Added Project and Report

2024-07-30 14:43:25 +02:00
parent c828453e94
commit 3ad6f7f86f
311 changed files with 13490 additions and 3280 deletions
--- a/Lessons/10-12/GRS.jl
+++ b/Lessons/10-12/GRS.jl
@ -0,0 +1,187 @@
+using Plots
+using LinearAlgebra
+using Printf
+
+function GRS(f;
+        rangeplt::Union{Nothing, Tuple{Real, Real}}=nothing,
+        delta::Real=1e-6,
+        MaxFeval::Integer=100,
+        plt::Union{Plots.Plot, Nothing}=nothing,
+        plotatend::Bool=true,
+        Plotg::Integer=0
+    )::Tuple{Real, String}
+
+    # Plotg
+    # 0 = nothing is plotted
+    # 1 = the function value / gap are plotted
+    # 2 = the function and the test points used are plotted
+
+    resolution = 1000
+
+    Interactive = false # if we pause at every iteration
+
+    # reading and checking input- - - - - - - - - - - - - - - - - - - - - - - -
+    # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+    if rangeplt == nothing
+        (fStar, _, _, rangeplt) = f(nothing)
+    else
+        fStar = -Inf
+    end
+
+    xm = rangeplt[1] # x_-
+    xp = rangeplt[2] # x_+
+
+    if xm > xp
+        throw(ArgumentError("rangeplt is empty"))
+        return (NaN, "empty")
+    end
+
+    if MaxFeval < 2
+        throw(ArgumentError("At least two function computations are required"))
+        return (NaN, "empty")
+    end
+
+    # initializations - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+    # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+    r = (sqrt( 5 ) - 1)/2
+
+    xmp = xm + (1 - r) * (xp - xm) # x'_-
+    xpp = xm + r * (xp - xm)       # x'_+
+
+    fxmp = f(xmp)[1]               # f(x'_-)
+    fxpp = f(xpp)[1]               # f(x'_+)
+
+    feval = 2
+
+    if fxmp ≤ fxpp
+        fx = fxmp
+    else
+        fx = fxpp
+    end
+
+    status = "optimal"
+
+    if Plotg > 0
+        gap = []
+    end
+
+    if Plotg == 1 && plt == nothing
+        plt = plot(yscale = :log,
+                   xlims=(0, 35),
+                   ylims=(1e-15, Inf),
+                   guidefontsize=16)
+    elseif Plotg == 2 && plt == nothing
+        plt = plot(legend = false)
+    end
+
+    print("Golden ratio search\n")
+    if fStar > -Inf
+       print("feval\trel gap\t\tx_-\t\tx_+\n")
+    else
+       print("feval\tfbest\t\tx_-\t\tx_+\n")
+    end
+
+    # main loop - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+    # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+    while xp - xm > delta
+
+        # output statistics - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+        if fStar > -Inf
+            gapk = (fx - fStar) / max(abs(fStar), 1)
+
+            if Plotg == 1
+                push!(gap, gapk)
+            end
+        else
+            gapk = fx
+        end
+        @printf("%4d\t%1.4e\t%1.8e\t%1.8e\n", feval, gapk, xm, xp)
+
+        if Plotg == 2
+            xbot = xm - ( xp - xm ) / 20;
+            xtop = xp + ( xp - xm ) / 20;
+
+            if !isempty(plt.series_list)
+                plt.series_list[end][:linealpha] = 0
+            end
+            xx = range(xbot, xtop, resolution)
+            yy = map(v -> v[1], f.(xx))
+            xlims!(plt, (xbot, xtop))
+            old_ylims = ylims(plt)
+            ylims!(plt, (old_ylims[1], max(fxmp, fxpp)))
+            plot!(plt, xx, yy)
+
+            # old_xticks = xticks(plt[1])
+            new_xticks = ([xbot, xm, xmp, xpp, xp, xtop],
+                [@sprintf("%1.1g", xbot), "x-", "x''-", "x''+", "x+", @sprintf("%1.1g", xtop)])
+            # keep_indices = findall(x -> all(x .≠ new_xticks[1]), old_xticks[1])
+            # merged_xticks = (old_xticks[1][keep_indices] ∪ new_xticks[1],
+            #                  old_xticks[2][keep_indices] ∪ new_xticks[2])
+            # xticks!(merged_xticks)
+            xticks!(plt, new_xticks)
+        end
+
+        # stopping criteria - - - - - - - - - - - - - - - - - - - - - - - - - -
+        if feval > MaxFeval
+            status = "stopped"
+            break
+        end
+
+        # main logic- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+        if fxmp <= fxpp
+            xp = xpp
+            xpp = xmp
+            xmp = xm + (1 - r) * (xp - xm)
+
+            fxpp = fxmp
+            fx = fxmp
+            fxmp = f(xmp)[1]
+        else
+            xm = xmp
+            xmp = xpp
+            xpp = xm + r * (xp - xm)
+            
+            fxmp = fxpp
+            fx = fxpp
+            fxpp = f(xpp)[1]
+        end
+
+        feval += 1
+
+        if Plotg ≠ 0 && Interactive
+            IJulia.clear_output(wait=true)
+            display(plt)
+            sleep(0.1)
+            readline()
+        end
+
+        # iterate - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+    end
+
+    # end of main loop- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+    # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+    # select final answer
+    if fxmp ≤ fxpp
+        x = xmp
+    else
+        x = xpp
+    end
+
+    if Plotg == 1
+        plot!(plt,
+            gap,
+            linewidth=2)
+    end
+
+    if plotatend && Plotg ≠ 0
+        display(plt)
+    end
+
+    (x, status)
+end