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Plotting Utilities for Accuracy vs Compute Experiment
Creates Pareto plots, scaling plots, calibration plots, etc.
"""
using CairoMakie
using Statistics
using DataFrames
# Include metrics for MetricsSummary type
include("metrics.jl")
# Color scheme for methods
const METHOD_COLORS = Dict(
"sparse_fvm" => :blue,
"ekf_fvm" => :purple,
"sparse_collocation" => :green,
"classical_fvm" => :orange,
)
const METHOD_MARKERS = Dict(
"sparse_fvm" => :circle,
"ekf_fvm" => :star5,
"sparse_collocation" => :diamond,
"classical_fvm" => :utriangle,
)
const METHOD_LABELS = Dict(
"sparse_fvm" => "Sparse GP-FVM",
"ekf_fvm" => "EKF GP-FVM",
"sparse_collocation" => "Sparse GP-Collocation",
"classical_fvm" => "Classical FVM",
)
"""
pareto_plot(results::DataFrame; kwargs...)
Create Pareto frontier plot: L2 error vs wall-clock time.
# Arguments
- `results`: DataFrame with columns: method, N, time_s, mean_l2_error (and optionally std columns)
# Keyword arguments
- `aggregate=true`: If true, aggregate over IC seeds showing mean ± std
- `title="Accuracy vs Compute"`: Plot title
- `filename=nothing`: If provided, save figure to this path
"""
function pareto_plot(results::DataFrame;
aggregate::Bool=true,
title::String="Accuracy vs Compute",
filename::Union{Nothing,String}=nothing)
fig = Figure(size=(800, 600), fontsize=14)
ax = Axis(fig[1, 1],
xlabel = "Wall-clock time (s)",
ylabel = "Relative L2 error",
xscale = log10,
yscale = log10,
title = title
)
methods = unique(results.method)
for method in methods
method_data = filter(row -> row.method == method, results)
if aggregate
# Group by N and aggregate
grouped = combine(
groupby(method_data, :N),
:time_s => mean => :time_mean,
:time_s => std => :time_std,
:mean_l2_error => mean => :error_mean,
:mean_l2_error => std => :error_std
)
sort!(grouped, :N)
times = grouped.time_mean
errors = grouped.error_mean
# Plot with error bars
scatter!(ax, times, errors,
color = METHOD_COLORS[method],
marker = METHOD_MARKERS[method],
markersize = 12,
label = METHOD_LABELS[method]
)
# Connect points with lines
lines!(ax, times, errors,
color = METHOD_COLORS[method],
linewidth = 2
)
# Add error bars if we have multiple samples
# On log scale, we need asymmetric error bars to avoid going negative
if any(grouped.error_std .> 0)
# Upper error is just std
error_high = grouped.error_std
# Lower error is clamped so we don't go below 10% of the mean (stays positive on log scale)
error_low = min.(grouped.error_std, errors .* 0.9)
errorbars!(ax, times, errors, error_low, error_high,
color = METHOD_COLORS[method],
linewidth = 1
)
end
# Label points with N
for row in eachrow(grouped)
text!(ax, row.time_mean, row.error_mean,
text = "N=$(row.N)",
fontsize = 9,
offset = (5, 5)
)
end
else
# Plot all points individually
scatter!(ax, method_data.time_s, method_data.mean_l2_error,
color = METHOD_COLORS[method],
marker = METHOD_MARKERS[method],
markersize = 8,
label = METHOD_LABELS[method]
)
end
end
axislegend(ax, position = :rt)
if !isnothing(filename)
mkpath(dirname(filename))
save(filename, fig)
println("Saved: $filename")
end
return fig
end
"""
scaling_plot(results::DataFrame; kwargs...)
Create scaling plot: wall-clock time vs grid size N on log-log scale.
Shows O(N) vs O(N³) scaling.
"""
function scaling_plot(results::DataFrame;
title::String="Computational Scaling",
filename::Union{Nothing,String}=nothing)
fig = Figure(size=(800, 600), fontsize=14)
ax = Axis(fig[1, 1],
xlabel = "Grid size N",
ylabel = "Wall-clock time (s)",
xscale = log10,
yscale = log10,
title = title
)
methods = unique(results.method)
for method in methods
method_data = filter(row -> row.method == method, results)
# Aggregate by N
grouped = combine(
groupby(method_data, :N),
:time_s => mean => :time_mean,
:time_s => std => :time_std
)
sort!(grouped, :N)
Ns = grouped.N
times = grouped.time_mean
scatter!(ax, Ns, times,
color = METHOD_COLORS[method],
marker = METHOD_MARKERS[method],
markersize = 12,
label = METHOD_LABELS[method]
)
lines!(ax, Ns, times,
color = METHOD_COLORS[method],
linewidth = 2
)
end
# Add reference slopes
N_ref = [minimum(results.N), maximum(results.N)]
t_base = 0.01 # Adjust based on data
# O(N) reference line
lines!(ax, N_ref, t_base .* (N_ref ./ N_ref[1]),
color = :gray, linestyle = :dash, linewidth = 1,
label = "O(N)"
)
# O(N³) reference line
lines!(ax, N_ref, t_base .* (N_ref ./ N_ref[1]).^3,
color = :gray, linestyle = :dot, linewidth = 1,
label = "O(N³)"
)
axislegend(ax, position = :lt)
if !isnothing(filename)
mkpath(dirname(filename))
save(filename, fig)
println("Saved: $filename")
end
return fig
end
"""
calibration_plot(results::DataFrame; kwargs...)
Create calibration plot: empirical coverage vs nominal coverage.
Shows if uncertainty quantification is well-calibrated.
"""
function calibration_plot(results::DataFrame;
nominal_levels::Vector{Float64}=[0.5, 0.8, 0.9, 0.95, 0.99],
title::String="UQ Calibration",
filename::Union{Nothing,String}=nothing)
fig = Figure(size=(700, 600), fontsize=14)
ax = Axis(fig[1, 1],
xlabel = "Nominal coverage",
ylabel = "Empirical coverage",
title = title,
aspect = 1
)
# Perfect calibration line
lines!(ax, [0, 1], [0, 1],
color = :black, linestyle = :dash, linewidth = 1,
label = "Perfect calibration"
)
# For now, we only have 95% coverage in the data
# This would need extension to compute coverage at multiple levels
methods = unique(results.method)
for method in methods
method_data = filter(row -> row.method == method, results)
# Mean coverage across all runs
mean_coverage = mean(method_data.coverage_95)
# Plot single point at 95% nominal
scatter!(ax, [0.95], [mean_coverage],
color = METHOD_COLORS[method],
marker = METHOD_MARKERS[method],
markersize = 15,
label = METHOD_LABELS[method]
)
end
xlims!(ax, 0.4, 1.0)
ylims!(ax, 0.4, 1.0)
axislegend(ax, position = :rb)
if !isnothing(filename)
mkpath(dirname(filename))
save(filename, fig)
println("Saved: $filename")
end
return fig
end
"""
convergence_plot(results::DataFrame; kwargs...)
Create convergence plot: L2 error vs grid size N.
Shows discretization convergence rate.
"""
function convergence_plot(results::DataFrame;
title::String="Discretization Convergence",
filename::Union{Nothing,String}=nothing)
fig = Figure(size=(800, 600), fontsize=14)
ax = Axis(fig[1, 1],
xlabel = "Grid size N",
ylabel = "Relative L2 error",
xscale = log10,
yscale = log10,
title = title
)
methods = unique(results.method)
for method in methods
method_data = filter(row -> row.method == method, results)
# Aggregate by N
grouped = combine(
groupby(method_data, :N),
:mean_l2_error => mean => :error_mean,
:mean_l2_error => std => :error_std
)
sort!(grouped, :N)
Ns = grouped.N
errors = grouped.error_mean
scatter!(ax, Ns, errors,
color = METHOD_COLORS[method],
marker = METHOD_MARKERS[method],
markersize = 12,
label = METHOD_LABELS[method]
)
lines!(ax, Ns, errors,
color = METHOD_COLORS[method],
linewidth = 2
)
end
# Add reference slopes
N_ref = [minimum(results.N), maximum(results.N)]
e_base = maximum(results.mean_l2_error)
# O(1/N) = O(Δx) first-order convergence
lines!(ax, N_ref, e_base .* (N_ref[1] ./ N_ref),
color = :gray, linestyle = :dash, linewidth = 1,
label = "O(1/N)"
)
# O(1/N²) = O(Δx²) second-order convergence
lines!(ax, N_ref, e_base .* (N_ref[1] ./ N_ref).^2,
color = :gray, linestyle = :dot, linewidth = 1,
label = "O(1/N²)"
)
axislegend(ax, position = :rt)
if !isnothing(filename)
mkpath(dirname(filename))
save(filename, fig)
println("Saved: $filename")
end
return fig
end
"""
summary_table(results::DataFrame)
Create summary table of results aggregated by method and N.
"""
function summary_table(results::DataFrame)
summary = combine(
groupby(results, [:method, :N]),
:time_s => mean => :time_mean,
:time_s => std => :time_std,
:mean_l2_error => mean => :error_mean,
:mean_l2_error => std => :error_std,
:coverage_95 => mean => :coverage_mean,
:fillin_pct => mean => :fillin_mean,
nrow => :n_samples
)
sort!(summary, [:method, :N])
return summary
end
"""
results_to_dataframe(metrics::Vector{MetricsSummary})
Convert vector of MetricsSummary to DataFrame.
"""
function results_to_dataframe(metrics::Vector{MetricsSummary})
rows = [metrics_to_namedtuple(m) for m in metrics]
return DataFrame(rows)
end
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