Possible solution of the Julia optimization task

material/5_fri/optimizing_julia/optimizing_julia_solution.jl

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+# # Optimizing Julia code: possible solution
+
+# First, we install all required packages
+import Pkg
+Pkg.activate(@__DIR__)
+Pkg.instantiate()
+
+# The markdown file is created from the source code using
+# [Literate.jl](https://github.com/fredrikekre/Literate.jl).
+# You can create the markdown file via
+
+using Literate
+Literate.markdown(joinpath(@__DIR__, "optimizing_julia_solution.jl");
+                  flavor = Literate.CommonMarkFlavor())
+
+# First, we generate initial data and store it in a file.
+using HDF5
+x = range(-1.0, 1.0, length = 1000)
+dx = step(x)
+h5open("initial_data.h5", "w") do io
+    u0 = sinpi.(x)
+    write_dataset(io, "x", collect(x))
+    write_dataset(io, "u0", u0)
+end
+
+function simulate(; kwargs...)
+    x, u0 = h5open("initial_data.h5", "r") do io
+        read_dataset(io, "x"), read_dataset(io, "u0")
+    end
+
+    u = copy(u0)
+    t = simulate!(u; kwargs...)
+
+    return t, x, u, u0
+end
+
+function simulate!(u; t_end, dt, dx)
+    du = similar(u)
+    t = zero(t_end)
+    while t < t_end
+        rhs!(du, u, dx)
+        # u = u + dt * du
+        # u .= u .+ dt .* du
+        @. u = u + dt * du
+        t = t + dt
+    end
+
+    return t
+end
+
+# function rhs!(du, u, dx)
+#     for i in eachindex(u)
+#         im1 = i == firstindex(u) ? lastindex(u) : (i - 1)
+#         du[i] = -(u[i] - u[im1]) / dx
+#     end
+#     return nothing
+# end
+
+function rhs!(du, u, dx)
+    inv_dx = inv(dx)
+
+    let i = firstindex(u)
+        im1 = lastindex(u)
+        # du[i] = -(u[i] - u[im1]) / dx
+        du[i] = -inv_dx * (u[i] - u[im1])
+    end
+
+    for i in (firstindex(u) + 1):lastindex(u)
+        im1 = i - 1
+        # du[i] = -(u[i] - u[im1]) / dx
+        du[i] = -inv_dx * (u[i] - u[im1])
+    end
+    return nothing
+end
+
+# Now, we can define our parameters, run a simulation,
+# and plot the results.
+using Plots, LaTeXStrings
+
+t_end = 2.5
+dt = 0.9 * dx
+t, x, u, u0 = simulate(; t_end, dt, dx)
+plot(x, u0; label = L"u_0", xguide = L"x")
+plot!(x, u; label = L"u")
+
+
+using BenchmarkTools
+@benchmark simulate(; t_end, dt, dx)
+
+let u = h5open("initial_data.h5", "r") do io
+        read_dataset(io, "u0")
+    end
+    @benchmark simulate!(u; t_end, dt, dx)
+end