Track Roots 3 find_zero convergence failures in quantile paths

[lrnv]

[writen by chatgpt]

Summary

Recent full test runs fail with Roots.ConvergenceFailed("Algorithm failed to converge") from quantile/root-finding paths that used to pass.

This started showing up after dependency updates around Roots/Optim. It may be a Roots 3 behavior/tolerance change, or it may expose that our quantile calls rely on overly strict/default convergence behavior.

Observed failures

From the attached test output:

1. BC2Copula sampling through ExtremeDist.quantile:

Roots.ConvergenceFailed("Algorithm failed to converge")
Stacktrace:
  Roots.find_zero(..., Roots.Brent())
  quantile @ src/UnivariateDistribution/ExtremeDist.jl:42
  rand @ src/UnivariateDistribution/ExtremeDist.jl:47
  _rand!(::StableRNGs.LehmerRNG, ::BC2Copula{Float64}, ::Matrix{Float64})
      @ src/ExtremeValueCopula.jl:80

Examples in the test output include:

• BC2Copula{Float64}(a = 0.5, b = 0.3)
• BC2Copula{Float64}(a = 0.5, b = 0.5)
• BC2Copula{Float64}(a = 0.5516353577049822, b = 0.33689370624999193)
• BC2Copula{Float64}(a = 0.7, b = 0.3)
• BC2Copula{Float64}(a = 0.6, b = 0.8)

The relevant code currently does:

Roots.find_zero(x -> Distributions.cdf(d, x) - p,
                (eps(), 1.0 - eps()), Roots.Brent())

2. Bernstein inverse Rosenblatt through Distributions mixture quantile:

Roots.ConvergenceFailed("Algorithm failed to converge")
Stacktrace:
  Roots.find_zero(...)
  quantile_bisect @ Distributions/src/quantilealgs.jl:18
  quantile @ Distributions/src/mixtures/mixturemodel.jl:449
  inverse_rosenblatt(::BernsteinCopula{2}, ...)
      @ src/Conditioning.jl:340

The failing test is the generic roundtrip:

rosenblatt ∘ inverse_rosenblatt = Id

Version trail

Current local manifest / failing run:

• Julia: 1.12.1
• Copulas: 0.1.35
• Roots: 3.0.2
• Optim: 2.2.1
• Distributions: 0.25.129

Recent compat history from this repo:

• Before ad9988b3 / PR #354, Project.toml had Roots = "1, 2".
• After ad9988b3 / PR #354, Project.toml has Roots = "1, 2, 3".
• Before a75b08cf / PR #355, Project.toml had Optim = "1.13.2".
• After a75b08cf / PR #355, Project.toml has Optim = "2".

Manifest.toml is not tracked historically in this repo, so I could not recover the exact old resolved Roots version from git. Installed local Roots versions include:

• 2.2.10 installed 2025-09-02
• 3.0.0 installed 2026-05-11
• 3.0.2 installed 2026-07-10

Given the old compat was Roots = "1, 2", the previous resolver target was presumably a Roots 2.x release, likely 2.2.10 in this local environment.

Initial hypothesis

This may be due to Roots 3 returning NaN / throwing ConvergenceFailed more readily when the bracketing solver reaches a plateau or a very tight tolerance near floating-point resolution. The two failure paths both rely on library quantile/root-finding defaults:

• our explicit Roots.find_zero(..., Roots.Brent()) in ExtremeDist.quantile;
• Distributions' quantile_bisect, which now delegates to find_zero(..., ITP()) and relies on Roots defaults.

Things to investigate

• Reproduce with Roots 3.0.2 versus Roots 2.2.10.
• Check whether ExtremeDist.quantile should use a more robust local bisection/ITP call with explicit tolerances or endpoint guards.
• Check whether the Bernstein failures are upstream in Distributions/Roots defaults or whether our inverse_rosenblatt passes probabilities close enough to a flat/atomic mixture boundary that we should clamp or handle endpoints.