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⚡ Bolt: [performance improvement] Replace double matrix inversion with direct covariance matrix usage #10

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⚡ Bolt: [performance improvement] Replace double matrix inversion with direct covariance matrix usage #10

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3 changes: 3 additions & 0 deletions .jules/bolt.md
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Original file line number Diff line number Diff line change
@@ -0,0 +1,3 @@
## 2024-05-24 - Avoid Double Matrix Inversion
**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`.
Comment on lines +2 to +3
14 changes: 9 additions & 5 deletions R/vuongtest.R
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Expand Up @@ -232,6 +232,10 @@ calcAB <- function(object, n, scfun, vc){
if(nrow(tmpvc) == 1 & is.na(tmpvc[1,1])) stop("Please re-estimate the mirt model with SE=TRUE")
}
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
Comment on lines 234 to +238

## Eq (2.2)
if(!is.null(scfun)){
Expand All @@ -253,7 +257,7 @@ calcAB <- function(object, n, scfun, vc){
sc.cp <- crossprod(sc)/n
B <- matrix(sc.cp, nrow(A), nrow(A))

list(A=A, B=B, sc=sc)
list(A=A, Ainv=Ainv, B=B, sc=sc)
}

## a function to get the cross-product from Eq (2.7)
Expand All @@ -271,10 +275,10 @@ calcLambda <- function(object1, object2, n, score1, score2, vc1, vc2) {
AB2 <- calcAB(object2, n, score2, vc2)
Bc <- calcBcross(AB1$sc, AB2$sc, n)

W <- cbind(rbind(-AB1$B %*% chol2inv(chol(AB1$A)),
t(Bc) %*% chol2inv(chol(AB1$A))),
rbind(-Bc %*% chol2inv(chol(AB2$A)),
AB2$B %*% chol2inv(chol(AB2$A))))
W <- cbind(rbind(-AB1$B %*% AB1$Ainv,
t(Bc) %*% AB1$Ainv),
rbind(-Bc %*% AB2$Ainv,
AB2$B %*% AB2$Ainv))
Comment on lines +278 to +281

lamstar <- eigen(W, only.values=TRUE)$values
## Discard imaginary part, as it only occurs for tiny eigenvalues?
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