Merge pull request #164 from QuantEcon/latexstrings

Finish #122: port plot text to LaTeXStrings

Author: jbrightuniverse

lectures/Manifest.toml

@@ -971,6 +971,12 @@ git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
 uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
 version = "3.100.1+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.LZO_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
@@ -1084,10 +1090,10 @@ uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
 version = "2.35.0+0"
 
 [[deps.Libtiff_jll]]
-deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
-git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
+deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
+git-tree-sha1 = "c9551dd26e31ab17b86cbd00c2ede019c08758eb"
 uuid = "89763e89-9b03-5906-acba-b20f662cd828"
-version = "4.3.0+0"
+version = "4.3.0+1"
 
 [[deps.Libuuid_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]

lectures/Project.toml

@@ -26,6 +26,7 @@ Ipopt = "b6b21f68-93f8-5de0-b562-5493be1d77c9"
 IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
 JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
 KernelDensity = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
+LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
 LeastSquaresOptim = "0fc2ff8b-aaa3-5acd-a817-1944a5e08891"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearMaps = "7a12625a-238d-50fd-b39a-03d52299707e"

lectures/continuous_time/covid_sde.md

@@ -54,7 +54,7 @@ Every other Levy Process can be represented by these building blocks (e.g. a [Di
 In this lecture, we will examine shocks driven by transformations of Brownian motion, as the prototypical Stochastic Differential Equation (SDE).
 
 ```{code-cell} julia
-using LinearAlgebra, Statistics, Random, SparseArrays
+using LaTeXStrings, LinearAlgebra, Random, SparseArrays, Statistics
 ```
 
 ```{code-cell} julia
@@ -284,25 +284,25 @@ If we take two solutions and plot the number of infections, we will see differen
 ```{code-cell} julia
 sol_2 = solve(prob, SOSRI())
 plot(sol_1, vars=[2], title = "Number of Infections", label = "Trajectory 1",
-     lm = 2, xlabel = "t", ylabel = "i(t)")
-plot!(sol_2, vars=[2], label = "Trajectory 2", lm = 2, ylabel = "i(t)")
+     lm = 2, xlabel = L"t", ylabel = L"i(t)")
+plot!(sol_2, vars=[2], label = "Trajectory 2", lm = 2, xlabel = L"t", ylabel = L"i(t)")
 ```
 
 The same holds for other variables such as the cumulative deaths, mortality, and $R_0$:
 
 ```{code-cell} julia
 plot_1 = plot(sol_1, vars=[4], title = "Cumulative Death Proportion", label = "Trajectory 1",
-              lw = 2, xlabel = "t", ylabel = "d(t)", legend = :topleft)
-plot!(plot_1, sol_2, vars=[4], label = "Trajectory 2", lw = 2)
+              lw = 2, xlabel = L"t", ylabel = L"d(t)", legend = :topleft)
+plot!(plot_1, sol_2, vars=[4], label = "Trajectory 2", lw = 2, xlabel = L"t")
 plot_2 = plot(sol_1, vars=[3], title = "Cumulative Recovered Proportion", label = "Trajectory 1",
-              lw = 2, xlabel = "t", ylabel = "d(t)", legend = :topleft)
-plot!(plot_2, sol_2, vars=[3], label = "Trajectory 2", lw = 2)
-plot_3 = plot(sol_1, vars=[5], title = "R_0 transition from lockdown", label = "Trajectory 1",
-              lw = 2, xlabel = "t", ylabel = "R_0(t)")
-plot!(plot_3, sol_2, vars=[5], label = "Trajectory 2", lw = 2)
+              lw = 2, xlabel = L"t", ylabel = L"d(t)", legend = :topleft)
+plot!(plot_2, sol_2, vars=[3], label = "Trajectory 2", lw = 2, xlabel = L"t")
+plot_3 = plot(sol_1, vars=[5], title = L"$R_0$ transition from lockdown", label = "Trajectory 1",
+              lw = 2, xlabel = L"t", ylabel = L"R_0(t)")
+plot!(plot_3, sol_2, vars=[5], label = "Trajectory 2", lw = 2, xlabel = L"t")
 plot_4 = plot(sol_1, vars=[6], title = "Mortality Rate", label = "Trajectory 1",
-              lw = 2, xlabel = "t", ylabel = "delta(t)", ylim = (0.006, 0.014))
-plot!(plot_4, sol_2, vars=[6], label = "Trajectory 2", lw = 2)
+              lw = 2, xlabel = L"t", ylabel = L"\delta(t)", ylim = (0.006, 0.014))
+plot!(plot_4, sol_2, vars=[6], label = "Trajectory 2", lw = 2, xlabel = L"t")
 plot(plot_1, plot_2, plot_3, plot_4, size = (900, 600))
 ```
 
@@ -324,7 +324,7 @@ For example:
 ```{code-cell} julia
 ensembleprob = EnsembleProblem(prob)
 sol = solve(ensembleprob, SOSRI(), EnsembleSerial(), trajectories = 10)
-plot(sol, vars = [2], title = "Infection Simulations", ylabel = "i(t)", xlabel = "t", lm = 2)
+plot(sol, vars = [2], title = "Infection Simulations", ylabel = L"i(t)", xlabel = L"t", lm = 2)
 ```
 
 Or, more frequently, you may want to run many trajectories and plot quantiles, which can be automatically run in [parallel](https://docs.sciml.ai/stable/features/ensemble/) using multiple threads, processes, or GPUs. Here we showcase `EnsembleSummary` which calculates summary information from an ensemble and plots the mean of the solution along with calculated quantiles of the simulation:
@@ -333,8 +333,8 @@ Or, more frequently, you may want to run many trajectories and plot quantiles, w
 trajectories = 100  # choose larger for smoother quantiles
 sol = solve(ensembleprob, SOSRI(), EnsembleThreads(), trajectories = trajectories)
 summ = EnsembleSummary(sol) # defaults to saving 0.05, 0.95 quantiles
-plot(summ, idxs = (2,), title = "Quantiles of Infections Ensemble", ylabel = "i(t)",
-     xlabel = "t", labels = "Middle 95% Quantile", legend = :topright)
+plot(summ, idxs = (2,), title = "Quantiles of Infections Ensemble", ylabel = L"i(t)",
+     xlabel = L"t", labels = "Middle 95% Quantile", legend = :topright)
 ```
 
 In addition, you can calculate more quantiles and stack graphs
@@ -345,8 +345,8 @@ summ = EnsembleSummary(sol) # defaults to saving 0.05, 0.95 quantiles
 summ2 = EnsembleSummary(sol, quantiles = (0.25, 0.75))
 
 plot(summ, idxs = (2,4,5,6),
-    title = ["Proportion Infected" "Proportion Dead" "R_0" "delta"],
-    ylabel = ["i(t)" "d(t)" "R_0(t)" "delta(t)"], xlabel = "t",
+    title = ["Proportion Infected" "Proportion Dead" L"R_0" L"\delta"],
+    ylabel = [L"i(t)" L"d(t)" L"R_0(t)" L"\delta(t)"], xlabel = L"t",
     legend = [:topleft :topleft :bottomright :bottomright],
     labels = "Middle 95% Quantile", layout = (2, 2), size = (900, 600))
 plot!(summ2, idxs = (2,4,5,6),
@@ -385,14 +385,14 @@ end
 summ_1 = generate_η_experiment(η_1)
 summ_2 = generate_η_experiment(η_2)
 plot(summ_1, idxs = (4,5),
-    title = ["Proportion Dead" "R_0"],
-    ylabel = ["d(t)" "R_0(t)"], xlabel = "t",
+    title = ["Proportion Dead" L"R_0"],
+    ylabel = [L"d(t)" L"R_0(t)"], xlabel = L"t",
     legend = [:topleft :bottomright],
-    labels = "Middle 95% Quantile, eta = $η_1",
+    labels = L"Middle 95% Quantile, $\eta = %$η_1$",
     layout = (2, 1), size = (900, 900), fillalpha = 0.5)
 plot!(summ_2, idxs = (4,5),
     legend = [:topleft :bottomright],
-    labels = "Middle 95% Quantile, eta = $η_2", size = (900, 900), fillalpha = 0.5)
+    labels = L"Middle 95% Quantile, $\eta = %$η_2$", size = (900, 900), fillalpha = 0.5)
 ```
 
 While the the mean of the $d(t)$ increases, unsurprisingly, we see that the 95% quantile for later time periods is also much larger - even after the $R_0$ has converged.
@@ -439,14 +439,14 @@ Simulating for a single realization of the shocks, we see the results are qualit
 sol_early = solve(prob_early, SOSRI())
 sol_late = solve(prob_late, SOSRI())
 plot(sol_early, vars = [5, 1,2,4],
-    title = ["R_0" "Susceptible" "Infected" "Dead"],
+    title = [L"R_0" "Susceptible" "Infected" "Dead"],
     layout = (2, 2), size = (900, 600),
-    ylabel = ["R_0(t)" "s(t)" "i(t)" "d(t)"], xlabel = "t",
+    ylabel = [L"R_0(t)" L"s(t)" L"i(t)" L"d(t)"], xlabel = L"t",
         legend = [:bottomright :topright :topright :topleft],
         label = ["Early" "Early" "Early" "Early"])
 plot!(sol_late, vars = [5, 1,2,4],
         legend = [:bottomright :topright :topright :topleft],
-        label = ["Late" "Late" "Late" "Late"])
+        label = ["Late" "Late" "Late" "Late"], xlabel = L"t")
 ```
 
 However, note that this masks highly volatile values induced by the in $R_0$ variation, as seen in the ensemble
@@ -462,8 +462,8 @@ summ_early = EnsembleSummary(ensemble_sol_early)
 summ_late = EnsembleSummary(ensemble_sol_late)
 
 plot(summ_early, idxs = (5, 1, 2, 4),
-    title = ["R_0" "Susceptible" "Infected" "Dead"], layout = (2, 2), size = (900, 600),
-    ylabel = ["R_0(t)" "s(t)" "i(t)" "d(t)"], xlabel = "t",
+    title = [L"R_0" "Susceptible" "Infected" "Dead"], layout = (2, 2), size = (900, 600),
+    ylabel = [L"R_0(t)" L"s(t)" L"i(t)" L"d(t)"], xlabel = L"t",
     legend = [:bottomright :topright :topright :topleft],
     label = ["Early" "Early" "Early" "Early"])
 plot!(summ_late, idxs = (5, 1,2,4),
@@ -485,12 +485,12 @@ bins_2 = 30  # number rather than grid.
 hist_1 = histogram([ensemble_sol_early.u[i](t_1)[4] for i in 1:trajectories],
                    fillalpha = 0.5, normalize = :probability,
                    legend = :topleft, bins = bins_1,
-                   label = "Early", title = "Death Proportion at t = $t_1")
+                   label = "Early", title = L"Death Proportion at $t = %$t_1$")
 histogram!(hist_1, [ensemble_sol_late.u[i](t_1)[4] for i in 1:trajectories],
            label = "Late", fillalpha = 0.5, normalize = :probability, bins = bins_1)
 hist_2 = histogram([ensemble_sol_early.u[i][4, end] for i in 1:trajectories],
                    fillalpha = 0.5, normalize = :probability, bins = bins_2,
-                   label = "Early", title = "Death Proportion at t = $t_2")
+                   label = "Early", title = L"Death Proportion at $t = %$t_2$")
 histogram!(hist_2, [ensemble_sol_late.u[i][4, end] for i in 1:trajectories],
            label = "Late", fillalpha = 0.5, normalize = :probability, bins = bins_2)
 plot(hist_1, hist_2, size = (600,600), layout = (2, 1))
@@ -572,12 +572,12 @@ The ensemble simulations for the $\nu = 0$ and $\nu > 0$ can be compared to see
 plot(summ_late, idxs = (1, 2, 3, 4),
     title = ["Susceptible" "Infected" "Recovered" "Dead"],
     layout = (2, 2), size = (900, 600),
-    ylabel = ["s(t)" "i(t)" "r(t)" "d(t)"], xlabel = "t",
+    ylabel = [L"s(t)" L"i(t)" L"r(t)" L"d(t)"], xlabel = L"t",
     legend = :topleft,
-    label = ["s(t)" "i(t)" "r(t)" "d(t)"])
+    label = [L"s(t)" L"i(t)" L"r(t)" L"d(t)"])
 plot!(summ_re_late, idxs =  (1, 2, 3, 4),
     legend = :topleft,
-    label = ["s(t); nu > 0" "i(t); nu > 0" "r(t); nu > 0" "d(t); nu > 0"])
+    label = [L"s(t); \nu > 0" L"i(t); \nu > 0" L"r(t); \nu > 0" L"d(t); \nu > 0"])
 ```
 
 Finally, we can examine the same early vs. late lockdown histogram
@@ -588,12 +588,12 @@ bins_re_2 = range(0.0085, 0.0102, length = 50)
 hist_re_1 = histogram([ensemble_sol_re_early.u[i](t_1)[4] for i in 1:trajectories],
                     fillalpha = 0.5, normalize = :probability,
                     legend = :topleft, bins = bins_re_1,
-                    label = "Early", title = "Death Proportion at t = $t_1")
+                    label = "Early", title = L"Death Proportion at $t = %$t_1$")
 histogram!(hist_re_1, [ensemble_sol_re_late.u[i](t_1)[4] for i in 1:trajectories],
         label = "Late", fillalpha = 0.5, normalize = :probability, bins = bins_re_1)
 hist_re_2 = histogram([ensemble_sol_re_early.u[i][4, end] for i in 1:trajectories],
                     fillalpha = 0.5, normalize = :probability, bins = bins_re_2,
-                    label = "Early", title = "Death Proportion at t = $t_2")
+                    label = "Early", title = L"Death Proportion at $t = %$t_2$")
 histogram!(hist_re_2, [ensemble_sol_re_late.u[i][4, end] for i in 1:trajectories],
         label = "Late", fillalpha = 0.5, normalize = :probability,
         bins =  bins = bins_re_2)

lectures/continuous_time/seir_model.md

@@ -53,7 +53,7 @@ The interest is primarily in
 
 
 ```{code-cell} julia
-using LinearAlgebra, Statistics, Random, SparseArrays
+using LaTeXStrings, LinearAlgebra, Random, SparseArrays, Statistics
 ```
 
 ```{code-cell} julia
@@ -199,15 +199,15 @@ With this, choose an ODE algorithm and solve the initial value problem.  A good
 
 ```{code-cell} julia
 sol = solve(prob, Tsit5())
-plot(sol, labels = ["s" "e" "i" "r"], title = "SEIR Dynamics", lw = 2)
+plot(sol, labels = [L"s" L"e" L"i" L"r"], title = "SEIR Dynamics", lw = 2, xlabel = L"t")
 ```
 
 We did not provide either a set of time steps or a `dt` time step size to the `solve`.  Most accurate and high-performance ODE solvers appropriate for this problem use adaptive time-stepping, changing the step size based the degree of curvature in the derivatives.
 
 Or, as an alternative visualization, the proportions in each state over time
 
 ```{code-cell} julia
-areaplot(sol.t, sol', labels = ["s" "e" "i" "r"], title = "SEIR Proportions")
+areaplot(sol.t, sol', labels = [L"s" L"e" L"i" L"r"], title = "SEIR Proportions", xlabel = L"t")
 ```
 
 While maintaining the core system of ODEs in $(s, e, i, r)$, we will extend the basic model to enable some policy experiments and calculations of aggregate values.
@@ -354,9 +354,9 @@ While it may seem that 45 time intervals is extremely small for that range, for
 The solution object has [built in](https://docs.sciml.ai/stable/basics/plot/) plotting support.
 
 ```{code-cell} julia
-plot(sol, vars = [6, 7], label = ["c(t)" "d(t)"], lw = 2,
+plot(sol, vars = [6, 7], label = [L"c(t)" L"d(t)"], lw = 2,
      title = ["Cumulative Infected" "Death Proportion"],
-     layout = (1,2), size = (900, 300))
+     xlabel = L"t", layout = (1,2), size = (900, 300))
 ```
 
 A few more comments:
@@ -384,10 +384,10 @@ Changing the saved points is just a question of storage/interpolation, and does
 Let's plot current cases as a fraction of the population.
 
 ```{code-cell} julia
-labels = permutedims(["R_0 = $r" for r in R₀_n_vals])
+labels = permutedims([L"R_0 = %$r" for r in R₀_n_vals])
 infecteds = [sol[3,:] for sol in sols]
-plot(infecteds, label=labels, legend=:topleft, lw = 2, xlabel = "t",
-     ylabel = "i(t)", title = "Current Cases")
+plot(infecteds, label=labels, legend=:topleft, lw = 2, xlabel = L"t",
+     ylabel = L"i(t)", title = "Current Cases")
 ```
 
 As expected, lower effective transmission rates defer the peak of infections.
@@ -398,8 +398,8 @@ Here is cumulative cases, as a fraction of population:
 
 ```{code-cell} julia
 cumulative_infected = [sol[6,:] for sol in sols]
-plot(cumulative_infected, label=labels ,legend=:topleft, lw = 2, xlabel = "t",
-     ylabel = "c(t)", title = "Cumulative Cases")
+plot(cumulative_infected, label=labels ,legend=:topleft, lw = 2, xlabel = L"t",
+     ylabel = L"c(t)", title = "Cumulative Cases")
 ```
 
 ### Experiment 2: Changing Mitigation
@@ -420,7 +420,7 @@ We consider several different rates:
 
 ```{code-cell} julia
 η_vals = [1/5, 1/10, 1/20, 1/50, 1/100]
-labels = permutedims(["eta = $η" for η in η_vals]);
+labels = permutedims([L"\eta = %$η" for η in η_vals]);
 ```
 
 Let's calculate the time path of infected people, current cases, and mortality
@@ -434,23 +434,23 @@ Next, plot the $R_0$ over time:
 
 ```{code-cell} julia
 Rs = [sol[5,:] for sol in sols]
-plot(Rs, label=labels, legend=:topright, lw = 2, xlabel = "t",
-     ylabel = "R_0(t)", title = "Basic Reproduction Number")
+plot(Rs, label=labels, legend=:topright, lw = 2, xlabel = L"t",
+     ylabel = L"R_0(t)", title = "Basic Reproduction Number")
 ```
 
 Now let's plot the number of infected persons and the cumulative number
 of infected persons:
 
 ```{code-cell} julia
 infecteds = [sol[3,:] for sol in sols]
-plot(infecteds, label=labels, legend=:topleft, lw = 2, xlabel = "t",
-     ylabel = "i(t)", title = "Current Infected")
+plot(infecteds, label=labels, legend=:topleft, lw = 2, xlabel = L"t",
+     ylabel = L"i(t)", title = "Current Infected")
 ```
 
 ```{code-cell} julia
 cumulative_infected = [sol[6,:] for sol in sols]
-plot(cumulative_infected, label=labels ,legend=:topleft, lw = 2, xlabel = "t",
-     ylabel = "c(t)", title = "Cumulative Infected")
+plot(cumulative_infected, label=labels ,legend=:topleft, lw = 2, xlabel = L"t",
+     ylabel = L"c(t)", title = "Cumulative Infected")
 ```
 
 ## Ending Lockdown
@@ -495,7 +495,7 @@ Let's calculate the paths:
 sol_early = solve(prob_early, Tsit5(), tstops = [30.0, 120.0])
 sol_late = solve(prob_late, Tsit5(), tstops = [30.0, 120.0])
 plot(sol_early, vars = [7], title = "Total Mortality", label = "Lift Early", legend = :topleft)
-plot!(sol_late, vars = [7], label = "Lift Late")
+plot!(sol_late, vars = [7], label = "Lift Late", xlabel = L"t")
 ```
 
 Next we examine the daily deaths, $\frac{d D(t)}{dt} = N \delta \gamma i(t)$.
@@ -504,7 +504,7 @@ Next we examine the daily deaths, $\frac{d D(t)}{dt} = N \delta \gamma i(t)$.
 flow_deaths(sol, p) = p.N * p.δ * p.γ * sol[3,:]
 
 plot(sol_early.t, flow_deaths(sol_early, p_early), title = "Flow Deaths", label = "Lift Early")
-plot!(sol_late.t, flow_deaths(sol_late, p_late), label = "Lift Late")
+plot!(sol_late.t, flow_deaths(sol_late, p_late), label = "Lift Late", xlabel = L"t")
 ```
 
 Pushing the peak of curve further into the future may reduce cumulative deaths

lectures/dynamic_programming/career.md

@@ -154,7 +154,7 @@ using Test
 ```
 
 ```{code-cell} julia
-using Plots, QuantEcon, Distributions
+using LaTeXStrings, Plots, QuantEcon, Distributions
 
 
 n = 50
@@ -163,7 +163,7 @@ b_vals = [0.5, 1, 100]
 
 plt = plot()
 for (a, b) in zip(a_vals, b_vals)
-    ab_label = "a = $a, b = $b"
+    ab_label = L"$a = %$a, b = %$b$"
     dist = BetaBinomial(n, a, b)
     plot!(plt, 0:n, pdf.(dist, support(dist)), label = ab_label)
 end
@@ -274,7 +274,7 @@ v_init = fill(100.0, wp.N, wp.N)
 func(x) = update_bellman(wp, x)
 v = compute_fixed_point(func, v_init, max_iter = 500, verbose = false)
 
-plot(linetype = :surface, wp.θ, wp.ϵ, transpose(v), xlabel="theta", ylabel="epsilon",
+plot(linetype = :surface, wp.θ, wp.ϵ, transpose(v), xlabel=L"\theta", ylabel=L"\epsilon",
      seriescolor=:plasma, gridalpha = 1)
 ```
 
@@ -392,8 +392,8 @@ end
 plot_array = Any[]
 for i in 1:2
     θ_path, ϵ_path = gen_path()
-    plt = plot(ϵ_path, label="epsilon")
-    plot!(plt, θ_path, label="theta")
+    plt = plot(ϵ_path, label=L"\epsilon")
+    plot!(plt, θ_path, label=L"\theta")
     plot!(plt, legend=:bottomright)
     push!(plot_array, plt)
 end
@@ -487,7 +487,7 @@ y_grid = range(0, 5, length = 50)
 
 contour(x_grid, y_grid, optimal_policy', fill=true, levels=lvls,color = :Blues,
         fillalpha=1, cbar = false)
-contour!(xlabel="theta", ylabel="epsilon")
+contour!(xlabel=L"\theta", ylabel=L"\epsilon")
 annotate!([(1.8,2.5, text("new life", 14, :white, :center))])
 annotate!([(4.5,2.5, text("new job", 14, :center))])
 annotate!([(4.0,4.5, text("stay put", 14, :center))])
@@ -505,7 +505,7 @@ y_grid = range(0, 5, length = 50)
 
 contour(x_grid, y_grid, optimal_policy', fill=true, levels=lvls,color = :Blues,
         fillalpha=1, cbar = false)
-contour!(xlabel="theta", ylabel="epsilon")
+contour!(xlabel=L"\theta", ylabel=L"\epsilon")
 annotate!([(1.8,2.5, text("new life", 14, :white, :center))])
 annotate!([(4.5,2.5, text("new job", 14, :center))])
 annotate!([(4.0,4.5, text("stay put", 14, :center))])