Rewrite QGQ into DQ module

[tovrstra]

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[Copilot]

Pull request overview

This PR rewrites the stacie.qgq (Quasi-Gaussian Quadrature) module into a new stacie.dq (Designed Quadrature) module. The new module uses a fundamentally different optimization approach — a custom modified Levenberg-Marquardt algorithm with an orthogonal regularization scheme — replacing the previous L-BFGS-B optimizer from scipy. This results in better numerical stability and more control over the optimization. An analytical dq3 helper for 3-point quadrature is also added.

Changes:

• New src/stacie/dq.py: Complete rewrite of the QGQ algorithm with the new DQ formulation using fixed (equal or user-specified) weights, a custom LM solver, and a new Equations class encapsulating the constraint system.
• Updated tests: tests/test_qgq.py removed and replaced by the more comprehensive tests/test_dq.py, adding unit tests for individual methods (apply_sym, backprop_sym, proj, pen, solve_weights, dq3).
• Updated documentation: docs/source/examples/qgq.py replaced by docs/source/examples/dq.py with an expanded tutorial, new BibTeX references added, changelog updated.

Reviewed changes

Copilot reviewed 9 out of 9 changed files in this pull request and generated 13 comments.

Show a summary per file

File	Description
src/stacie/dq.py	New DQ module (699 lines) replacing qgq.py; new Equations class, solve_modified_lm, dq3 function, and public API
tests/test_dq.py	New test file with more granular unit tests for the DQ internals
tests/test_qgq.py	Removed (replaced by test_dq.py)
src/stacie/qgq.py	Removed (replaced by dq.py)
docs/source/examples/dq.py	New example notebook (450 lines) with DQ tutorial and regression tests
docs/source/examples/qgq.py	Removed (replaced by dq.py)
docs/source/examples/index.md	Updated to reference dq.py instead of qgq.py
docs/source/references.bib	Added two new BibTeX entries for Chebyshev quadrature literature
docs/source/development/changelog.md	Added changelog entry for the new stacie.dq module

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[Copilot]

Pull request overview

Copilot reviewed 9 out of 9 changed files in this pull request and generated 2 comments.

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