Added Project and Report
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elvis
223
Lessons/10-12/DIS.jl
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223
Lessons/10-12/DIS.jl
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using LinearAlgebra
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using Printf
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using Plots
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function DIS(f;
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rangeplt::Union{Nothing, Tuple{Real, Real}}=nothing,
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sfgrd::Real=0,
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eps::Real=1e-6,
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MaxFeval::Integer=100,
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plt::Union{Plots.Plot, Nothing}=nothing,
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plotatend::Bool=true,
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Plotg::Integer=0
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)::Tuple{Real, String}
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# Plotg
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# 1 = the function value / gap are plotted
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# 2 = the function and the model (if used) are plotted
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# all the rest: nothing is plotted
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resolution = 1000
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Interactive = false # if we pause at every iteration
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# reading and checking input- - - - - - - - - - - - - - - - - - - - - - - -
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# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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if rangeplt == nothing
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(fStar, _, _, rangeplt) = f(nothing)
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else
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fStar = -Inf
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end
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xm = rangeplt[1] # x_-
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xp = rangeplt[2] # x_+
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if xm > xp
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throw(ArgumentError("rangeplt is empty"))
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return (NaN, "empty")
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end
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(fxm, f1xm, _) = f(xm)
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if( f1xm > 0 )
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throw(DomainError(rangeplt, "f'(x_-) must be ≤ 0"))
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return (NaN, "empty")
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end
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(fxp, f1xp, _) = f(xp)
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if( f1xp < 0 )
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throw(DomainError(rangeplt, "f'(x_+) must be ≥ 0"))
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return (NaN, "empty")
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end
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if (sfgrd < 0) || (sfgrd ≥ 0.5)
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throw(DomainError(sfgrd, "sfgrd must be in [ 0 , 1/2 )"))
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return (NaN, "empty")
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end
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if MaxFeval < 2
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throw(ArgumentError("At least two function computations are required"))
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return (NaN, "empty")
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end
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# initializations - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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feval = 2
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status = "optimal"
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if f1xm ≥ -eps
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return (xm, status)
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end
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if f1xp ≤ eps
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return (xp, status)
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end
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fbest = min(fxp, fxm)
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f1x = min(-f1xp, f1xm)
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if Plotg == 1
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gap = []
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end
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if Plotg == 1 && plt == nothing
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plt = plot(yscale = :log,
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xlims=(0, 35),
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ylims=(1e-15, Inf),
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guidefontsize=16)
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elseif Plotg == 2 && plt == nothing
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plt = plot(legend = false)
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end
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if iszero(sfgrd)
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println("Dichotomic search")
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else
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@printf("Dichotomic search with safeguarded interpolation (%1.4f)\n", sfgrd)
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end
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if fStar > -Inf
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println("feval\trel gap\t\tx_-\t\tx_+\t\tx\t\tf'(x)")
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else
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println("feval\tfbest\t\tx_-\t\tx_+\t\tx\t\tf'(x)")
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end
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# main loop - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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x = 0
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while true
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# stopping criteria - - - - - - - - - - - - - - - - - - - - - - - - - -
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if feval > MaxFeval
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status = "stopped"
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break
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end
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# main logic- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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if iszero(sfgrd)
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# compute the new point as the middle of the inteval
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x = (xm + xp) / 2
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else
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# compute the new point by safeguarded quadratic interpolation
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sfxp = xp - (xp - xm) * sfgrd
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sfxm = xm + (xp - xm) * sfgrd
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x = (xm * f1xp - xp * f1xm) / (f1xp - f1xm)
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x = max(sfxm, min(sfxp, x))
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end
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(fx, f1x, _) = f(x) # compute f(x) and f'(x)
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if fx < fbest
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fbest = fx
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end
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feval += 1
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# output statistics - - - - - - - - - - - - - - - - - - - - - - - - - -
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if fStar > -Inf
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gapk = (fbest - fStar) / max(abs(fStar), 1)
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if Plotg == 1
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push!(gap, gapk)
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end
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else
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gapk = fbest
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end
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@printf("%4d\t%1.4e\t%1.8e\t%1.8e\t%1.8e\t%1.4e\n", feval, gapk, xm, xp, x, f1x)
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if Plotg == 2
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xmp = xm - (xp - xm) / 20
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xpp = xp + (xp - xm) / 20
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for e in plt.series_list
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e[:linealpha] = 0
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end
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xx = range(xmp, xpp, resolution)
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yy = map(v -> v[1], f.(xx))
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xlims!(plt, (xmp, xpp))
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old_ylims = ylims(plt)
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ylims!(plt, (old_ylims[1], max(fxm, fxp)))
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plot!(plt, xx, yy)
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if !iszero(sfgrd)
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a = (f1xp - f1xm) / (2 * (xp - xm))
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b = (xp * f1xm - xm * f1xp) / (xp - xm)
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# a xm^2 + b xm + c == fxm ==>
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# c == fxm - a xm^2 - b xm
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c = fxm - a * xm^2 - b * xm
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xlims!(plt, (xmp, xpp))
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new_xticks = ([xmp, xm, sfxm, sfxp, xp, xpp],
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[@sprintf("%1.1g", xmp), "x-", "sx-", "sx+", "x+", @sprintf("%1.1g", xpp)])
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xticks!(plt, new_xticks)
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plot!(plt, xx, @. a*xx^2 + b*xx + c)
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else
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new_xticks = ([xmp, xm, x, xp, xpp],
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[@sprintf("%1.1g", xmp), "x-", "x", "x+", @sprintf("%1.1g", xpp)])
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xticks!(plt, new_xticks)
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end
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end
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# stopping criteria - - - - - - - - - - - - - - - - - - - - - - - - - -
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if abs(f1x) ≤ eps
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break
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end
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# restrict the interval based on sign of the derivative in xn - - - - -
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if f1x < 0
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xm = x
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fxm = fx
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f1xm = f1x
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else
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xp = x
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fxp = fx
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f1xp = f1x
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end
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if Plotg ≠ 0 && Interactive
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IJulia.clear_output(wait=true)
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display(plt)
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sleep(0.1)
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readline()
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end
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# iterate - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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end
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if Plotg == 1
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plot!(plt,
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gap,
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linewidth=2)
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end
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if plotatend && Plotg ≠ 0
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display(plt)
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end
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(x, status)
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end
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