y ← outer_ci[i] 128 | iy ← index_map(ind_y, locs_y) 129 | branch_keeper ← zeros(Bool, size(inner_ci)...) 130 | pl ← ones(T, size(inner_ci)...) 131 | for ind_x in inner_ci 132 | pli ← one(T) 133 | ind_xy ← CartesianIndex(TupleTools.vcat(ind_y.I, ind_x.I)) 134 | for I=1:N 135 | pli *= xs[I][index_map(ind_xy, locs_xs[I])] 136 | end 137 | if (el.n < pli.n, branch_keeper[ind_x]) 138 | FLIP(branch_keeper[ind_x]) 139 | SWAP(el, pli) 140 | end 141 | SWAP(pl[ind_x], pli) 142 | pli → one(T) 143 | end 144 | end 145 | @inbounds y[iy] *= el 146 | ~@routine 147 | end 148 | end 149 | 150 | # patches 151 | Base.zero(x::Tropical{GVar{T,GT}}) where {T,GT} =zero(Tropical{GVar{T,GT}}) 152 | Base.zero(::Type{Tropical{GVar{T,T}}}) where T = Tropical(GVar(zero(Tropical{T}).n, zero(T))) 153 | 154 | NiLang.AD.GVar(x::Tropical{T}) where T = Tropical(GVar{T,T}(x.n, zero(T))) 155 | 156 | function NiLangCore.deanc(x::T, v::T) where T<:Tropical 157 | x === v || NiLangCore.deanc(content(x), content(v)) 158 | end 159 | end 160 | 161 | # ╔═╡ d8669492-8c98-11eb-1cf5-374da9bd4556 162 | html"" 163 | 164 | # ╔═╡ f0b4563a-8b0b-11eb-3085-458f5d9f88b8 165 | md""" 166 | ```math 167 | \newcommand{\comment}[1]{{\bf \color{blue}{\text{◂~ #1}}}} 168 | ``` 169 | """ 170 | 171 | # ╔═╡ ce5af22a-8830-11eb-13c8-49c680526bd9 172 | md"# Cool automatic differentiation applications 173 | 174 | -- Jinguo Liu" 175 | 176 | # ╔═╡ 22768818-8a95-11eb-1cfe-69534f8b0314 177 | md""" 178 | * What is automatic differentiation (AD)? 179 | * A true history of AD 180 | * Forward mode AD 181 | * Reverse mode AD 182 | * primitves on tensors (including tensorflow, pytorch et al.) 183 | * primitves on elementary instructions (usually source code transformation based) 184 | * defined on a reversible program 185 | * Some applications in **scientific computing** 186 | * solving the graph embedding problem 187 | * inverse engineering a hamiltonian 188 | * obtaining maximum independent set (MIS) configurations 189 | * towards differentiating `expmv` ``\comment{will be used in our emulator}`` 190 | """ 191 | 192 | # ╔═╡ 68be48da-8a93-11eb-226b-7b1f2be99cb6 193 | md""" 194 | ## The true history of automatic differentiation 195 | """ 196 | 197 | # ╔═╡ da08c542-8a93-11eb-3375-d79ccd2de122 198 | md""" 199 | * 1964 ~ Robert Edwin Wengert, A simple automatic derivative evaluation program. ``\comment{first forward mode AD}`` 200 | * 1970 ~ Seppo Linnainmaa, Taylor expansion of the accumulated rounding error. ``\comment{first backward mode AD}`` 201 | * 1986 ~ Rumelhart, D. E., Hinton, G. E., and Williams, R. J., Learning representations by back-propagating errors. 202 | * 1992 ~ Andreas Griewank, Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation. ``\comment{foundation of source code transformation based AD.}`` 203 | * 2000s ~ The boom of tensor based AD frameworks for machine learning. 204 | * 2018 ~ People re-invented AD as differential programming ([wiki](https://en.wikipedia.org/wiki/Differentiable_programming) and this [quora answer](https://www.quora.com/What-is-Differentiable-Programming).) 205 | ![](https://qph.fs.quoracdn.net/main-qimg-fb2f8470f2120eb49c8142b08d9c4132) 206 | * 2020 ~ Me, Differentiate everything with a reversible embeded domain-specific language ``\comment{AD based on reversible programming}``. 207 | """ 208 | 209 | # ╔═╡ 0c80347a-8aff-11eb-0862-1d551e3af00b 210 | md"## Forward mode automatic differentiation" 211 | 212 | # ╔═╡ f55f9cba-8afe-11eb-3bf9-e3e5ecbf3a56 213 | md""" 214 | Forward mode AD attaches a infitesimal number $\epsilon$ to a variable, when applying a function $f$, it does the following transformation 215 | ```math 216 | \begin{align} 217 | f(x+g \epsilon) = f(x) + f'(x) g\epsilon + \mathcal{O}(\epsilon^2) 218 | \end{align} 219 | ``` 220 | 221 | The higher order infinitesimal is ignored. 222 | 223 | **In the program**, we can define a *dual number* with two fields, just like a complex number 224 | ``` 225 | f((x, g)) = (f(x), f'(x)*g) 226 | ``` 227 | """ 228 | 229 | # ╔═╡ 662c94c4-8b0a-11eb-39a2-9f37e689fbd3 230 | res = sin(Dual(π/4, 2.0)) 231 | 232 | # ╔═╡ 9e24dd6c-8b0a-11eb-020a-a1d7bf2e87bf 233 | res === Dual(sin(π/4), cos(π/4)*2.0) 234 | 235 | # ╔═╡ fc682956-8b00-11eb-3102-952881130049 236 | md" 237 | We can apply this transformation consecutively, it reflects the chain rule. 238 | ```math 239 | \begin{align} 240 | \frac{\partial \vec y_{i+1}}{\partial x} &= \boxed{\frac{\partial \vec y_{i+1}}{\partial \vec y_i}}\frac{\partial \vec y_i}{\partial x}\\ 241 | &\text{local Jacobian} 242 | \end{align} 243 | ``` 244 | " 245 | 246 | # ╔═╡ 167cbe40-8bf5-11eb-077b-bdd217c9bd78 247 | let 248 | lb = textstyle(:math, fontsize(8), width=0.5, height=0.5) 249 | tb = textstyle(:default, fontsize(10), Compose.font("monospace")) 250 | tb_big = textstyle(:default, fontsize(3.5), fill("white"), Compose.font("monospace")) 251 | nb = nodestyle(:circle, fill("white"), Compose.stroke("black"); r=0.08) 252 | tri = nodestyle(:triangle, Compose.stroke("transparent"), fill("black"); r=0.02) 253 | eb = bondstyle(:default, linewidth(0.5mm)) 254 | ebr = bondstyle(:default, Compose.stroke("red"), linewidth(0.5mm)) 255 | ebd = bondstyle(:default, linewidth(0.5mm), dashed=true) 256 | eba = bondstyle(:default, linewidth(0.5mm), Compose.arrow(), Compose.stroke("red"), Compose.fill("red")) 257 | 258 | function arrow(x, y) 259 | mid = (x .+ y) ./ 2 260 | t = nodestyle(:triangle, fill("red"), θ=π/2-atan((y .- x)...)-1π/6) 261 | ebr >> (x, y) 262 | t >> mid 263 | end 264 | 265 | Compose.set_default_graphic_size(15cm, 5cm) 266 | x = (0.1, 0.5) 267 | fi0 = (0.35, 0.5) 268 | fi1 = (0.7, 0.5) 269 | fi2 = (1.0, 0.5) 270 | img = canvas() do 271 | nb >> fi0 272 | nb >> fi1 273 | lb >> (fi0 .- (0.05, 0.1), "f_{i-1}") 274 | lb >> (fi1 .- (0.02, 0.1), "f_{i}") 275 | lb >> (x, "x") 276 | lb >> ((fi1 .+ fi0) ./ 2 .- (0.02, 0.0), raw"\vec{y}_{i}") 277 | lb >> ((fi1 .+ fi2) ./ 2 .- (0.05, 0.0), raw"\vec{y}_{i+1}") 278 | lb >> ((fi1 .+ fi2) ./ 2 .- (0.05, 0.0), "\\vec{y}_{i+1}") 279 | lb >> (x .- (0.00, 0.25), raw"\color{red}{1}") 280 | lb >> ((fi1 .+ fi0) ./ 2 .- (0.05, 0.45), raw"\color{red}{\frac{\partial \vec{y}_{i}}{\partial x}}") 281 | lb >> ((fi1 .+ fi2) ./ 2 .- (0.08, 0.45), raw"\color{red}{\frac{\partial \vec{y}_{i+1}}{\partial x}}") 282 | ebd >> (x, fi0) 283 | eb >> (fi0, fi1) 284 | eb >> (fi1, fi2) 285 | #arrow((fi1 .+ fi0) ./ 2 .+ (0.08, -0.3), (fi1 .+ fi2) ./ 2 .+ (-0.08, -0.3)) 286 | arrow((fi1 .+ fi0) ./ 2 .+ (0.08, -0.3), (fi1 .+ fi2) ./ 2 .+ (-0.08, -0.3)) 287 | end 288 | img 289 | end 290 | 291 | # ╔═╡ d29a56a4-8d86-11eb-1749-0972a594a0e4 292 | let 293 | x = Dual(π/4, 1.0) 294 | for i=1:10 295 | x = sin(x) 296 | end 297 | x 298 | end 299 | 300 | # ╔═╡ 0ba6245c-8bf5-11eb-1005-1b72ffae3412 301 | md""" 302 | **Example:** Computing two gradients $\frac{\partial z\sin x}{\partial x}$ and $\frac{\partial \sin^2x}{\partial x}$ at one sweep 303 | """ 304 | 305 | # ╔═╡ aa316d52-8b00-11eb-1e7e-43e6f504977f 306 | let 307 | lb = textstyle(:math, fontsize(8), width=1.0, height=0.5) 308 | tb = textstyle(:default, fontsize(3.5), Compose.font("monospace")) 309 | tb_big = textstyle(:default, fontsize(4.5), fill("white"), Compose.font("monospace")) 310 | nb = nodestyle(:circle, fill("black"), Compose.stroke("transparent"); r=0.05) 311 | tri = nodestyle(:triangle, Compose.stroke("transparent"), fill("black"); r=0.02) 312 | eb = bondstyle(:default, linewidth(0.5mm)) 313 | 314 | x_x = (0.1, 0.25) 315 | x_y = (0.9, 0.5) 316 | x_y2 = (0.9, 0.25) 317 | x_z = (0.3, 0.5) 318 | x_sin = (0.3, 0.25) 319 | x_mul = (0.5, 0.5) 320 | x_square = (0.5, 0.25) 321 | 322 | function arrow(x, y) 323 | mid = (x .+ y) ./ 2 324 | t = nodestyle(:triangle, θ=π/2-atan((y .- x)...)-1π/6) 325 | eb >> (x, y) 326 | t >> mid 327 | end 328 | 329 | img = canvas() do 330 | nb >> x_sin 331 | nb >> x_mul 332 | nb >> x_square 333 | tb_big >> (x_sin, "sin") 334 | tb_big >> (x_mul .+ (0, 0.01), "*") 335 | tb_big >> (x_square, "^2") 336 | arrow(x_sin, x_mul) 337 | arrow(x_x, x_sin) 338 | arrow(x_mul, x_y) 339 | arrow(x_square, x_y2) 340 | arrow(x_z, x_mul) 341 | arrow(x_sin, x_square) 342 | tb >> ((x_x .+ x_sin) ./ 2 .- (0.02, 0.04), "x+ϵˣ") 343 | tb >> ((x_sin .+ x_mul) ./ 2 .- (0.08, 0.04), "sin(x)+cos(x)*ϵˣ") 344 | tb >> ((x_y .+ x_mul) ./ 2 .- (-0.04, 0.055), "z*sin(x)\n+z*cos(x)*ϵˣ") 345 | tb >> ((x_y2 .+ x_square) ./ 2 .- (-0.04, 0.055), "sin(x)^2\n+2*sin(x)*cos(x)*ϵˣ") 346 | tb >> ((x_z .+ x_mul) ./ 2 .- (0.05, 0.02), "z") 347 | end 348 | 349 | Compose.set_default_graphic_size(100mm, 100mm/2) 350 | Compose.compose(context(0, -0.15, 1, 2), img) 351 | end 352 | 353 | # ╔═╡ 8a55b3e4-8d67-11eb-203e-0b49c8e3e4aa 354 | md"so the gradients are $z\cos x$ and $2\sin x\cos x$" 355 | 356 | # ╔═╡ f0468078-8b0c-11eb-1bdb-9f6f9496dcf2 357 | md""" 358 | **What if we want to compute gradients for multiple inputs?** 359 | 360 | The computing time grows **linearly** as the number of variables that we want to differentiate. But does not grow significantly with the number of outputs. 361 | """ 362 | 363 | # ╔═╡ 6335bc36-8b15-11eb-3731-5b76661d10fa 364 | md""" 365 | ## Reverse mode automatic differentiation 366 | 367 | """ 368 | 369 | # ╔═╡ 2f60bb2c-8b2e-11eb-04f9-b79f81439af3 370 | md"On the other side, the back-propagation can differentiate **many inputs** with respect to a **single output** efficiently" 371 | 372 | # ╔═╡ 61be9354-8b25-11eb-3205-db9b03a18f18 373 | md""" 374 | ```math 375 | \begin{align} 376 | \frac{\partial \mathcal{L}}{\partial \vec y_i} = \frac{\partial \mathcal{L}}{\partial \vec y_{i+1}}&\boxed{\frac{\partial \vec y_{i+1}}{\partial \vec y_i}}\\ 377 | &\text{local jacobian?} 378 | \end{align} 379 | ``` 380 | """ 381 | 382 | # ╔═╡ 30f3b718-8bfc-11eb-02cc-777ebc108429 383 | let 384 | lb = textstyle(:math, fontsize(8), width=0.5, height=0.5) 385 | tb = textstyle(:default, fontsize(10), Compose.font("monospace")) 386 | tb_big = textstyle(:default, fontsize(3.5), fill("white"), Compose.font("monospace")) 387 | nb = nodestyle(:circle, fill("white"), Compose.stroke("black"); r=0.08) 388 | tri = nodestyle(:triangle, Compose.stroke("transparent"), fill("black"); r=0.02) 389 | eb = bondstyle(:default, linewidth(0.5mm)) 390 | ebr = bondstyle(:default, Compose.stroke("red"), linewidth(0.5mm)) 391 | ebd = bondstyle(:default, linewidth(0.5mm), dashed=true) 392 | eba = bondstyle(:default, linewidth(0.5mm), Compose.arrow(), Compose.stroke("red"), Compose.fill("red")) 393 | 394 | function arrow(x, y) 395 | mid = (x .+ y) ./ 2 396 | t = nodestyle(:triangle, fill("red"), θ=π/2-atan((y .- x)...)-1π/6) 397 | ebr >> (x, y) 398 | t >> mid 399 | end 400 | 401 | Compose.set_default_graphic_size(15cm, 5cm) 402 | x = (0.1, 0.5) 403 | fi0 = (0.35, 0.5) 404 | fi1 = (0.7, 0.5) 405 | fi2 = (0.9, 0.5) 406 | img = canvas() do 407 | nb >> fi0 408 | nb >> fi1 409 | lb >> (fi0 .- (0.02, 0.1), "f_{i}") 410 | lb >> (fi1 .- (0.05, 0.1), "f_{i+1}") 411 | lb >> (fi2 .- (0.05, 0.0), raw"\mathcal{L}") 412 | lb >> ((fi0 .+ x) ./ 2 .- (0.05, 0.0), raw"\vec{y}_{i}") 413 | lb >> ((fi0 .+ fi1) ./ 2 .- (0.05, 0.0), raw"\vec{y}_{i+1}") 414 | lb >> ((fi0 .+ fi1) ./ 2 .- (0.05, 0.0), "\\vec{y}_{i+1}") 415 | lb >> (fi2 .- (0.05, 0.25), raw"\color{red}{1}") 416 | lb >> ((fi0 .+ x) ./ 2 .- (0.08, 0.45), raw"\color{red}{\frac{\partial \vec{y}_{i}}{\partial x}}") 417 | lb >> ((fi0 .+ fi1) ./ 2 .- (0.08, 0.45), raw"\color{red}{\frac{\partial \vec{y}_{i+1}}{\partial x}}") 418 | ebd >> (fi1, fi2) 419 | eb >> (fi0, fi1) 420 | eb >> (x, fi0) 421 | #arrow((fi1 .+ fi0) ./ 2 .+ (0.08, -0.3), (fi1 .+ fi2) ./ 2 .+ (-0.08, -0.3)) 422 | arrow( (fi0 .+ fi1) ./ 2 .+ (-0.08, -0.3), (fi0 .+ x) ./ 2 .+ (0.05, -0.3),) 423 | end 424 | img 425 | end 426 | 427 | # ╔═╡ f67d1d28-8d6c-11eb-2e47-09e0aece0967 428 | md"### How to visite local Jacobians in the reversed order? " 429 | 430 | # ╔═╡ 0ebb6588-8b52-11eb-21c0-4fd9e70a77e7 431 | md" 432 | **Design Decision** 433 | 434 | 1. Compute forward pass and caching inetermediate results into a global stack $\Sigma$ （packages except NiLang）， 435 | 2. reversible programming." 436 | 437 | # ╔═╡ 085145dc-8c10-11eb-12dc-3be1d68fe85c 438 | md""" 439 | **Example:** Computing the gradient $\frac{\partial z\sin x}{\partial x}$ and $\frac{\partial z\sin x}{\partial z}$ by back propagating cached local information. 440 | """ 441 | 442 | # ╔═╡ 80caf3ba-8b1f-11eb-3030-5378078e2df9 443 | let 444 | lb = textstyle(:math, fontsize(10), width=1.0, height=0.5) 445 | tb = textstyle(:default, fontsize(3.5), Compose.font("monospace")) 446 | tbc = textstyle(:default, fontsize(3.5), fill("red"), Compose.font("monospace")) 447 | tb_big = textstyle(:default, fontsize(4), fill("white"), Compose.font("monospace")) 448 | nb = nodestyle(:circle, fill("black"), Compose.stroke("transparent"); r=0.05) 449 | tri = nodestyle(:triangle, Compose.stroke("transparent"), fill("black"); r=0.02) 450 | eb = bondstyle(:default, linewidth(0.5mm)) 451 | 452 | x_x = (0.1, 0.2) 453 | x_y = (0.9, 0.5) 454 | x_z = (0.1, 0.7) 455 | x_sin = (0.3, 0.3) 456 | x_mul = (0.5, 0.5) 457 | 458 | function arrow(x, y) 459 | mid = (x .+ y) ./ 2 460 | t = nodestyle(:triangle, θ=π/2-atan((y .- x)...)-1π/6) 461 | eb >> (x, y) 462 | t >> mid 463 | end 464 | img1 = canvas() do 465 | nb >> x_sin 466 | nb >> x_mul 467 | tb_big >> (x_sin, "sin") 468 | tb_big >> (x_mul .+ (0, 0.01), "*") 469 | arrow(x_sin, x_mul) 470 | arrow(x_x, x_sin) 471 | arrow(x_mul, x_y) 472 | arrow(x_z, x_mul) 473 | tb >> ((x_x .+ x_sin) ./ 2 .- (0.0, 0.1), "x \n push(Σ,x)") 474 | tb >> ((x_sin .+ x_mul) ./ 2 .- (-0.15, 0.04), "s = sin(x) \n push(Σ,s)") 475 | tb >> ((x_y .+ x_mul) ./ 2 .- (-0.05, 0.04), "y = z*sin(x)") 476 | tb >> ((x_z .+ x_mul) ./ 2 .- (0.05, 0.07), "z\n push(Σ,z)") 477 | end 478 | img2 = canvas() do 479 | nb >> x_sin 480 | nb >> x_mul 481 | tb_big >> (x_sin, "sin") 482 | tb_big >> (x_mul .+ (0, 0.01), "*") 483 | arrow(x_mul, x_sin) 484 | arrow(x_sin, x_x) 485 | arrow(x_y, x_mul) 486 | arrow(x_mul, x_z) 487 | tb >> ((x_x .+ x_sin) ./ 2 .- (0.0, 0.1), "x = pop(Σ)\nx̄ = cos(x)*s̄") 488 | tb >> ((x_sin .+ x_mul) ./ 2 .- (-0.12, 0.04), "z = pop(Σ)\ns̄ = z*ȳ") 489 | tb >> ((x_y .+ x_mul) ./ 2 .- (-0.05, 0.06), "y\nȳ=1") 490 | tb >> ((x_z .+ x_mul) ./ 2 .- (0.05, 0.07), "s = pop(Σ)\nz̄ = s*ȳ") 491 | end 492 | 493 | Compose.set_default_graphic_size(150mm, 75mm/1.4) 494 | Compose.compose(context(), 495 | (context(0, -0.1, 0.5, 1.4), img1), 496 | (context(0.5, -0.1, 0.5, 1.4), img2) 497 | ) 498 | end 499 | 500 | 501 | 502 | # ╔═╡ 8bed03b2-8c1b-11eb-1043-23ff31b46991 503 | md"Here, we use $\overline y$ for $\frac{\partial \mathcal{L}}{\partial y}$, which is also called the adjoint." 504 | 505 | # ╔═╡ 0790392e-8d04-11eb-3585-d17e29d379d9 506 | md"### Primitives on different scales" 507 | 508 | # ╔═╡ 330ccb76-8d04-11eb-3bfd-434a93465975 509 | md"We call the leaf nodes defining AD rules \"**primitives**\"" 510 | 511 | # ╔═╡ dfb179fe-8cae-11eb-24b6-3bdfa57a0d45 512 | md" 513 | **Design Decision** 514 | 515 | * A: If we define primitives on **arrays**, we need tons of manually defined backward rules. (Jax, Pytorch, Zygote.jl, ReverseDiff.jl et al.) 516 | * B: If we define primitives on **scalar instructions**, we will have worse tensor performance. (Tapenade, Adept, NiLang et al.) 517 | 518 | *Note*: Here, implementing AD on scalars means specifically the **optimal checkpointing** approach, rather than a package like Jax, Zygote and ReverseDiff that having scalar support. 519 | " 520 | 521 | # ╔═╡ f2c75336-8cab-11eb-09ce-e99acb20aee8 522 | let 523 | w, h = 0.22, 0.1 524 | lb = Compose.compose(context(), polygon([(-w, -h), (-w, h), (w, h), (w, -h)]), Compose.stroke("transparent")) 525 | lb2 = Compose.compose(context(), polygon([(-w, -h), (-w, h), (w, h), (w, -h)]), Compose.stroke("transparent"), fill("red")) 526 | tb = Compose.compose(context(), Compose.text(0.0, 0.0, ""), fontsize(3), Compose.font("monospace")) 527 | tb_big = textstyle(:default, fontsize(3), fill("white"), Compose.font("monospace")) 528 | eb = bondstyle(:default, linewidth(0.5mm)) 529 | ar = bondstyle(:default, linewidth(0.3mm), Compose.arrow()) 530 | xprog = (0.25, 0.15) 531 | xtensors = (0.25, 0.5) 532 | t1 = (0.5, 0.15) 533 | t2 = (0.5, 0.5) 534 | t3 = (0.5, 0.85) 535 | xscalars2 = (0.25, 0.85) 536 | 537 | function box(loc, text; color="black") 538 | (color=="black" ? lb : lb2) >> loc 539 | tb_big >> (loc, text) 540 | end 541 | Compose.set_default_graphic_size(10cm, 5cm) 542 | canvas() do 543 | box(xprog, "Program") 544 | ar >> (xprog, xtensors .+ (0, -h-0.03)) 545 | #ar >> (xprog, xscalars .+ (-w/2, -h-0.03)) 546 | ar >> (xtensors, xscalars2 .+ (0, -h-0.05)) 547 | box(xtensors, "Functions on arrays") 548 | #box(xscalars, "Functions on Scalars") 549 | box(xscalars2, "Finite instructions"; color="red") 550 | tb >> (t1, "Neural networks") 551 | tb >> (t2, "matrix multiplication") 552 | tb >> (t3, "+, -, *") 553 | end 554 | end 555 | 556 | # ╔═╡ d1760114-8b52-11eb-3241-252292bf96ac 557 | html""" 558 | 559 | 560 | 561 | 562 | 563 | 564 | 565 | 566 | 567 | 568 | 569 | 570 | 571 | 578 | 584 | 586 | 587 | 588 | 589 | 590 | 594 | 595 |
on tensorson finite instructions
meaningdefining backward rules manully for functions on tensorsdefining backward rules on a limited set of basic scalar operations, and generate gradient code using source code transformation
pros and cons 572 |
    573 |
  1. Good tensor performance
    2. 574 |
  2. Mature machine learning ecosystem
    3. 575 |
  3. Need to define backward rules manually
    4. 576 |
577 | 		579 |
    580 |
  1. Reasonalbe scalar performance
    2. 581 |
  2. hard to utilize GPU kernels (except NiLang.jl) and BLAS
    3. 582 |
583 | 		585 |
packagesJax
PyTorch		Tapenade
591 | Adept
592 | NiLang.jl 593 |
596 | """ 597 | 598 | # ╔═╡ 8cab36f8-8c1a-11eb-009a-3d6dbdb83d85 599 | md""" 600 | ## The AD ecosystem in Julia 601 | 602 | Please check JuliaDiff: [https://juliadiff.org/](https://juliadiff.org/) 603 | 604 | A short list: 605 | * Forward mode AD: ForwardDiff.jl 606 | * Reverse mode AD (tensor): ReverseDiff.jl/Zygote.jl 607 | * Reverse mode AD (scalar): NiLang.jl 608 | 609 | Warnings 610 | * The main authors of `Tracker`, `ReverseDiff` and `Zygote` are not maintaining them anymore. 611 | """ 612 | #= 613 | | | Rules | Favors Tensor? | Type | 614 | | ---- | ---- | --- | --- | 615 | | Zygote | C | ✓ | R | 616 | | ReverseDiff | D | ✓ | R | 617 | | Nabla | D→C | ✓ | R | 618 | | Tracker | D | ✓ | R | 619 | | Yota | C | ✓ | R | 620 | | NiLang | - | × | R | 621 | | Enzyme | - | × | R | 622 | | ForwardDiff | - | × | F | 623 | | Diffractor | ? | ? | ? | 624 | 625 | * R: reverse mode 626 | * F: forward mode 627 | * C: ChainRules 628 | * D: DiffRules 629 | """ 630 | =# 631 | 632 | # ╔═╡ 01e46500-8ced-11eb-04b7-a1e05a81b1b2 633 | md"# Quick summary 634 | 1. The history of AD is longer than many people have thought. People are most familar with *reverse mode AD with primitives implemented on tensors* that brings the boom of machine learning. There are also AD frameworks that can differentiate a general program directly, which does not require users defining AD rules manually. 635 | 2. **Forward mode AD** propagate gradients forward, it has a computational overhead propotional to the number of input parameters. 636 | 2. **Backward mode AD** propagate gradients backward, it has a computational overhead propotional to the number of output parameters. 637 | * primitives on **tensors** v.s. **scalars** 638 | * reverse the program tape by **caching/checkpointing** v.s. **reversible programming** 639 | 4. Julia has one of the most active AD community! 640 | 641 | #### Forward v.s. Backward 642 | when is forward mode AD more useful? 643 | 644 | * It is often combined with backward mode AD for obtaining Hessians (forward over backward). 645 | * Having <20 input parameters. 646 | 647 | when is backward mode AD more useful? 648 | * In most variational optimizations, especially when we are training a neural network with ~ 100M parameters. 649 | " 650 | 651 | # ╔═╡ eb0cba98-8a54-11eb-132f-6320f3893da9 652 | md"## 1. Embedding a peterson Graph" 653 | 654 | # ╔═╡ 43c6b8ec-8a79-11eb-2ff1-cb8fd958b693 655 | md""" 656 | One day, A postdoc of Anders Sandvik Jun Takahashi went to me, said "Hey, Jinguo, can you help me figure out what is the minimum embedding dimension of a Peterson graph?" 657 | 658 | A Peterson graph is a famous 3-regular graph with very high symmetry. It is well know to graph theory people. It looks like 659 | """ 660 | 661 | # ╔═╡ 99839afc-8a83-11eb-3f38-1bef2960f969 662 | md"It has 10 vertices, 15 edges, while these vertices are all equivalent to each other. By embedding a graph into a k-dimensional space, it requires 663 | 1. assigning a k-dimensional vector to each node as the Euclidean coordinate, 664 | 2. the distance between each pair of connected nodes are the same, meanwhile, the distance between each pair of disconnected nodes are same too. 665 | 3. the distance between disconnected vertices are larger than connect vertices" 666 | 667 | # ╔═╡ a8a92160-88c5-11eb-0a7e-cbec45b627f0 668 | # connected vertex-pairs in a petersen graph 669 | const L1 = [(1, 6), (2, 7), (3, 8), (4, 9), (5, 10), 670 | (1, 2), (2, 3), (3, 4), (4, 5), (1, 5), (6, 8), 671 | (8, 10), (7, 10), (7, 9), (6, 9)]; 672 | 673 | # ╔═╡ b1016e9c-88c5-11eb-12a5-41a914a794d3 674 | # disconnected vertex-pairs in a petersen graph 675 | const L2 = [(1, 3), (1, 4), (1, 7), (1, 8), (1, 9), 676 | (1, 10), (2, 4), (2, 5), (2, 6), (2, 8), (2, 9), 677 | (2, 10), (3, 5), (3, 6), (3, 7), (3, 9), (3, 10), 678 | (4, 6), (4, 7), (4, 8), (4, 10), (5, 6), (5, 7), 679 | (5, 8), (5, 9), (6, 7), (6, 10), (7, 8), (8, 9), 680 | (9, 10)]; 681 | 682 | # ╔═╡ 385638ea-8a81-11eb-166b-a9caf2b2792f 683 | let 684 | L1 = [(1, 6), (2, 7), (3, 8), (4, 9), (5, 10), 685 | (1, 2), (2, 3), (3, 4), (4, 5), (1, 5), (6, 8), 686 | (8, 10), (7, 10), (7, 9), (6, 9)] 687 | x1 = (0.0, -0.45) 688 | x2 = (0.0, -0.25) 689 | nodes = [ 690 | [Viznet.rot(x1..., 2π/5*i) .+ 0.5 for i=0:4]..., 691 | [Viznet.rot(x2..., 2π/5*i) .+ 0.5 for i=0:4]... 692 | ] 693 | Compose.set_default_graphic_size(8cm, 8cm) 694 | nb = nodestyle(:circle, fill("white"), Compose.stroke("black")) 695 | eb = bondstyle(:default) 696 | eb2 = bondstyle(:default, Compose.stroke("#DDDDDD")) 697 | canvas() do 698 | for n in nodes 699 | nb >> n 700 | end 701 | for (i,j) in L1 702 | eb >> (nodes[i], nodes[j]) 703 | end 704 | for (i,j) in L2 705 | eb2 >> (nodes[i], nodes[j]) 706 | end 707 | end 708 | end 709 | 710 | # ╔═╡ 38a9382e-8b58-11eb-3e0b-656260c672cd 711 | md"For dimension $k\in 1,2,\dots,10$, we assign a coordinate to each vertex. Then we define the loss as 712 | ```math 713 | \begin{align} 714 | \begin{split} 715 | D_1 &= \{d_{(i,j)} | (i,j) \in L_1\}\\ 716 | D_2 &= \{d_{(i,j)} | (i,j) \in L_2\}\\ 717 | \mathcal{L} &= {\rm var}(D_1) + {\rm var}(D_2) \\ 718 | &+\exp({\rm relu}({\rm mean}(D_1)- {\rm mean}(D_2) + 0.1)) - 1 \comment{if $d_2$ < $d_1$, punish} 719 | \end{split} 720 | \end{align} 721 | ``` 722 | 723 | " 724 | 725 | # ╔═╡ 1d503598-8d7c-11eb-1cf4-cf0755194043 726 | md""" 727 | `relu` is defined as `x > 0 ? x : 0` 728 | """ 729 | 730 | # ╔═╡ bf5702ae-88c5-11eb-2bb2-d7d5cf4eccdf 731 | @i function sqdistance(dist!, x1::AbstractVector{T}, x2::AbstractVector) where T 732 | for i=1:length(x1) 733 | @routine begin 734 | diff ← zero(T) 735 | diff += x1[i] - x2[i] 736 | end 737 | dist! += diff ^ 2 738 | ~@routine 739 | end 740 | end 741 | 742 | # ╔═╡ 9a474d6a-885f-11eb-2db5-2145c0b9183f 743 | """The loss of graph embedding problem.""" 744 | @i function embedding_loss(out!::T, x) where T 745 | @routine @invcheckoff begin 746 | @zeros T v1 varsum1 varsum2 s1 s2 m1 v2 m2 diff 747 | d1 ← zeros(T, length(L1)) 748 | d2 ← zeros(T, length(L2)) 749 | # 1. compute distances 750 | for i=1:length(L1) 751 | sqdistance(d1[i], x[:,L1[i][1]],x[:,L1[i][2]]) 752 | end 753 | for i=1:length(L2) 754 | sqdistance(d2[i], x[:,L2[i][1]],x[:,L2[i][2]]) 755 | end 756 | # 2. compute variances 757 | NiLang.i_var_mean_sum(v1, varsum1, m1, s1, d1) 758 | NiLang.i_var_mean_sum(v2, varsum2, m2, s2, d2) 759 | m1 -= m2 - 0.1 760 | end 761 | out! += v1 + v2 762 | if m1 > 0 763 | # to ensure mean(v2) > mean(v1) 764 | # if mean(v1)+0.1 - mean(v2) > 0, punish it. 765 | out! += exp(m1) 766 | out! -= 1 767 | end 768 | ~@routine 769 | end 770 | 771 | # ╔═╡ 5ef95fa8-8a50-11eb-35e7-9354bf50b0e7 772 | md"Seed = $(@bind seed Slider(1:10000))" 773 | 774 | # ╔═╡ 8f2d529c-8a50-11eb-1910-29b61b1b8f82 775 | md"dimension $(@bind dimension NumberField(1:10; default=5))" 776 | 777 | # ╔═╡ 9b86ac04-8a4c-11eb-278e-5777f3552f25 778 | x_minimizer, x_minimum = let 779 | Random.seed!(seed) 780 | x = randn(dimension,10) 781 | # `NiLang.AD.gradient` to obtain the gradients 782 | res = Optim.optimize(x->embedding_loss(0.0, x)[1], x->NiLang.AD.gradient(embedding_loss, (0.0, x); iloss=1)[2], x, LBFGS(), Optim.Options(f_abstol=1e-12, f_reltol=1e-12, g_abstol=1e-12, g_reltol=1e-12), inplace=false) 783 | res.minimizer, res.minimum 784 | end; 785 | 786 | # ╔═╡ c697cf2c-8d76-11eb-1817-132326c4a92e 787 | x_minimum 788 | 789 | # ╔═╡ 8cae97aa-8d76-11eb-1740-0752e4297de2 790 | d1s = [norm(x_minimizer[:,a] .- x_minimizer[:,b]) for (a, b) in L1] 791 | 792 | # ╔═╡ 01e6cbb4-8d77-11eb-2519-23c89d5de971 793 | d2s = [norm(x_minimizer[:,a] .- x_minimizer[:,b]) for (a, b) in L2] 794 | 795 | # ╔═╡ 071bc508-8d77-11eb-01e6-950e171e6b45 796 | mean(d2s)/mean(d1s) 797 | 798 | # ╔═╡ 77562ce2-8a79-11eb-389a-a35e42e65171 799 | md""" 800 | His work of finding the SO(5) symmetric tensor order representation is later published as 801 | 802 | "Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet." (Phys. Rev. Research 2, 033459, Jun Takahashi, Anders W. Sandvik) 803 | """ 804 | 805 | # ╔═╡ 0f5cc712-8a84-11eb-0f31-91b30ad895af 806 | md"## 2. Inverse engineering a Hamiltonian" 807 | 808 | # ╔═╡ be1a31d8-8a91-11eb-2ead-fb4b7de74afc 809 | md""" 810 | This problem is from "Notes on Adjoint Methods for 18.335", Steven G. Johnson 811 | 812 | Consider a 1D Shrodinger equation 813 | ```math 814 | \left[-\frac{d^2}{dx^2} + V(x)\right]\Psi(x) = E\Psi(x), x \in [-1,1] 815 | ``` 816 | 817 | """ 818 | 819 | # ╔═╡ 25bc662a-8c14-11eb-0689-45ac05c280aa 820 | md"We can solve its gound state numerically by discretizing the space and diagonalize the Hamiltonian matrix. The Hamiltonian matrix is 821 | 822 | ```math 823 | A = \frac{1}{Δx^2}\left( 824 | \begin{matrix} 825 | 2 & -1 & 0 & \ldots & 0 & -1\\ 826 | -1 & 2 & -1 & 0 & \ldots & \\ 827 | 0 & -1 & 2 & -1 & 0 & \ldots \\ 828 | \vdots & & & \ddots & & \\ 829 | & & & -1 & 2 & -1\\ 830 | -1 & 0 & \ldots & 0 & -1 & 2 831 | \end{matrix} 832 | \right) + {\rm diag}(V) 833 | ``` 834 | " 835 | 836 | # ╔═╡ 3aa7ea18-8c15-11eb-010e-9d6a9e7dd952 837 | md"where the matrix size is equal the descretized lattice size" 838 | 839 | # ╔═╡ 4eda1c4c-8b5f-11eb-2485-6b34cdef4ef8 840 | dx = 0.02; 841 | 842 | # ╔═╡ 40ec8444-8b5f-11eb-0de5-97ed546aa4a1 843 | xgrid = -1.0:dx:1.0; 844 | 845 | # ╔═╡ cf8235b6-8b5d-11eb-2997-41da626b503f 846 | @i function hamiltonian!(a, x, V::AbstractVector{T}) where T 847 | @routine begin 848 | @zeros T dx2 invdx2 849 | n ← length(x) 850 | dx2 += (@const Float64(x.step))^2 851 | invdx2 += 1/dx2 852 | end 853 | @safe @assert size(a) == (n, n) 854 | for i=1:n 855 | a[i, i] += 2 * invdx2 856 | a[i, i] += V[i] 857 | a[i, mod1(i+1, n)] -= invdx2 858 | a[mod1(i+1, n), i] -= invdx2 859 | end 860 | ~@routine 861 | end 862 | 863 | # ╔═╡ 82c60414-8c4a-11eb-27c2-e9294ecbebba 864 | hamiltonian(x, V) = hamiltonian!(zeros(length(x), length(x)), x, V)[1] 865 | 866 | # ╔═╡ 3dcc9014-8c4b-11eb-0a15-a5e9e495c7b7 867 | hamiltonian(xgrid, randn(length(xgrid))) 868 | 869 | # ╔═╡ eb77b59a-8c9b-11eb-2683-c150952cf85b 870 | md"Because we are going to use Zygote (with rules set defined in ChainRules)" 871 | 872 | # ╔═╡ 63d9c6ce-8c4a-11eb-384d-a1fa4fe5ccd6 873 | function ChainRules.rrule(::typeof(hamiltonian), x, V) 874 | y = hamiltonian(x, V) 875 | function hamiltonian_pullback(Δy) 876 | gV = NiLang.AD.grad((~hamiltonian!)(GVar.(y, Δy), x, GVar.(V))[3]) 877 | return (ChainRules.NO_FIELDS, ChainRules.DoesNotExist(), gV) 878 | end 879 | return y, hamiltonian_pullback 880 | end 881 | 882 | # ╔═╡ 8e9f00ca-8c15-11eb-3079-a147fd2b0149 883 | md"We want the ground state be a house." 884 | 885 | # ╔═╡ 20e1c2ae-8b5f-11eb-334c-d74f310f9cc5 886 | ψ0 = [abs(xi)<0.5 ? 1 - abs(xi) : 0 for xi in xgrid]; normalize!(ψ0); 887 | 888 | # ╔═╡ 88757052-8b5f-11eb-189c-5b74c7c9acde 889 | plot(xgrid, ψ0) 890 | 891 | # ╔═╡ 5b357e9e-8c15-11eb-1ce8-6b91fac05cc0 892 | md"So we define a loss function 893 | ```math 894 | \begin{align} 895 | E, \psi &= {\rm eigensolve}(A)\\ 896 | \mathcal{L} &= \sum_i |(|(\psi_0)_i| - |(\psi_G)_i|)| 897 | \end{align} 898 | ``` 899 | " 900 | 901 | # ╔═╡ bd15d5ca-8c18-11eb-33a8-7306b70c02e0 902 | md"where $\psi_G$ is state vector in $\psi$ that corresponds to the minimum energy." 903 | 904 | # ╔═╡ 2a7a0da4-8b63-11eb-2d1c-9b852a39dacf 905 | function solve_wave(x, V) 906 | a = hamiltonian(x, V) 907 | ψ = LinearAlgebra.eigen(LinearAlgebra.Hermitian(a)).vectors[:,1] 908 | end 909 | 910 | # ╔═╡ a0918e24-8b61-11eb-3f39-69bd8ce0c618 911 | function loss(x, V, ψ0) 912 | ψ = solve_wave(x, V) 913 | sum(map(abs, map(abs, ψ) - map(abs, ψ0))) * dx 914 | end 915 | 916 | # ╔═╡ eaa8f57e-8b61-11eb-28b7-bf487a201b80 917 | loss(xgrid, randn(length(xgrid)), ψ0) 918 | 919 | # ╔═╡ 4543b0b2-8b64-11eb-0984-71f0a8027e6b 920 | solve_wave(xgrid, randn(length(xgrid))) |> norm 921 | 922 | # ╔═╡ c21f7c16-8b66-11eb-1502-8362d656896a 923 | loss(xgrid, randn(length(xgrid)), ψ0) 924 | 925 | # ╔═╡ 4b667f7a-8b60-11eb-1773-6904f0858ad7 926 | Zygote.gradient(v->loss(xgrid, v, ψ0), randn(length(xgrid))) 927 | 928 | # ╔═╡ a0a78f52-8b62-11eb-2e7a-4d3f975461ce 929 | @bind clock Clock(0.1) 930 | 931 | # ╔═╡ e64c8508-8b62-11eb-191c-45ec2ae6cd8c 932 | it = adam(v->loss(xgrid, v, ψ0), x->Zygote.gradient(v->loss(xgrid, v, ψ0), x)[1], randn(length(xgrid)); η=1.0); 933 | 934 | # ╔═╡ a910ae42-8b62-11eb-0474-7f81c709a77c 935 | let 936 | clock 937 | state = step!(it) 938 | v = minimizer(state) 939 | ψ = solve_wave(xgrid, v) 940 | @show loss(xgrid, v, ψ0) 941 | plot(xgrid, abs.(ψ); label="ψ") 942 | plot!(xgrid, abs.(ψ0); label="ψ0") 943 | plot!(xgrid, normalize(v); label="V") 944 | end |> PlutoUI.as_svg 945 | 946 | # ╔═╡ a1e7dd02-8bc8-11eb-29e0-91df4126872a 947 | md"""## 3. Obtaining MIS configurations""" 948 | 949 | # ╔═╡ 7919105e-8ce4-11eb-3f31-ff0fc17ca375 950 | md"We are able to get the weighted maximum independent set (MIS) size of the following graph 951 | 952 | ```math 953 | S = \max_{\vec s}\left(\sum_i w_i s_i-\infty \sum_{ij\in E} s_i s_j\right), s_i \in \{0,1\} 954 | ``` 955 | where $s_i$ and $w_i$ are the configuration (in MIS: 1, not in MIS: 0) and weight of node $i$. 956 | " 957 | 958 | # ╔═╡ 1e954d20-8ce7-11eb-078e-0baaaa7132d4 959 | md"Question: how to get the configuration with MIS?" 960 | 961 | # ╔═╡ ee3c1284-8d7d-11eb-3f4c-59ceabbd180c 962 | md"The optimal configuration is a gradient!" 963 | 964 | # ╔═╡ 32fdc4e0-8ce7-11eb-3acd-ed90c6e2e780 965 | md""" 966 | ```math 967 | \frac{\partial S}{\partial w_i} = \begin{cases} 968 | 1 & s_i \in \vec s_{\rm max}\\ 969 | 0 & otherwise 970 | \end{cases} 971 | ``` 972 | """ 973 | 974 | # ╔═╡ 083f13f0-8cea-11eb-0b3a-a96ab05aece9 975 | md"The actual problem is harder, if we fix the boundary configurations `a, b, c, d`, what is the optimal configurations for interior?" 976 | 977 | # ╔═╡ f96dc3b4-8bcf-11eb-15ec-232d15b3e075 978 | function vizconfig(nodes, edges, config=zeros(Int, length(nodes))) 979 | Compose.set_default_graphic_size(12cm, 12cm) 980 | tb = textstyle(:default, fill("white")) 981 | nb = nodestyle(:default) 982 | nb2 = nodestyle(:default, fill("red")) 983 | eb = bondstyle(:default) 984 | canvas() do 985 | for (i, (t, p)) in enumerate(nodes) 986 | (config[i]==1 ? nb2 : nb) >> p 987 | tb >> (p, t) 988 | end 989 | for (i,j) in edges 990 | eb >> (nodes[i].second, nodes[j].second) 991 | end 992 | end 993 | end; 994 | 995 | # ╔═╡ beee2d1e-8bcf-11eb-295c-a3b45bfc3aa8 996 | nodes_simple = let 997 | a = 0.12 998 | ymid = xmid = 0.5 999 | X = 0.33 1000 | Y = 0.17 1001 | D = 0.15 1002 | y = [ymid-Y, ymid-Y+D, ymid-a/2, ymid+a/2, ymid+Y-D, ymid+Y] 1003 | x = [xmid-X, xmid-X+D, xmid-1.5a, xmid-a/2, xmid+a/2, xmid+1.5a, xmid+X-D, xmid+X] 1004 | xmin, xmax, ymin, ymax = x[1], x[end], y[1], y[end] 1005 | ["a"=>(xmid, y[1]), "b"=>(xmin, ymid), "c"=>(xmid, ymax), "d"=>(xmax, ymid), 1006 | "i"=>(x[3], y[3]), "j"=>(x[4], y[3]), 1007 | "k"=>(x[5], y[3]), "l"=>(x[6], y[3]), "m"=>(x[3], y[4]), 1008 | "n"=>(x[4], y[4]), "o"=>(x[5], y[4]), "p"=>(x[6], y[4])] 1009 | end; 1010 | 1011 | # ╔═╡ 13bc3822-8bd0-11eb-1caa-1d49b3b74272 1012 | function find_edges(nodes, distance) 1013 | edges = Tuple{Int,Int}[] 1014 | for (i, p) in enumerate(nodes) 1015 | for (j,p2) in enumerate(nodes) 1016 | if i tget(i), 1, x[i]) 1050 | end 1051 | for j=length(x)+1:length(x)+28 1052 | bond_tensor(xs |> tget(j)) 1053 | end 1054 | end 1055 | # contract tropical tensors 1056 | i_einsum!(ixs, xs, iy, out) 1057 | # store the entry with specific boundary configuration to `optsize` 1058 | optsize += out[config...].n 1059 | ~@routine 1060 | end 1061 | 1062 | # ╔═╡ 546c8fb4-8bd2-11eb-30e4-5de043658636 1063 | compute_mis(0, ones(Tropical{Int},2,2,2,2), Tropical.(ones(Int,12)), [1,1,2,2]) 1064 | 1065 | # ╔═╡ c1aa24ce-8cea-11eb-3dd1-bd817acf2d8b 1066 | md" 1067 | We want to differentiate the weights (3rd argument) with respect to the loss (1st argument). 1068 | " 1069 | 1070 | # ╔═╡ d34fc06e-8ce8-11eb-0604-7139a6e1fbc3 1071 | md" $(@bind ca CheckBox()) a $(@bind cb CheckBox()) b $(@bind cc CheckBox()) c $(@bind cd CheckBox()) d " 1072 | 1073 | # ╔═╡ 85978e48-8bd9-11eb-340d-1f60d233522a 1074 | configs = NiLang.AD.gradient(compute_mis, (0, ones(Tropical{Int64},2,2,2,2), Tropical.(ones(Int,12)), 1 .+ [ca,cb,cc,cd]); iloss=1)[3]; 1075 | 1076 | # ╔═╡ 0a3f57c2-8be2-11eb-11f9-d1c6d78f0af0 1077 | vizconfig(nodes_simple, edges_simple, content.(configs)) 1078 | 1079 | # ╔═╡ 4180d4ee-8cec-11eb-139d-f9a0b79dcf3f 1080 | md"Here is a quick reference of the function definitions of Tropical algebra and Tropical einsum. 1081 | 1082 | Note: For regular tensors, we can use existing backward rules defined in `ChainRules`. 1083 | " 1084 | 1085 | # ╔═╡ 57e182e2-8bd4-11eb-2c36-835b43413c1c 1086 | vertex_tensor(ones(TropicalF64,2), 1, Tropical(1.0))[1] 1087 | 1088 | # ╔═╡ 2dad711e-8cec-11eb-1b78-a79d8201a019 1089 | bond_tensor(ones(TropicalF64,2, 2)) 1090 | 1091 | # ╔═╡ abb3b8c0-8a94-11eb-35b9-fbfd31f19501 1092 | md""" 1093 | ## 4. Towards differentiating `expmv` 1094 | """ 1095 | 1096 | # ╔═╡ 4bd1668e-8cb5-11eb-2ea7-f5398916dd60 1097 | let 1098 | F = 1.7 1099 | W, w, h = 0.47, 0.22, 0.1/F 1100 | lb = Compose.compose(context(), polygon([(-w, -h), (-w, h), (w, h), (w, -h)]), Compose.stroke("transparent")) 1101 | lb2 = Compose.compose(context(), polygon([(-W, -h), (-W, h), (W, h), (W, -h)]), Compose.stroke("transparent"), fill("red")) 1102 | lb3 = Compose.compose(context(), polygon([(-w/2, -h), (-w/2, h), (w/2, h), (w/2, -h)]), Compose.stroke("transparent"), fill("black")) 1103 | lb4 = Compose.compose(context(), polygon([(-w, -h), (-w, h), (w, h), (w, -h)]), Compose.stroke("transparent"), fill("green")) 1104 | tb = textstyle(:default, fontsize(3.5), Compose.font("monospace")) 1105 | tb_big = textstyle(:default, fontsize(3), fill("white"), Compose.font("monospace")) 1106 | eb = bondstyle(:default, linewidth(0.5mm)) 1107 | ar = bondstyle(:default, linewidth(0.3mm), Compose.arrow()) 1108 | xprog = (0.5, 0.15/F) 1109 | xtensors = (0.25, 0.5/F) 1110 | xscalars = (0.75, 0.5/F) 1111 | xscalars2 = (0.25, 0.85/F) 1112 | xscalars3 = (0.25, 1.2/F) 1113 | xscalars4 = (0.5, 1.55/F) 1114 | xpade = (0.6, 0.85/F) 1115 | 1116 | function box(loc, text; color="black") 1117 | (color=="black" ? lb : (color=="red" ? lb2 : lb4)) >> loc 1118 | tb_big >> (loc, text) 1119 | end 1120 | Compose.set_default_graphic_size(10cm, F*5cm) 1121 | img = canvas() do 1122 | box(xprog, "expmv") 1123 | ar >> (xprog, xtensors .+ (w/2, -h-0.03/F)) 1124 | ar >> (xprog, xscalars .+ (-w/2, -h-0.03/F)) 1125 | ar >> (xtensors, xscalars2 .+ (0, -h-0.05/F)) 1126 | ar >> (xscalars2, xscalars3 .+ (0, -h-0.05/F)) 1127 | ar >> (xscalars3, xscalars3 .+ (0, 0.2/F)) 1128 | ar >> (xscalars, xscalars3 .+ (0.5, 0.2/F)) 1129 | ar >> (xtensors, xpade .+ (-w/2, -h-0.02/F)) 1130 | box(xtensors, "expm (small dense)") 1131 | lb3 >> xpade 1132 | tb_big >> (xpade, "Pade") 1133 | box(xscalars, "Sparse mv (Lanczos)") 1134 | box(xscalars2, "Linear solver") 1135 | box(xscalars3, "QR decomp."; color="green") 1136 | box(xscalars4, "+, -, *, /"; color="red") 1137 | end 1138 | end 1139 | 1140 | # ╔═╡ 5482dd8a-8cba-11eb-182e-6d7fed2543f5 1141 | md""" 1142 | ### Resouces 1143 | * [Differentiating sparse operations](https://nextjournal.com/giggle/how-to-write-a-program-differentiably) 1144 | * [How to compute expm](http://eprints.ma.man.ac.uk/634/1/covered/MIMS_ep2006_394.pdf) 1145 | """ 1146 | 1147 | # ╔═╡ b1b8ccb4-8ce5-11eb-36c7-f5be8f8d1115 1148 | md"## More interesting AD examples 1149 | 1150 | * **Gate based quantum simulation**, Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design, Xiu-Zhe Luo, Jin-Guo Liu, Pan Zhang, Lei Wang [arxiv: 1912.10877](https://arxiv.org/abs/1912.10877) 1151 | * **Reverse time migration**, Reverse time migration with optimal checkpointing, William W. Symes [DOI](https://doi.org/10.1190/1.2742686) 1152 | * **Gaussian mixture models, Bundle adjustment and hand tracking**, A benchmark of selected algorithmic differentiation tools on some problems in computer vision and machine learning, Filip Srajer,Zuzana Kukelova &Andrew Fitzgibbon [DOI](https://doi.org/10.1080/10556788.2018.1435651) 1153 | 1154 | ### Videos 1155 | 1156 | * [Transformations & AutoDiff | MIT Computational Thinking Spring 2021 | Lecture 3](https://www.youtube.com/watch?v=AAREeuaKCic&ab_channel=TheJuliaProgrammingLanguage) ``\comment{AD in image processing}`` 1157 | " 1158 | 1159 | # ╔═╡ f8a2feee-8d63-11eb-0e4a-874a49df59ed 1160 | md""" 1161 | ## Quick Summary 1162 | 1163 | * Every program is differentiable 1164 | * For packages implementing AD rules on tensors, they have problems handling effective codes. 1165 | """ 1166 | 1167 | # ╔═╡ Cell order: 1168 | # ╠═b9a9214e-8830-11eb-1751-9d9161202c76 1169 | # ╟─d8669492-8c98-11eb-1cf5-374da9bd4556 1170 | # ╟─f0b4563a-8b0b-11eb-3085-458f5d9f88b8 1171 | # ╟─ce5af22a-8830-11eb-13c8-49c680526bd9 1172 | # ╟─22768818-8a95-11eb-1cfe-69534f8b0314 1173 | # ╟─68be48da-8a93-11eb-226b-7b1f2be99cb6 1174 | # ╟─da08c542-8a93-11eb-3375-d79ccd2de122 1175 | # ╟─0c80347a-8aff-11eb-0862-1d551e3af00b 1176 | # ╟─f55f9cba-8afe-11eb-3bf9-e3e5ecbf3a56 1177 | # ╠═bd3a4ece-8b09-11eb-2fcb-0710286e9892 1178 | # ╠═662c94c4-8b0a-11eb-39a2-9f37e689fbd3 1179 | # ╠═9e24dd6c-8b0a-11eb-020a-a1d7bf2e87bf 1180 | # ╟─fc682956-8b00-11eb-3102-952881130049 1181 | # ╟─167cbe40-8bf5-11eb-077b-bdd217c9bd78 1182 | # ╠═d29a56a4-8d86-11eb-1749-0972a594a0e4 1183 | # ╟─0ba6245c-8bf5-11eb-1005-1b72ffae3412 1184 | # ╟─aa316d52-8b00-11eb-1e7e-43e6f504977f 1185 | # ╟─8a55b3e4-8d67-11eb-203e-0b49c8e3e4aa 1186 | # ╟─f0468078-8b0c-11eb-1bdb-9f6f9496dcf2 1187 | # ╟─6335bc36-8b15-11eb-3731-5b76661d10fa 1188 | # ╟─2f60bb2c-8b2e-11eb-04f9-b79f81439af3 1189 | # ╟─61be9354-8b25-11eb-3205-db9b03a18f18 1190 | # ╟─30f3b718-8bfc-11eb-02cc-777ebc108429 1191 | # ╟─f67d1d28-8d6c-11eb-2e47-09e0aece0967 1192 | # 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╟─5482dd8a-8cba-11eb-182e-6d7fed2543f5 1277 | # ╟─b1b8ccb4-8ce5-11eb-36c7-f5be8f8d1115 1278 | # ╟─f8a2feee-8d63-11eb-0e4a-874a49df59ed 1279 | -------------------------------------------------------------------------------- /autodiff/coolad.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/CodingThrust/CodingClub/d6acc0c44858c5a2c0f6d0b81beaa2e85144a91c/autodiff/coolad.pdf -------------------------------------------------------------------------------- /copilot/README.md: -------------------------------------------------------------------------------- 1 | # How to setup Copilot for lecturing 2 | The recommended workflow contains the following three building blocks 3 | 1. Markdown: A file format for writing plain text documents that can be converted to HTML for preview. Or equivalently, you could use latex to write your lecture notes. 4 | 2. Editor: Visual Studio Code (VS Code), a lightweight but powerful source code editor which runs on your desktop and is available for Windows, macOS and Linux. We use it to write and preview markdown files. 5 | 3. Github Copilot: An extension of VSCode that helps you write code. Here we use it to generate lecture notes. 6 | 7 | 8 | ## Step 1: Link to Github Copilot 9 | To use Github Copilot, you need to have a Github account first. Github is a code hosting platform for version control and collaboration, which can host your markdown files and provide preview. You should go to [Github website](https://github.com/) and sign up an account. 10 | ## Step 2: Get Visual Studio Code 11 | 1. Go to [VS Code website](https://code.visualstudio.com/) and download the latest version. 12 | 2. Install & open VS Code. 13 | 3. Add the following VS Code extensions. To add an VS Code extension, please click the `Extensions` button in the left side bar, search for the extension name and click the `Install` button. 14 | - [Markdown Preview Enhanced](https://marketplace.visualstudio.com/items?itemName=shd101wyy.markdown-preview-enhanced) 15 | - [Markdown All in One](https://marketplace.visualstudio.com/items?itemName=yzhang.markdown-all-in-one) 16 | 5. Open a new file and save it as `test.md`. Then, click the `Open Preview to the Side` button in the top right corner of the VS Code window. The left side is the editor and the right side is the preview. You can edit the file on the left side and the preview will be updated automatically. 17 | 6. Now, you can start writing your own markdown file. You can learn markdown from [here](https://www.markdownguide.org/basic-syntax/). The GitHub website also renders math equations in Markdown. For example, the following code 18 | ~~~ 19 | ```math 20 | \frac{1}{2} 21 | ``` 22 | ~~~ 23 | will be rendered as 24 | ```math 25 | \frac{1}{2} 26 | ``` 27 | I think is better than latex because the preview is dynamically rendered. 28 | 29 | 7. Install the following VS Code extension 30 | - [Github Copilot](https://marketplace.visualstudio.com/items?itemName=GitHub.copilot). It requires you to connect with your Github account, and you can use it for free for 30 days. After 30 days, you can still use it for free but you need to join the waitlist. You can also use it for free if you are a student. You can apply for a student account [here](https://education.github.com/pack). Please check this [YouTube video](https://youtu.be/HDG4PQK7DK8?si=sOR7PqNcGAnrV4Tm) for more details 31 | 8. You might need to activate the Github Copilot extension by clicking the `Activate` button in the bottom right corner of the VS Code window to make it work. Then you can type some text in the editor and press `Tab` to generate lecture notes. 32 | ## Step 3: Using Github to sync your files (optional) 33 | If you want to sync your files across different devices, you can use Github. Github is a code hosting platform for version control and collaboration. It lets you and others work together on projects from anywhere. You can use Github to host your markdown files and provide preview. 34 | 35 | This tutorial does not cover how to use Github. You can learn it from the [YouTube video](https://www.youtube.com/watch?v=RGOj5yH7evk) or the [official guide](https://guides.github.com/activities/hello-world/). -------------------------------------------------------------------------------- /error-float/error_estimate.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "attachments": {}, 5 | "cell_type": "markdown", 6 | "metadata": {}, 7 | "source": [ 8 | "# Error in Floating Point System\n", 9 | "\n", 10 | "Let's start from a simple example" 11 | ] 12 | }, 13 | { 14 | "cell_type": "code", 15 | "execution_count": 1, 16 | "metadata": {}, 17 | "outputs": [ 18 | { 19 | "name": "stdout", 20 | "output_type": "stream", 21 | "text": [ 22 | "a64 + b64 = 0.21000000000000002\n", 23 | "a32 + b32 = 0.21000001f0\n" 24 | ] 25 | } 26 | ], 27 | "source": [ 28 | "a64 = 0.01\n", 29 | "b64 = 0.2\n", 30 | "@show a64 + b64;\n", 31 | "a32 = Float32(0.01)\n", 32 | "b32 = Float32(0.2)\n", 33 | "@show a32 + b32;" 34 | ] 35 | }, 36 | { 37 | "attachments": {}, 38 | "cell_type": "markdown", 39 | "metadata": {}, 40 | "source": [ 41 | "## IEEE 754: Standard of Floating Point Number\n", 42 | "\n", 43 | "The IEEE 754 standard is a binary floating-point arithmetic standard used to represent and process real numbers in computers and other digital devices. The standard defines two floating-point formats: single-precision and double-precision, which use 32 bits and 64 bits respectively to represent a floating-point number. These formats use scientific notation to represent real numbers, with three parts: sign, exponent, and mantissa.\n", 44 | "\n", 45 | "The IEEE 754 standard also defines arithmetic operations such as addition, subtraction, multiplication, and division, as well as rounding rules for performing arithmetic operations on these floating-point numbers. These rules ensure the precision and reproducibility of floating-point arithmetic operations performed in computers.\n", 46 | "\n", 47 | "A floating point number can be give as\n", 48 | "$$\n", 49 | "a = ±m \\cdot \\beta^e, m = (0.d_1 d_2 ... d_t)_\\beta, 0 ≤ d_i< \\beta\\;,\n", 50 | "$$\n", 51 | "so that the rounding error will be $\\frac{1}{2} \\beta^{1-t}$ and the chopping error will be $\\beta^{1-t}$.\n", 52 | "\n", 53 | "By IEEE 754, in single precision a floating-point number $a$ is stored as the sign $s$ (one bit), the exponent $e$ (8 bits), and the mantissa $m$ (23 bits).\n", 54 | "In double precision 11 of the 64 bits are used for the exponent, and 52 bits are used for the mantissa.\n", 55 | "So that the rounding error of Float32 and Float64 are about $5.94 \\cdot 10^{-8}$ and $1.11 \\cdot 10^{-16}$.\n", 56 | "\n", 57 | "The IEEE standard also includes two extended precision formats that offer extra precision and exponent range. The standard only specifies a lower bound on how many extra bits it provides. 33 Most modern processors use 80-bit registers for processing real numbers and store results as 64-bit numbers according to the IEEE double precision standard. Extended formats simplify tasks such as computing elementary functions accurately in single or double precision. Extended precision formats are used also by hand calculators. These will often display 10 decimal digits but use 13 digits internally—“the calculator knows more than it shows.”\n", 58 | "\n", 59 | "\n", 60 | "### Guard digits\n", 61 | "\n", 62 | "The guard digit is an extra digit used in floating-point arithmetic to improve the accuracy of computations. It is a bit that is added to the least significant bit of the mantissa of a floating-point number, and it represents an additional bit of precision that is used during arithmetic operations.\n", 63 | "\n", 64 | "The guard digit is used to prevent rounding errors that may occur during arithmetic operations, especially when intermediate results are very close to the boundary between two representable floating-point numbers. By adding an extra bit of precision, the guard digit helps to ensure that the final result is as accurate as possible.\n", 65 | "\n", 66 | "For example, consider the addition of two floating-point numbers that have a very small difference between their values. Without a guard digit, the result of the addition may need to be rounded, which could introduce a small error. With a guard digit, the addition can be performed with greater precision, reducing the likelihood of rounding errors and improving the accuracy of the final result.\n", 67 | "\n", 68 | "![image.png](./figs/flIEEE.png)" 69 | ] 70 | }, 71 | { 72 | "attachments": {}, 73 | "cell_type": "markdown", 74 | "metadata": {}, 75 | "source": [ 76 | "## Error Propragration\n", 77 | "\n", 78 | "### Operations in Floating Point Number System\n", 79 | "\n", 80 | "Define the basic floating-point operations are given as\n", 81 | "$$\n", 82 | "fl(x + y),~fl(x-y),~fl(x\\times y)~\\text{and}~fl(x / y)\n", 83 | "$$\n", 84 | "and the standard model holds because of the existence of the guard digits:\n", 85 | "$$\n", 86 | "fl(x ~\\text{op} ~y) = (x ~\\text{op} ~y) (1 + \\delta),~|\\delta| \\leq u \\;.\n", 87 | "$$\n", 88 | "In computers support a *fused multiply-add* operation and have only one rounding error\n", 89 | "$$\n", 90 | "fl(a\\times x + y) = (a \\times x + y) (1 + \\delta),~|\\delta| \\leq u \\;,\n", 91 | "$$\n", 92 | "so it is not only about speed but also accuracy.\n", 93 | "\n", 94 | "The rule for the complex number is a litte bit different, given by\n", 95 | "\n", 96 | "![image.png](./figs/complex_rule.png)\n", 97 | "\n", 98 | "where $\\gamma_n = \\frac{nu}{1 - nu}$." 99 | ] 100 | }, 101 | { 102 | "attachments": {}, 103 | "cell_type": "markdown", 104 | "metadata": {}, 105 | "source": [ 106 | "Here we can have a check on another example" 107 | ] 108 | }, 109 | { 110 | "cell_type": "code", 111 | "execution_count": 9, 112 | "metadata": {}, 113 | "outputs": [ 114 | { 115 | "name": "stdout", 116 | "output_type": "stream", 117 | "text": [ 118 | "error natural = 0.00010874912467651043\n", 119 | "error opposite = 3.0252606197933574e-8\n" 120 | ] 121 | } 122 | ], 123 | "source": [ 124 | "sum_natural = sum(Float32(Float32(1)/Float32(i)^Float32(2)) for i= 1:10000)\n", 125 | "sum_opposite = sum(Float32(Float32(1)/Float32(10001 - i)^Float32(2)) for i= 1:10000)\n", 126 | "sum_exact = sum(1.0/(i^2) for i in 1:10000)\n", 127 | "println(\"error natural = \", abs(sum_exact - sum_natural))\n", 128 | "println(\"error opposite = \", abs(sum_exact - sum_opposite))" 129 | ] 130 | }, 131 | { 132 | "attachments": {}, 133 | "cell_type": "markdown", 134 | "metadata": {}, 135 | "source": [ 136 | "This clearly shows the error of the $fl(x~\\text{op}~y)$ depends on value of $x~\\text{op}~y$, changing the summation order may change a lot.\n", 137 | "\n", 138 | "The compensated summation method can be used in such cases." 139 | ] 140 | }, 141 | { 142 | "cell_type": "code", 143 | "execution_count": 10, 144 | "metadata": {}, 145 | "outputs": [ 146 | { 147 | "data": { 148 | "text/plain": [ 149 | "compensated_summation (generic function with 1 method)" 150 | ] 151 | }, 152 | "metadata": {}, 153 | "output_type": "display_data" 154 | } 155 | ], 156 | "source": [ 157 | "function compensated_summation(x::Vector{T}) where T\n", 158 | " s = x[1]\n", 159 | " c = zero(T)\n", 160 | " for i in 2:length(x)\n", 161 | " y = c + x[i]\n", 162 | " t = s + y\n", 163 | " c = (s - t) + y\n", 164 | " s = t\n", 165 | " end\n", 166 | " return s\n", 167 | "end" 168 | ] 169 | }, 170 | { 171 | "cell_type": "code", 172 | "execution_count": 11, 173 | "metadata": {}, 174 | "outputs": [ 175 | { 176 | "name": "stdout", 177 | "output_type": "stream", 178 | "text": [ 179 | "error special = 3.0252606197933574e-8\n" 180 | ] 181 | } 182 | ], 183 | "source": [ 184 | "error_special = abs(compensated_summation([Float32(1 / i^2) for i in 1:10000]) - sum_exact)\n", 185 | "println(\"error special = \", error_special)" 186 | ] 187 | }, 188 | { 189 | "attachments": {}, 190 | "cell_type": "markdown", 191 | "metadata": {}, 192 | "source": [ 193 | "### Error Propragation\n", 194 | "\n", 195 | "The very basic rule of error propragation can be given as \n", 196 | "$$\n", 197 | "|\\Delta f| \\leq \\sum_i |\\frac{\\partial f}{\\partial x_i} \\Delta x_i|\\;.\n", 198 | "$$\n", 199 | "\n", 200 | "We can also define conditional number as\n", 201 | "$$\n", 202 | "\\kappa(f;x) = \\frac{||J(x)||~||x||}{||f(x)||}\\;.\n", 203 | "$$" 204 | ] 205 | }, 206 | { 207 | "attachments": {}, 208 | "cell_type": "markdown", 209 | "metadata": {}, 210 | "source": [ 211 | "![image.png](./figs/conditional_number.png)" 212 | ] 213 | }, 214 | { 215 | "attachments": {}, 216 | "cell_type": "markdown", 217 | "metadata": {}, 218 | "source": [] 219 | } 220 | ], 221 | "metadata": { 222 | "kernelspec": { 223 | "display_name": "Julia 1.9.0", 224 | "language": "julia", 225 | "name": "julia-1.9" 226 | }, 227 | "language_info": { 228 | "file_extension": ".jl", 229 | "mimetype": "application/julia", 230 | "name": "julia", 231 | "version": "1.9.0" 232 | }, 233 | "orig_nbformat": 4 234 | }, 235 | "nbformat": 4, 236 | "nbformat_minor": 2 237 | } 238 | -------------------------------------------------------------------------------- /error-float/figs/complex_rule.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/CodingThrust/CodingClub/d6acc0c44858c5a2c0f6d0b81beaa2e85144a91c/error-float/figs/complex_rule.png -------------------------------------------------------------------------------- /error-float/figs/conditional_number.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/CodingThrust/CodingClub/d6acc0c44858c5a2c0f6d0b81beaa2e85144a91c/error-float/figs/conditional_number.png -------------------------------------------------------------------------------- /error-float/figs/flIEEE.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/CodingThrust/CodingClub/d6acc0c44858c5a2c0f6d0b81beaa2e85144a91c/error-float/figs/flIEEE.png -------------------------------------------------------------------------------- /franklin/README.md: -------------------------------------------------------------------------------- 1 | # How to write your own blog with Franklin 2 | 3 | The workflow is detailed in this web-page: 4 | https://franklinjl.org/workflow/ -------------------------------------------------------------------------------- /helpdesk/README.md: -------------------------------------------------------------------------------- 1 | 2 | 3 | # Purpose 4 | 5 | - Setup environments 6 | - Help find solution to your coding problems 7 | - … 8 | 9 | 10 | # Git 11 | 12 | 13 | ## Basics 14 | 15 | 16 | ### Before Starting: Configuring git 17 | 18 | - Configs 19 | 1. Global use `/.gitconfig` 20 | 2. Repo specific use `.git/config` 21 | 3. Repo specific config file will overwrite the global one 22 | - How to view your current config 23 | `$ git config --list --show-origin` 24 | - Config editor 25 | `$ git config --global core.editor emacs` 26 | 27 | 28 | ### Git-Basics-Undoing-Things: 29 | 30 | - Introduction to undoing changes in Git 31 | - Three basic ways to undo changes in Git: 32 | - `git reset` 33 | - `git revert` 34 | - `git checkout` 35 | - `git commit --ammend` is your pal for fixing a commit not pushed 36 | - `git reset HEAD ` – Unstage a staged file 37 | - `git checkout -- ` – Discard changes in a file since the last commit 38 | - `git revert HEAD` – Create a new commit that undoes the changes made in the 39 | previous commit 40 | - `git push --force origin ` – Force push changes to a remote branch 41 | that has already been pushed with unwanted changes. 42 | 43 | - [Reference](https://git-scm.com/book/en/v2/Git-Basics-Undoing-Things#_undoing) 44 | 45 | 46 | ### What is remote? 47 | 48 | Remote on Git refers to a repository that is located on a server or another 49 | computer, rather than the user’s local machine. It’s a version of the repository 50 | that is used by teams to collaborate on a project. Remote repositories can be 51 | accessed and manipulated through Git commands, allowing users to push changes or 52 | fetch changes made by others. Remote repositories can be hosted on Git hosting 53 | services like GitHub, GitLab, or Bitbucket, or set up on a personal server. 54 | Multiple users can access and modify the same remote repository, making it easy 55 | for teams to work on a project together. 56 | 57 | 58 | ### What is branch? 59 | 60 | A branch in Git is a lightweight pointer to a specific commit. It allows 61 | developers to work on new features or make changes to the codebase without 62 | affecting the main codebase. Branches are created and can be switched between 63 | easily, and changes made in one branch do not affect other branches. 64 | 65 | To create a new branch in Git, you can use the command `git branch 66 | `. This creates a new branch but does not switch to it, so you will 67 | be working in the same branch until you use the command `git checkout 68 | ` to switch to the new branch. Alternatively, you can use the 69 | command `git checkout -b ` to create and switch to the new branch 70 | at the same time. 71 | 72 | To end a branch, you can use the command `git branch -d `. This 73 | deletes the specified branch, but only if it has been fully merged into the main 74 | branch. If you want to delete a branch whether it has been fully merged or not, 75 | you can use the command `git branch -D `. It’s important to note 76 | that once a branch has been deleted, you cannot restore its commit history. 77 | 78 | 79 | ## Resources 80 | 81 | - [Visualization of Commands](https://dev.to/lydiahallie/cs-visualized-useful-git-commands-37p1) 82 | - 83 | - 84 | - [Missing semester video](https://missing.csail.mit.edu/2020/version-control/) 85 | - 86 | 87 | 88 | # Julia Package Management 89 | 90 | - This section is really well presented by Prof Liu at [here](https://github.com/exAClior/CodingClub/blob/main/julia-packages/README.md) and [here](https://github.com/exAClior/CodingClub/blob/main/julia/2.first-package.md). 91 | - Ask me anything and let’s do a quick demo. 92 | 93 | 94 | # Shell Tools 95 | 96 | 97 | ## Shells 98 | 99 | Shell, zsh and bash are all command-line interface (CLI) interpreters used in 100 | Unix-like operating systems. 101 | 102 | - Shell is the simplest and most basic interpreter. Its primary function is to 103 | provide a command-line interface to the system. It can execute scripts, launch 104 | programs, manage files and directories, and perform basic system 105 | administrative tasks. 106 | 107 | - Bash (Bourne-Again SHell) is the default shell on most Linux distributions. It 108 | is backward-compatible with the original Bourne shell and includes many 109 | additional features, such as command-line editing, job control, and shell 110 | scripting capabilities. Bash is widely used as it is both easy to use and has 111 | a large user community, resulting in a plethora of available resources 112 | (tutorials, scripts, etc.) online. 113 | 114 | - Zsh (Z shell) is an extended version of the shell, with a more powerful 115 | command-line editing and completion system. It includes features like spelling 116 | correction and tab-completion, and it also supports plugins and themes. Zsh is 117 | commonly used by power users who require more productivity and efficiency from 118 | their command-line interface. 119 | 120 | 121 | ## Path Variable 122 | 123 | On Linux, the PATH variable is an environment variable that contains a list of 124 | directories that the shell searches for executable files. When a user enters a 125 | command in the shell, the shell looks for the executable file in each directory 126 | listed in the PATH variable, in the order they are listed. The PATH variable can 127 | be modified to add or remove directories, and it can also be set on a per-user 128 | or system-wide basis. The PATH variable is important because it allows users to 129 | easily run programs without having to specify the full path to the executable 130 | file each time. 131 | 132 | 133 | ## File Permission 134 | 135 | In Linux, file permissions determine who can access, edit, and execute files and 136 | directories. Each file and directory has three permission settings: owner, 137 | group, and other. The owner is the user who created the file or directory, the 138 | group is a set of users with specific permissions, and other is anyone else who 139 | has permission to access the file or directory. Each permission setting can have 140 | three levels of access: read, write, and execute. Read permission allows the 141 | user to view the contents of the file or directory, write permission allows the 142 | user to edit or delete the file or directory, and execute permission allows the 143 | user to run the file or access the directory. File and directory permissions can 144 | be changed using the chmod command in Linux. 145 | 146 | 147 | ## Common Shell Commands 148 | 149 | 1. `cd` - Change directory 150 | 2. `ls` - List directory contents 151 | 3. `mv` - Move or rename files or directories 152 | 4. `cp` - Copy files or directories 153 | 5. `rm` - Remove files or directories 154 | 6. `mkdir` - Create directories 155 | 7. `rmdir` - Remove empty directories 156 | 8. `touch` - Create an empty file or update the modification timestamp of a file 157 | 9. `cat` - Display the content of a file 158 | 10. `grep` - Search for a pattern in files 159 | 11. `ps` - Display information about running processes 160 | 12. `kill` - Terminate a process 161 | 13. `echo` - Print a message to the console 162 | 14. `chmod` - Change permissions of files or directories 163 | 15. `history` - Display a list of recently used commands 164 | 16. `ssh` - Connect to a remote server through ssh protocol 165 | 17. `scp` - Copy files between local and remote machines over ssh protocol 166 | 18. `tar` - Create or extract archive files 167 | 19. `df` - Display information about disk usage 168 | 20. `wget` - Download files from the internet. 169 | 170 | 171 | ## Tools 172 | 173 | 1. `ripgrep` (rg): A fast text search tool that recursively searches a directory 174 | hierarchy for a regex pattern. 175 | 2. `Tmux`: A terminal multiplexer that allows you to divide your terminal into 176 | multiple panes and windows. 177 | 3. `Ncdu`: A disk usage analyzer that helps you visualize which files and 178 | directories are consuming the most space on your filesystem. 179 | 4. `tldr`: A simplified and community-driven version of man pages that provides 180 | practical examples of command line usage. 181 | 5. `Bat`: A cat replacement that provides syntax highlighting, line numbering, and 182 | Git integration. 183 | 6. `Exa`: A modern replacement for ls that supports additional features like file 184 | icons, Git status, and color themes. 185 | 7. `Bandwhich`: A bandwidth usage analyzer that helps you see which processes are 186 | using the most network bandwidth. 187 | 8. `fd`: A more user-friendly alternative to find that allows you to search for 188 | files and directories using a streamlined syntax. 189 | 9. `htop`: An interactive process viewer that provides detailed information about 190 | system resource usage and allows you to manage processes. 191 | 10. `Tmuxp`: A command line tool that allows you to easily manage and share your 192 | Tmux configurations. 193 | 11. `direnv`: direnv is a shell extension that allows users to manage environment 194 | variables for different directories. It is designed to alleviate the 195 | inconvenience of constantly setting and unsetting environmental variables 196 | within different development environments. 197 | 198 | 199 | ## Resources 200 | 201 | - [Shell Script Learning](https://www.shellscript.sh/) 202 | - [The Art of Command Line](https://github.com/jlevy/the-art-of-command-line/blob/master/README.md) 203 | 204 | 205 | # Editors 206 | 207 | - Vim 208 | - Emacs 209 | - VSCode 210 | 211 | -------------------------------------------------------------------------------- /helpdesk/README.org: -------------------------------------------------------------------------------- 1 | #+TITLE: Coding Help Desk 2 | #+AUTHOR: Yusheng Zhao (+ ChatGPT) 3 | #+OPTIONS: toc:nil 4 | * Purpose 5 | - Setup environments 6 | - Help find solution to your coding problems 7 | - ... 8 | 9 | * Git 10 | ** Basics 11 | *** Before Starting: Configuring git 12 | - Configs 13 | 1) Global use ~/.gitconfig~ 14 | 2) Repo specific use ~.git/config~ 15 | 3) Repo specific config file will overwrite the global one 16 | - How to view your current config 17 | ~$ git config --list --show-origin~ 18 | - Config editor 19 | ~$ git config --global core.editor emacs~ 20 | 21 | *** Git-Basics-Undoing-Things: 22 | - Introduction to undoing changes in Git 23 | - Three basic ways to undo changes in Git: 24 | - ~git reset~ 25 | - ~git revert~ 26 | - ~git checkout~ 27 | - ~git commit --ammend~ is your pal for fixing a commit not pushed 28 | - ~git reset HEAD ~ – Unstage a staged file 29 | - ~git checkout -- ~ – Discard changes in a file since the last commit 30 | - ~git revert HEAD~ – Create a new commit that undoes the changes made in the 31 | previous commit 32 | - ~git push --force origin ~ – Force push changes to a remote branch 33 | that has already been pushed with unwanted changes. 34 | 35 | - [[https://git-scm.com/book/en/v2/Git-Basics-Undoing-Things#_undoing][Reference]] 36 | *** What is remote? 37 | Remote on Git refers to a repository that is located on a server or another 38 | computer, rather than the user's local machine. It's a version of the repository 39 | that is used by teams to collaborate on a project. Remote repositories can be 40 | accessed and manipulated through Git commands, allowing users to push changes or 41 | fetch changes made by others. Remote repositories can be hosted on Git hosting 42 | services like GitHub, GitLab, or Bitbucket, or set up on a personal server. 43 | Multiple users can access and modify the same remote repository, making it easy 44 | for teams to work on a project together. 45 | 46 | *** What is branch? 47 | A branch in Git is a lightweight pointer to a specific commit. It allows 48 | developers to work on new features or make changes to the codebase without 49 | affecting the main codebase. Branches are created and can be switched between 50 | easily, and changes made in one branch do not affect other branches. 51 | 52 | To create a new branch in Git, you can use the command ~git branch 53 | ~. This creates a new branch but does not switch to it, so you will 54 | be working in the same branch until you use the command ~git checkout 55 | ~ to switch to the new branch. Alternatively, you can use the 56 | command ~git checkout -b ~ to create and switch to the new branch 57 | at the same time. 58 | 59 | To end a branch, you can use the command ~git branch -d ~. This 60 | deletes the specified branch, but only if it has been fully merged into the main 61 | branch. If you want to delete a branch whether it has been fully merged or not, 62 | you can use the command ~git branch -D ~. It's important to note 63 | that once a branch has been deleted, you cannot restore its commit history. 64 | 65 | ** Resources 66 | - [[https://dev.to/lydiahallie/cs-visualized-useful-git-commands-37p1][Visualization of Commands]] 67 | - [[https://ohshitgit.com/]] 68 | - [[https://learngitbranching.js.org/?locale=zh_CN]] 69 | - [[https://missing.csail.mit.edu/2020/version-control/][Missing semester video]] 70 | - [[https://git-scm.com/book/en/v2]] 71 | 72 | * Julia Package Management 73 | - This section is really well presented by Prof Liu at [[https://github.com/exAClior/CodingClub/blob/main/julia-packages/README.md][here]] and [[https://github.com/exAClior/CodingClub/blob/main/julia/2.first-package.md][here]]. 74 | - Ask me anything and let's do a quick demo. 75 | 76 | * Shell Tools 77 | ** Shells 78 | Shell, zsh and bash are all command-line interface (CLI) interpreters used in 79 | Unix-like operating systems. 80 | 81 | - Shell is the simplest and most basic interpreter. Its primary function is to 82 | provide a command-line interface to the system. It can execute scripts, launch 83 | programs, manage files and directories, and perform basic system 84 | administrative tasks. 85 | 86 | - Bash (Bourne-Again SHell) is the default shell on most Linux distributions. It 87 | is backward-compatible with the original Bourne shell and includes many 88 | additional features, such as command-line editing, job control, and shell 89 | scripting capabilities. Bash is widely used as it is both easy to use and has 90 | a large user community, resulting in a plethora of available resources 91 | (tutorials, scripts, etc.) online. 92 | 93 | - Zsh (Z shell) is an extended version of the shell, with a more powerful 94 | command-line editing and completion system. It includes features like spelling 95 | correction and tab-completion, and it also supports plugins and themes. Zsh is 96 | commonly used by power users who require more productivity and efficiency from 97 | their command-line interface. 98 | 99 | ** Path Variable 100 | On Linux, the PATH variable is an environment variable that contains a list of 101 | directories that the shell searches for executable files. When a user enters a 102 | command in the shell, the shell looks for the executable file in each directory 103 | listed in the PATH variable, in the order they are listed. The PATH variable can 104 | be modified to add or remove directories, and it can also be set on a per-user 105 | or system-wide basis. The PATH variable is important because it allows users to 106 | easily run programs without having to specify the full path to the executable 107 | file each time. 108 | 109 | ** File Permission 110 | In Linux, file permissions determine who can access, edit, and execute files and 111 | directories. Each file and directory has three permission settings: owner, 112 | group, and other. The owner is the user who created the file or directory, the 113 | group is a set of users with specific permissions, and other is anyone else who 114 | has permission to access the file or directory. Each permission setting can have 115 | three levels of access: read, write, and execute. Read permission allows the 116 | user to view the contents of the file or directory, write permission allows the 117 | user to edit or delete the file or directory, and execute permission allows the 118 | user to run the file or access the directory. File and directory permissions can 119 | be changed using the chmod command in Linux. 120 | 121 | ** Common Shell Commands 122 | 1. ~cd~ - Change directory 123 | 2. ~ls~ - List directory contents 124 | 3. ~mv~ - Move or rename files or directories 125 | 4. ~cp~ - Copy files or directories 126 | 5. ~rm~ - Remove files or directories 127 | 6. ~mkdir~ - Create directories 128 | 7. ~rmdir~ - Remove empty directories 129 | 8. ~touch~ - Create an empty file or update the modification timestamp of a file 130 | 9. ~cat~ - Display the content of a file 131 | 10. ~grep~ - Search for a pattern in files 132 | 11. ~ps~ - Display information about running processes 133 | 12. ~kill~ - Terminate a process 134 | 13. ~echo~ - Print a message to the console 135 | 14. ~chmod~ - Change permissions of files or directories 136 | 15. ~history~ - Display a list of recently used commands 137 | 16. ~ssh~ - Connect to a remote server through ssh protocol 138 | 17. ~scp~ - Copy files between local and remote machines over ssh protocol 139 | 18. ~tar~ - Create or extract archive files 140 | 19. ~df~ - Display information about disk usage 141 | 20. ~wget~ - Download files from the internet. 142 | 143 | ** Tools 144 | 1. ~ripgrep~ (rg): A fast text search tool that recursively searches a directory 145 | hierarchy for a regex pattern. 146 | 2. ~Tmux~: A terminal multiplexer that allows you to divide your terminal into 147 | multiple panes and windows. 148 | 3. ~Ncdu~: A disk usage analyzer that helps you visualize which files and 149 | directories are consuming the most space on your filesystem. 150 | 4. ~tldr~: A simplified and community-driven version of man pages that provides 151 | practical examples of command line usage. 152 | 5. ~Bat~: A cat replacement that provides syntax highlighting, line numbering, and 153 | Git integration. 154 | 6. ~Exa~: A modern replacement for ls that supports additional features like file 155 | icons, Git status, and color themes. 156 | 7. ~Bandwhich~: A bandwidth usage analyzer that helps you see which processes are 157 | using the most network bandwidth. 158 | 8. ~fd~: A more user-friendly alternative to find that allows you to search for 159 | files and directories using a streamlined syntax. 160 | 9. ~htop~: An interactive process viewer that provides detailed information about 161 | system resource usage and allows you to manage processes. 162 | 10. ~Tmuxp~: A command line tool that allows you to easily manage and share your 163 | Tmux configurations. 164 | 11. ~direnv~: direnv is a shell extension that allows users to manage environment 165 | variables for different directories. It is designed to alleviate the 166 | inconvenience of constantly setting and unsetting environmental variables 167 | within different development environments. 168 | 169 | ** Resources 170 | - [[https://www.shellscript.sh/][Shell Script Learning]] 171 | - [[https://github.com/jlevy/the-art-of-command-line/blob/master/README.md][The Art of Command Line]] 172 | 173 | * Editors 174 | - Vim 175 | - Emacs 176 | - VSCode 177 | -------------------------------------------------------------------------------- /julia-packages/.gitignore: -------------------------------------------------------------------------------- 1 | _test.dat -------------------------------------------------------------------------------- /julia-packages/Manifest.toml: -------------------------------------------------------------------------------- 1 | # This file is machine-generated - editing it directly is not advised 2 | 3 | julia_version = "1.9.0-rc1" 4 | manifest_format = "2.0" 5 | project_hash = "c5949bca6853aa4235adab4bfc66c533b58e57a1" 6 | 7 | [[deps.AbstractFFTs]] 8 | deps = ["LinearAlgebra"] 9 | git-tree-sha1 = "16b6dbc4cf7caee4e1e75c49485ec67b667098a0" 10 | uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c" 11 | version = "1.3.1" 12 | weakdeps = ["ChainRulesCore"] 13 | 14 | [deps.AbstractFFTs.extensions] 15 | AbstractFFTsChainRulesCoreExt = "ChainRulesCore" 16 | 17 | [[deps.AbstractTrees]] 18 | git-tree-sha1 = "faa260e4cb5aba097a73fab382dd4b5819d8ec8c" 19 | uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c" 20 | version = "0.4.4" 21 | 22 | [[deps.Adapt]] 23 | deps = ["LinearAlgebra", "Requires"] 24 | git-tree-sha1 = "cc37d689f599e8df4f464b2fa3870ff7db7492ef" 25 | uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" 26 | version = "3.6.1" 27 | weakdeps = ["StaticArrays"] 28 | 29 | [deps.Adapt.extensions] 30 | AdaptStaticArraysExt = "StaticArrays" 31 | 32 | [[deps.Animations]] 33 | deps = ["Colors"] 34 | git-tree-sha1 = "e81c509d2c8e49592413bfb0bb3b08150056c79d" 35 | uuid = "27a7e980-b3e6-11e9-2bcd-0b925532e340" 36 | version = "0.4.1" 37 | 38 | [[deps.ArgTools]] 39 | uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" 40 | version = "1.1.1" 41 | 42 | [[deps.Artifacts]] 43 | uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" 44 | 45 | [[deps.Atomix]] 46 | deps = ["UnsafeAtomics"] 47 | git-tree-sha1 = "c06a868224ecba914baa6942988e2f2aade419be" 48 | uuid = "a9b6321e-bd34-4604-b9c9-b65b8de01458" 49 | version = "0.1.0" 50 | 51 | [[deps.Automa]] 52 | deps = ["Printf", "ScanByte", "TranscodingStreams"] 53 | git-tree-sha1 = "d50976f217489ce799e366d9561d56a98a30d7fe" 54 | uuid = "67c07d97-cdcb-5c2c-af73-a7f9c32a568b" 55 | version = "0.8.2" 56 | 57 | [[deps.AxisAlgorithms]] 58 | deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"] 59 | git-tree-sha1 = "66771c8d21c8ff5e3a93379480a2307ac36863f7" 60 | uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950" 61 | version = "1.0.1" 62 | 63 | [[deps.AxisArrays]] 64 | deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"] 65 | git-tree-sha1 = "1dd4d9f5beebac0c03446918741b1a03dc5e5788" 66 | uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9" 67 | version = "0.4.6" 68 | 69 | [[deps.BFloat16s]] 70 | deps = ["LinearAlgebra", "Printf", "Random", "Test"] 71 | git-tree-sha1 = "dbf84058d0a8cbbadee18d25cf606934b22d7c66" 72 | uuid = "ab4f0b2a-ad5b-11e8-123f-65d77653426b" 73 | version = "0.4.2" 74 | 75 | [[deps.Base64]] 76 | uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" 77 | 78 | [[deps.Bzip2_jll]] 79 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 80 | git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2" 81 | uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0" 82 | version = "1.0.8+0" 83 | 84 | [[deps.CEnum]] 85 | git-tree-sha1 = "eb4cb44a499229b3b8426dcfb5dd85333951ff90" 86 | uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82" 87 | version = "0.4.2" 88 | 89 | [[deps.CRC32c]] 90 | uuid = "8bf52ea8-c179-5cab-976a-9e18b702a9bc" 91 | 92 | [[deps.CUDA]] 93 | deps = ["AbstractFFTs", "Adapt", "BFloat16s", "CEnum", "CUDA_Driver_jll", "CUDA_Runtime_Discovery", "CUDA_Runtime_jll", "CompilerSupportLibraries_jll", "ExprTools", "GPUArrays", "GPUCompiler", "KernelAbstractions", "LLVM", "LazyArtifacts", "Libdl", "LinearAlgebra", "Logging", "Preferences", "Printf", "Random", "Random123", "RandomNumbers", "Reexport", "Requires", "SparseArrays", "SpecialFunctions", "UnsafeAtomicsLLVM"] 94 | git-tree-sha1 = "2dbdec5c010bed6c6b1e0e5fd213bfe47925abc3" 95 | uuid = "052768ef-5323-5732-b1bb-66c8b64840ba" 96 | version = "4.1.0" 97 | 98 | [[deps.CUDA_Driver_jll]] 99 | deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"] 100 | git-tree-sha1 = "a1efe2bfb96c10906dede10f1580aca0ae6d092f" 101 | uuid = "4ee394cb-3365-5eb0-8335-949819d2adfc" 102 | version = "0.4.0+2" 103 | 104 | [[deps.CUDA_Runtime_Discovery]] 105 | deps = ["Libdl"] 106 | git-tree-sha1 = "58dd8ec29f54f08c04b052d2c2fa6760b4f4b3a4" 107 | uuid = "1af6417a-86b4-443c-805f-a4643ffb695f" 108 | version = "0.1.1" 109 | 110 | [[deps.CUDA_Runtime_jll]] 111 | deps = ["Artifacts", "CUDA_Driver_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "TOML"] 112 | git-tree-sha1 = "96e06a24c89a9945c57278fd09fb717f71476d87" 113 | uuid = "76a88914-d11a-5bdc-97e0-2f5a05c973a2" 114 | version = "0.4.0+2" 115 | 116 | [[deps.Cairo_jll]] 117 | 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"] 118 | git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2" 119 | uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" 120 | version = "1.16.1+1" 121 | 122 | [[deps.Calculus]] 123 | deps = ["LinearAlgebra"] 124 | git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad" 125 | uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9" 126 | version = "0.5.1" 127 | 128 | [[deps.ChainRulesCore]] 129 | deps = ["Compat", "LinearAlgebra", "SparseArrays"] 130 | git-tree-sha1 = "c6d890a52d2c4d55d326439580c3b8d0875a77d9" 131 | uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" 132 | version = "1.15.7" 133 | 134 | [[deps.ColorBrewer]] 135 | deps = ["Colors", "JSON", "Test"] 136 | git-tree-sha1 = "61c5334f33d91e570e1d0c3eb5465835242582c4" 137 | uuid = "a2cac450-b92f-5266-8821-25eda20663c8" 138 | version = "0.4.0" 139 | 140 | [[deps.ColorSchemes]] 141 | deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "Random", "SnoopPrecompile"] 142 | git-tree-sha1 = "aa3edc8f8dea6cbfa176ee12f7c2fc82f0608ed3" 143 | uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4" 144 | version = "3.20.0" 145 | 146 | [[deps.ColorTypes]] 147 | deps = ["FixedPointNumbers", "Random"] 148 | git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4" 149 | uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f" 150 | version = "0.11.4" 151 | 152 | [[deps.ColorVectorSpace]] 153 | deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"] 154 | git-tree-sha1 = "600cc5508d66b78aae350f7accdb58763ac18589" 155 | uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4" 156 | version = "0.9.10" 157 | 158 | [[deps.Colors]] 159 | deps = ["ColorTypes", "FixedPointNumbers", "Reexport"] 160 | git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a" 161 | uuid = "5ae59095-9a9b-59fe-a467-6f913c188581" 162 | version = "0.12.10" 163 | 164 | [[deps.Compat]] 165 | deps = ["UUIDs"] 166 | git-tree-sha1 = "7a60c856b9fa189eb34f5f8a6f6b5529b7942957" 167 | uuid = "34da2185-b29b-5c13-b0c7-acf172513d20" 168 | version = "4.6.1" 169 | weakdeps = ["Dates", "LinearAlgebra"] 170 | 171 | [deps.Compat.extensions] 172 | CompatLinearAlgebraExt = "LinearAlgebra" 173 | 174 | [[deps.CompilerSupportLibraries_jll]] 175 | deps = ["Artifacts", "Libdl"] 176 | uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" 177 | version = "1.0.2+0" 178 | 179 | [[deps.ConstructionBase]] 180 | deps = ["LinearAlgebra"] 181 | git-tree-sha1 = "89a9db8d28102b094992472d333674bd1a83ce2a" 182 | uuid = 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"3c712976c47707ff893cf6ba4354aa14db1d8938" 1255 | uuid = "9d95972d-f1c8-5527-a6e0-b4b365fa01f6" 1256 | version = "1.3.0" 1257 | 1258 | [[deps.UUIDs]] 1259 | deps = ["Random", "SHA"] 1260 | uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" 1261 | 1262 | [[deps.Unicode]] 1263 | uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" 1264 | 1265 | [[deps.UnicodeFun]] 1266 | deps = ["REPL"] 1267 | git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf" 1268 | uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1" 1269 | version = "0.4.1" 1270 | 1271 | [[deps.UnsafeAtomics]] 1272 | git-tree-sha1 = "6331ac3440856ea1988316b46045303bef658278" 1273 | uuid = "013be700-e6cd-48c3-b4a1-df204f14c38f" 1274 | version = "0.2.1" 1275 | 1276 | [[deps.UnsafeAtomicsLLVM]] 1277 | deps = ["LLVM", "UnsafeAtomics"] 1278 | git-tree-sha1 = "33af9d2031d0dc09e2be9a0d4beefec4466def8e" 1279 | uuid = "d80eeb9a-aca5-4d75-85e5-170c8b632249" 1280 | version = "0.1.0" 1281 | 1282 | [[deps.WoodburyMatrices]] 1283 | deps = ["LinearAlgebra", "SparseArrays"] 1284 | git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3" 1285 | uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6" 1286 | version = "0.5.5" 1287 | 1288 | [[deps.XML2_jll]] 1289 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"] 1290 | git-tree-sha1 = "93c41695bc1c08c46c5899f4fe06d6ead504bb73" 1291 | uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a" 1292 | version = "2.10.3+0" 1293 | 1294 | [[deps.XSLT_jll]] 1295 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"] 1296 | git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a" 1297 | uuid = "aed1982a-8fda-507f-9586-7b0439959a61" 1298 | version = "1.1.34+0" 1299 | 1300 | [[deps.Xorg_libX11_jll]] 1301 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"] 1302 | git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527" 1303 | uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc" 1304 | version = "1.6.9+4" 1305 | 1306 | [[deps.Xorg_libXau_jll]] 1307 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1308 | git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e" 1309 | uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec" 1310 | version = "1.0.9+4" 1311 | 1312 | [[deps.Xorg_libXcursor_jll]] 1313 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"] 1314 | git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd" 1315 | uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724" 1316 | version = "1.2.0+4" 1317 | 1318 | [[deps.Xorg_libXdmcp_jll]] 1319 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1320 | git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4" 1321 | uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05" 1322 | version = "1.1.3+4" 1323 | 1324 | [[deps.Xorg_libXext_jll]] 1325 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] 1326 | git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3" 1327 | uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3" 1328 | version = "1.3.4+4" 1329 | 1330 | [[deps.Xorg_libXfixes_jll]] 1331 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] 1332 | git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4" 1333 | uuid = "d091e8ba-531a-589c-9de9-94069b037ed8" 1334 | version = "5.0.3+4" 1335 | 1336 | [[deps.Xorg_libXi_jll]] 1337 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"] 1338 | git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246" 1339 | uuid = "a51aa0fd-4e3c-5386-b890-e753decda492" 1340 | version = "1.7.10+4" 1341 | 1342 | [[deps.Xorg_libXinerama_jll]] 1343 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"] 1344 | git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123" 1345 | uuid = "d1454406-59df-5ea1-beac-c340f2130bc3" 1346 | version = "1.1.4+4" 1347 | 1348 | [[deps.Xorg_libXrandr_jll]] 1349 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"] 1350 | git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631" 1351 | uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484" 1352 | version = "1.5.2+4" 1353 | 1354 | [[deps.Xorg_libXrender_jll]] 1355 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] 1356 | git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96" 1357 | uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa" 1358 | version = "0.9.10+4" 1359 | 1360 | [[deps.Xorg_libpthread_stubs_jll]] 1361 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1362 | git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb" 1363 | uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74" 1364 | version = "0.1.0+3" 1365 | 1366 | [[deps.Xorg_libxcb_jll]] 1367 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"] 1368 | git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6" 1369 | uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b" 1370 | version = "1.13.0+3" 1371 | 1372 | [[deps.Xorg_xtrans_jll]] 1373 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1374 | git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845" 1375 | uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10" 1376 | version = "1.4.0+3" 1377 | 1378 | [[deps.Zlib_jll]] 1379 | deps = ["Libdl"] 1380 | uuid = "83775a58-1f1d-513f-b197-d71354ab007a" 1381 | version = "1.2.13+0" 1382 | 1383 | [[deps.isoband_jll]] 1384 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1385 | git-tree-sha1 = "51b5eeb3f98367157a7a12a1fb0aa5328946c03c" 1386 | uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4" 1387 | version = "0.2.3+0" 1388 | 1389 | [[deps.libaom_jll]] 1390 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1391 | git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4" 1392 | uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b" 1393 | version = "3.4.0+0" 1394 | 1395 | [[deps.libass_jll]] 1396 | deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] 1397 | git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47" 1398 | uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" 1399 | version = "0.15.1+0" 1400 | 1401 | [[deps.libblastrampoline_jll]] 1402 | deps = ["Artifacts", "Libdl"] 1403 | uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" 1404 | version = "5.4.0+0" 1405 | 1406 | [[deps.libfdk_aac_jll]] 1407 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1408 | git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55" 1409 | uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" 1410 | version = "2.0.2+0" 1411 | 1412 | [[deps.libpng_jll]] 1413 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] 1414 | git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c" 1415 | uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" 1416 | version = "1.6.38+0" 1417 | 1418 | [[deps.libsixel_jll]] 1419 | deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "libpng_jll"] 1420 | git-tree-sha1 = "d4f63314c8aa1e48cd22aa0c17ed76cd1ae48c3c" 1421 | uuid = "075b6546-f08a-558a-be8f-8157d0f608a5" 1422 | version = "1.10.3+0" 1423 | 1424 | [[deps.libvorbis_jll]] 1425 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] 1426 | git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c" 1427 | uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" 1428 | version = "1.3.7+1" 1429 | 1430 | [[deps.nghttp2_jll]] 1431 | deps = ["Artifacts", "Libdl"] 1432 | uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" 1433 | version = "1.48.0+0" 1434 | 1435 | [[deps.p7zip_jll]] 1436 | deps = ["Artifacts", "Libdl"] 1437 | uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" 1438 | version = "17.4.0+0" 1439 | 1440 | [[deps.x264_jll]] 1441 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1442 | git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" 1443 | uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" 1444 | version = "2021.5.5+0" 1445 | 1446 | [[deps.x265_jll]] 1447 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 1448 | git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" 1449 | uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" 1450 | version = "3.5.0+0" 1451 | -------------------------------------------------------------------------------- /julia-packages/Project.toml: -------------------------------------------------------------------------------- 1 | [deps] 2 | CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" 3 | DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab" 4 | GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a" 5 | LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" 6 | Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a" 7 | -------------------------------------------------------------------------------- /julia-packages/README.md: -------------------------------------------------------------------------------- 1 | # Essential Julia packages 2 | You may find trending Julia packages here: https://juliahub.com/ui/Packages 3 | 4 | ## Development 5 | 1. [PkgTemplates](https://github.com/JuliaCI/PkgTemplates.jl) `package development`, `continuous integration` 6 | 7 | Create new Julia packages, the easy way. 8 | 9 | ```julia 10 | julia> using PkgTemplates 11 | 12 | julia> tpl = Template(; user="GiggleLiu", plugins=[ 13 | GitHubActions(; extra_versions=["nightly"]), 14 | Git(), 15 | Codecov(), 16 | Documenter{GitHubActions}(), 17 | ]) 18 | 19 | julia> tpl("PkgName") 20 | ``` 21 | 22 | 2. [Revise](https://github.com/timholy/Revise.jl) `package development`, `reload` 23 | 24 | `Revise.jl` allows you to modify code and use the changes without restarting Julia. With Revise, you can be in the middle of a session and then update packages, switch git branches, and/or edit the source code in the editor of your choice; any changes will typically be incorporated into the very next command you issue from the REPL. This can save you the overhead of restarting Julia, loading packages, and waiting for code to JIT-compile. 25 | 26 | ## High performance computing 27 | 1. [CUDA](https://github.com/JuliaGPU/CUDA.jl) `CUDA`, `kernels` 28 | 29 | The CUDA.jl package is the main programming interface for working with NVIDIA CUDA GPUs using Julia. It features a user-friendly array abstraction, a compiler for writing CUDA kernels in Julia, and wrappers for various CUDA libraries. 30 | 31 | Example: [cuda.jl](cuda.jl) 32 | 33 | 2. [LoopVectorization](https://github.com/JuliaSIMD/LoopVectorization.jl) `AVX`, `SIMD`, `CPU`, `speed` 34 | 35 | Macro(s) for vectorizing loops. 36 | 37 | 3. [StaticArrays](https://github.com/JuliaArrays/StaticArrays.jl) `small arrays`, `static` 38 | 39 | StaticArrays provides a framework for implementing statically sized arrays in Julia, using the abstract type StaticArray{Size,T,N} <: AbstractArray{T,N}. Subtypes of StaticArray will provide fast implementations of common array and linear algebra operations. Note that here "statically sized" means that the size can be determined from the type, and "static" does not necessarily imply immutable. 40 | 41 | ## Optimization 42 | 1. [Optim.jl](https://github.com/JuliaNLSolvers/Optim.jl) `optimize`, `LBFGS`, `Nelder-Mead` 43 | 44 | Univariate and multivariate optimization in Julia. 45 | 46 | Example: [optim.jl](optim.jl) 47 | 48 | 2. [JuMP](https://github.com/jump-dev/JuMP.jl) `mathematical optimization`, `fast` 49 | 50 | JuMP is a domain-specific modeling language for mathematical optimization embedded in Julia. You can find out more about us by visiting jump.dev. 51 | 52 | 3. [ForwradDiff](https://github.com/JuliaDiff/ForwardDiff.jl) and [Enzyme](https://github.com/EnzymeAD/Enzyme.jl) `autodiff`, `llvm`, `NIPS best paper`, `forward`, `reverse` 53 | 54 | Enzyme is a plugin that performs automatic differentiation (AD) of statically analyzable LLVM. It is highly-efficient and its ability perform AD on optimized code allows Enzyme to meet or exceed the performance of state-of-the-art AD tools. 55 | 56 | 57 | ## Linear Algebra 58 | 1. [ITensors](https://github.com/ITensor/ITensors.jl), [TensorOperations](https://github.com/Jutho/TensorOperations.jl) and [OMEinsum](https://github.com/under-Peter/OMEinsum.jl) `tensor`, `contraction`, `physics` 59 | 60 | * ITensor is a library for rapidly creating correct and efficient tensor network algorithms. 61 | * TensorOperations provides fast tensor operations using a convenient Einstein index notation. 62 | * This is a repository for the Google Summer of Code project on Differentiable Tensor Networks. It implements one function that both computer scientists and physicists love, the Einstein summation. It features large scale tensor network contraction. 63 | 64 | 2. [KrylovKit](https://github.com/Jutho/KrylovKit.jl) `sparse matrix`, `linear operator`, `eigen value problem`, `iterative solver`, `krylov space` 65 | 66 | A Julia package collecting a number of Krylov-based algorithms for linear problems, singular value and eigenvalue problems and the application of functions of linear maps or operators to vectors. 67 | 68 | 3. [ExponentialUtilities](https://github.com/SciML/ExponentialUtilities.jl) `expmv`, `krylov space` 69 | 70 | ExponentialUtilities is a package of utility functions for matrix functions of exponential type, including functionality for the matrix exponential and phi-functions. These methods are more numerically stable, generic (thus support a wider range of number types), and faster than the matrix exponentiation tools in Julia's Base. The tools are used by the exponential integrators in OrdinaryDiffEq. The package has no external dependencies, so it can also be used independently. 71 | 72 | ## Plotting 73 | 74 | 1. [Makie](https://github.com/MakieOrg/Makie.jl) `plot`, `gpu` 75 | 76 | Example: [makie.jl](cuda.jl) 77 | 78 | 79 | 2. [Luxor](https://github.com/JuliaGraphics/Luxor.jl) 80 | 81 | Luxor is a Julia package for drawing simple 2D vector graphics. Think of it as a high-level easier to use interface to Cairo.jl, with shorter names, fewer underscores, default contexts, and simplified functions. In Luxor, the emphasis is on simplicity and ease of use. 82 | 83 | 3. [UnicodePlots](https://github.com/JuliaPlots/UnicodePlots.jl) 84 | Advanced Unicode plotting library designed for use in Julia's REPL. 85 | 86 | ## Scientific Computing 87 | 1. [DifferetialEquations](https://github.com/SciML/DifferentialEquations.jl) `ODE`, `PDE`, `fast` 88 | 89 | This is a suite for numerically solving differential equations written in Julia and available for use in Julia, Python, and R. The purpose of this package is to supply efficient Julia implementations of solvers for various differential equations. Equations within the realm of this package include: 90 | 91 | * Discrete equations (function maps, discrete stochastic (Gillespie/Markov) simulations) 92 | * Ordinary differential equations (ODEs) 93 | * Split and Partitioned ODEs (Symplectic integrators, IMEX Methods) 94 | * Stochastic ordinary differential equations (SODEs or SDEs) 95 | * Stochastic differential-algebraic equations (SDAEs) 96 | * Random differential equations (RODEs or RDEs) 97 | * Differential algebraic equations (DAEs) 98 | * Delay differential equations (DDEs) 99 | * Neutral, retarded, and algebraic delay differential equations (NDDEs, RDDEs, and DDAEs) 100 | * Stochastic delay differential equations (SDDEs) 101 | * Experimental support for stochastic neutral, retarded, and algebraic delay differential equations (SNDDEs, SRDDEs, and SDDAEs) 102 | * Mixed discrete and continuous equations (Hybrid Equations, Jump Diffusions) 103 | * (Stochastic) partial differential equations ((S)PDEs) (with both finite difference and finite element methods) 104 | 105 | 2. [Yao](https://github.com/QuantumBFS/Yao.jl) `quantum`, `differentiable`, `fast`, `gpu` 106 | 107 | Yao is an open source framework that aims to empower quantum information research with software tools. It is designed with following in mind: 108 | * quantum algorithm design; 109 | * quantum software 2.0; 110 | * quantum computation education. 111 | 112 | 113 | ## FileIO 114 | 115 | 1. DelimitedFiles 116 | 117 | ```julia 118 | julia> using DelimitedFiles 119 | 120 | julia> x = randn(100, 100);julia> writedlm(x); 121 | 122 | julia> writedlm("_test.dat", x); 123 | 124 | julia> y = readdlm("_test.dat"); 125 | 126 | julia> x ≈ y 127 | true 128 | ``` 129 | 130 | 2. [JLD2](https://github.com/JuliaIO/JLD2.jl) 131 | 132 | JLD2 saves and loads Julia data structures in a format comprising a subset of HDF5, without any dependency on the HDF5 C library. JLD2 is able to read most HDF5 files created by other HDF5 implementations supporting HDF5 File Format Specification Version 3.0 (i.e. libhdf5 1.10 or later) and similarly those should be able to read the files that JLD2 produces. JLD2 provides read-only support for files created with the JLD package. -------------------------------------------------------------------------------- /julia-packages/cuda.jl: -------------------------------------------------------------------------------- 1 | using CUDA, CUDA.GPUArrays 2 | 3 | function my_permutedims!(dest::AbstractGPUArray, src::AbstractGPUArray, 4 | perm::NTuple{N}) where N 5 | Base.checkdims_perm(dest, src, perm) 6 | 7 | # get the new strides of destination tensor 8 | dest_strides = ntuple(k->k==1 ? 1 : prod(i->size(dest, i), 1:k-1), N) 9 | dest_strides_perm = ntuple(i->dest_strides[findfirst(==(i), perm)], N) 10 | 11 | function permutedims_kernel(ctx, dest, src, dest_strides_perm) 12 | # find the cartesian index in source tensor 13 | LI = @linearidx src 14 | I = @inbounds CartesianIndices(src)[LI] 15 | 16 | # the corresponding linear index in the destination tensor 17 | dest_index = map_index(I.I, dest_strides_perm) 18 | @inbounds dest[dest_index] = src[LI] 19 | return 20 | end 21 | gpu_call(permutedims_kernel, dest, src, dest_strides_perm) 22 | return dest 23 | end 24 | 25 | # get linear index from cartesian indices and strides. 26 | @inline @generated function map_index(I::NTuple{N}, dest_strides::NTuple{N,T}) where {N,T} 27 | Expr(:call, :+, one(T), [:(@inbounds (I[$i]-1) * dest_strides[$i]) for i in 1:N]...) 28 | end 29 | 30 | using Test 31 | @testset "permutedims" begin 32 | a = randn(10, 10, 4, 6, 20) 33 | b = randn(20, 4, 6, 10, 10) 34 | c1 = my_permutedims!(CuArray(a), CuArray(b), (5, 4, 2, 3, 1)) 35 | c2 = permutedims!(a, b, (5, 4, 2, 3, 1)) 36 | @test c1 isa CuArray 37 | @test Array(c1) ≈ c2 38 | end -------------------------------------------------------------------------------- /julia-packages/makie.jl: -------------------------------------------------------------------------------- 1 | using GLMakie, GLMakie.FileIO 2 | using LinearAlgebra: norm 3 | using DelimitedFiles 4 | 5 | f = Figure(resolution = (1400, 1000)) 6 | a = readdlm(assetpath("airportlocations.csv")) # reduce this number if your GPU is not powerful enough 7 | n_points = 10_000_000 8 | a_rep = repeat(a, n_points ÷ size(a, 1), 1) .+ randn.() 9 | scatter(f[1, 1], a_rep, color = (:black, 0.01), markersize = 1.0, 10 | strokewidth = 0, axis = (title = "Airports (100 Million points)", 11 | limits = (-200, 200, -70, 80))) 12 | 13 | r = LinRange(-5, 5, 100) 14 | volume = [sin(x) + sin(y) + 0.1z^2 for x = r, y = r, z = r] 15 | ax, c = contour(f[2, 1][1, 1], volume, levels = 8, colormap = :viridis, 16 | axis = (type = Axis3, viewmode = :stretch, title = "3D contour")) 17 | Colorbar(f[2, 1][1, 2], c, label = "intensity") 18 | 19 | function mandelbrot(x, y) 20 | z = c = x + y*im 21 | for i in 1:30.0 22 | abs(z) > 2 && return i 23 | z = z^2 + c 24 | end 25 | 0 26 | end 27 | ax2, hm = heatmap(f[1:2, 2][1, 2], -2:0.005:1, -1.1:0.005:1.1, mandelbrot, 28 | colormap = Reverse(:deep), axis = (title = "Mandelbrot set",)) 29 | hidedecorations!(ax2) 30 | Colorbar(f[1:2, 2][1, 1], hm, flipaxis = false, 31 | label = "Iterations", height = 300) 32 | Axis3(f[1:2, 2][2, 1:2], aspect = :data, title = "Brain mesh") 33 | brain = load(assetpath("brain.stl")) 34 | color = [-norm(x[1] .- Point(-40, 10, 45)) for x in brain for i in 1:3] 35 | mesh!(brain, color = color, colormap = :thermal) 36 | Label(f[0, :], "Makie.jl Example Figure") 37 | save("paper_example.png", f) -------------------------------------------------------------------------------- /julia-packages/optim.jl: -------------------------------------------------------------------------------- 1 | using Optim, ForwardDiff 2 | 3 | f(x) = (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2 4 | x0 = [0.0, 0.0] 5 | 6 | # gradient free optimizers 7 | optimize(f, x0, NelderMead()) 8 | 9 | # gradient based optimizers 10 | function g(x) 11 | return ForwardDiff.gradient(f, x) 12 | end 13 | optimize(f, g, x0, LBFGS(); inplace = false) -------------------------------------------------------------------------------- /julia/1.julia-setup.md: -------------------------------------------------------------------------------- 1 | ## Setup Julia development environment in mainland China 2 | 3 | ### Step 1: Installing Julia 4 | For Linux/Mac users, please open a terminal and type the following command to install [Julia](https://julialang.org/) with [juliaup](https://github.com/JuliaLang/juliaup). `Juliaup` is a tool to manage Julia versions and installations. It allows you to install multiple versions of Julia and switch between them easily. 5 | 6 | ```Bash 7 | curl -fsSL https://install.julialang.org | sh # Linux and macOS 8 | ``` 9 | 10 | For Windows users, please open execute the following command in a `cmd`, 11 | ```PowerShell 12 | winget install julia -s msstore # Windows 13 | ``` 14 | You can also install Juliaup directly from [Windows Store](https://www.microsoft.com/store/apps/9NJNWW8PVKMN). 15 | 16 | 17 | #### For users suffering from the slow download speed 18 | 19 | You may need to specify another server for installing Juliaup. To do so, execute the following command in your terminal before running the script above. 20 | 21 | **Linux and macOS** 22 | ```bash 23 | export JULIAUP_SERVER=https://mirror.nju.edu.cn/julia-releases/ # Linux & macOS 24 | ``` 25 | **Windows** 26 | ```PowerShell 27 | $env:JULIAUP_SERVER="https://mirror.nju.edu.cn/julia-releases/" # Windows 28 | ``` 29 | An alternative approach is downloading the corresponding Julia binary from the [Nanjing university mirror website](https://mirror.nju.edu.cn/julia-releases/). 30 | After installing the binary, please set the Julia binary path properly if you want to start a Julia REPL from a terminal, check this [manual page](https://julialang.org/downloads/platform/) to learn more. 31 | 32 | 33 | #### Installing Julia 34 | To verify that Julia is installed, run the following command in your terminal. 35 | ```bash 36 | julia 37 | ``` 38 | - It should start a Julia REPL(Read-Eval-Print-Loop) session like this 39 | ![REPL Session](https://miro.medium.com/v2/resize:fit:4800/format:webp/1*lxjWRvH3EzSa1N3Pg4iNag.png) 40 | - If you wish to install a specific version of Julia, please refer to the [documentation](https://github.com/JuliaLang/juliaup). 41 | 42 | ### Step 2: Package Management 43 | - `Julia` has a mature eco-system for scientific computing. 44 | - `Pkg` is the built-in package manager for Julia. 45 | - To enter the package manager, press `]` in the REPL. 46 | ![PackageMangement](https://github.com/exAClior/QMBCTutorial/blob/ys/julia-tutorial/notebooks/resources/scripts/Packages.gif?raw=true) 47 | - The environment is indicated by the `(@v1.9)`. 48 | - To add a package, type `add `. 49 | - To exit the package manager press `backspace` key 50 | - [Read More](https://pkgdocs.julialang.org/v1/managing-packages/) 51 | 52 | ### Step 3. Configure the startup file and add `Revise` 53 | First create a new file `~/.julia/config/startup.jl` by executing the following commands 54 | 55 | `mkdir -r ~/.julia/config` 56 | `touch ~/.julia/config/startup.jl` 57 | 58 | You could open the file with your favourite editor and add the following content 59 | ```julia 60 | ENV["JULIA_PKG_SERVER"] = "http://cn-southeast.pkg.juliacn.com/" 61 | try 62 | using Revise 63 | catch e 64 | @warn "fail to load Revise." 65 | end 66 | ``` 67 | 68 | The contents in the startup file is executed immediately after you open a new Julia session. 69 | 70 | Then you need to install [Revise](https://github.com/timholy/Revise.jl), which is an Julia package that can greatly improve the using experience of Julia. To install `Revise`, open Julia REPL and type 71 | ```julia 72 | julia> using Pkg; Pkg.add("Revise") 73 | ``` 74 | 75 | If you don't know about `startup.jl` and where to find it, [here](https://docs.julialang.org/en/v1/manual/command-line-interface/#Startup-file) is a good place for further information. Windows users can find their Julia config file in `JULIA_INSTALL_FOLDER\etc\julia\startup.jl` 76 | 77 | #### More Packages 78 | - You may find more Julia packages [here](https://juliahub.com/). 79 | 80 | 81 | As a final step, please verify your Julia configuration by openning a Julia REPL and type 82 | ```julia 83 | julia> versioninfo() 84 | Julia Version 1.9.2 85 | Commit e4ee485e909 (2023-07-05 09:39 UTC) 86 | Platform Info: 87 | OS: macOS (arm64-apple-darwin22.4.0) 88 | CPU: 10 × Apple M2 Pro 89 | WORD_SIZE: 64 90 | LIBM: libopenlibm 91 | LLVM: libLLVM-14.0.6 (ORCJIT, apple-m1) 92 | Threads: 1 on 6 virtual cores 93 | Environment: 94 | JULIA_NUM_THREADS = 1 95 | JULIA_PROJECT = @. 96 | JULIA_PKG_SERVER = http://cn-southeast.pkg.juliacn.com/ 97 | ``` 98 | 99 | #### Step 3. Download an editor: VSCode 100 | 101 | Install VSCode by downloading the correct binary for your platform from [here](https://code.visualstudio.com/download). 102 | Open VSCode and open the `Extensions` tab on the left side-bar of the window, search `Julia` and install the most popular extension. 103 | [read more...](https://github.com/julia-vscode/julia-vscode) 104 | ![VSCode Julia Layout](https://code.visualstudio.com/assets/docs/languages/julia/overview.png) 105 | 106 | You are ready to go, cheers! 107 | 108 | ### A quick introduction to the Julia REPL 109 | 110 | A Julia REPL has four modes, 111 | 112 | 1. Julian mode is the default mode that can interpret your Julia code. 113 | 114 | 2. Shell mode is the mode that you can run shell commands. Press `;` in the Julian mode and type 115 | ```julia 116 | shell> date 117 | Sun Nov 6 10:50:21 PM CST 2022 118 | ``` 119 | To return to the Julian mode, type the Backspace key. 120 | 121 | 3. Package mode is the mode that you can manage packages. Press `]` in the Julian mode and type 122 | ```julia 123 | (@v1.8) pkg> st 124 | Status `~/.julia/environments/v1.8/Project.toml` 125 | [295af30f] Revise v3.4.0 126 | ``` 127 | To return to the Julian mode, type the Backspace key. 128 | 129 | 4. Help mode is the mode that you can access the docstrings of functions. Press `?` in the Julian mode and type 130 | ```julia 131 | help> sum 132 | ... docstring for sum ... 133 | ``` 134 | To return to the Julian mode, type the Backspace key. 135 | 136 | [read more...](https://docs.julialang.org/en/v1/stdlib/REPL/) 137 | -------------------------------------------------------------------------------- /julia/2.first-package.md: -------------------------------------------------------------------------------- 1 | # Packages and projects 2 | 3 | Julia packages are scattered on Github, e.g. the package `Yao` is in a Github repo [Yao.jl](https://github.com/QuantumBFS/Yao.jl). 4 | To locate these packages, Julia uses the a special Github repository as the registry of packages. 5 | The default one is called `General` registry. 6 | 7 | ```julia 8 | (@v1.8) pkg> registry status 9 | Registry Status 10 | [23338594] General (https://github.com/JuliaRegistries/General.git) 11 | ``` 12 | 13 | Each package has a special file called `Project.toml` in the top level folder, which includes the dependency information. 14 | When you install a package, Julia resolves this dependency tree and install the dependencies and generate the `Manifest.toml` file. 15 | 16 | [read more...]() 17 | 18 | ## Create and release your first package 19 | 20 | ### 1. Create a package using `PkgTemplates` 21 | It is recommended to start a new Julia project as a Julia package so that the dependency can be resolved properly. 22 | It is very simple to create a new Julia package with [PkgTemplates](https://github.com/JuliaCI/PkgTemplates.jl). 23 | A minimum example is as follows. 24 | 25 | ```julia 26 | pkg> add PkgTemplates 27 | 28 | julia> using PkgTemplates 29 | 30 | julia> tpl = Template(; user="MyGithubUserOrOrg", plugins=[ 31 | GitHubActions(; extra_versions=["nightly"]), 32 | Git(), 33 | Codecov(), 34 | Documenter{GitHubActions}(), 35 | ]) 36 | 37 | julia> tpl("Demo") 38 | ``` 39 | 40 | A fresh new project will be generate in folder `~/.julia/dev/Demo` (or `%HOME%/.julia/dev/Demo` for Windows users). The file structure of this project is 41 | ```zsh 42 | (base) ➜ Demo git:(main) tree . 43 | . 44 | ├── docs 45 | │   ├── make.jl # The make file for the documents 46 | │   ├── Manifest.toml # The resolved dependency for the `docs` environment 47 | │   ├── Project.toml # The dependency specification for the `docs` environment 48 | │   └── src 49 | │   └── index.md # The document home page 50 | ├── .github 51 | │   └── workflows # Files in this folder specify jobs run by Github Action automatically. 52 | │   ├── CI.yml # Run tests and calculate the test coverage 53 | │   ├── CompatHelper.yml # Help your package dependency up to date by creating a pull request. 54 | │   └── TagBot.yml # Auto-tag a version after registering a new version in a Julia registry. 55 | ├── .gitignore # Ignored files will not be considered a part of the `git` repo. 56 | ├── LICENSE # MIT license by default 57 | ├── Manifest.toml # The resolved dependency 58 | ├── Project.toml # The package name, UUID and dependencies 59 | ├── README.md # README in markdown format 60 | ├── src # The folder for Julia source code 61 | │   └── Demo.jl # The main file for the `Demo` module 62 | └── test # The folder for Julia test code 63 | └── runtests.jl # The main file for testing. 64 | ``` 65 | References 66 | 67 | * [Github Action](https://docs.github.com/en/actions) 68 | 69 | Some extra steps are required, 70 | 71 | * Setup the Github pages, 72 | * Connect your repo with [CodeCov](https://about.codecov.io/) correctly. 73 | 74 | ### 2. Create a Github repo 75 | The github repo name should be the same as your Julia package name. 76 | In our example, it is `Demo.jl`. Push your local files to the remote. 77 | 78 | ### 3. Develop and manage your package dependency 79 | 80 | ### 4. Release your package 81 | You can offically release this package to make it accessible to the public by registering your package in Julia's [General registry](https://github.com/JuliaRegistries/General). 82 | You may find an instruction about how to register a package in the github repo [Registrator.jl](https://github.com/JuliaRegistries/Registrator.jl). 83 | After a 3 days review procedure, your package will be installable in the Pkg mode. 84 | 85 | ### How to contribute to a package 86 | 87 | Fork a package, 88 | 89 | ```julia 90 | pkg> dev 91 | ``` 92 | 93 | 94 | Explain package management. 95 | Local and global environment 96 | 97 | Remove access. 98 | 99 | How to create a package, specify project.toml 100 | -------------------------------------------------------------------------------- /julia/3.basic-grammar.md: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/CodingThrust/CodingClub/d6acc0c44858c5a2c0f6d0b81beaa2e85144a91c/julia/3.basic-grammar.md -------------------------------------------------------------------------------- /julia/linear-algebra.md: -------------------------------------------------------------------------------- 1 | # Linear Algebra 2 | 3 | ## Setup BLAS backend and multi-threading 4 | ```julia 5 | julia> using LinearAlgebra 6 | 7 | julia> BLAS.get_config() 8 | LinearAlgebra.BLAS.LBTConfig 9 | Libraries: 10 | └ [ILP64] libopenblas64_.so 11 | 12 | julia> BLAS.get_num_threads() 13 | 4 14 | ``` 15 | 16 | If you want to switch to MKL, please type 17 | ```julia 18 | julia> using Pkg; Pkg.add("MKL") 19 | 20 | julia> using LinearAlgebra, MKL 21 | 22 | julia> BLAS.get_config() 23 | LinearAlgebra.BLAS.LBTConfig 24 | Libraries: 25 | └ [ILP64] libmkl_rt.1.dylib 26 | ``` 27 | 28 | [read more...](https://github.com/JuliaLinearAlgebra/MKL.jl) 29 | 30 | Input unicode characters 31 | https://docs.julialang.org/en/v1/manual/unicode-input/ 32 | -------------------------------------------------------------------------------- /mpi/.gitignore: -------------------------------------------------------------------------------- 1 | *.err 2 | *.out 3 | -------------------------------------------------------------------------------- /mpi/LocalPreferences.toml: -------------------------------------------------------------------------------- 1 | [MPIPreferences] 2 | _format = "1.0" 3 | abi = "OpenMPI" 4 | binary = "system" 5 | libmpi = "libmpi" 6 | mpiexec = "mpiexec" 7 | -------------------------------------------------------------------------------- /mpi/Manifest.toml: -------------------------------------------------------------------------------- 1 | # This file is machine-generated - editing it directly is not advised 2 | 3 | julia_version = "1.9.0" 4 | manifest_format = "2.0" 5 | project_hash = "74a6e625983937d7da55b3762da71de816c3ebfa" 6 | 7 | [[deps.ArgTools]] 8 | uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" 9 | version = "1.1.1" 10 | 11 | [[deps.Artifacts]] 12 | uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" 13 | 14 | [[deps.Base64]] 15 | uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" 16 | 17 | [[deps.CompilerSupportLibraries_jll]] 18 | deps = ["Artifacts", "Libdl"] 19 | uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" 20 | version = "1.0.2+0" 21 | 22 | [[deps.Dates]] 23 | deps = ["Printf"] 24 | uuid = "ade2ca70-3891-5945-98fb-dc099432e06a" 25 | 26 | [[deps.Distributed]] 27 | deps = ["Random", "Serialization", "Sockets"] 28 | uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b" 29 | 30 | [[deps.DocStringExtensions]] 31 | deps = ["LibGit2"] 32 | git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d" 33 | uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" 34 | version = "0.9.3" 35 | 36 | [[deps.Downloads]] 37 | deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"] 38 | uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6" 39 | version = "1.6.0" 40 | 41 | [[deps.FileWatching]] 42 | uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee" 43 | 44 | [[deps.InteractiveUtils]] 45 | deps = ["Markdown"] 46 | uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240" 47 | 48 | [[deps.JLLWrappers]] 49 | deps = ["Preferences"] 50 | git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1" 51 | uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210" 52 | version = "1.4.1" 53 | 54 | [[deps.LazyArtifacts]] 55 | deps = ["Artifacts", "Pkg"] 56 | uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3" 57 | 58 | [[deps.LibCURL]] 59 | deps = ["LibCURL_jll", "MozillaCACerts_jll"] 60 | uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21" 61 | version = "0.6.3" 62 | 63 | [[deps.LibCURL_jll]] 64 | deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"] 65 | uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0" 66 | version = "7.84.0+0" 67 | 68 | [[deps.LibGit2]] 69 | deps = ["Base64", "NetworkOptions", "Printf", "SHA"] 70 | uuid = "76f85450-5226-5b5a-8eaa-529ad045b433" 71 | 72 | [[deps.LibSSH2_jll]] 73 | deps = ["Artifacts", "Libdl", "MbedTLS_jll"] 74 | uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8" 75 | version = "1.10.2+0" 76 | 77 | [[deps.Libdl]] 78 | uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb" 79 | 80 | [[deps.Logging]] 81 | uuid = "56ddb016-857b-54e1-b83d-db4d58db5568" 82 | 83 | [[deps.MPI]] 84 | deps = ["Distributed", "DocStringExtensions", "Libdl", "MPICH_jll", "MPIPreferences", "MPItrampoline_jll", "MicrosoftMPI_jll", "OpenMPI_jll", "PrecompileTools", "Requires", "Serialization", "Sockets"] 85 | git-tree-sha1 = "cef80bd5aad97224a3937596066c21a37dca3990" 86 | uuid = "da04e1cc-30fd-572f-bb4f-1f8673147195" 87 | version = "0.20.9" 88 | 89 | [deps.MPI.extensions] 90 | AMDGPUExt = "AMDGPU" 91 | CUDAExt = "CUDA" 92 | 93 | [deps.MPI.weakdeps] 94 | AMDGPU = "21141c5a-9bdb-4563-92ae-f87d6854732e" 95 | CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" 96 | 97 | [[deps.MPICH_jll]] 98 | deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "MPIPreferences", "TOML"] 99 | git-tree-sha1 = "d790fbd913f85e8865c55bf4725aff197c5155c8" 100 | uuid = "7cb0a576-ebde-5e09-9194-50597f1243b4" 101 | version = "4.1.1+1" 102 | 103 | [[deps.MPIPreferences]] 104 | deps = ["Libdl", "Preferences"] 105 | git-tree-sha1 = "71f937129731a29eabe6969db2c90368a4408933" 106 | uuid = "3da0fdf6-3ccc-4f1b-acd9-58baa6c99267" 107 | version = "0.1.7" 108 | 109 | [[deps.MPItrampoline_jll]] 110 | deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "MPIPreferences", "TOML"] 111 | git-tree-sha1 = "b3dcf8e1c610a10458df3c62038c8cc3a4d6291d" 112 | uuid = "f1f71cc9-e9ae-5b93-9b94-4fe0e1ad3748" 113 | version = "5.3.0+0" 114 | 115 | [[deps.Markdown]] 116 | deps = ["Base64"] 117 | uuid = "d6f4376e-aef5-505a-96c1-9c027394607a" 118 | 119 | [[deps.MbedTLS_jll]] 120 | deps = ["Artifacts", "Libdl"] 121 | uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1" 122 | version = "2.28.2+0" 123 | 124 | [[deps.MicrosoftMPI_jll]] 125 | deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] 126 | git-tree-sha1 = "a8027af3d1743b3bfae34e54872359fdebb31422" 127 | uuid = "9237b28f-5490-5468-be7b-bb81f5f5e6cf" 128 | version = "10.1.3+4" 129 | 130 | [[deps.MozillaCACerts_jll]] 131 | uuid = "14a3606d-f60d-562e-9121-12d972cd8159" 132 | version = "2022.10.11" 133 | 134 | [[deps.NetworkOptions]] 135 | uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" 136 | version = "1.2.0" 137 | 138 | [[deps.OpenMPI_jll]] 139 | deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "MPIPreferences", "TOML"] 140 | git-tree-sha1 = "f3080f4212a8ba2ceb10a34b938601b862094314" 141 | uuid = "fe0851c0-eecd-5654-98d4-656369965a5c" 142 | version = "4.1.5+0" 143 | 144 | [[deps.Pkg]] 145 | deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"] 146 | uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" 147 | version = "1.9.0" 148 | 149 | [[deps.PrecompileTools]] 150 | deps = ["Preferences"] 151 | git-tree-sha1 = "259e206946c293698122f63e2b513a7c99a244e8" 152 | uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a" 153 | version = "1.1.1" 154 | 155 | [[deps.Preferences]] 156 | deps = ["TOML"] 157 | git-tree-sha1 = "7eb1686b4f04b82f96ed7a4ea5890a4f0c7a09f1" 158 | uuid = "21216c6a-2e73-6563-6e65-726566657250" 159 | version = "1.4.0" 160 | 161 | [[deps.Printf]] 162 | deps = ["Unicode"] 163 | uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" 164 | 165 | [[deps.REPL]] 166 | deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"] 167 | uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb" 168 | 169 | [[deps.Random]] 170 | deps = ["SHA", "Serialization"] 171 | uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" 172 | 173 | [[deps.Requires]] 174 | deps = ["UUIDs"] 175 | git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7" 176 | uuid = "ae029012-a4dd-5104-9daa-d747884805df" 177 | version = "1.3.0" 178 | 179 | [[deps.SHA]] 180 | uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" 181 | version = "0.7.0" 182 | 183 | [[deps.Serialization]] 184 | uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" 185 | 186 | [[deps.Sockets]] 187 | uuid = "6462fe0b-24de-5631-8697-dd941f90decc" 188 | 189 | [[deps.TOML]] 190 | deps = ["Dates"] 191 | uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76" 192 | version = "1.0.3" 193 | 194 | [[deps.Tar]] 195 | deps = ["ArgTools", "SHA"] 196 | uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e" 197 | version = "1.10.0" 198 | 199 | [[deps.UUIDs]] 200 | deps = ["Random", "SHA"] 201 | uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" 202 | 203 | [[deps.Unicode]] 204 | uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" 205 | 206 | [[deps.Zlib_jll]] 207 | deps = ["Libdl"] 208 | uuid = "83775a58-1f1d-513f-b197-d71354ab007a" 209 | version = "1.2.13+0" 210 | 211 | [[deps.nghttp2_jll]] 212 | deps = ["Artifacts", "Libdl"] 213 | uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" 214 | version = "1.48.0+0" 215 | 216 | [[deps.p7zip_jll]] 217 | deps = ["Artifacts", "Libdl"] 218 | uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" 219 | version = "17.4.0+0" 220 | -------------------------------------------------------------------------------- /mpi/Project.toml: -------------------------------------------------------------------------------- 1 | [deps] 2 | MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195" 3 | MPIPreferences = "3da0fdf6-3ccc-4f1b-acd9-58baa6c99267" 4 | -------------------------------------------------------------------------------- /mpi/README.md: -------------------------------------------------------------------------------- 1 | # Message Passing Interface (MPI) 2 | ## Mindset 3 | Multi-Universe model: all processors run exactly the same program without sharing memories. Without communication, they will end up with returning the same result. 4 | Then, we introduce a web-based oracle object `MPI.COMM_WORLD`. When a processor queries that object with the `Get_rank()` function, that object returns a number that corresponds to the processor ID. 5 | ## Watch YouTube Video 6 | * [MPI Basic](https://youtu.be/c0C9mQaxsD4) 7 | * [MPI Advancd](https://youtu.be/q9OfXis50Rg) 8 | ## List of packages 9 | 1. Python: [mpi4py](https://mpi4py.readthedocs.io/en/stable/) 10 | 2. Julia: [MPI.jl](https://juliaparallel.org/MPI.jl/dev/) 11 | 3. Backends: [MPICH](https://www.mpich.org/), [OpenMPI](https://www.open-mpi.org/), Intel MPI et al. 12 | 13 | ## Coding example: Distributed hello-world with MPI.jl 14 | We are working in the Julia project folder, using the project's [local environment](https://pkgdocs.julialang.org/v1/environments/) 15 | 16 | 1. Add `MPI.jl` to your project dependencies. 17 | ```julia 18 | julia> using Pkg; Pkg.activate("."); Pkg.add("MPI") 19 | ``` 20 | 21 | 2. Configure the MPI backend ([doc](https://juliaparallel.org/MPI.jl/dev/configuration/)) 22 | ```julia 23 | julia> using Pkg; Pkg.add("MPIPreferences"); 24 | 25 | julia> using MPIPreferences; MPIPreferences.use_system_binary() 26 | ``` 27 | You will see a [LocalPreferences.toml](LocalPreferences.toml) in your working folder. 28 | 29 | 3. You need to build the MPI package again for the new MPI backend. 30 | ```bash 31 | julia --project -e 'using Pkg; Pkg.build("MPI")' 32 | ``` 33 | 34 | 4. You may test the program with 35 | ```bash 36 | mpiexec -n 3 julia --project mpi.jl 37 | ``` 38 | 39 | ## Another example 40 | Go through this example: https://juliaparallel.org/MPI.jl/dev/examples/06-scatterv/ 41 | 42 | ## Using school cluster. 43 | 1. Please check the tested [LSF script](julia-helloworld-lsf.job). This script can be executed on a cluster with 44 | ```bash 45 | bsub < julia-helloworld-lsf.job 46 | ``` 47 | 48 | 2. The [slurm script](julia-helloworld-slurm.slurm) is not tested. It can be executed on a cluster with 49 | ```bash 50 | sbatch < julia-helloworld-slurm.slurm 51 | ``` 52 | -------------------------------------------------------------------------------- /mpi/julia-helloworld-lsf.job: -------------------------------------------------------------------------------- 1 | #!/bin/bash 2 | 3 | ############## SLURM SETUP ############### 4 | #BSUB -W 10:00 5 | #BSUB -n 4 6 | #BSUB -R "span[ptile=2]" 7 | #BSUB -e $PWD/%J.err 8 | #BSUB -o $PWD/%J.out 9 | 10 | ############## MODULE LOADING ############### 11 | # Clear the environment from any previously loaded modules 12 | # module purge > /dev/null 2>&1 13 | # Show available modules with module avail 14 | module load openmpi 15 | 16 | ############## RUN ###################### 17 | /usr/mpi/gcc/openmpi-4.1.2a1/bin/mpirun $HOME/.local/bin/julia --project=$PWD mpi.jl 18 | -------------------------------------------------------------------------------- /mpi/julia-helloworld-slurm.slurm: -------------------------------------------------------------------------------- 1 | #!/bin/bash 2 | 3 | ############## SLURM SETUP ############### 4 | #SBATCH --job-name=mpi_job 5 | #SBATCH --ntasks=128 6 | # less than 10 hours 7 | #SBATCH --time=10:00:00 8 | #SBATCH --output=log.%j 9 | 10 | ############## MODULE LOADING ############### 11 | # Clear the environment from any previously loaded modules 12 | # module purge > /dev/null 2>&1 13 | # Show available modules with module avail 14 | module load mpi/openmpi-4.1.5 15 | 16 | ############## RUN ###################### 17 | export OMP_NUM_THREADS=$SLURM_CPUS_PER_TASK 18 | mpirun $HOME/.juliaup/bin/julia --project=$PWD mpi.jl 19 | -------------------------------------------------------------------------------- /mpi/mpi.jl: -------------------------------------------------------------------------------- 1 | # examples/06-scatterv.jl 2 | # This example shows how to use MPI.Scatterv! and MPI.Gatherv! 3 | # roughly based on the example from 4 | # https://stackoverflow.com/a/36082684/392585 5 | # source: https://juliaparallel.org/MPI.jl/dev/examples/06-scatterv/ 6 | 7 | using MPI 8 | 9 | # initialize global variables 10 | MPI.Init() 11 | 12 | comm = MPI.COMM_WORLD 13 | 14 | # get the id for the current processor 15 | rank = MPI.Comm_rank(comm) 16 | 17 | # total number of processors 18 | comm_size = MPI.Comm_size(comm) 19 | 20 | print("Hello world, I am rank $(MPI.Comm_rank(comm)) of $(MPI.Comm_size(comm))\n") 21 | 22 | MPI.Barrier(comm) 23 | 24 | # root = 0 25 | 26 | # if rank == root 27 | # M, N = 4, 7 28 | 29 | # test = Float64[i for i = 1:M, j = 1:N] 30 | # output = similar(test) 31 | 32 | # # Julia arrays are stored in column-major order, so we need to split along the last dimension 33 | # # dimension 34 | # M_counts = [M for i = 1:comm_size] 35 | # N_counts = split_count(N, comm_size) 36 | 37 | # # store sizes in 2 * comm_size Array 38 | # sizes = vcat(M_counts', N_counts') 39 | # size_ubuf = UBuffer(sizes, 2) 40 | 41 | # # store number of values to send to each rank in comm_size length Vector 42 | # counts = vec(prod(sizes, dims=1)) 43 | 44 | # test_vbuf = VBuffer(test, counts) # VBuffer for scatter 45 | # output_vbuf = VBuffer(output, counts) # VBuffer for gather 46 | # else 47 | # # these variables can be set to `nothing` on non-root processes 48 | # size_ubuf = UBuffer(nothing) 49 | # output_vbuf = test_vbuf = VBuffer(nothing) 50 | # end 51 | 52 | # if rank == root 53 | # println("Original matrix") 54 | # println("================") 55 | # @show test sizes counts 56 | # println() 57 | # println("Each rank") 58 | # println("================") 59 | # end 60 | # MPI.Barrier(comm) 61 | 62 | # local_size = MPI.Scatter(size_ubuf, NTuple{2,Int}, root, comm) 63 | # local_test = MPI.Scatterv!(test_vbuf, zeros(Float64, local_size), root, comm) 64 | 65 | # for i = 0:comm_size-1 66 | # if rank == i 67 | # @show rank local_test 68 | # end 69 | # MPI.Barrier(comm) 70 | # end 71 | 72 | # MPI.Gatherv!(local_test, output_vbuf, root, comm) 73 | 74 | # if rank == root 75 | # println() 76 | # println("Final matrix") 77 | # println("================") 78 | # @show output 79 | # end -------------------------------------------------------------------------------- /prompt/prompt.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/CodingThrust/CodingClub/d6acc0c44858c5a2c0f6d0b81beaa2e85144a91c/prompt/prompt.pdf -------------------------------------------------------------------------------- /simulated-annealing/README.md: -------------------------------------------------------------------------------- 1 | # Solving the spin-glass problem with simulated annealing 2 | 3 | ### Get started 4 | 5 | This tutorial is contained in the Pluto notebook file: [notebook.jl](notebook.jl) [[pdf](notebook.pdf)]. 6 | You can open it with [Pluto](https://github.com/fonsp/Pluto.jl). 7 | 8 | ## The SSSS-Challenge 9 | [Github repo](https://github.com/QuantumBFS/SSSS) 10 | 11 | The challenge description could be found in the challenge section of the README of SSSS. Where submissions are also available. 12 | -------------------------------------------------------------------------------- /simulated-annealing/example.txt: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/CodingThrust/CodingClub/d6acc0c44858c5a2c0f6d0b81beaa2e85144a91c/simulated-annealing/example.txt -------------------------------------------------------------------------------- /simulated-annealing/notebook.jl: -------------------------------------------------------------------------------- 1 | ### A Pluto.jl notebook ### 2 | # v0.19.19 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 $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) 13 | el 14 | end 15 | end 16 | 17 | # ╔═╡ 2ec32c9d-0216-48a8-848d-79f7cc84798e 18 | using DelimitedFiles, Test, BenchmarkTools, Statistics 19 | 20 | # ╔═╡ 701dfc92-4891-477b-9e15-8083f8ca5531 21 | begin 22 | using PlutoUI 23 | 24 | struct BondWrapper 25 | content 26 | end 27 | 28 | function Base.show(io::IO, mime::MIME"text/html", b::BondWrapper) 29 | print(io, 30 | """$(b.content.defines) = """) 31 | Base.show(io, mime, b.content) 32 | end 33 | 34 | #macro xbind(args...) 35 | # esc(quote 36 | # let 37 | # bond = @bind $(args...) 38 | # $BondWrapper(bond) 39 | # end 40 | # end) 41 | #end 42 | end; 43 | 44 | # ╔═╡ 0b0e674d-688d-491d-8a51-36334ad40b1a 45 | using Random 46 | 47 | # ╔═╡ 8c702004-0534-43cb-b92c-1b494a1145b3 48 | using Profile 49 | 50 | # ╔═╡ c96ce06a-bd6a-419c-8c77-cc76ea0f8593 51 | # pip install viznet, matplotlib 52 | using PythonCall, CondaPkg 53 | 54 | # ╔═╡ 0c3000cf-46d3-4481-9d6d-61980443dd93 55 | """General Annealing Problem""" 56 | abstract type AnnealingProblem end 57 | 58 | # ╔═╡ 9ec34d03-e9e6-460c-bc8b-39b70b6b8a37 59 | """ 60 | SpinAnnealingProblem{T<:Real} <: AnnealingProblem 61 | 62 | Annealing problem defined by coupling matrix of spins. 63 | """ 64 | struct SpinAnnealingProblem{T<:Real} <: AnnealingProblem # immutable, with type parameter T (a subtype of Real). 65 | num_spin::Int 66 | coupling::Matrix{T} 67 | function SpinAnnealingProblem(coupling::Matrix{T}) where T 68 | size(coupling, 1) == size(coupling, 2) || throw(DimensionMismatch("input must be square matrix.")) 69 | new{T}(size(coupling, 1), coupling) 70 | end 71 | end 72 | 73 | # ╔═╡ a7e70b41-9184-4127-b66f-dfc03b8b3004 74 | """ 75 | load_coupling(filename::String) -> SpinAnnealingProblem 76 | 77 | Load the data file into symmtric coupling matrix. 78 | """ 79 | function load_coupling(filename::String) 80 | data = readdlm(filename) 81 | is = Int.(view(data, :, 1)) .+ 1 #! @. means broadcast for the following functions, is here used correctly? 82 | js = Int.(view(data, :, 2)) .+ 1 83 | weights = data[:,3] 84 | num_spin = max(maximum(is), maximum(js)) 85 | J = zeros(eltype(weights), num_spin, num_spin) 86 | @inbounds for (i, j, weight) = zip(is, js, weights) 87 | J[i,j] = weight/2 88 | J[j,i] = weight/2 89 | end 90 | SpinAnnealingProblem(J) 91 | end 92 | 93 | # ╔═╡ 35b7dcfe-717f-48b0-bd4f-4c72f880a229 94 | @testset "loading" begin 95 | sap = load_coupling("programs/example.txt") 96 | @test size(sap.coupling) == (300, 300) 97 | end 98 | 99 | # ╔═╡ 6cc6e9a2-4409-4ad1-b8d1-be0826fe9592 100 | abstract type AnnealingConfig end 101 | 102 | # ╔═╡ a2a174b8-28d0-461f-97c6-8364ccada6c4 103 | struct SpinConfig{Ts, Tf} <: AnnealingConfig 104 | config::Vector{Ts} 105 | field::Vector{Tf} 106 | end 107 | 108 | # ╔═╡ f1c1eae7-102f-4ca3-9fd2-d81529ada0a3 109 | """ 110 | random_config(prblm::AnnealingProblem) -> SpinConfig 111 | 112 | Random spin configuration. 113 | """ 114 | function random_config end # where to put the docstring of a multiple-dispatch function is a problem. Using `abstract function` is proper. 115 | 116 | # ╔═╡ caa805be-6c98-4b59-8404-c0db284c58e9 117 | function random_config(prblm::SpinAnnealingProblem) 118 | config = rand([-1,1], prblm.num_spin) 119 | SpinConfig(config, prblm.coupling*config) 120 | end 121 | 122 | # ╔═╡ e692876e-72eb-4a19-a0b9-367ab3e84783 123 | @testset "random config" begin 124 | sap = load_coupling("programs/example.txt") 125 | initial_config = random_config(sap) 126 | @test initial_config.config |> length == 300 127 | @test eltype(initial_config.config) == Int 128 | end 129 | 130 | # ╔═╡ 0d37406b-f16a-4b91-a138-ee59a92e2ca4 131 | md"## Main program" 132 | 133 | # ╔═╡ 6116801e-e6a8-4e75-9e04-6c07e4a17305 134 | """ 135 | get_cost(config::AnnealingConfig, ap::AnnealingProblem) -> Real 136 | 137 | Get the cost of specific configuration. 138 | """ 139 | get_cost(config::SpinConfig, sap::SpinAnnealingProblem) = sum(config.config'*sap.coupling*config.config) 140 | 141 | # ╔═╡ 92c83b32-668a-4adb-8531-4258d094403c 142 | """ 143 | propose(config::AnnealingConfig, ap::AnnealingProblem) -> (Proposal, Real) 144 | 145 | Propose a change, as well as the energy change. 146 | """ 147 | @inline function propose(config::SpinConfig, ::SpinAnnealingProblem) # ommit the name of argument, since not used. 148 | ispin = rand(1:length(config.config)) 149 | @inbounds ΔE = -config.field[ispin] * config.config[ispin] * 4 # 2 for spin change, 2 for mutual energy. 150 | ispin, ΔE 151 | end 152 | 153 | # ╔═╡ 83211927-e0b7-4439-90e1-9d348328be16 154 | """ 155 | flip!(config::AnnealingConfig, ispin::Proposal, ap::AnnealingProblem) -> SpinConfig 156 | 157 | Apply the change to the configuration. 158 | """ 159 | @inline function flip!(config::SpinConfig, ispin::Int, sap::SpinAnnealingProblem) 160 | @inbounds config.config[ispin] = -config.config[ispin] # @inbounds can remove boundary check, and improve performance 161 | @simd for i=1:sap.num_spin 162 | @inbounds config.field[i] += 2 * config.config[ispin] * sap.coupling[i,ispin] 163 | end 164 | config 165 | end 166 | 167 | # ╔═╡ 30ea57fc-f6ce-4fdf-b880-fc83012ed49f 168 | """ 169 | anneal_singlerun!(config::AnnealingConfig, prblm, tempscales::Vector{Float64}, num_update_each_temp::Int) 170 | 171 | Perform Simulated Annealing using Metropolis updates for the single run. 172 | 173 | * configuration that can be updated. 174 | * prblm: problem with `get_cost`, `flip!` and `random_config` interfaces. 175 | * tempscales: temperature scales, which should be a decreasing array. 176 | * num_update_each_temp: the number of update in each temprature scale. 177 | 178 | Returns (minimum cost, optimal configuration). 179 | """ 180 | function anneal_singlerun!(config, prblm, tempscales::Vector{Float64}, num_update_each_temp::Int) 181 | cost = get_cost(config, prblm) 182 | 183 | opt_config = config 184 | opt_cost = cost 185 | for beta = 1 ./ tempscales 186 | @simd for m = 1:num_update_each_temp # single instriuction multiple data, see julia performance tips. 187 | proposal, ΔE = propose(config, prblm) 188 | if exp(-beta*ΔE) > rand() #accept 189 | flip!(config, proposal, prblm) 190 | cost += ΔE 191 | if cost < opt_cost 192 | opt_cost = cost 193 | opt_config = config 194 | end 195 | end 196 | end 197 | end 198 | opt_cost, opt_config 199 | end 200 | 201 | # ╔═╡ 01275de9-c88b-4404-94f9-8a9129b06e70 202 | """ 203 | anneal(nrun::Int, prblm, tempscales::Vector{Float64}, num_update_each_temp::Int) 204 | 205 | Perform Simulated Annealing with multiple runs. 206 | """ 207 | function anneal(nrun::Int, prblm, tempscales::Vector{Float64}, num_update_each_temp::Int) 208 | local opt_config, opt_cost 209 | for r = 1:nrun 210 | initial_config = random_config(prblm) 211 | cost, config = anneal_singlerun!(initial_config, prblm, tempscales, num_update_each_temp) 212 | if r == 1 || cost < opt_cost 213 | opt_cost = cost 214 | opt_config = config 215 | end 216 | end 217 | opt_cost, opt_config 218 | end 219 | 220 | # ╔═╡ dcac0777-ff00-4ccb-91bb-678680413826 221 | Random.seed!(2) 222 | 223 | # ╔═╡ 53510c2f-ed40-4dee-84c0-436cc8281076 224 | tempscales = 10 .- (1:64 .- 1) .* 0.15 |> collect 225 | 226 | # ╔═╡ a4269932-e5af-4966-a0a9-4757066048b8 227 | sap = load_coupling("programs/example.txt") 228 | 229 | # ╔═╡ 61b6649e-04cd-45ab-ab40-19283a556bd8 230 | @testset "anneal" begin 231 | opt_cost, opt_config = anneal(30, sap, tempscales, 4000) 232 | @test anneal(30, sap, tempscales, 4000)[1] == -3858 233 | anneal(30, sap, tempscales, 4000) 234 | res = median(@benchmark anneal(30, $sap, $tempscales, 4000)) 235 | @test res.time/1e9 < 2 236 | @test res.allocs < 500 237 | end 238 | 239 | # ╔═╡ a883bf1a-f38c-4759-9287-7bad55d9ac37 240 | @bind run_julia_benchmark CheckBox() 241 | 242 | # ╔═╡ 0aebe7f7-3a88-4bf3-ab81-2d817f2d56b8 243 | if run_julia_benchmark @benchmark anneal(30, $sap, $tempscales, 4000) end 244 | 245 | # ╔═╡ 6a658549-c1e5-4ce2-bcce-ca08a5b0fe2c 246 | with_terminal() do 247 | Profile.clear() 248 | @profile anneal(100, sap, tempscales, 4000) 249 | Profile.print() 250 | end 251 | 252 | # ╔═╡ 8fa64302-22ac-49b1-ae0d-035660eacdac 253 | md""" 254 | ## Calling a Fortran program 255 | * https://docs.julialang.org/en/v1/manual/calling-c-and-fortran-code/index.html 256 | * https://craftofcoding.wordpress.com/2017/02/26/calling-fortran-from-julia-i/ 257 | * https://craftofcoding.wordpress.com/2017/03/01/calling-fortran-from-julia-ii/ 258 | """ 259 | 260 | # ╔═╡ 8dac622d-b115-46e5-8dd8-2150fcf53cc5 261 | cd(joinpath(@__DIR__, "programs")) do 262 | run(`gfortran -shared -fPIC problem.f90 fsa.f90 -o fsa.so` & `nm fsa.so`) 263 | end 264 | 265 | # ╔═╡ e9ffb48e-8d57-468e-b47c-466d827faa78 266 | @bind run_fortran_benchmark CheckBox() 267 | 268 | # ╔═╡ ef586d7e-adbc-44b3-b6eb-6685b3e13378 269 | # crash! 270 | # @benchmark ccall(((:test_, joinpath(@__DIR__, "fsa.so"))), Int32, ()) 271 | 272 | # ╔═╡ 1acd9c9b-6a01-44ab-9cbe-9d0c94544f39 273 | md""" 274 | ## What about Python? 275 | We can use [PyCall](https://github.com/JuliaPy/PyCall.jl) to call python programs! 276 | 277 | ### **Challenge!** 278 | 1. use Python package [viznet](https://github.com/GiggleLiu/viznet) and [matplotlib](https://matplotlib.org/) for visualization 279 | 2. benchmark pure python version of simulated annealing, show the time 280 | """ 281 | 282 | # ╔═╡ 92e7af60-0566-4769-b90c-e0abbb2b2f76 283 | # ╠═╡ show_logs = false 284 | CondaPkg.add("seaborn") 285 | 286 | # ╔═╡ c9d2f737-c034-4394-b18b-70e9f9ec28ea 287 | plt = pyimport("matplotlib.pyplot") 288 | 289 | # ╔═╡ 83d904d3-cdfe-499b-bfaa-c2ae643526a7 290 | let 291 | N = 400 292 | t = LinRange(0, 2π, N) 293 | r = 0.5 .+ cos.(t) 294 | x, y = r .* cos.(t), r .* sin.(t) 295 | 296 | fig, ax = plt.subplots() 297 | ax.plot(x, y, "k") 298 | ax.set(aspect=1) 299 | plt.show() 300 | end; 301 | 302 | # ╔═╡ 0a1ad6b8-f848-4147-a4aa-b4edc0caa42b 303 | pysa = try 304 | pyimport("testsa") 305 | catch e 306 | pyimport("sys").path.append(joinpath(@__DIR__, "programs")) # add current folder into path 307 | pyimport("testsa") 308 | end 309 | 310 | # ╔═╡ 01dd7234-f600-4597-b372-049e000ced1b 311 | @bind benchmark_python CheckBox() 312 | 313 | # ╔═╡ a3575bea-e521-47e1-9167-62e999728786 314 | if benchmark_python @benchmark pysa.test_codec() end 315 | 316 | # ╔═╡ 00000000-0000-0000-0000-000000000001 317 | PLUTO_PROJECT_TOML_CONTENTS = """ 318 | [deps] 319 | BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" 320 | CondaPkg = "992eb4ea-22a4-4c89-a5bb-47a3300528ab" 321 | DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab" 322 | PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" 323 | Profile = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79" 324 | PythonCall = "6099a3de-0909-46bc-b1f4-468b9a2dfc0d" 325 | Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" 326 | Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" 327 | Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" 328 | 329 | [compat] 330 | BenchmarkTools = "~1.3.2" 331 | CondaPkg = "~0.2.18" 332 | PlutoUI = "~0.7.50" 333 | PythonCall = "~0.9.12" 334 | """ 335 | 336 | # ╔═╡ 00000000-0000-0000-0000-000000000002 337 | PLUTO_MANIFEST_TOML_CONTENTS = """ 338 | # This file is machine-generated - editing it directly is not advised 339 | 340 | julia_version = "1.9.0-rc2" 341 | manifest_format = "2.0" 342 | project_hash = "3c9743b42aefe8f050872f1389dfdc77f9f22d5f" 343 | 344 | [[deps.AbstractPlutoDingetjes]] 345 | deps = ["Pkg"] 346 | git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481" 347 | uuid = "6e696c72-6542-2067-7265-42206c756150" 348 | version = "1.1.4" 349 | 350 | [[deps.ArgTools]] 351 | uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" 352 | version = "1.1.1" 353 | 354 | [[deps.Artifacts]] 355 | uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" 356 | 357 | [[deps.Base64]] 358 | uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" 359 | 360 | [[deps.BenchmarkTools]] 361 | deps = ["JSON", "Logging", "Printf", "Profile", "Statistics", "UUIDs"] 362 | git-tree-sha1 = "d9a9701b899b30332bbcb3e1679c41cce81fb0e8" 363 | uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" 364 | version = "1.3.2" 365 | 366 | [[deps.ColorTypes]] 367 | deps = ["FixedPointNumbers", "Random"] 368 | git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4" 369 | uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f" 370 | version = "0.11.4" 371 | 372 | [[deps.CompilerSupportLibraries_jll]] 373 | deps = ["Artifacts", "Libdl"] 374 | uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" 375 | version = "1.0.2+0" 376 | 377 | [[deps.CondaPkg]] 378 | deps = ["JSON3", "Markdown", "MicroMamba", "Pidfile", "Pkg", "TOML"] 379 | git-tree-sha1 = "741146cf2ced5859faae76a84b541aa9af1a78bb" 380 | uuid = "992eb4ea-22a4-4c89-a5bb-47a3300528ab" 381 | version = "0.2.18" 382 | 383 | [[deps.DataAPI]] 384 | git-tree-sha1 = "e8119c1a33d267e16108be441a287a6981ba1630" 385 | uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a" 386 | version = "1.14.0" 387 | 388 | [[deps.DataValueInterfaces]] 389 | git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6" 390 | uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464" 391 | version = "1.0.0" 392 | 393 | [[deps.Dates]] 394 | deps = ["Printf"] 395 | uuid = "ade2ca70-3891-5945-98fb-dc099432e06a" 396 | 397 | [[deps.DelimitedFiles]] 398 | deps = ["Mmap"] 399 | git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae" 400 | uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab" 401 | version = "1.9.1" 402 | 403 | [[deps.Downloads]] 404 | deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"] 405 | uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6" 406 | version = "1.6.0" 407 | 408 | [[deps.FileWatching]] 409 | uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee" 410 | 411 | [[deps.FixedPointNumbers]] 412 | deps = ["Statistics"] 413 | git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc" 414 | uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93" 415 | version = "0.8.4" 416 | 417 | [[deps.Hyperscript]] 418 | deps = ["Test"] 419 | git-tree-sha1 = "8d511d5b81240fc8e6802386302675bdf47737b9" 420 | uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91" 421 | version = "0.0.4" 422 | 423 | [[deps.HypertextLiteral]] 424 | deps = ["Tricks"] 425 | git-tree-sha1 = "c47c5fa4c5308f27ccaac35504858d8914e102f9" 426 | uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2" 427 | version = "0.9.4" 428 | 429 | [[deps.IOCapture]] 430 | deps = ["Logging", "Random"] 431 | git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a" 432 | uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89" 433 | version = "0.2.2" 434 | 435 | [[deps.InteractiveUtils]] 436 | deps = ["Markdown"] 437 | uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240" 438 | 439 | [[deps.IteratorInterfaceExtensions]] 440 | git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856" 441 | uuid = "82899510-4779-5014-852e-03e436cf321d" 442 | version = "1.0.0" 443 | 444 | [[deps.JLLWrappers]] 445 | deps = ["Preferences"] 446 | git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1" 447 | uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210" 448 | version = "1.4.1" 449 | 450 | [[deps.JSON]] 451 | deps = ["Dates", "Mmap", "Parsers", "Unicode"] 452 | git-tree-sha1 = "3c837543ddb02250ef42f4738347454f95079d4e" 453 | uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6" 454 | version = "0.21.3" 455 | 456 | [[deps.JSON3]] 457 | deps = ["Dates", "Mmap", "Parsers", "SnoopPrecompile", "StructTypes", "UUIDs"] 458 | git-tree-sha1 = "84b10656a41ef564c39d2d477d7236966d2b5683" 459 | uuid = "0f8b85d8-7281-11e9-16c2-39a750bddbf1" 460 | version = "1.12.0" 461 | 462 | [[deps.LazyArtifacts]] 463 | deps = ["Artifacts", "Pkg"] 464 | uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3" 465 | 466 | [[deps.LibCURL]] 467 | deps = ["LibCURL_jll", "MozillaCACerts_jll"] 468 | uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21" 469 | version = "0.6.3" 470 | 471 | [[deps.LibCURL_jll]] 472 | deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"] 473 | uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0" 474 | version = "7.84.0+0" 475 | 476 | [[deps.LibGit2]] 477 | deps = ["Base64", "NetworkOptions", "Printf", "SHA"] 478 | uuid = "76f85450-5226-5b5a-8eaa-529ad045b433" 479 | 480 | [[deps.LibSSH2_jll]] 481 | deps = ["Artifacts", "Libdl", "MbedTLS_jll"] 482 | uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8" 483 | version = "1.10.2+0" 484 | 485 | [[deps.Libdl]] 486 | uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb" 487 | 488 | [[deps.LinearAlgebra]] 489 | deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"] 490 | uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" 491 | 492 | [[deps.Logging]] 493 | uuid = "56ddb016-857b-54e1-b83d-db4d58db5568" 494 | 495 | [[deps.MIMEs]] 496 | git-tree-sha1 = "65f28ad4b594aebe22157d6fac869786a255b7eb" 497 | uuid = "6c6e2e6c-3030-632d-7369-2d6c69616d65" 498 | version = "0.1.4" 499 | 500 | [[deps.MacroTools]] 501 | deps = ["Markdown", "Random"] 502 | git-tree-sha1 = "42324d08725e200c23d4dfb549e0d5d89dede2d2" 503 | uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09" 504 | version = "0.5.10" 505 | 506 | [[deps.Markdown]] 507 | deps = ["Base64"] 508 | uuid = "d6f4376e-aef5-505a-96c1-9c027394607a" 509 | 510 | [[deps.MbedTLS_jll]] 511 | deps = ["Artifacts", "Libdl"] 512 | uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1" 513 | version = "2.28.2+0" 514 | 515 | [[deps.MicroMamba]] 516 | deps = ["Pkg", "Scratch", "micromamba_jll"] 517 | git-tree-sha1 = "a6a4771aba1dc8942bc0f44ff9f8ee0f893ef888" 518 | uuid = "0b3b1443-0f03-428d-bdfb-f27f9c1191ea" 519 | version = "0.1.12" 520 | 521 | [[deps.Mmap]] 522 | uuid = "a63ad114-7e13-5084-954f-fe012c677804" 523 | 524 | [[deps.MozillaCACerts_jll]] 525 | uuid = "14a3606d-f60d-562e-9121-12d972cd8159" 526 | version = "2022.10.11" 527 | 528 | [[deps.NetworkOptions]] 529 | uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" 530 | version = "1.2.0" 531 | 532 | [[deps.OpenBLAS_jll]] 533 | deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"] 534 | uuid = "4536629a-c528-5b80-bd46-f80d51c5b363" 535 | version = "0.3.21+4" 536 | 537 | [[deps.OrderedCollections]] 538 | git-tree-sha1 = "d321bf2de576bf25ec4d3e4360faca399afca282" 539 | uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d" 540 | version = "1.6.0" 541 | 542 | [[deps.Parsers]] 543 | deps = ["Dates", "SnoopPrecompile"] 544 | git-tree-sha1 = "478ac6c952fddd4399e71d4779797c538d0ff2bf" 545 | uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0" 546 | version = "2.5.8" 547 | 548 | [[deps.Pidfile]] 549 | deps = ["FileWatching", "Test"] 550 | git-tree-sha1 = "2d8aaf8ee10df53d0dfb9b8ee44ae7c04ced2b03" 551 | uuid = "fa939f87-e72e-5be4-a000-7fc836dbe307" 552 | version = "1.3.0" 553 | 554 | [[deps.Pkg]] 555 | deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"] 556 | uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" 557 | version = "1.9.0" 558 | 559 | [[deps.PlutoUI]] 560 | deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"] 561 | git-tree-sha1 = "5bb5129fdd62a2bbbe17c2756932259acf467386" 562 | uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8" 563 | version = "0.7.50" 564 | 565 | [[deps.Preferences]] 566 | deps = ["TOML"] 567 | git-tree-sha1 = "47e5f437cc0e7ef2ce8406ce1e7e24d44915f88d" 568 | uuid = "21216c6a-2e73-6563-6e65-726566657250" 569 | version = "1.3.0" 570 | 571 | [[deps.Printf]] 572 | deps = ["Unicode"] 573 | uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" 574 | 575 | [[deps.Profile]] 576 | deps = ["Printf"] 577 | uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79" 578 | 579 | [[deps.PythonCall]] 580 | deps = ["CondaPkg", "Dates", "Libdl", "MacroTools", "Markdown", "Pkg", "REPL", "Requires", "Serialization", "Tables", "UnsafePointers"] 581 | git-tree-sha1 = "f27dabb05ec811675a9eefe49325a14ae7266b0b" 582 | uuid = "6099a3de-0909-46bc-b1f4-468b9a2dfc0d" 583 | version = "0.9.12" 584 | 585 | [[deps.REPL]] 586 | deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"] 587 | uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb" 588 | 589 | [[deps.Random]] 590 | deps = ["SHA", "Serialization"] 591 | uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" 592 | 593 | [[deps.Reexport]] 594 | git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b" 595 | uuid = "189a3867-3050-52da-a836-e630ba90ab69" 596 | version = "1.2.2" 597 | 598 | [[deps.Requires]] 599 | deps = ["UUIDs"] 600 | git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7" 601 | uuid = "ae029012-a4dd-5104-9daa-d747884805df" 602 | version = "1.3.0" 603 | 604 | [[deps.SHA]] 605 | uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" 606 | version = "0.7.0" 607 | 608 | [[deps.Scratch]] 609 | deps = ["Dates"] 610 | git-tree-sha1 = "30449ee12237627992a99d5e30ae63e4d78cd24a" 611 | uuid = "6c6a2e73-6563-6170-7368-637461726353" 612 | version = "1.2.0" 613 | 614 | [[deps.Serialization]] 615 | uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" 616 | 617 | [[deps.SnoopPrecompile]] 618 | deps = ["Preferences"] 619 | git-tree-sha1 = "e760a70afdcd461cf01a575947738d359234665c" 620 | uuid = "66db9d55-30c0-4569-8b51-7e840670fc0c" 621 | version = "1.0.3" 622 | 623 | [[deps.Sockets]] 624 | uuid = "6462fe0b-24de-5631-8697-dd941f90decc" 625 | 626 | [[deps.SparseArrays]] 627 | deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"] 628 | uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" 629 | 630 | [[deps.Statistics]] 631 | deps = ["LinearAlgebra", "SparseArrays"] 632 | uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" 633 | version = "1.9.0" 634 | 635 | [[deps.StructTypes]] 636 | deps = ["Dates", "UUIDs"] 637 | git-tree-sha1 = "ca4bccb03acf9faaf4137a9abc1881ed1841aa70" 638 | uuid = "856f2bd8-1eba-4b0a-8007-ebc267875bd4" 639 | version = "1.10.0" 640 | 641 | [[deps.SuiteSparse_jll]] 642 | deps = ["Artifacts", "Libdl", "Pkg", "libblastrampoline_jll"] 643 | uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c" 644 | version = "5.10.1+6" 645 | 646 | [[deps.TOML]] 647 | deps = ["Dates"] 648 | uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76" 649 | version = "1.0.3" 650 | 651 | [[deps.TableTraits]] 652 | deps = ["IteratorInterfaceExtensions"] 653 | git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39" 654 | uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c" 655 | version = "1.0.1" 656 | 657 | [[deps.Tables]] 658 | deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits", "Test"] 659 | git-tree-sha1 = "1544b926975372da01227b382066ab70e574a3ec" 660 | uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c" 661 | version = "1.10.1" 662 | 663 | [[deps.Tar]] 664 | deps = ["ArgTools", "SHA"] 665 | uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e" 666 | version = "1.10.0" 667 | 668 | [[deps.Test]] 669 | deps = ["InteractiveUtils", "Logging", "Random", "Serialization"] 670 | uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" 671 | 672 | [[deps.Tricks]] 673 | git-tree-sha1 = "aadb748be58b492045b4f56166b5188aa63ce549" 674 | uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775" 675 | version = "0.1.7" 676 | 677 | [[deps.URIs]] 678 | git-tree-sha1 = "074f993b0ca030848b897beff716d93aca60f06a" 679 | uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4" 680 | version = "1.4.2" 681 | 682 | [[deps.UUIDs]] 683 | deps = ["Random", "SHA"] 684 | uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" 685 | 686 | [[deps.Unicode]] 687 | uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" 688 | 689 | [[deps.UnsafePointers]] 690 | git-tree-sha1 = "c81331b3b2e60a982be57c046ec91f599ede674a" 691 | uuid = "e17b2a0c-0bdf-430a-bd0c-3a23cae4ff39" 692 | version = "1.0.0" 693 | 694 | [[deps.Zlib_jll]] 695 | deps = ["Libdl"] 696 | uuid = "83775a58-1f1d-513f-b197-d71354ab007a" 697 | version = "1.2.13+0" 698 | 699 | [[deps.libblastrampoline_jll]] 700 | deps = ["Artifacts", "Libdl"] 701 | uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" 702 | version = "5.4.0+0" 703 | 704 | [[deps.micromamba_jll]] 705 | deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl"] 706 | git-tree-sha1 = "087555b0405ed6adf526cef22b6931606b5af8ac" 707 | uuid = "f8abcde7-e9b7-5caa-b8af-a437887ae8e4" 708 | version = "1.4.1+0" 709 | 710 | [[deps.nghttp2_jll]] 711 | deps = ["Artifacts", "Libdl"] 712 | uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" 713 | version = "1.48.0+0" 714 | 715 | [[deps.p7zip_jll]] 716 | deps = ["Artifacts", "Libdl"] 717 | uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" 718 | version = "17.4.0+0" 719 | """ 720 | 721 | # ╔═╡ Cell order: 722 | # ╠═2ec32c9d-0216-48a8-848d-79f7cc84798e 723 | # ╟─701dfc92-4891-477b-9e15-8083f8ca5531 724 | # ╠═0c3000cf-46d3-4481-9d6d-61980443dd93 725 | # ╠═9ec34d03-e9e6-460c-bc8b-39b70b6b8a37 726 | # ╠═a7e70b41-9184-4127-b66f-dfc03b8b3004 727 | # ╠═35b7dcfe-717f-48b0-bd4f-4c72f880a229 728 | # ╠═6cc6e9a2-4409-4ad1-b8d1-be0826fe9592 729 | # ╠═a2a174b8-28d0-461f-97c6-8364ccada6c4 730 | # ╠═f1c1eae7-102f-4ca3-9fd2-d81529ada0a3 731 | # ╠═caa805be-6c98-4b59-8404-c0db284c58e9 732 | # ╠═e692876e-72eb-4a19-a0b9-367ab3e84783 733 | # 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╠═92e7af60-0566-4769-b90c-e0abbb2b2f76 755 | # ╠═c9d2f737-c034-4394-b18b-70e9f9ec28ea 756 | # ╠═83d904d3-cdfe-499b-bfaa-c2ae643526a7 757 | # ╠═0a1ad6b8-f848-4147-a4aa-b4edc0caa42b 758 | # ╟─01dd7234-f600-4597-b372-049e000ced1b 759 | # ╠═a3575bea-e521-47e1-9167-62e999728786 760 | # ╟─00000000-0000-0000-0000-000000000001 761 | # ╟─00000000-0000-0000-0000-000000000002 762 | -------------------------------------------------------------------------------- /simulated-annealing/notebook.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/CodingThrust/CodingClub/d6acc0c44858c5a2c0f6d0b81beaa2e85144a91c/simulated-annealing/notebook.pdf -------------------------------------------------------------------------------- /simulated-annealing/programs/fsa.f90: -------------------------------------------------------------------------------- 1 | ! initialize a random seed from the system clock at every run (fortran 95 code) 2 | subroutine init_random_seed() 3 | INTEGER :: i, n, clock 4 | INTEGER, DIMENSION(:), ALLOCATABLE :: seed 5 | 6 | CALL RANDOM_SEED(size = n) 7 | ALLOCATE(seed(n)) 8 | CALL SYSTEM_CLOCK(COUNT=clock) 9 | seed = clock + 37 * (/ (i - 1, i = 1, n) /) 10 | CALL RANDOM_SEED(PUT = seed) 11 | DEALLOCATE(seed) 12 | end subroutine init_random_seed 13 | 14 | !Perform Simulated Annealing using Metropolis updates for the single run. 15 | ! 16 | !Parameters: 17 | ! :ann: , the app. 18 | ! :initial_config: config, 19 | ! :tempscales: 1D array, the time scale from high temperature to low temperature. 20 | ! 21 | !Return: 22 | ! (minimum cost, optimal configuration) 23 | subroutine anneal_singlerun(config,field,opt_cost,opt_config) 24 | use problem 25 | implicit none 26 | integer,intent(inout) :: config(num_spin) 27 | real,intent(inout) :: field(num_spin) 28 | integer :: it,ispin,m 29 | real :: cost,delta 30 | real :: uni01(nms),beta 31 | integer,intent(out) :: opt_config(num_spin) 32 | real,intent(out) :: opt_cost 33 | 34 | opt_config=config 35 | call get_cost(config,cost) 36 | opt_cost=cost 37 | 38 | do it=1,num_tempscales 39 | beta=1/tempscales(it) 40 | call random_number(uni01) 41 | do m=1,nms 42 | call propose(config,field,ispin,delta) 43 | if(exp(-beta*delta)>uni01(m)) then !accept 44 | call accept(ispin,config,field) 45 | cost=cost+delta 46 | if(cost, the app. 71 | :initial_state: state, 72 | :tempscales: 1D array, the time scale from high temperature to low temperature. 73 | :nms: int, the number of Monte Carlo updates in each time scale. 74 | 75 | Return: 76 | (minimum cost, optimal configuration) 77 | ''' 78 | state=initial_state 79 | opt_state=copy.deepcopy(initial_state) 80 | opt_cost=cost=ann.get_cost(state) 81 | for T in tempscales: 82 | uni01=random.random(nms) 83 | beta=1./T 84 | for m in range(nms): 85 | info,dE=ann.propose(state) 86 | if exp(-beta*dE)>uni01[m]: #accept 87 | state=ann.accept((info,dE),state) 88 | cost+=dE 89 | if cost, the app. 99 | :tempscales: 1D array, the time scale from high temperature to low temperature. 100 | :nrun: int, the number of runs. 101 | :nms: int, the number of Monte Carlo updates in each time scale. 102 | 103 | Return: 104 | (minimum cost, optimal configuration) 105 | ''' 106 | opt_cost=Inf 107 | for r in range(nrun): 108 | t0=time.time() 109 | initial_state=ann.get_random_state() 110 | cost,state=anneal_singlerun(ann,initial_state,tempscales,nms=nms) 111 | if cost %s'%(r,cost,t1-t0)) 116 | return opt_cost,opt_state 117 | 118 | ''' 119 | Flexible way to construct . 120 | 121 | e.g. sap(get_cost,propose,accept,get_random_state) 122 | ''' 123 | sap=namedtuple('SAP','get_cost propose accept get_random_state') 124 | -------------------------------------------------------------------------------- /simulated-annealing/programs/testsa.py: -------------------------------------------------------------------------------- 1 | ''' 2 | Tests for nrg. 3 | ''' 4 | from numpy import * 5 | from numpy.testing import dec,assert_,assert_raises,assert_almost_equal,assert_allclose 6 | from scipy.sparse import coo_matrix 7 | import pdb,sys 8 | 9 | from sa import SAP,anneal 10 | 11 | class CC(SAP): 12 | def __init__(self,J): 13 | self.J=J 14 | 15 | def get_cost(self,state): 16 | config=state[0] 17 | return (self.J*config[:,newaxis]*config).sum() 18 | 19 | def propose(self,state): 20 | config,field=state 21 | N=len(self.J) 22 | i = random.randint(N) 23 | dE=-field[i]*config[i]*4 #2 for spin change, 2 for mutual energy. 24 | return i,dE 25 | 26 | def accept(self,proposal,state): 27 | i,dE=proposal 28 | config,field=state 29 | config[i]*=-1 30 | #update field 31 | ci=config[i] 32 | field+=(2*ci)*self.J[:,i] 33 | return (config,field) 34 | 35 | def get_random_state(self): 36 | config=sign(random.random(len(self.J))-0.5) 37 | field=self.J.dot(config) 38 | return (config,field) 39 | 40 | def test_codec(): 41 | #run a simple test: code challenge 42 | N=300 43 | import os 44 | dirname = os.path.dirname(__file__) 45 | data=loadtxt(os.path.join(dirname, 'example.txt')) 46 | J=coo_matrix((data[:,2],(data[:,0],data[:,1])),shape=(N,N),dtype='int32').toarray() 47 | J=(J+J.T)/2. 48 | cc=CC(J) 49 | Emin,Config=anneal(cc,tempscales=linspace(10,0.6,51),nms=4000,nrun=30) 50 | assert_(Emin==-3858 and cc.get_cost(Config)==Emin) 51 | 52 | if __name__=='__main__': 53 | test_codec() 54 | --------------------------------------------------------------------------------