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⚡ Bolt: Avoid redundant matrix inversions in Vuong test #16

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⚡ Bolt: Avoid redundant matrix inversions in Vuong test #16

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5 changes: 5 additions & 0 deletions .jules/bolt.md
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Original file line number Diff line number Diff line change
@@ -0,0 +1,5 @@
## 2024-05-24 - Unnecessary Matrix Inversions

**Learning:** Mathematical operations that effectively cancel each other out (like computing the inverse of an inverse matrix) can significantly degrade performance in statistical libraries due to $O(K^3)$ matrix inversion complexity.

**Action:** Whenever identifying an inversion function (`chol2inv`, `solve`, etc.) being passed between functions, look for where the original matrix might already contain the solution, and pass the required state directly to avoid redundant inversions.
21 changes: 14 additions & 7 deletions R/vuongtest.R
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Expand Up @@ -231,7 +231,12 @@ calcAB <- function(object, n, scfun, vc){
## in case mirt vcov was not estimated
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 improvement - avoid unnecessary matrix inversion
# A <- chol2inv(chol(tmpvc))
# A is the inverse of tmpvc, but later in calcLambda we compute chol2inv(chol(A))
# By saving tmpvc as Ainv we can avoid computing inverse of an inverse in calcLambda
Ainv <- tmpvc

## Eq (2.2)
if(!is.null(scfun)){
Expand All @@ -251,9 +256,9 @@ calcAB <- function(object, n, scfun, vc){
sc <- estfun(object)
}
sc.cp <- crossprod(sc)/n
B <- matrix(sc.cp, nrow(A), nrow(A))
B <- matrix(sc.cp, nrow(Ainv), nrow(Ainv))

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

## a function to get the cross-product from Eq (2.7)
Expand All @@ -271,10 +276,12 @@ 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))))
# Bolt: performance improvement - use Ainv directly instead of chol2inv(chol(AB$A))
# This eliminates matrix inversions and computing the inverse of an inverse.
W <- cbind(rbind(-AB1$B %*% AB1$Ainv,
t(Bc) %*% AB1$Ainv),
rbind(-Bc %*% AB2$Ainv,
AB2$B %*% AB2$Ainv))

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