⚡ Bolt: Remove redundant matrix inversions in Vuong test

[seonghobae]

💡 What: Optimized calcAB to return the original matrix tmpvc as Ainv, and updated calcLambda to use Ainv directly instead of computing the inverse of A.

🎯 Why: The function calcAB computes the inverse of a covariance matrix (tmpvc) as A <- chol2inv(chol(tmpvc)). The function calcLambda then computes the inverse of A using chol2inv(chol(A)) to get back the original matrix tmpvc. Computing the inverse of the inverse is a redundant double inversion that wastes significant computational time (both Cholesky decomposition and matrix inversion are $O(N^3)$ operations) and can introduce unnecessary floating-point inaccuracies.

📊 Impact: This optimization removes four redundant $O(N^3)$ matrix operations per test run, delivering a massive performance boost, especially for models with a large number of parameters, while remaining mathematically identical.

🔬 Measurement: Run the Vuong test on models with a large number of parameters (e.g. latent variable models) and measure the execution time using system.time(vuongtest(fit1, fit2)). Execution time should be significantly shorter.

---

PR created automatically by Jules for task 9478210095186241521 started by @seonghobae

[google-labs-jules]

👋 Jules, reporting for duty! I'm here to lend a hand with this pull request.

When you start a review, I'll add a 👀 emoji to each comment to let you know I've read it. I'll focus on feedback directed at me and will do my best to stay out of conversations between you and other bots or reviewers to keep the noise down.

I'll push a commit with your requested changes shortly after. Please note there might be a delay between these steps, but rest assured I'm on the job!

For more direct control, you can switch me to Reactive Mode. When this mode is on, I will only act on comments where you specifically mention me with @jules. You can find this option in the Pull Request section of your global Jules UI settings. You can always switch back!

New to Jules? Learn more at jules.google/docs.

---

For security, I will only act on instructions from the user who triggered this task.

[Copilot]

Pull request overview

Optimizes the Vuong test implementation by removing redundant matrix inversions: calcAB() now returns the original covariance matrix so calcLambda() can avoid inverting the inverse of that covariance matrix.

Changes:

• Cache the original covariance matrix (tmpvc) from calcAB() as Ainv and return it alongside A, B, and sc.
• Update calcLambda() to use the cached matrix directly instead of calling chol2inv(chol(A)).
• Add a .jules/bolt.md note documenting the optimization rationale.

Reviewed changes

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

File	Description
R/vuongtest.R	Caches the pre-inversion covariance matrix and reuses it in calcLambda() to avoid redundant O(N^3) operations.
.jules/bolt.md	Adds an automation/learning note describing the redundant inversion optimization.

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.