### A Pluto.jl notebook ### # v0.19.46 using Markdown using InteractiveUtils # 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). macro bind(def, element) quote local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end local el = $(esc(element)) global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) el end end # ╔═╡ 9c61c9d5-0d3d-47b7-8e7d-f929cfec3311 begin # using LaTeXStrings using JuMP using Plots using Ipopt using GLPK using Distributions using Statistics using OrderedCollections using LinearAlgebra using Test using NLopt using PlutoUI end # ╔═╡ aa1f0719-5e1d-4294-815e-349d1cebc004 html""" """ # ╔═╡ aae2e545-198c-42bb-9e97-6d6635bee02a html"" # ╔═╡ 4468041e-4472-11ec-16b7-553f4def2b18 md""" # Constraints Recall our core optimization problem: $$\min_{x\in\mathbb{R}^n} f(x) \text{ s.t. } x \in \mathcal{X}$$ * Up to now, the feasible set was $\mathcal{X} \in \mathbb{R}^n$. * In **constrained problems** $\mathcal{X}$ is a subset thereof. * We already encountered *box constraints*, e.g. $x \in [a,b]$. * Sometimes the contrained solution coincides with the unconstrained one, sometimes it does not. * There are *equality constraints* and *inequality constraints*. """ # ╔═╡ e66005ad-1f51-462a-9329-d77f7695cbfc md""" ## Lagrange Multipliers * Used to optimize a function subject to equality constraints. $$\begin{aligned} \min_x & f(x) \\ \text{subject to } & h(x) = 0 \end{aligned}$$ where both $f$ and $h$ have continuous partial derivatives. * We look for contour lines of $f$ that are aligned to contours of $h(x) = 0$. In other words, we want to find the best $x$ s.t. $h(x) = 0$ and we have $$\nabla f(x) = \lambda \nabla h(x)$$ for some *Lagrange Mutliplier* $\lambda$ * Notice that we need the scalar $\lambda$ because the magnitudes of the gradients may be different. * We therefore form the the **Lagrangian**: $$\mathcal{L}(x,\lambda) = f(x) - \lambda h(x)$$ """ # ╔═╡ 5bc7c8ce-3a4a-4505-a2fa-2b25f041437a md""" ## Example Suppose we have $$\begin{align} \min_x & -\exp\left( -\left( x_1 x_2 - \frac{3}{2} \right)^2 - \left(x_2 - \frac{3}{2}\right)^2 \right) \\ \text{subject to } & x_1 - x_2^2 = 0 \end{align}$$ We form the Lagrangiagn: $$\mathcal{L}(x_1,x_2,\lambda) = -\exp\left( -\left( x_1 x_2 - \frac{3}{2} \right)^2 - \left(x_2 - \frac{3}{2}\right)^2 \right) - \lambda(x_1 - x_2^2)$$ Then we compute the gradient wrt to $x_1,x_2,\lambda$, set to zero and solve. """ # ╔═╡ 9a92426e-bc9a-4ead-a93c-ec1c3f23ca57 begin f(x1,x2) = -exp.(-(x1.*x2 - 3/2).^2 - (x2-3/2).^2) c(z) = sqrt(z) x=0:0.01:3.5 end # ╔═╡ d7acef71-fe0d-4062-9342-9061afde1293 let p1 = surface(x,x,(x,y)->f(x,y),xlab = L"x_1", ylab = L"x_2") scatter3d!(p1,[1.358],[1.165],[f(1.358,1.165)],markercolor=:red,leg=false) p2 = contour(x,x,(x,y)->f(x,y),lw=1.5,levels=[collect(0:-0.1:-0.85)...,-0.887,-0.95,-1],xlab = L"x_1", ylab = L"x_2") plot!(p2,c,0.01,3.5,label="",lw=2,color=:black) scatter!(p2,[1.358],[1.165],markersize=5,markercolor=:red,label="Constr. Optimum") plot(p1,p2,size=(900,300)) end # ╔═╡ de879e63-fdc9-486e-9aaa-1a55c32d93d5 md""" * If we had multiple constraints ($l$), we'd just add them up to get $$ \mathcal{L}(\mathbf{x},\mathbf{\lambda}) = f(\mathbf{x}) - \sum_{i=1}^l \lambda_i h_i(\mathbf{x})$$ """ # ╔═╡ 54a17a40-fd67-4040-99b9-d0d460385155 md""" ## Inequality Constraints Suppose now we had $$\begin{align} \min_\mathbf{x} & f(\mathbf{x}) \\ \text{subject to } & g(\mathbf{x}) \leq 0 \end{align}$$ which, if the solution lies *on* the constraint *boundary*, means that $$\nabla f - \mu \nabla g = 0$$ for some scalar $\mu$ - as before. * In this case, we say the **constraint is active**. * In the opposite case, i.e. the solution lies **inside** the contrained region, we way the contraint is **inactive**. * In that case, we are back to an *unconstrained* problem, look for $\nabla f = 0$, and set $\mu=0$. """ # ╔═╡ 9f1f0926-b1b3-4ef3-aebe-277531abfd33 let # the blue area shows the FEASIBLE SET contour(x,x,(x,y)->f(x,y),lw=1.5,levels=[collect(0:-0.1:-0.85)...,-0.887,-0.95,-1], title = "Constraint is Active or Binding") plot!(c,0.01,3.5,label="",lw=2,color=:black,fill=(0,0.5,:blue)) scatter!([1.358],[1.165],markersize=5,markercolor=:red,label="Constr. Optimum") end # ╔═╡ 2f8d4513-0871-48f3-acfb-f7a0254f7b8e let c2(x1) = 1+sqrt(x1) contour(x,x,(x,y)->f(x,y),lw=1.5,levels=[collect(0:-0.1:-0.85)...,-0.887,-0.95,-1], title = "Constraint is Inactive or Slack") plot!(c2,0.01,3.5,label="",lw=2,color=:black,fill=(0,0.5,:blue)) scatter!([1],[1.5],markersize=5,markercolor=:red,label="Unconstr. Optimum") end # ╔═╡ 8901f1e5-f243-4fe7-afda-6cc951b234a5 md""" ## Infinity Step * We could do an **infinite step** to avoid *infeasible points*: $$\begin{align} f_{\infty\text{-step}} &= \begin{cases} f(\mathbf{x}) & \text{if } g(\mathbf{x}) \leq 0 \\ \infty & \text{else. } \end{cases}\\ &= f(\mathbf{x}) + \infty (g(\mathbf{x} > 0) \end{align}$$ * Unfortunately, this is discontinous and non-differentiable, i.e. hard to handle for algorithms. * Instead, we use a *linear penalty* $\mu g(\mathbf{x})$ on the objective if the constraint is violated. """ # ╔═╡ fe6b7d74-1c6f-4253-9254-57d536bb24c5 md""" * The penalty provides a lower bound to $\infty$: $$\mathcal{L}(\mathbf{x},\mu) = f(\mathbf{x}) + \mu g(\mathbf{x})$$ * We can get back the infinite step by maximizing the penalty: $$f_{\infty\text{-step}} = \max_{\mu\geq 0} \mathcal{L}(\mathbf{x},\mu)$$ * Every infeasible $\mathbf{x}$ returns $\infty$, all others return $f(\mathbf{x})$ """ # ╔═╡ 19d12886-3980-4116-8772-2c1d17b14270 md""" ## Kuhn-Karush-Tucker (KKT) * Our problem thus becomes $$\min_\mathbf{x} \max_{\mu\geq 0} \mathcal{L}(\mathbf{x},\mu)$$ * This is called the **primal problem**. Optimizing this requires: 1. Point is feasible.: $g(\mathbf{x}^*) \leq 0$. 2. Penalty goes into the right direction: $\mu \geq 0$. *Dual feasibility*. 3. Feasible point on the boundary: $\mu g(\mathbf{x}^*) = 0$ has $g(\mathbf{x}) = 0$, otherwise $g(\mathbf{x}) < 0$ and $\mu =0$. 4. Active constraint: $\nabla f(\mathbf{x}^*) - \mu \nabla g(\mathbf{x}^*) = 0$. With an active constraint, we want parallel contours of objective and constraint. When inactive, our optimum just has $\nabla f(\mathbf{x}^*) = 0$, which means $\mu = 0$. The preceding four conditions are called the **Kuhn-Karush-Tucker (KKT)** conditions. In the above order, and in general terms, they are: 1. Feasibility 2. Dual Feasibility 3. Complementary Slackness 4. Stationarity. The KKT conditions are the FONCs for problems with smooth constraints. """ # ╔═╡ 583a5640-adde-4f4f-a344-4e77e04e431d md""" ## Duality We can combine equality and inequality constraints: $$\mathcal{L}(\mathbf{x},\mathbf{\lambda},\mathbf{\mu}) = f(\mathbf{x}) + \sum_{i} \lambda_i h_i(\mathbf{x}) + \sum_j \mu_j g_j(\mathbf{x})$$ where, notice, we reverted the sign of $\lambda$ since this is unrestricted. * The Primal problem is identical to the original problem and just as difficult to solve: $$\min_\mathbf{x} \max_{\mathbf{\mu}\geq 0,\mathbf{\lambda}} \mathcal{L}(\mathbf{x},\mathbf{\mu},\mathbf{\lambda})$$ * The Dual problem reverses min and max: $$\max_{\mathbf{\mu}\geq 0,\mathbf{\lambda}} \min_\mathbf{x} \mathcal{L}(\mathbf{x},\mathbf{\mu},\mathbf{\lambda})$$ ### Dual Values * The *max-min-inequality* states that for any function $f(a,b)$ $$\max_\mathbf{a} \min_\mathbf{b} f(\mathbf{a},\mathbf{b}) \leq \min_\mathbf{b} \max_\mathbf{a} f(\mathbf{a},\mathbf{b})$$ * Hence, the solution to the dual is a lower bound to the solution of the primal problem. * The solution to the *dual function*, $\min_\mathbf{x} \mathcal{L}(\mathbf{x},\mathbf{\mu},\mathbf{\lambda})$ is the min of a collection of linear functions, and thus always concave. * It is easy to optimize this. * In general, solving the dual is easy whenever minimizing $\mathcal{L}$ wrt $x$ is easy. """ # ╔═╡ 9be3cbee-7949-42da-9496-6afc94785f98 md""" ## Penalty Methods * We can convert the constrained problem back to unconstrained by adding penalty terms for constraint violoations. * A simple method could just count the number of violations: $$p_\text{count}(\mathbf{x}) = \sum_{i} (h_i(\mathbf{x}) \neq 0 ) + \sum_j (g_j(\mathbf{x} > 0)$$ * and add this to the objective in an *unconstrained* problem with penalty $\rho > 0$ $$\min_\mathbf{x} f(\mathbf{x}) + \rho p_\text{count}(\mathbf{x})$$ * One can choose the penalty function: for example, a quadratic penaly will produce a smooth objective function * Notice that $\rho$ needs to become very large sometimes here. """ # ╔═╡ 91da671d-7602-490c-a94c-bc9ff4eca59a md""" ## Interior Point Method * Also called *barrier method*. * These methods make sure that the search point remains always feasible. * As one approaches the constraint boundary, the barrier function goes to infinity. Properties: 1. continuous: $p_\text{barrier}(\mathbf{x})$ 2. non negative: $p_\text{barrier}(\mathbf{x})$ 3. goes to infinitey : $p_\text{barrier}(\mathbf{x})$ as one approaches the constraint boundary ### Barriers * Inverse Barrier $$p_\text{barrier}(\mathbf{x}) = -\sum_i \frac{1}{g_i(\mathbf{x})}$$ * Log Barrier $$p_\text{barrier}(\mathbf{x}) = -\sum_i \begin{cases}\log(-g_i(\mathbf{x})) & \text{if } g_i(\mathbf{x}) \geq -1 \\ 0& \text{else.} \end{cases}$$ * The approach is as before, one transforms the problem to an unconstrained one and increases $\rho$ until convergence: $$\min_\mathbf{x} f(\mathbf{x}) + \frac{1}{\rho} p_\text{barrier}(\mathbf{x})$$ ### Examples $$\min_{x \in \mathbb{R}^2} \sqrt{x_2} \text{ subject to }\begin{array}{c} \\ x_2 \geq 0 \\ x_2 \geq (a_1 x_1 + b_1)^3 \\ x_2 \geq (a_2 x_1 + b_2)^3 \end{array}$$ ## Constrained Optimisation with [`NLopt.jl`](https://github.com/JuliaOpt/NLopt.jl) * We need to specify one function for each objective and constraint. * Both of those functions need to compute the function value (i.e. objective or constraint) *and* it's respective gradient. * `NLopt` expects contraints **always** to be formulated in the format $$g(x) \leq 0$$ where $g$ is your constraint function * The constraint function is formulated for each constraint at $x$. it returns a number (the value of the constraint at $x$), and it fills out the gradient vector, which is the partial derivative of the current constraint wrt $x$. * There is also the option to have vector valued constraints, see the documentation. * We set this up as follows: """ # ╔═╡ 7e5cedbf-05da-4573-994f-42099fe4b33a begin function objective(x::Vector, grad::Vector) if length(grad) > 0 grad[1] = 0 grad[2] = 0.5/sqrt(x[2]) end sqrt(x[2]) end function constraint(x::Vector, grad::Vector, a, b) if length(grad) > 0 grad[1] = 3a * (a*x[1] + b)^2 grad[2] = -1 end (a*x[1] + b)^3 - x[2] end end # ╔═╡ b1720238-495e-47f7-ae75-866723f5fca4 x -> x^2 # ╔═╡ 1e31dc48-e849-4045-8dcc-d05889f8609b let opt = Opt(:LD_MMA, 2) lower_bounds!(opt, [-Inf, 0.]) xtol_rel!(opt,1e-4) min_objective!(opt, objective) inequality_constraint!(opt, (x,g) -> constraint(x,g,2,0), 1e-8) inequality_constraint!(opt, (x,g) -> constraint(x,g,-1,1), 1e-8) (minfunc,minx,ret) = NLopt.optimize(opt, [1.234, 5.678]) end # ╔═╡ 70893b5f-51e8-4536-b5aa-4e353768bc52 md""" ## NLopt: Rosenbrock * Let's tackle the rosenbrock example again. * To make it more interesting, let's add an inequality constraint. $$\min_{x\in \mathbb{R}^2} (1-x_1)^2 + 100(x_2-x_1^2)^2 \text{ subject to } 0.8 - x_1^2 -x_2^2 \geq 0$$ * in `NLopt` format, the constraint is $x_1^2 + x_2^2 - 0.8 \leq 0$ """ # ╔═╡ 2a74858c-6d13-4961-86fa-125e4c01e232 function rosenbrockf(x::Vector,grad::Vector) if length(grad) > 0 grad[1] = -2.0 * (1.0 - x[1]) - 400.0 * (x[2] - x[1]^2) * x[1] grad[2] = 200.0 * (x[2] - x[1]^2) end return (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2 end # ╔═╡ ec0c21da-c517-4d2e-9832-18eca242621b function r_constraint(x::Vector, grad::Vector; radius = 0.8) if length(grad) > 0 grad[1] = 2*x[1] grad[2] = 2*x[2] end return x[1]^2 + x[2]^2 - radius end # ╔═╡ ade668a5-87d6-40aa-b670-d0cc41148757 md""" radius = $(@bind rad Slider(0.1:0.1:2.0,show_value = true,default = 0.2)) """ # ╔═╡ 52a1ca3b-8a10-4c0a-b4d4-82f995b4b3df let grad = zeros(2) xrange = collect(-2.5:0.01:2) cc = contour(xrange,xrange, (x,y)->sqrt(rosenbrockf([x, y],grad)), fill=false, color=:viridis, ylab = L"x_2",xlab = L"x_1", leg = :topleft,levels = exp.(range(log(0.1), stop = log(70.0), length = 50)), cbar = false) contour!(cc,xrange,xrange,(x,y)->r_constraint([x, y],grad,radius = rad), levels = [0],lw = 3) scatter!(cc,[1],[1],color = :red, lab = "unconstrained optimizer") # let's compute the constrained optimizer now! opt = Opt(:LD_MMA, 2) lower_bounds!(opt, [-5, -5.0]) min_objective!(opt,(x,g) -> rosenbrockf(x,g)) inequality_constraint!(opt, (x,g) -> r_constraint(x,g,radius = rad)) ftol_rel!(opt,1e-9) (minfunc,minx,ret) = NLopt.optimize(opt, [-1.0,0.0]) scatter!(cc, [minx[1]], [minx[2]], label = "constrained optimizer", leg = :topleft) end # ╔═╡ 9cc92292-4531-4f4c-b9b1-2a7a698529ac md""" ## JuMP.jl * Introduce [`JuMP.jl`](https://jump.dev/) * JuMP is a mathematical programming interface for Julia. It is like AMPL, but for free and with a decent programming language. * The main highlights are: * It uses automatic differentiation to compute derivatives from your expression. * It supplies this information, as well as the sparsity structure of the Hessian to your preferred solver. * It decouples your problem completely from the type of solver you are using. This is great, since you don't have to worry about different solvers having different interfaces. * In order to achieve this, `JuMP` uses [`MathProgBase.jl`](https://github.com/JuliaOpt/MathProgBase.jl), which converts your problem formulation into a standard representation of an optimization problem. * Let's look at the readme * The technical citation is Lubin et al """ # ╔═╡ fc75bc7b-0fe0-4f90-a425-6ed6e63acb4a let model = Model(GLPK.Optimizer) @variable(model, 0 <= x <= 2) @variable(model, 0 <= y <= 30) # next, we set an objective function @objective(model, Max, 5x + 3 * y) # maybe add a constraint called "con"? @constraint(model, con, 1x + 5y <= 3) #At this stage JuMP has a mathematical representation of our model internalized #The MathProgBase machinery knows now exactly how to translate that to different solver interfaces #For us the only thing left: hit the button! JuMP.optimize!(model) (termination_status(model),value(x),value(y)) end # ╔═╡ 2d7bdf41-85fc-4d0c-a387-60f9c9b36fcb # JuMP: nonlinear Rosenbrock Example # Instead of hand-coding first and second derivatives, you only have to give `JuMP` expressions for objective and constraints. # Here is an example. let m = Model(Ipopt.Optimizer) @variable(m, x) @variable(m, y) @NLobjective(m, Min, (1-x)^2 + 100(y-x^2)^2) @constraint(m, x + y <= 1.5) JuMP.optimize!(m) (termination_status(m),value(x),value(y)) end # ╔═╡ 3ba47370-c4df-4d22-8bda-0b7264927ae6 md""" ## JuMP: Maximium Likelihood * Let's redo the maximum likelihood example in JuMP. * Let $\mu,\sigma^2$ be the unknown mean and variance of a random sample generated from the normal distribution. * Find the maximum likelihood estimator for those parameters! * density: $$f(x_i|\mu,\sigma^2) = \frac{1}{\sigma \sqrt{2\pi}} \exp\left(-\frac{(x_i - \mu)^2}{2\sigma^2}\right)$$ * Likelihood Function $$\begin{aligned} L(\mu,\sigma^2) = \Pi_{i=1}^N f(x_i|\mu,\sigma^2) =& \frac{1}{(\sigma \sqrt{2\pi})^n} \exp\left(-\frac{1}{2\sigma^2} \sum_{i=1}^N (x_i-\mu)^2 \right) \\ =& \left(\sigma^2 2\pi\right)^{-\frac{n}{2}} \exp\left(-\frac{1}{2\sigma^2} \sum_{i=1}^N (x_i-\mu)^2 \right) \end{aligned}$$ * Constraints: $\mu\in \mathbb{R},\sigma>0$ * log-likelihood: $$\log L = l = -\frac{n}{2} \log \left( 2\pi \sigma^2 \right) - \frac{1}{2\sigma^2} \sum_{i=1}^N (x_i-\mu)^2$$ """ # ╔═╡ 84b81d87-d015-4cc2-8649-c94ba7770bd9 let distrib = Normal(4.5,3.5) n = 10000 data = rand(distrib,n); m = Model(Ipopt.Optimizer) set_optimizer_attribute(m, MOI.Silent(), true) @variable(m, μ, start = 0.0) @variable(m, σ >= 0.0, start = 1.0) # notice bound constraint @NLobjective(m, Max, -(n/2) * log(2π * σ^2) - sum( (data[i] - μ)^2 for i = 1:n)/(2 * σ^2) ) JuMP.optimize!(m) md""" parameter | data (truth) | estimate -------- | ------------ | -------- μ | $(value(μ)) | $(mean(data)) σ | $(value(σ)) | $(std(data)) """ end # ╔═╡ 061de138-b6fe-4437-aa26-0afaec2e66f0 md""" # Linear Constrained Problems (LPs) * Very similar to before, just that both objective and constraints are *linear*. $$\begin{align} \min_\mathbf{x} & \mathbf{c}^T \mathbf{x}\\ \text{subject to } & \mathbf{w}_{LE}^{(i)T} \mathbf{x} \leq b_i \text{ for }i\in{1,2,3,\dots}\\ & \mathbf{w}_{GE}^{(j)T} \mathbf{x} \geq b_j \text{ for }j\in{1,2,3,\dots}\\ & \mathbf{w}_{EQ}^{(k)T} \mathbf{x} = b_k \text{ for }k\in{1,2,3,\dots}\\ \end{align}$$ * Our initial JuMP example was of that sort. ## A Cannery Problem * A can factory (a cannery) has plants in Seattle and San Diego * They need to decide how to serve markets New-York, Chicago, Topeka * Firm wants to 1. minimize shipping costs 2. shipments cannot exceed capacity 3. shipments must satisfy demand * Formalize that! * Plant capacity $cap_i$, demands $d_j$ and transport costs from plant $i$ to market $j$, $dist_{i,j} c$ are all given. * Let $\mathbf{x}$ be a matrix with element $x_{i,j}$ for number of cans shipped from $i$ to $j$. ## From Maths ... $$\begin{align} \min_\mathbf{x} & \sum_{i=1}^2 \sum_{j=1}^3 dist_{i,j}c \times x_{i,j}\\ \text{subject to } & \sum_{j=1}^3 x(i,j) \leq cap_i , \forall i \\ & \sum_{i=1}^2 x(i,j) \geq d_j , \forall j \end{align}$$ ## ... to `JuMP` """ # ╔═╡ febc5df1-4ddd-48a7-94f8-251d316c72d0 # ... to JuMP # https://github.com/JuliaOpt/JuMP.jl/blob/release-0.19/examples/cannery.jl # Copyright 2017, Iain Dunning, Joey Huchette, Miles Lubin, and contributors # This Source Code Form is subject to the terms of the Mozilla Public # License, v. 2.0. If a copy of the MPL was not distributed with this # file, You can obtain one at http://mozilla.org/MPL/2.0/. ############################################################################# # JuMP # An algebraic modeling language for Julia # See http://github.com/JuliaOpt/JuMP.jl ############################################################################# """ example_cannery(; verbose = true) JuMP implementation of the cannery problem from Dantzig, Linear Programming and Extensions, Princeton University Press, Princeton, NJ, 1963. Author: Louis Luangkesorn Date: January 30, 2015 """ function example_cannery(; verbose = true) plants = ["Seattle", "San-Diego"] markets = ["New-York", "Chicago", "Topeka"] # Capacity and demand in cases. capacity = [350, 600] demand = [300, 300, 300] # Distance in thousand miles. distance = [2.5 1.7 1.8; 2.5 1.8 1.4] # Cost per case per thousand miles. freight = 90 num_plants = length(plants) num_markets = length(markets) cannery = Model(GLPK.Optimizer) @variable(cannery, ship[1:num_plants, 1:num_markets] >= 0) # Ship no more than plant capacity @constraint(cannery, capacity_con[i in 1:num_plants], sum(ship[i,j] for j in 1:num_markets) <= capacity[i] ) # Ship at least market demand @constraint(cannery, demand_con[j in 1:num_markets], sum(ship[i,j] for i in 1:num_plants) >= demand[j] ) # Minimize transporatation cost @objective(cannery, Min, sum(distance[i, j] * freight * ship[i, j] for i in 1:num_plants, j in 1:num_markets) ) JuMP.optimize!(cannery) if verbose println("RESULTS:") for i in 1:num_plants for j in 1:num_markets println(" $(plants[i]) $(markets[j]) = $(JuMP.value(ship[i, j]))") end end end @test JuMP.termination_status(cannery) == MOI.OPTIMAL @test JuMP.primal_status(cannery) == MOI.FEASIBLE_POINT @test JuMP.objective_value(cannery) == 151200.0 end # ╔═╡ 1334fc66-23bb-4a9a-9534-6f4d7a88d235 example_cannery() # ╔═╡ 520c3423-01d4-4794-893c-f7e5546d26f6 md""" # Discrete Optimization / Integer Programming * Here the choice variable is contrained to come from a discrete set $\mathcal{X}$. * If this set is $\mathcal{X} = \mathbb{N}$, we have an **integer program** * If only *some* $x$ have to be discrete, this is a **mixed integer program** ## Example $$\begin{align} \min_\mathbf{x} & x_1 + x_2\\ \text{subject to } & ||\mathbf{x}|| \leq 2\\ \text{and } & \mathbf{x} \in \mathbb{N} \end{align}$$ * continuous optimum is $(-\sqrt{2},-\sqrt{2})$ and objective is $y=-2\sqrt{2}=-2.828$ * Integer constrained problem is only delivering $y=-2$, and $\mathbf{x}^*\in \{(-2,0),(-1,-1),(0,-2)\}$ """ # ╔═╡ ee374307-043c-473d-b561-192718ea612b let x = -3:0.01:3 dx = repeat(range(-3,stop = 3, length = 7),1,7) contourf(x,x,(x,y)->x+y,color=:heat) scatter!(dx,dx',legend=false,markercolor=:white) plot!(x->sqrt(4-x^2),-2,2,c=:white) plot!(x->-sqrt(4-x^2),-2,2,c=:white) scatter!([-2,-1,0],[0,-1,-2],c=:red) scatter!([-sqrt(2)],[-sqrt(2)],c=:red,markershape=:cross,markersize=11) end # ╔═╡ 636f7fe1-a518-4f09-bdbd-bcb79703dda5 md""" ## Rounding * One solution is to just *round the continuous solution to the nearest integer* * We compute the **relaxed** problem, i.e. the one where $x$ is continuous. * Then we round up or down. * Can go terribly wrong. ## Cutting Planes * This is an exact method * We solve the relaxed problem first. * Then we add linear constraints that result in the solution becoming integral. ## Branch and Bound * This enumerates all possible soultions. * Branch and bound does this, without having to compute all of them. """ # ╔═╡ 2fcf8444-202a-453a-af28-0eade00e3981 md""" ## Example: The Knapsack Problem * We are packing our knapsack for a trip but only have space for the most valuable items. * We have $x_i=0$ if item $i$ is not in the sack, 1 else. $$\begin{align} \max_x & \sum_{i=1}^n v_i x_i \\ \text{s.t. } & \sum_{i=1}^n w_i x_i \leq w_{max} \\ w_i \in \mathbb{N}_+, & v_i \in \mathbb{R} \end{align}$$ * If there are $n$ items, we have $2^n$ possible design vectors. * But there is a useful recursive relationship. * If we solved $n-1$ knapsack problems so far and deliberate about item $n$ * If it's not worth including item $n$, then the solution **is** the knapsack problem for $n-1$ items and capacity $w_{\max}$ * If it IS worth including it: solution will have value of knapsack with $n-1$ items and reduced capacity, plus the value of the new item * This is dynamic progamming. """ # ╔═╡ 3f231741-12f6-4426-8d46-b6cfe623a248 (1:10).^2 # ╔═╡ 8eef8fc6-2272-46ff-a5ab-b2a4e63d9b7a let n , w , v , W = 5, [ 2, 8, 4, 2, 5 ] , [ 5, 3, 2, 7, 4 ] , 10 m = zeros(n,W+1) # m[i,j] is value of including i if capacity is j for i in 1:n for (jx,jw) in enumerate(0:W) # if current capacity is if w[i] > jw m[i,jx] = i == 1 ? 0.0 : m[i-1,jx] # if weight exceeds current capacity, value of problem is identical to value of problem without the i-th item at that capacity. else # weight is feasible to add: should we add it? m[i,jx] = i == 1 ? v[i] : max(m[i-1,jx], m[i-1, jx - jw] + v[i]) end end end m end # ╔═╡ b1f21cfe-ebc2-4321-9636-49739568a7de md""" ...or, a bit more elegant: """ # ╔═╡ b175638b-db07-41c5-a409-f7814d14dc42 let # Maximization problem m = Model(GLPK.Optimizer) set_optimizer_attribute(m, MOI.Silent(), true) @variable(m, x[1:5], Bin) profit = [ 5, 3, 2, 7, 4 ] weight = [ 2, 8, 4, 2, 5 ] capacity = 10 # Objective: maximize profit @objective(m, Max, dot(profit, x)) # Constraint: can carry all @constraint(m, dot(weight, x) <= capacity) # Solve problem using MIP solver JuMP.optimize!(m) OrderedDict( i => Dict(:included => convert(Bool,JuMP.value(x[i])), :profit_over_weight => profit[i]/weight[i]) for i in 1:5 ) end # ╔═╡ 9644fbd5-298c-4041-822b-1b44917b2c41 begin danger(head,text) = Markdown.MD(Markdown.Admonition("danger", head, [text])); danger(text) = Markdown.MD(Markdown.Admonition("danger", "Attention", [text])); info(text) = Markdown.MD(Markdown.Admonition("info", "Info", [text])); tip(text) = Markdown.MD(Markdown.Admonition("tip", "Tip", [text])); midbreak = html"


"; end # ╔═╡ 9cb9f9cc-fe89-44c3-8115-6a5c48b58ca0 midbreak # ╔═╡ 7f033067-2216-4532-baa3-6d099bbfc034 sb = md""" # """ # ╔═╡ c5f6d941-7161-44bb-8ec8-8644636234c0 sb # ╔═╡ 00000000-0000-0000-0000-000000000001 PLUTO_PROJECT_TOML_CONTENTS = """ [deps] Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" GLPK = "60bf3e95-4087-53dc-ae20-288a0d20c6a6" Ipopt = "b6b21f68-93f8-5de0-b562-5493be1d77c9" JuMP = "4076af6c-e467-56ae-b986-b466b2749572" LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" NLopt = "76087f3c-5699-56af-9a33-bf431cd00edd" OrderedCollections = "bac558e1-5e72-5ebc-8fee-abe8a469f55d" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [compat] Distributions = "~0.25.86" GLPK = "~1.1.1" Ipopt = "~1.2.0" JuMP = "~1.9.0" LaTeXStrings = "~1.3.0" NLopt = "~0.6.5" OrderedCollections = "~1.4.1" Plots = "~1.38.8" PlutoUI = "~0.7.58" """ # ╔═╡ 00000000-0000-0000-0000-000000000002 PLUTO_MANIFEST_TOML_CONTENTS = """ # This file is machine-generated - editing it directly is not advised julia_version = "1.11.0" manifest_format = "2.0" project_hash = "20712d38f49755ba31fe87c1b65533bd1f841cf6" [[deps.ASL_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "6252039f98492252f9e47c312c8ffda0e3b9e78d" uuid = "ae81ac8f-d209-56e5-92de-9978fef736f9" version = "0.1.3+0" [[deps.AbstractPlutoDingetjes]] deps = ["Pkg"] git-tree-sha1 = "6e1d2a35f2f90a4bc7c2ed98079b2ba09c35b83a" uuid = "6e696c72-6542-2067-7265-42206c756150" version = "1.3.2" [[deps.AliasTables]] deps = ["PtrArrays", "Random"] git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff" uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8" version = "1.1.3" [[deps.ArgTools]] uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" version = "1.1.2" [[deps.Artifacts]] uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" version = "1.11.0" [[deps.Base64]] uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" version = "1.11.0" [[deps.BenchmarkTools]] deps = ["JSON", "Logging", "Printf", "Profile", "Statistics", "UUIDs"] git-tree-sha1 = "f1dff6729bc61f4d49e140da1af55dcd1ac97b2f" uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" version = "1.5.0" [[deps.BitFlags]] git-tree-sha1 = "0691e34b3bb8be9307330f88d1a3c3f25466c24d" uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35" version = "0.1.9" [[deps.Bzip2_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd" uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0" version = "1.0.8+1" [[deps.Cairo_jll]] deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] git-tree-sha1 = "009060c9a6168704143100f36ab08f06c2af4642" uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" version = "1.18.2+1" [[deps.CodecBzip2]] deps = ["Bzip2_jll", "TranscodingStreams"] git-tree-sha1 = "e7c529cc31bb85b97631b922fa2e6baf246f5905" uuid = "523fee87-0ab8-5b00-afb7-3ecf72e48cfd" version = "0.8.4" [[deps.CodecZlib]] deps = ["TranscodingStreams", "Zlib_jll"] git-tree-sha1 = "bce6804e5e6044c6daab27bb533d1295e4a2e759" uuid = "944b1d66-785c-5afd-91f1-9de20f533193" version = "0.7.6" [[deps.ColorSchemes]] deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"] git-tree-sha1 = "b5278586822443594ff615963b0c09755771b3e0" uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4" version = "3.26.0" [[deps.ColorTypes]] deps = ["FixedPointNumbers", "Random"] git-tree-sha1 = "b10d0b65641d57b8b4d5e234446582de5047050d" uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f" version = "0.11.5" [[deps.ColorVectorSpace]] deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"] git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249" uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4" version = "0.10.0" weakdeps = ["SpecialFunctions"] [deps.ColorVectorSpace.extensions] SpecialFunctionsExt = "SpecialFunctions" [[deps.Colors]] deps = ["ColorTypes", "FixedPointNumbers", "Reexport"] git-tree-sha1 = "362a287c3aa50601b0bc359053d5c2468f0e7ce0" uuid = "5ae59095-9a9b-59fe-a467-6f913c188581" version = "0.12.11" [[deps.CommonSubexpressions]] deps = ["MacroTools"] git-tree-sha1 = "cda2cfaebb4be89c9084adaca7dd7333369715c5" uuid = "bbf7d656-a473-5ed7-a52c-81e309532950" version = "0.3.1" [[deps.Compat]] deps = ["TOML", "UUIDs"] git-tree-sha1 = "8ae8d32e09f0dcf42a36b90d4e17f5dd2e4c4215" uuid = "34da2185-b29b-5c13-b0c7-acf172513d20" version = "4.16.0" weakdeps = ["Dates", "LinearAlgebra"] [deps.Compat.extensions] CompatLinearAlgebraExt = "LinearAlgebra" [[deps.CompilerSupportLibraries_jll]] deps = ["Artifacts", "Libdl"] uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" version = "1.1.1+0" [[deps.ConcurrentUtilities]] deps = ["Serialization", "Sockets"] git-tree-sha1 = "ea32b83ca4fefa1768dc84e504cc0a94fb1ab8d1" uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb" version = "2.4.2" [[deps.Contour]] git-tree-sha1 = "439e35b0b36e2e5881738abc8857bd92ad6ff9a8" uuid = "d38c429a-6771-53c6-b99e-75d170b6e991" version = "0.6.3" [[deps.DataAPI]] git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe" uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a" version = "1.16.0" [[deps.DataStructures]] deps = ["Compat", "InteractiveUtils", "OrderedCollections"] git-tree-sha1 = "1d0a14036acb104d9e89698bd408f63ab58cdc82" uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8" version = "0.18.20" [[deps.Dates]] deps = ["Printf"] uuid = "ade2ca70-3891-5945-98fb-dc099432e06a" version = "1.11.0" [[deps.Dbus_jll]] deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl"] git-tree-sha1 = "fc173b380865f70627d7dd1190dc2fce6cc105af" uuid = "ee1fde0b-3d02-5ea6-8484-8dfef6360eab" version = "1.14.10+0" [[deps.DelimitedFiles]] deps = ["Mmap"] git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae" uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab" version = "1.9.1" [[deps.DiffResults]] deps = ["StaticArraysCore"] git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621" uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5" version = "1.1.0" [[deps.DiffRules]] deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"] git-tree-sha1 = "23163d55f885173722d1e4cf0f6110cdbaf7e272" uuid = "b552c78f-8df3-52c6-915a-8e097449b14b" version = "1.15.1" [[deps.Distributions]] deps = ["AliasTables", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SpecialFunctions", "Statistics", "StatsAPI", "StatsBase", "StatsFuns"] git-tree-sha1 = "d7477ecdafb813ddee2ae727afa94e9dcb5f3fb0" uuid = "31c24e10-a181-5473-b8eb-7969acd0382f" version = "0.25.112" [deps.Distributions.extensions] DistributionsChainRulesCoreExt = "ChainRulesCore" DistributionsDensityInterfaceExt = "DensityInterface" DistributionsTestExt = "Test" [deps.Distributions.weakdeps] ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" DensityInterface = "b429d917-457f-4dbc-8f4c-0cc954292b1d" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [[deps.DocStringExtensions]] deps = ["LibGit2"] git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d" uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" version = "0.9.3" [[deps.Downloads]] deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"] uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6" version = "1.6.0" [[deps.EpollShim_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "8e9441ee83492030ace98f9789a654a6d0b1f643" uuid = "2702e6a9-849d-5ed8-8c21-79e8b8f9ee43" version = "0.0.20230411+0" [[deps.ExceptionUnwrapping]] deps = ["Test"] git-tree-sha1 = "dcb08a0d93ec0b1cdc4af184b26b591e9695423a" uuid = "460bff9d-24e4-43bc-9d9f-a8973cb893f4" version = "0.1.10" [[deps.Expat_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "1c6317308b9dc757616f0b5cb379db10494443a7" uuid = "2e619515-83b5-522b-bb60-26c02a35a201" version = "2.6.2+0" [[deps.FFMPEG]] deps = ["FFMPEG_jll"] git-tree-sha1 = "53ebe7511fa11d33bec688a9178fac4e49eeee00" uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a" version = "0.4.2" [[deps.FFMPEG_jll]] deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"] git-tree-sha1 = "466d45dc38e15794ec7d5d63ec03d776a9aff36e" uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5" version = "4.4.4+1" [[deps.FileWatching]] uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee" version = "1.11.0" [[deps.FillArrays]] deps = ["LinearAlgebra"] git-tree-sha1 = "6a70198746448456524cb442b8af316927ff3e1a" uuid = "1a297f60-69ca-5386-bcde-b61e274b549b" version = "1.13.0" weakdeps = ["PDMats", "SparseArrays", "Statistics"] [deps.FillArrays.extensions] FillArraysPDMatsExt = "PDMats" FillArraysSparseArraysExt = "SparseArrays" FillArraysStatisticsExt = "Statistics" [[deps.FixedPointNumbers]] deps = ["Statistics"] git-tree-sha1 = "05882d6995ae5c12bb5f36dd2ed3f61c98cbb172" uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93" version = "0.8.5" [[deps.Fontconfig_jll]] deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Zlib_jll"] git-tree-sha1 = "db16beca600632c95fc8aca29890d83788dd8b23" uuid = "a3f928ae-7b40-5064-980b-68af3947d34b" version = "2.13.96+0" [[deps.Format]] git-tree-sha1 = "9c68794ef81b08086aeb32eeaf33531668d5f5fc" uuid = "1fa38f19-a742-5d3f-a2b9-30dd87b9d5f8" version = "1.3.7" [[deps.ForwardDiff]] deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"] git-tree-sha1 = "cf0fe81336da9fb90944683b8c41984b08793dad" uuid = "f6369f11-7733-5829-9624-2563aa707210" version = "0.10.36" [deps.ForwardDiff.extensions] ForwardDiffStaticArraysExt = "StaticArrays" [deps.ForwardDiff.weakdeps] StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" [[deps.FreeType2_jll]] deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"] git-tree-sha1 = "5c1d8ae0efc6c2e7b1fc502cbe25def8f661b7bc" uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7" version = "2.13.2+0" [[deps.FriBidi_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "1ed150b39aebcc805c26b93a8d0122c940f64ce2" uuid = "559328eb-81f9-559d-9380-de523a88c83c" version = "1.0.14+0" [[deps.GLFW_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll", "libdecor_jll", "xkbcommon_jll"] git-tree-sha1 = "532f9126ad901533af1d4f5c198867227a7bb077" uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89" version = "3.4.0+1" [[deps.GLPK]] deps = ["GLPK_jll", "MathOptInterface"] git-tree-sha1 = "e37c68890d71c2e6555d3689a5d5fc75b35990ef" uuid = "60bf3e95-4087-53dc-ae20-288a0d20c6a6" version = "1.1.3" [[deps.GLPK_jll]] deps = ["Artifacts", "GMP_jll", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "fe68622f32828aa92275895fdb324a85894a5b1b" uuid = "e8aa6df9-e6ca-548a-97ff-1f85fc5b8b98" version = "5.0.1+0" [[deps.GMP_jll]] deps = ["Artifacts", "Libdl"] uuid = "781609d7-10c4-51f6-84f2-b8444358ff6d" version = "6.3.0+0" [[deps.GR]] deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"] git-tree-sha1 = "27442171f28c952804dede8ff72828a96f2bfc1f" uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71" version = "0.72.10" [[deps.GR_jll]] deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"] git-tree-sha1 = "025d171a2847f616becc0f84c8dc62fe18f0f6dd" uuid = "d2c73de3-f751-5644-a686-071e5b155ba9" version = "0.72.10+0" [[deps.Gettext_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"] git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046" uuid = "78b55507-aeef-58d4-861c-77aaff3498b1" version = "0.21.0+0" [[deps.Glib_jll]] deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"] git-tree-sha1 = "674ff0db93fffcd11a3573986e550d66cd4fd71f" uuid = "7746bdde-850d-59dc-9ae8-88ece973131d" version = "2.80.5+0" [[deps.Graphite2_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011" uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472" version = "1.3.14+0" [[deps.Grisu]] git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2" uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe" version = "1.0.2" [[deps.HTTP]] deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"] git-tree-sha1 = "d1d712be3164d61d1fb98e7ce9bcbc6cc06b45ed" uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3" version = "1.10.8" [[deps.HarfBuzz_jll]] deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll"] git-tree-sha1 = "401e4f3f30f43af2c8478fc008da50096ea5240f" uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566" version = "8.3.1+0" [[deps.HypergeometricFunctions]] deps = ["LinearAlgebra", "OpenLibm_jll", "SpecialFunctions"] git-tree-sha1 = "7c4195be1649ae622304031ed46a2f4df989f1eb" uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a" version = "0.3.24" [[deps.Hyperscript]] deps = ["Test"] git-tree-sha1 = "179267cfa5e712760cd43dcae385d7ea90cc25a4" uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91" version = "0.0.5" [[deps.HypertextLiteral]] deps = ["Tricks"] git-tree-sha1 = "7134810b1afce04bbc1045ca1985fbe81ce17653" uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2" version = "0.9.5" [[deps.IOCapture]] deps = ["Logging", "Random"] git-tree-sha1 = "b6d6bfdd7ce25b0f9b2f6b3dd56b2673a66c8770" uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89" version = "0.2.5" [[deps.InteractiveUtils]] deps = ["Markdown"] uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240" version = "1.11.0" [[deps.Ipopt]] deps = ["Ipopt_jll", "LinearAlgebra", "MathOptInterface", "OpenBLAS32_jll", "SnoopPrecompile"] git-tree-sha1 = "392d19287155a54d0053360a90dd1b43037a8ef2" uuid = "b6b21f68-93f8-5de0-b562-5493be1d77c9" version = "1.2.1" [[deps.Ipopt_jll]] deps = ["ASL_jll", "Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "MUMPS_seq_jll", "OpenBLAS32_jll", "Pkg", "libblastrampoline_jll"] git-tree-sha1 = "97c0e9fa36e93448fe214fea5366fac1ba3d1bfa" uuid = "9cc047cb-c261-5740-88fc-0cf96f7bdcc7" version = "300.1400.1000+0" [[deps.IrrationalConstants]] git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2" uuid = "92d709cd-6900-40b7-9082-c6be49f344b6" version = "0.2.2" [[deps.JLFzf]] deps = ["Pipe", "REPL", "Random", "fzf_jll"] git-tree-sha1 = "39d64b09147620f5ffbf6b2d3255be3c901bec63" uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c" version = "0.1.8" [[deps.JLLWrappers]] deps = ["Artifacts", "Preferences"] git-tree-sha1 = "be3dc50a92e5a386872a493a10050136d4703f9b" uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210" version = "1.6.1" [[deps.JSON]] deps = ["Dates", "Mmap", "Parsers", "Unicode"] git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a" uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6" version = "0.21.4" [[deps.JpegTurbo_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "25ee0be4d43d0269027024d75a24c24d6c6e590c" uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8" version = "3.0.4+0" [[deps.JuMP]] deps = ["LinearAlgebra", "MathOptInterface", "MutableArithmetics", "OrderedCollections", "Printf", "SnoopPrecompile", "SparseArrays"] git-tree-sha1 = "611b9f12f02c587d860c813743e6cec6264e94d8" uuid = "4076af6c-e467-56ae-b986-b466b2749572" version = "1.9.0" [[deps.LAME_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "170b660facf5df5de098d866564877e119141cbd" uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d" version = "3.100.2+0" [[deps.LERC_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434" uuid = "88015f11-f218-50d7-93a8-a6af411a945d" version = "3.0.0+1" [[deps.LLVMOpenMP_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "78211fb6cbc872f77cad3fc0b6cf647d923f4929" uuid = "1d63c593-3942-5779-bab2-d838dc0a180e" version = "18.1.7+0" [[deps.LZO_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "854a9c268c43b77b0a27f22d7fab8d33cdb3a731" uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac" version = "2.10.2+1" [[deps.LaTeXStrings]] git-tree-sha1 = "50901ebc375ed41dbf8058da26f9de442febbbec" uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f" version = "1.3.1" [[deps.Latexify]] deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"] git-tree-sha1 = "ce5f5621cac23a86011836badfedf664a612cee4" uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316" version = "0.16.5" [deps.Latexify.extensions] DataFramesExt = "DataFrames" SparseArraysExt = "SparseArrays" SymEngineExt = "SymEngine" [deps.Latexify.weakdeps] DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8" [[deps.LibCURL]] deps = ["LibCURL_jll", "MozillaCACerts_jll"] uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21" version = "0.6.4" [[deps.LibCURL_jll]] deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"] uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0" version = "8.6.0+0" [[deps.LibGit2]] deps = ["Base64", "LibGit2_jll", "NetworkOptions", "Printf", "SHA"] uuid = "76f85450-5226-5b5a-8eaa-529ad045b433" version = "1.11.0" [[deps.LibGit2_jll]] deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll"] uuid = "e37daf67-58a4-590a-8e99-b0245dd2ffc5" version = "1.7.2+0" [[deps.LibSSH2_jll]] deps = ["Artifacts", "Libdl", "MbedTLS_jll"] uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8" version = "1.11.0+1" [[deps.Libdl]] uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb" version = "1.11.0" [[deps.Libffi_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290" uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490" version = "3.2.2+1" [[deps.Libgcrypt_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll"] git-tree-sha1 = "9fd170c4bbfd8b935fdc5f8b7aa33532c991a673" uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4" version = "1.8.11+0" [[deps.Libglvnd_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"] git-tree-sha1 = "6f73d1dd803986947b2c750138528a999a6c7733" uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29" version = "1.6.0+0" [[deps.Libgpg_error_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "fbb1f2bef882392312feb1ede3615ddc1e9b99ed" uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8" version = "1.49.0+0" [[deps.Libiconv_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "f9557a255370125b405568f9767d6d195822a175" uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531" version = "1.17.0+0" [[deps.Libmount_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "0c4f9c4f1a50d8f35048fa0532dabbadf702f81e" uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9" version = "2.40.1+0" [[deps.Libtiff_jll]] deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"] git-tree-sha1 = "2da088d113af58221c52828a80378e16be7d037a" uuid = "89763e89-9b03-5906-acba-b20f662cd828" version = "4.5.1+1" [[deps.Libuuid_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "5ee6203157c120d79034c748a2acba45b82b8807" uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700" version = "2.40.1+0" [[deps.LinearAlgebra]] deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"] uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" version = "1.11.0" [[deps.LogExpFunctions]] deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"] git-tree-sha1 = "a2d09619db4e765091ee5c6ffe8872849de0feea" uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688" version = "0.3.28" [deps.LogExpFunctions.extensions] LogExpFunctionsChainRulesCoreExt = "ChainRulesCore" LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables" LogExpFunctionsInverseFunctionsExt = "InverseFunctions" [deps.LogExpFunctions.weakdeps] ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0" InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112" [[deps.Logging]] uuid = "56ddb016-857b-54e1-b83d-db4d58db5568" version = "1.11.0" [[deps.LoggingExtras]] deps = ["Dates", "Logging"] git-tree-sha1 = "c1dd6d7978c12545b4179fb6153b9250c96b0075" uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36" version = "1.0.3" [[deps.METIS_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "1fd0a97409e418b78c53fac671cf4622efdf0f21" uuid = "d00139f3-1899-568f-a2f0-47f597d42d70" version = "5.1.2+0" [[deps.MIMEs]] git-tree-sha1 = "65f28ad4b594aebe22157d6fac869786a255b7eb" uuid = "6c6e2e6c-3030-632d-7369-2d6c69616d65" version = "0.1.4" [[deps.MUMPS_seq_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "METIS_jll", "OpenBLAS32_jll", "Pkg", "libblastrampoline_jll"] git-tree-sha1 = "f429d6bbe9ad015a2477077c9e89b978b8c26558" uuid = "d7ed1dd3-d0ae-5e8e-bfb4-87a502085b8d" version = "500.500.101+0" [[deps.MacroTools]] deps = ["Markdown", "Random"] git-tree-sha1 = "2fa9ee3e63fd3a4f7a9a4f4744a52f4856de82df" uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09" version = "0.5.13" [[deps.Markdown]] deps = ["Base64"] uuid = "d6f4376e-aef5-505a-96c1-9c027394607a" version = "1.11.0" [[deps.MathOptInterface]] deps = ["BenchmarkTools", "CodecBzip2", "CodecZlib", "DataStructures", "ForwardDiff", "JSON", "LinearAlgebra", "MutableArithmetics", "NaNMath", "OrderedCollections", "PrecompileTools", "Printf", "SparseArrays", "SpecialFunctions", "Test", "Unicode"] git-tree-sha1 = "5b246fca5420ae176d65ed43a2d0ee5897775216" uuid = "b8f27783-ece8-5eb3-8dc8-9495eed66fee" version = "1.31.2" [[deps.MathProgBase]] deps = ["LinearAlgebra", "SparseArrays"] git-tree-sha1 = "9abbe463a1e9fc507f12a69e7f29346c2cdc472c" uuid = "fdba3010-5040-5b88-9595-932c9decdf73" version = "0.7.8" [[deps.MbedTLS]] deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "NetworkOptions", "Random", "Sockets"] git-tree-sha1 = "c067a280ddc25f196b5e7df3877c6b226d390aaf" uuid = "739be429-bea8-5141-9913-cc70e7f3736d" version = "1.1.9" [[deps.MbedTLS_jll]] deps = ["Artifacts", "Libdl"] uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1" version = "2.28.6+0" [[deps.Measures]] git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102" uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e" version = "0.3.2" [[deps.Missings]] deps = ["DataAPI"] git-tree-sha1 = "ec4f7fbeab05d7747bdf98eb74d130a2a2ed298d" uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28" version = "1.2.0" [[deps.Mmap]] uuid = "a63ad114-7e13-5084-954f-fe012c677804" version = "1.11.0" [[deps.MozillaCACerts_jll]] uuid = "14a3606d-f60d-562e-9121-12d972cd8159" version = "2023.12.12" [[deps.MutableArithmetics]] deps = ["LinearAlgebra", "SparseArrays", "Test"] git-tree-sha1 = "7768a4e5f2b372777a90c1758809333081a096a8" uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0" version = "1.5.1" [[deps.NLopt]] deps = ["MathOptInterface", "MathProgBase", "NLopt_jll"] git-tree-sha1 = "5a7e32c569200a8a03c3d55d286254b0321cd262" uuid = "76087f3c-5699-56af-9a33-bf431cd00edd" version = "0.6.5" [[deps.NLopt_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "3d1eefa627faeabc59ab9edbf00d17f70123ad69" uuid = "079eb43e-fd8e-5478-9966-2cf3e3edb778" version = "2.8.0+0" [[deps.NaNMath]] deps = ["OpenLibm_jll"] git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4" uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3" version = "1.0.2" [[deps.NetworkOptions]] uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" version = "1.2.0" [[deps.Ogg_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f" uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051" version = "1.3.5+1" [[deps.OpenBLAS32_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"] git-tree-sha1 = "dd806c813429ff09878ea3eeb317818f3ca02871" uuid = "656ef2d0-ae68-5445-9ca0-591084a874a2" version = "0.3.28+3" [[deps.OpenBLAS_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"] uuid = "4536629a-c528-5b80-bd46-f80d51c5b363" version = "0.3.27+1" [[deps.OpenLibm_jll]] deps = ["Artifacts", "Libdl"] uuid = "05823500-19ac-5b8b-9628-191a04bc5112" version = "0.8.1+2" [[deps.OpenSSL]] deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"] git-tree-sha1 = "38cb508d080d21dc1128f7fb04f20387ed4c0af4" uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c" version = "1.4.3" [[deps.OpenSSL_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "7493f61f55a6cce7325f197443aa80d32554ba10" uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95" version = "3.0.15+1" [[deps.OpenSpecFun_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1" uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e" version = "0.5.5+0" [[deps.Opus_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "6703a85cb3781bd5909d48730a67205f3f31a575" uuid = "91d4177d-7536-5919-b921-800302f37372" version = "1.3.3+0" [[deps.OrderedCollections]] git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c" uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d" version = "1.4.1" [[deps.PCRE2_jll]] deps = ["Artifacts", "Libdl"] uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15" version = "10.42.0+1" [[deps.PDMats]] deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"] git-tree-sha1 = "949347156c25054de2db3b166c52ac4728cbad65" uuid = "90014a1f-27ba-587c-ab20-58faa44d9150" version = "0.11.31" [[deps.Pango_jll]] deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"] git-tree-sha1 = "e127b609fb9ecba6f201ba7ab753d5a605d53801" uuid = "36c8627f-9965-5494-a995-c6b170f724f3" version = "1.54.1+0" [[deps.Parsers]] deps = ["Dates", "PrecompileTools", "UUIDs"] git-tree-sha1 = "8489905bcdbcfac64d1daa51ca07c0d8f0283821" uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0" version = "2.8.1" [[deps.Pipe]] git-tree-sha1 = "6842804e7867b115ca9de748a0cf6b364523c16d" uuid = "b98c9c47-44ae-5843-9183-064241ee97a0" version = "1.3.0" [[deps.Pixman_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl"] git-tree-sha1 = "35621f10a7531bc8fa58f74610b1bfb70a3cfc6b" uuid = "30392449-352a-5448-841d-b1acce4e97dc" version = "0.43.4+0" [[deps.Pkg]] deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "Random", "SHA", "TOML", "Tar", "UUIDs", "p7zip_jll"] uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" version = "1.11.0" weakdeps = ["REPL"] [deps.Pkg.extensions] REPLExt = "REPL" [[deps.PlotThemes]] deps = ["PlotUtils", "Statistics"] git-tree-sha1 = "6e55c6841ce3411ccb3457ee52fc48cb698d6fb0" uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a" version = "3.2.0" [[deps.PlotUtils]] deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"] git-tree-sha1 = "7b1a9df27f072ac4c9c7cbe5efb198489258d1f5" uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043" version = "1.4.1" [[deps.Plots]] deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Preferences", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"] git-tree-sha1 = "9f8675a55b37a70aa23177ec110f6e3f4dd68466" uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" version = "1.38.17" [deps.Plots.extensions] FileIOExt = "FileIO" GeometryBasicsExt = "GeometryBasics" IJuliaExt = "IJulia" ImageInTerminalExt = "ImageInTerminal" UnitfulExt = "Unitful" [deps.Plots.weakdeps] FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549" GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a" ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254" Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" [[deps.PlutoUI]] deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"] git-tree-sha1 = "eba4810d5e6a01f612b948c9fa94f905b49087b0" uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8" version = "0.7.60" [[deps.PrecompileTools]] deps = ["Preferences"] git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f" uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a" version = "1.2.1" [[deps.Preferences]] deps = ["TOML"] git-tree-sha1 = "9306f6085165d270f7e3db02af26a400d580f5c6" uuid = "21216c6a-2e73-6563-6e65-726566657250" version = "1.4.3" [[deps.Printf]] deps = ["Unicode"] uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" version = "1.11.0" [[deps.Profile]] uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79" version = "1.11.0" [[deps.PtrArrays]] git-tree-sha1 = "77a42d78b6a92df47ab37e177b2deac405e1c88f" uuid = "43287f4e-b6f4-7ad1-bb20-aadabca52c3d" version = "1.2.1" [[deps.Qt6Base_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Vulkan_Loader_jll", "Xorg_libSM_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_cursor_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "libinput_jll", "xkbcommon_jll"] git-tree-sha1 = "37b7bb7aabf9a085e0044307e1717436117f2b3b" uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56" version = "6.5.3+1" [[deps.QuadGK]] deps = ["DataStructures", "LinearAlgebra"] git-tree-sha1 = "cda3b045cf9ef07a08ad46731f5a3165e56cf3da" uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc" version = "2.11.1" [deps.QuadGK.extensions] QuadGKEnzymeExt = "Enzyme" [deps.QuadGK.weakdeps] Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9" [[deps.REPL]] deps = ["InteractiveUtils", "Markdown", "Sockets", "StyledStrings", "Unicode"] uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb" version = "1.11.0" [[deps.Random]] deps = ["SHA"] uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" version = "1.11.0" [[deps.RecipesBase]] deps = ["PrecompileTools"] git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff" uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01" version = "1.3.4" [[deps.RecipesPipeline]] deps = ["Dates", "NaNMath", "PlotUtils", "PrecompileTools", "RecipesBase"] git-tree-sha1 = "45cf9fd0ca5839d06ef333c8201714e888486342" uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c" version = "0.6.12" [[deps.Reexport]] git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b" uuid = "189a3867-3050-52da-a836-e630ba90ab69" version = "1.2.2" [[deps.RelocatableFolders]] deps = ["SHA", "Scratch"] git-tree-sha1 = "ffdaf70d81cf6ff22c2b6e733c900c3321cab864" uuid = "05181044-ff0b-4ac5-8273-598c1e38db00" version = "1.0.1" [[deps.Requires]] deps = ["UUIDs"] git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7" uuid = "ae029012-a4dd-5104-9daa-d747884805df" version = "1.3.0" [[deps.Rmath]] deps = ["Random", "Rmath_jll"] git-tree-sha1 = "852bd0f55565a9e973fcfee83a84413270224dc4" uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa" version = "0.8.0" [[deps.Rmath_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "58cdd8fb2201a6267e1db87ff148dd6c1dbd8ad8" uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f" version = "0.5.1+0" [[deps.SHA]] uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" version = "0.7.0" [[deps.Scratch]] deps = ["Dates"] git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386" uuid = "6c6a2e73-6563-6170-7368-637461726353" version = "1.2.1" [[deps.Serialization]] uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" version = "1.11.0" [[deps.Showoff]] deps = ["Dates", "Grisu"] git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de" uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f" version = "1.0.3" [[deps.SimpleBufferStream]] git-tree-sha1 = "f305871d2f381d21527c770d4788c06c097c9bc1" uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7" version = "1.2.0" [[deps.SnoopPrecompile]] deps = ["Preferences"] git-tree-sha1 = "e760a70afdcd461cf01a575947738d359234665c" uuid = "66db9d55-30c0-4569-8b51-7e840670fc0c" version = "1.0.3" [[deps.Sockets]] uuid = "6462fe0b-24de-5631-8697-dd941f90decc" version = "1.11.0" [[deps.SortingAlgorithms]] deps = ["DataStructures"] git-tree-sha1 = "66e0a8e672a0bdfca2c3f5937efb8538b9ddc085" uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c" version = "1.2.1" [[deps.SparseArrays]] deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"] uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" version = "1.11.0" [[deps.SpecialFunctions]] deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"] git-tree-sha1 = "2f5d4697f21388cbe1ff299430dd169ef97d7e14" uuid = "276daf66-3868-5448-9aa4-cd146d93841b" version = "2.4.0" [deps.SpecialFunctions.extensions] SpecialFunctionsChainRulesCoreExt = "ChainRulesCore" [deps.SpecialFunctions.weakdeps] ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" [[deps.StaticArraysCore]] git-tree-sha1 = "192954ef1208c7019899fbf8049e717f92959682" uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c" version = "1.4.3" [[deps.Statistics]] deps = ["LinearAlgebra"] git-tree-sha1 = "ae3bb1eb3bba077cd276bc5cfc337cc65c3075c0" uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" version = "1.11.1" weakdeps = ["SparseArrays"] [deps.Statistics.extensions] SparseArraysExt = ["SparseArrays"] [[deps.StatsAPI]] deps = ["LinearAlgebra"] git-tree-sha1 = "1ff449ad350c9c4cbc756624d6f8a8c3ef56d3ed" uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0" version = "1.7.0" [[deps.StatsBase]] deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"] git-tree-sha1 = "5cf7606d6cef84b543b483848d4ae08ad9832b21" uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" version = "0.34.3" [[deps.StatsFuns]] deps = ["HypergeometricFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"] git-tree-sha1 = "b423576adc27097764a90e163157bcfc9acf0f46" uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c" version = "1.3.2" [deps.StatsFuns.extensions] StatsFunsChainRulesCoreExt = "ChainRulesCore" StatsFunsInverseFunctionsExt = "InverseFunctions" [deps.StatsFuns.weakdeps] ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112" [[deps.StyledStrings]] uuid = "f489334b-da3d-4c2e-b8f0-e476e12c162b" version = "1.11.0" [[deps.SuiteSparse]] deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"] uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9" [[deps.SuiteSparse_jll]] deps = ["Artifacts", "Libdl", "libblastrampoline_jll"] uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c" version = "7.7.0+0" [[deps.TOML]] deps = ["Dates"] uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76" version = "1.0.3" [[deps.Tar]] deps = ["ArgTools", "SHA"] uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e" version = "1.10.0" [[deps.TensorCore]] deps = ["LinearAlgebra"] git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6" uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50" version = "0.1.1" [[deps.Test]] deps = ["InteractiveUtils", "Logging", "Random", "Serialization"] uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" version = "1.11.0" [[deps.TranscodingStreams]] git-tree-sha1 = "0c45878dcfdcfa8480052b6ab162cdd138781742" uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa" version = "0.11.3" [[deps.Tricks]] git-tree-sha1 = "7822b97e99a1672bfb1b49b668a6d46d58d8cbcb" uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775" version = "0.1.9" [[deps.URIs]] git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b" uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4" version = "1.5.1" [[deps.UUIDs]] deps = ["Random", "SHA"] uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" version = "1.11.0" [[deps.Unicode]] uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" version = "1.11.0" [[deps.UnicodeFun]] deps = ["REPL"] git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf" uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1" version = "0.4.1" [[deps.Unitful]] deps = ["Dates", "LinearAlgebra", "Random"] git-tree-sha1 = "d95fe458f26209c66a187b1114df96fd70839efd" uuid = "1986cc42-f94f-5a68-af5c-568840ba703d" version = "1.21.0" [deps.Unitful.extensions] ConstructionBaseUnitfulExt = "ConstructionBase" InverseFunctionsUnitfulExt = "InverseFunctions" [deps.Unitful.weakdeps] ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9" InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112" [[deps.UnitfulLatexify]] deps = ["LaTeXStrings", "Latexify", "Unitful"] git-tree-sha1 = "975c354fcd5f7e1ddcc1f1a23e6e091d99e99bc8" uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728" version = "1.6.4" [[deps.Unzip]] git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78" uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d" version = "0.2.0" [[deps.Vulkan_Loader_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Xorg_libX11_jll", "Xorg_libXrandr_jll", "xkbcommon_jll"] git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59" uuid = "a44049a8-05dd-5a78-86c9-5fde0876e88c" version = "1.3.243+0" [[deps.Wayland_jll]] deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"] git-tree-sha1 = "7558e29847e99bc3f04d6569e82d0f5c54460703" uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89" version = "1.21.0+1" [[deps.Wayland_protocols_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "93f43ab61b16ddfb2fd3bb13b3ce241cafb0e6c9" uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91" version = "1.31.0+0" [[deps.XML2_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"] git-tree-sha1 = "1165b0443d0eca63ac1e32b8c0eb69ed2f4f8127" uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a" version = "2.13.3+0" [[deps.XSLT_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "XML2_jll", "Zlib_jll"] git-tree-sha1 = "a54ee957f4c86b526460a720dbc882fa5edcbefc" uuid = "aed1982a-8fda-507f-9586-7b0439959a61" version = "1.1.41+0" [[deps.XZ_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "ac88fb95ae6447c8dda6a5503f3bafd496ae8632" uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800" version = "5.4.6+0" [[deps.Xorg_libICE_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "326b4fea307b0b39892b3e85fa451692eda8d46c" uuid = "f67eecfb-183a-506d-b269-f58e52b52d7c" version = "1.1.1+0" [[deps.Xorg_libSM_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libICE_jll"] git-tree-sha1 = "3796722887072218eabafb494a13c963209754ce" uuid = "c834827a-8449-5923-a945-d239c165b7dd" version = "1.2.4+0" [[deps.Xorg_libX11_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"] git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495" uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc" version = "1.8.6+0" [[deps.Xorg_libXau_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8" uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec" version = "1.0.11+0" [[deps.Xorg_libXcursor_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"] git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd" uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724" version = "1.2.0+4" [[deps.Xorg_libXdmcp_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7" uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05" version = "1.1.4+0" [[deps.Xorg_libXext_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"] git-tree-sha1 = "d2d1a5c49fae4ba39983f63de6afcbea47194e85" uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3" version = "1.3.6+0" [[deps.Xorg_libXfixes_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"] git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4" uuid = "d091e8ba-531a-589c-9de9-94069b037ed8" version = "5.0.3+4" [[deps.Xorg_libXi_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"] git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246" uuid = "a51aa0fd-4e3c-5386-b890-e753decda492" version = "1.7.10+4" [[deps.Xorg_libXinerama_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"] git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123" uuid = "d1454406-59df-5ea1-beac-c340f2130bc3" version = "1.1.4+4" [[deps.Xorg_libXrandr_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"] git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631" uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484" version = "1.5.2+4" [[deps.Xorg_libXrender_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"] git-tree-sha1 = "47e45cd78224c53109495b3e324df0c37bb61fbe" uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa" version = "0.9.11+0" [[deps.Xorg_libpthread_stubs_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9" uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74" version = "0.1.1+0" [[deps.Xorg_libxcb_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"] git-tree-sha1 = "bcd466676fef0878338c61e655629fa7bbc69d8e" uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b" version = "1.17.0+0" [[deps.Xorg_libxkbfile_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"] git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4" uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a" version = "1.1.2+0" [[deps.Xorg_xcb_util_cursor_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"] git-tree-sha1 = "04341cb870f29dcd5e39055f895c39d016e18ccd" uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43" version = "0.1.4+0" [[deps.Xorg_xcb_util_image_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97" uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b" version = "0.4.0+1" [[deps.Xorg_xcb_util_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"] git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1" uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5" version = "0.4.0+1" [[deps.Xorg_xcb_util_keysyms_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00" uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7" version = "0.4.0+1" [[deps.Xorg_xcb_util_renderutil_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e" uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e" version = "0.3.9+1" [[deps.Xorg_xcb_util_wm_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67" uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361" version = "0.4.1+1" [[deps.Xorg_xkbcomp_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"] git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb" uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4" version = "1.4.6+0" [[deps.Xorg_xkeyboard_config_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"] git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3" uuid = "33bec58e-1273-512f-9401-5d533626f822" version = "2.39.0+0" [[deps.Xorg_xtrans_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77" uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10" version = "1.5.0+0" [[deps.Zlib_jll]] deps = ["Libdl"] uuid = "83775a58-1f1d-513f-b197-d71354ab007a" version = "1.2.13+1" [[deps.Zstd_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "555d1076590a6cc2fdee2ef1469451f872d8b41b" uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" version = "1.5.6+1" [[deps.eudev_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"] git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba" uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06" version = "3.2.9+0" [[deps.fzf_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "936081b536ae4aa65415d869287d43ef3cb576b2" uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09" version = "0.53.0+0" [[deps.gperf_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033" uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70" version = "3.1.1+0" [[deps.libaom_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "1827acba325fdcdf1d2647fc8d5301dd9ba43a9d" uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b" version = "3.9.0+0" [[deps.libass_jll]] deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"] git-tree-sha1 = "e17c115d55c5fbb7e52ebedb427a0dca79d4484e" uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" version = "0.15.2+0" [[deps.libblastrampoline_jll]] deps = ["Artifacts", "Libdl"] uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" version = "5.11.0+0" [[deps.libdecor_jll]] deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"] git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f" uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f" version = "0.2.2+0" [[deps.libevdev_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22" uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc" version = "1.11.0+0" [[deps.libfdk_aac_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "8a22cf860a7d27e4f3498a0fe0811a7957badb38" uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" version = "2.0.3+0" [[deps.libinput_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"] git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce" uuid = "36db933b-70db-51c0-b978-0f229ee0e533" version = "1.18.0+0" [[deps.libpng_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"] git-tree-sha1 = "b70c870239dc3d7bc094eb2d6be9b73d27bef280" uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" version = "1.6.44+0" [[deps.libvorbis_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3" uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" version = "1.3.7+2" [[deps.mtdev_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11" uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e" version = "1.1.6+0" [[deps.nghttp2_jll]] deps = ["Artifacts", "Libdl"] uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" version = "1.59.0+0" [[deps.p7zip_jll]] deps = ["Artifacts", "Libdl"] uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" version = "17.4.0+2" [[deps.x264_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" version = "2021.5.5+0" [[deps.x265_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" version = "3.5.0+0" [[deps.xkbcommon_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37" uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" version = "1.4.1+1" """ # ╔═╡ Cell order: # ╟─aa1f0719-5e1d-4294-815e-349d1cebc004 # ╟─aae2e545-198c-42bb-9e97-6d6635bee02a # ╠═9c61c9d5-0d3d-47b7-8e7d-f929cfec3311 # ╟─4468041e-4472-11ec-16b7-553f4def2b18 # ╟─e66005ad-1f51-462a-9329-d77f7695cbfc # ╟─5bc7c8ce-3a4a-4505-a2fa-2b25f041437a # ╟─c5f6d941-7161-44bb-8ec8-8644636234c0 # ╠═9a92426e-bc9a-4ead-a93c-ec1c3f23ca57 # ╠═d7acef71-fe0d-4062-9342-9061afde1293 # ╟─de879e63-fdc9-486e-9aaa-1a55c32d93d5 # ╟─54a17a40-fd67-4040-99b9-d0d460385155 # ╟─9f1f0926-b1b3-4ef3-aebe-277531abfd33 # ╟─2f8d4513-0871-48f3-acfb-f7a0254f7b8e # ╟─8901f1e5-f243-4fe7-afda-6cc951b234a5 # ╟─fe6b7d74-1c6f-4253-9254-57d536bb24c5 # ╟─19d12886-3980-4116-8772-2c1d17b14270 # ╟─583a5640-adde-4f4f-a344-4e77e04e431d # ╟─9be3cbee-7949-42da-9496-6afc94785f98 # ╟─91da671d-7602-490c-a94c-bc9ff4eca59a # ╠═7e5cedbf-05da-4573-994f-42099fe4b33a # ╠═b1720238-495e-47f7-ae75-866723f5fca4 # ╠═1e31dc48-e849-4045-8dcc-d05889f8609b # ╟─70893b5f-51e8-4536-b5aa-4e353768bc52 # ╠═2a74858c-6d13-4961-86fa-125e4c01e232 # ╠═ec0c21da-c517-4d2e-9832-18eca242621b # ╟─ade668a5-87d6-40aa-b670-d0cc41148757 # ╠═52a1ca3b-8a10-4c0a-b4d4-82f995b4b3df # ╟─9cc92292-4531-4f4c-b9b1-2a7a698529ac # ╠═fc75bc7b-0fe0-4f90-a425-6ed6e63acb4a # ╠═2d7bdf41-85fc-4d0c-a387-60f9c9b36fcb # ╟─3ba47370-c4df-4d22-8bda-0b7264927ae6 # ╠═84b81d87-d015-4cc2-8649-c94ba7770bd9 # ╟─061de138-b6fe-4437-aa26-0afaec2e66f0 # ╠═febc5df1-4ddd-48a7-94f8-251d316c72d0 # ╠═1334fc66-23bb-4a9a-9534-6f4d7a88d235 # ╟─520c3423-01d4-4794-893c-f7e5546d26f6 # ╟─ee374307-043c-473d-b561-192718ea612b # ╟─636f7fe1-a518-4f09-bdbd-bcb79703dda5 # ╟─2fcf8444-202a-453a-af28-0eade00e3981 # ╠═3f231741-12f6-4426-8d46-b6cfe623a248 # ╟─8eef8fc6-2272-46ff-a5ab-b2a4e63d9b7a # ╟─b1f21cfe-ebc2-4321-9636-49739568a7de # ╠═b175638b-db07-41c5-a409-f7814d14dc42 # ╠═9cb9f9cc-fe89-44c3-8115-6a5c48b58ca0 # ╠═9644fbd5-298c-4041-822b-1b44917b2c41 # ╟─7f033067-2216-4532-baa3-6d099bbfc034 # ╟─00000000-0000-0000-0000-000000000001 # ╟─00000000-0000-0000-0000-000000000002