```
## A random sparse matrix :
set.seed(7)
m <- matrix(0, 5, 5)
m[sample(length(m), size = 14)] <- rep(1:9, length=14)
(mm <- as(m, "CsparseMatrix"))
tril(mm) # lower triangle
tril(mm, -1) # strict lower triangle
triu(mm, 1) # strict upper triangle
band(mm, -1, 2) # general band
(m5 <- Matrix(rnorm(25), ncol = 5))
tril(m5) # lower triangle
tril(m5, -1) # strict lower triangle
triu(m5, 1) # strict upper triangle
band(m5, -1, 2) # general band
(m65 <- Matrix(rnorm(30), ncol = 5)) # not square
triu(m65) # result not "dtrMatrix" unless square
(sm5 <- crossprod(m65)) # symmetric
band(sm5, -1, 1)# "dsyMatrix": symmetric band preserves symmetry property
as(band(sm5, -1, 1), "sparseMatrix")# often preferable
(sm <- round(crossprod(triu(mm/2)))) # sparse symmetric ("dsC*")
band(sm, -1,1) # remains "dsC", *however*
band(sm, -2,1) # -> "dgC"
## this uses special methods
(x.x <- crossprod(mm))
tril(x.x)
xx <- tril(x.x) + triu(x.x, 1) ## the same as x.x (but stored differently):
txx <- t(as(xx, "symmetricMatrix"))
stopifnot(identical(triu(x.x), t(tril(x.x))),
identical(class(x.x), class(txx)),
identical(as(x.x, "generalMatrix"), as(txx, "generalMatrix")))
```

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