⚡ Pluto.jl ⚡

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begin
    using Distributions, Gadfly, Random, LinearAlgebra,LaTeXStrings,RDatasets,Compose
end

17.2 s

f (generic function with 1 method)

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begin
x = range(-3,stop=3,length=200)
y = range(-3,stop=10,length=200)
N = 1000
Sampleₙ = 5
f(x,y) = exp(-((1 - x)^2 + 100(y - x^2)^2) / 20)
end

158 ms

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plot((x,y)->f(x,y),-3,3,-3,10,Stat.contour(levels=10))

561 ms

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using DataFrames

2.1 ms

DiagNormal(
dim: 2
μ: [0.0, 0.0]
Σ: [0.1 0.0; 0.0 0.1]
)

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q = MvNormal(zeros(2),Diagonal(ones(2))*0.1)

75.9 ms

 
begin
    p = nothing
    D = DataFrame(x=repeat(x, inner=length(x)), y=repeat(y,outer=length(y)))
    D.z =  map((x)->f(x...),zip(D.x,D.y))
    p = []
    push!(p,layer(D, x=:x, y=:y,z=:z,Geom.contour(levels=5)))
    push!(p,layer(x=[1],y=[1],shape=[Shape.star2],alpha=[1.0],                  
            Geom.point,
            Theme(point_size=3mm,default_color=color("black")),
            order=1))
    push!(p,layer(x=[1,2.5],y=[1,-2.5],Geom.line,
            Theme(default_color=color("black"),line_width=0.3mm)))
    push!(p,Guide.annotation(compose(context(), text(2.3, -2.9, "fₘₐₓ(1,1)=1"))))
    colors = ["orange","purple","darkgreen","red","blue"]
    for sᵢ in 1:Sampleₙ
        samples = Array{Float64,2}(zeros(N,2))
        samples[1,:] = [rand(Uniform(-3,3)),rand(Uniform(-3,10))]
        udist = Uniform()
        for i in 2:N
            curr = samples[i-1,:]
            prop = curr + rand(q)
            alpha = f(prop...) / f(curr...)     
            if rand(udist) < alpha
                curr = prop
            end
            samples[i,:] = curr
        end 
        #Geom.path는 Geom.line(preserve_order=true)과 동일
        push!(p,layer(x=samples[:,1],y=samples[:,2],Geom.path ,Geom.point,
                Theme(point_size=0.8mm,line_width=0.05mm,
                    default_color=color(colors[sᵢ]),
                    point_shapes=[Shape.circle],
                    alphas=[0.6],highlight_width=0.1mm),order=1))
    end
    plot(p...,
        Coord.cartesian(xmin=-3, xmax=3, ymin=-3, ymax=10),
        Guide.title("Rosenbrock densityt f(x)"),
        Guide.xticks(ticks = -3:1:3),
        Guide.yticks(ticks = -2:2:10))
end

7.6 ms