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⚡ Bolt: Remove redundant matrix inversions in Vuong test #13

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⚡ Bolt: Remove redundant matrix inversions in Vuong test #13

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3 changes: 3 additions & 0 deletions .jules/bolt.md
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@@ -0,0 +1,3 @@
## 2024-05-24 - Redundant Matrix Inversions in Statistical Operations
**Learning:** Inverting a matrix and then inverting it again is a redundant O(N^3) operation that causes a massive performance bottleneck and potential precision loss. In `nonnest2`, the code computed `A <- chol2inv(chol(tmpvc))` and then later computed `chol2inv(chol(A))` to get back the original matrix `tmpvc`.
**Action:** When reviewing statistical/mathematical code, trace the lifecycle of expensive matrices to find opportunities to pass pre-computed forms rather than recalculating inverses or Cholesky decompositions.
Comment on lines +1 to +3
16 changes: 11 additions & 5 deletions R/vuongtest.R
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Expand Up @@ -231,6 +231,10 @@ 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")
}

# Optimization: We also pre-compute Ainv = tmpvc to save O(N^3) time later
# in calcLambda by avoiding chol2inv(chol(A)).
Ainv <- tmpvc
A <- chol2inv(chol(tmpvc))
Comment on lines +235 to 238

## Eq (2.2)
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 +275,12 @@ 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))))
# Optimization: AB1$Ainv and AB2$Ainv are already A^-1, so we use them directly
# instead of computing chol2inv(chol(A)).
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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