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

> #
> # A test of the backsolve function
> #
> aeq <- function(x,y) all.equal(as.vector(x), as.vector(y))
> 
> tmat <- matrix(rep(1:5,5), 5, 5)
> tmat <- tmat + t(tmat)
> diag(tmat) <- diag(tmat) + 10
> 
> gt <- gchol(tmat)
> g1 <- as.matrix(gt)
> gd <- diag(sqrt(diag(gt)))
> gc <- gd %*% t(g1)  #usual cholesky form
> 
> xmat <- cbind(1:5, 11:15)
> 
> s1 <- backsolve(gt, xmat, upper=TRUE)  #the default
> aeq(gd %*% t(g1) %*% s1, xmat)
[1] TRUE
> all.equal(s1, backsolve(gc, xmat)) 
[1] TRUE
> 
> s2 <- backsolve(gt, xmat, upper=FALSE)
> aeq(g1 %*% gd %*% s2, xmat)
[1] TRUE
> all.equal(backsolve(gt,xmat, upper=F), backsolve(t(gc),xmat, upper=F)) 
[1] TRUE
> 
> 
> # Now for bdsmatrix objects
> 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)
> 
> gt <- gchol(tmat)
> gs <- gchol(smat)
> 
> xmat <- cbind(1:13, 1:13*2 + 3)
> 
> s1 <- backsolve(gt, xmat)
> s2 <- backsolve(gs, xmat)
> s3 <- backsolve(gt, xmat, upper=FALSE)
> s4 <- backsolve(gs, xmat, upper=FALSE)
> 
> aeq(s1, s2)
[1] TRUE
> aeq(s3, s4)
[1] TRUE
> 
> g1 <- as.matrix(gt)
> gd <- diag(sqrt(diag(gt)))
> aeq(gd %*% t(g1) %*% s1, xmat)
[1] TRUE
> aeq(g1 %*% gd %*% s3, xmat)
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.29    0.06    0.34