From 48665653ce235b58f45ae108efea95345147650d Mon Sep 17 00:00:00 2001
From: seonghobae <8172694+seonghobae@users.noreply.github.com>
Date: Mon, 29 Jun 2026 04:10:28 +0000
Subject: [PATCH] =?UTF-8?q?=E2=9A=A1=20Bolt:=20Remove=20redundant=20matrix?=
 =?UTF-8?q?=20inversions?=
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- Updated `calcAB` to return `Ainv` (the asymptotic covariance matrix directly, without inversion) and updated the `B` matrix construction.
- Updated `calcLambda` to use `Ainv` directly, removing `chol2inv(chol(AB1$A))` and `chol2inv(chol(AB2$A))` and avoiding redundant matrix inversions.
---
 .jules/bolt.md |  5 +++++
 R/vuongtest.R  | 21 ++++++++++++++-------
 2 files changed, 19 insertions(+), 7 deletions(-)
 create mode 100644 .jules/bolt.md

diff --git a/.jules/bolt.md b/.jules/bolt.md
new file mode 100644
index 0000000..e53b99d
--- /dev/null
+++ b/.jules/bolt.md
@@ -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.
diff --git a/R/vuongtest.R b/R/vuongtest.R
index 57c5f6b..5edcca7 100644
--- a/R/vuongtest.R
+++ b/R/vuongtest.R
@@ -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)){
@@ -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)
@@ -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?