using Gadfly
using DataFrames
using Isotonic

set_default_plot_size(21cm, 13cm);

function logistic_data(n::Int64)
    X = sort(randn(n))
    return X, float64(1.0 / (1.0 + exp(X)) .< rand(n))
end;

X, Y = logistic_data(200)
plot(x=X, y=Y, Geom.point)

function timing(n::Int64, iters::Int64, regression::Function)
    gc()
    _, Y = logistic_data(n)
    weights = ones(n)
    times = zeros(iters)
    for i in 1 : iters
        t_start = time()
        scratch = copy(Y)
        regression(scratch, weights)
        t_end = time()
        times[i] = t_end - t_start
    end
    return mean(times)
end;

xs = logspace(2, 7, 10)

run(algorithm, fn) =  DataFrame(X=xs, Y=map(x -> timing(int64(x), 1, fn), xs), algorithm=algorithm)
df = [
    run("Active Set", active_set_isotonic_regression), 
    run("Linear PAVA", isotonic_regression), 
    run("Pooled PAVA", pooled_pava_isotonic_regression)];

plot(df, x="X", y="Y", color="algorithm", Geom.line, Geom.point, Scale.x_log10, Scale.y_log10)