⚡ Bolt: [performance improvement] Replace double matrix inversion with direct covariance matrix usage#10
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…h direct covariance matrix usage What: Prevent unnecessary double inversions of the covariance matrix in `R/vuongtest.R` by saving the un-inverted covariance matrix in `calcAB` and using it directly in `calcLambda`. Why: Double inverting matrices (e.g. `chol2inv(chol(A))` where `A` is already inverted) adds significant $O(p^3)$ time complexity per execution, and can lead to precision loss. Impact: Substantially reduces computational overhead for Vuong tests, especially with larger numbers of parameters. Measurement: Compare execution time of `vuongtest(fit1, fit2)` for models with many parameters. Time reduction and exactness of results guarantee improvement.
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Pull request overview
Optimizes vuongtest()’s calcLambda() path by avoiding redundant inversion of the information/covariance matrix, aiming to reduce cubic-time overhead and improve numerical stability for large parameter counts.
Changes:
calcAB()now returnstmpvcasAinvsocalcLambda()can use the covariance matrix directly.calcLambda()replaces repeatedchol2inv(chol(AB$A))calls withAB$Ainvto eliminate the extra inversion.- Adds a Bolt performance note in
.jules/bolt.mddocumenting the optimization.
Reviewed changes
Copilot reviewed 2 out of 2 changed files in this pull request and generated 3 comments.
| File | Description |
|---|---|
R/vuongtest.R |
Uses Ainv to avoid re-inverting matrices when building W in calcLambda(). |
.jules/bolt.md |
Documents the double-inversion performance pitfall and the intended remediation. |
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| A <- chol2inv(chol(tmpvc)) | ||
| ## Bolt performance optimization: return un-inverted matrix `tmpvc` as `Ainv` | ||
| ## to avoid the $O(p^3)$ performance overhead and precision loss of | ||
| ## double-inverting in `calcLambda`. | ||
| Ainv <- tmpvc |
| W <- cbind(rbind(-AB1$B %*% AB1$Ainv, | ||
| t(Bc) %*% AB1$Ainv), | ||
| rbind(-Bc %*% AB2$Ainv, | ||
| AB2$B %*% AB2$Ainv)) |
| **Learning:** Found a performance bottleneck where a covariance matrix is inverted, passed to another function, and then inverted again (`chol2inv(chol(A))`). This is not only an unnecessary $O(p^3)$ performance overhead, but also risks precision loss due to repeated floating point calculations. | ||
| **Action:** When a matrix and its inverse are needed, consider whether passing the original un-inverted matrix is sufficient, or pass both. In `vuongtest.R`, we can just pass the original variance-covariance matrix (`tmpvc`) rather than inverting it in `calcAB` and inverting it back in `calcLambda`. |
💡 What: Prevent unnecessary double inversions of the covariance matrix in$O(p^3)$ performance bottlenecks and risks precision loss due to floating-point representation limits.$p$ . Better numerical stability.
R/vuongtest.Rby returning the un-inverted covariance matrixtmpvcasAinvincalcABand using it directly incalcLambdainstead of redundantly runningchol2inv(chol(AB$A)).🎯 Why: Double inverting a dense matrix creates unnecessary
📊 Impact: Considerably faster computation speeds for the
vuongtestfunction, specially when testing models with a large number of parameters🔬 Measurement: Comparing the time profile of
vuongtest()operations on larger datasets should show an elimination of overhead associated with redundant Cholesky and inverse calculations. The optimization was also recorded in.jules/bolt.md.PR created automatically by Jules for task 3585486672558178911 started by @seonghobae