R Under development (unstable) (2024-03-01 r86033 ucrt) -- "Unsuffered Consequences"
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> library(bdsmatrix)

Attaching package: 'bdsmatrix'

The following object is masked from 'package:base':

    backsolve

> aeq <- function(x,y) all.equal(as.vector(x), as.vector(y))
> 
> tmat <- bdsmatrix(c(3,2,2,4), 
+ 	      c(22,1,2,21,3,20,19,4,18,17,5,16,15,6,7, 8,14,9,10,13,11,12),
+ 	      matrix(c(1,0,1,1,0,0,1,1,0,1,0,10,0,
+                        0,1,1,0,1,1,0,1,1,0,1,0,10), ncol=2))
> dimnames(tmat) <- list(NULL, letters[1:13])
> 
> smat <- as.matrix(tmat)
> yy <- c(30,35,42,56,34,45,32,37,78,56,40,52,39)
> # look at inverses more closely
> #  (I needed this when some of the other tests weren't being passed,
> #  to figure out where in the decomposition/inversion/multiply process
> #  the flaw was).
> 
> ch1 <- gchol(smat)
> ch2 <- gchol(tmat)
> 
> inv1 <- solve(as.matrix(ch1))
> inv2 <- solve(ch2,full=F)  #inverse of the cholesky, not of tmat
> aeq(inv1, as.matrix(inv2))
[1] TRUE
> 
> # Full matrix tests
> inv3 <- solve(smat)
> inv4 <- solve(tmat)
> inv5 <- solve(gchol(smat), full=T)
> aeq(inv3, inv4)
[1] TRUE
> aeq(inv3, inv5)
[1] TRUE
> 
> # The following test is false by design: when called with a bdsmatrix
> #  object that has an rmat portion, the true inverse is dense.  But
> #  coxme only needs the trace for one calcluation; solve(gchol(tmat))
> #  cheats and only returns the block diagonal portion of the inverse.
> #inv6 <- solve(gchol(tmat), full=T)
> #aeq(inv3, inv6)
> 
> #
> # Now test the solution to a partial solve
> #  We want to be able to transform a matrix to uncorrelated form
> #  If tmat= LDL', and A is general, I want (D^{-1/2}) L^{-1} A
> #
> amat <- matrix(runif(5*nrow(tmat)), nrow=nrow(tmat))
> xx1 <- diag(1/sqrt(diag(ch1))) %*% solve(as.matrix(ch1), amat) 
> xx2 <- solve(ch2, amat, full=F)
> aeq(xx1, xx2)
[1] TRUE
> 
> xx1 <- diag(1/sqrt(diag(ch1))) %*% solve(as.matrix(ch1), yy)
> xx2 <- solve(ch2, yy, full=F)
> aeq(xx1, xx2)
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.35    0.03    0.32