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)
> 
> # matrix multiplication
> zz <- runif(13)
> aeq(zz%*% smat, zz%*% tmat)
[1] TRUE
> aeq(smat%*%zz, tmat%*% zz)
[1] TRUE
> 
> xx <- matrix(1:39, ncol=3)
> aeq(smat %*% zz, tmat %*% zz)
[1] TRUE
> aeq(t(xx) %*% smat, t(xx) %*% tmat)
[1] TRUE
> 
> 
> amat <- tmat
> amat@offdiag <- pi
> bmat <- as.matrix(amat)
> 
> aeq(zz%*% amat, zz%*% bmat)
[1] TRUE
> aeq(amat%*%zz, bmat%*% zz)
[1] TRUE
> 
> 
> # Solve the right-hand side wrt a matrix
> yy2 <- cbind(yy, -yy, yy+3)
> zz1 <- solve(smat, yy2)
> zz2 <- solve(tmat, yy2)
> aeq(zz1, zz2)
[1] TRUE
> aeq(zz2[,1], solve(tmat, yy))
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.26    0.07    0.34