File size: 3,047 Bytes
c711202 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 | """
QQ plot of z-scores against N(0,1) for UQ calibration diagnostic.
Reads z-score NPZ files saved by the scalability study.
Usage:
julia --project=../.. plot_qq.jl results/scalability/zscores/zscores_N31.npz
julia --project=../.. plot_qq.jl results/scalability/zscores/zscores_N31.npz results/calibrated/zscores/zscores_N31.npz --labels "Default,Calibrated"
"""
using NPZ
using CairoMakie
using Statistics
using SpecialFunctions
# Normal quantile function (inverse CDF of N(0,1))
norminv(p) = √2 * erfinv(2p - 1)
function qq_theoretical(z_empirical)
n = length(z_empirical)
z_sorted = sort(z_empirical)
# Theoretical quantiles: use (i - 0.5) / n to avoid ±∞
p = [(i - 0.5) / n for i in 1:n]
z_theoretical = norminv.(p)
return z_theoretical, z_sorted
end
function plot_qq(npz_paths::Vector{String}, labels::Vector{String};
filename::Union{Nothing,String}=nothing,
grid_size::Union{Nothing,Int}=nothing)
fig = Figure(size=(800, 380), fontsize=12)
colors = [:royalblue, :crimson, :seagreen, :darkorange]
for (col_idx, (field, title)) in enumerate([("z_c", "Concentration"), ("z_s", "Source")])
ax = Axis(fig[1, col_idx];
xlabel="Theoretical quantiles (N(0,1))",
ylabel="Empirical quantiles",
title=title,
aspect=1,
)
# Reference diagonal
lines!(ax, [-4, 4], [-4, 4]; color=:gray60, linestyle=:dash, linewidth=1,
label="N(0,1)")
for (i, (path, label)) in enumerate(zip(npz_paths, labels))
data = npzread(path)
z = vec(data[field])
z_th, z_emp = qq_theoretical(z)
# Subsample for plotting if too many points
if length(z_th) > 500
idx = round.(Int, range(1, length(z_th), length=500))
z_th = z_th[idx]
z_emp = z_emp[idx]
end
scatter!(ax, z_th, z_emp; color=(colors[i], 0.6), markersize=3,
label="$label (σ̂=$(round(std(vec(data[field])), digits=2)))")
end
xlims!(ax, -4, 4)
ylims!(ax, -4, 4)
axislegend(ax; position=:lt, labelsize=10)
end
if !isnothing(filename)
mkpath(dirname(filename))
save(filename, fig, px_per_unit=3)
println("Saved: $filename")
end
return fig
end
if abspath(PROGRAM_FILE) == @__FILE__
local npz_paths = String[]
local labels = String[]
local output = joinpath(@__DIR__, "results", "scalability", "qq_plot.pdf")
local idx = 1
while idx <= length(ARGS)
if ARGS[idx] == "--labels"
idx += 1
labels = String.(split(ARGS[idx], ","))
elseif ARGS[idx] == "-o"
idx += 1
output = ARGS[idx]
else
push!(npz_paths, ARGS[idx])
end
idx += 1
end
if isempty(labels)
labels = ["Run $j" for j in 1:length(npz_paths)]
end
plot_qq(npz_paths, labels; filename=output)
end
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