Integrate with hints

[alexandrehoffmann]

The goal of this PR is to use adaptive quadrature over $\mathbb{R}$ with hints on where the most relevant features of the integrate functions are.

The user provides a std::span of mean and a single variance corresponding to the function's peaks the adaptive quadrature then computes an initial subdivision of $\mathbb{R}$ from theses informations.

[Copilot]

Pull request overview

This PR refactors the finite-interval adaptive quadrature implementation by extracting the iterative “adaptation” loop into a reusable helper, likely as groundwork for alternative initialization strategies (e.g., hinted subdivision).

Changes:

• Extracted the core adaptive refinement loop into a new private helper (addaptQuadrature).
• Reworked integrate(xmin, xmax) to only build the initial subdivision and then delegate refinement to the helper.
• Minor local cleanup in the refinement loop (structured binding for the second interval estimate).

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 4 comments.

File	Description
include/LNIT/AdaptiveQuadratures/AdaptiveQuadratureBase.hpp	Declares a new private helper to run the adaptive refinement loop.
include/LNIT/AdaptiveQuadratures/AdaptiveQuadratureBase_impl.hpp	Moves the refinement loop into the helper and makes integrate delegate to it after initial subdivision.

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[Copilot]

Pull request overview

Copilot reviewed 2 out of 2 changed files in this pull request and generated 2 comments.

Comments suppressed due to low confidence (3)

include/LNIT/AdaptiveQuadratures/AdaptiveQuadratureBase_impl.hpp:125

• Range-for iterates mu as const double&, which forces a conversion from Scalar to double and can lose precision (and breaks if Scalar isn’t implicitly convertible to double). Iterate using Scalar instead.

	for (const double& mu_i : mu)

include/LNIT/AdaptiveQuadratures/AdaptiveQuadratureBase_impl.hpp:123

• If mu is empty, no sub-intervals are created and adaptQuadrature() will call max_element() on an empty error vector (UB). Consider falling back to the existing infinite-range integrate(f) behavior when no hints are provided.

	m_intervals.clear();
	m_subIntergrals.clear();
	m_subIntergralsErr.clear();

	m_intervals.reserve(2*mu.size());

include/LNIT/AdaptiveQuadratures/AdaptiveQuadratureBase_impl.hpp:179

• fmt::print(..., "{}", m_intervals) requires fmt range formatting support (e.g., <fmt/ranges.h>) and a formatter for Interval/pair. With only <fmt/core.h> included here, this is likely to fail to compile. Consider logging only the number of intervals, or include the necessary fmt headers.

	if (m_out) { fmt::print(m_out, "#NumericalIntegrator adapting quadrature over {}\n", m_intervals); }

[alexandrehoffmann]

PR comment was fixed to a std::span of means and a single sigma.