```
# NOT RUN {
data(KNex)
mtm <- with(KNex, crossprod(mm))
str(mtm@factors) # empty list()
(C1 <- Cholesky(mtm)) # uses show(<MatrixFactorization>)
str(mtm@factors) # 'sPDCholesky' (simpl)
(Cm <- Cholesky(mtm, super = TRUE))
c(C1 = isLDL(C1), Cm = isLDL(Cm))
str(mtm@factors) # 'sPDCholesky' *and* 'SPdCholesky'
str(cm1 <- as(C1, "sparseMatrix"))
str(cmat <- as(Cm, "sparseMatrix"))# hmm: super is *less* sparse here
cm1[1:20, 1:20]
b <- matrix(c(rep(0, 711), 1), nc = 1)
## solve(Cm, b) by default solves Ax = b, where A = Cm'Cm (= mtm)!
## hence, the identical() check *should* work, but fails on some GOTOblas:
x <- solve(Cm, b)
stopifnot(identical(x, solve(Cm, b, system = "A")),
all.equal(x, solve(mtm, b)))
Cn <- Cholesky(mtm, perm = FALSE)# no permutation -- much worse:
sizes <- c(simple = object.size(C1),
super = object.size(Cm),
noPerm = object.size(Cn))
## simple is 100, super= 137, noPerm= 812 :
noquote(cbind(format(100 * sizes / sizes[1], digits=4)))
## Visualize the sparseness:
dq <- function(ch) paste('"',ch,'"', sep="") ## dQuote(<UTF-8>) gives bad plots
image(mtm, main=paste("crossprod(mm) : Sparse", dq(class(mtm))))
image(cm1, main= paste("as(Cholesky(crossprod(mm)),\"sparseMatrix\"):",
dq(class(cm1))))
# }
# NOT RUN {
## Smaller example, with same matrix as in help(chol) :
(mm <- Matrix(toeplitz(c(10, 0, 1, 0, 3)), sparse = TRUE)) # 5 x 5
(opts <- expand.grid(perm = c(TRUE,FALSE), LDL = c(TRUE,FALSE), super = c(FALSE,TRUE)))
rr <- lapply(seq_len(nrow(opts)), function(i)
do.call(Cholesky, c(list(A = mm), opts[i,])))
nn <- do.call(expand.grid, c(attr(opts, "out.attr")$dimnames,
stringsAsFactors=FALSE,KEEP.OUT.ATTRS=FALSE))
names(rr) <- apply(nn, 1, function(r)
paste(sub("(=.).*","\\1", r), collapse=","))
# }
# NOT RUN {
<!-- % extra '\\' in Rd -->
# }
# NOT RUN {
str(rr, max=1)
str(re <- lapply(rr, expand), max=2) ## each has a 'P' and a 'L' matrix
# }
# NOT RUN {
<!-- %% FIXME !! --- "check" them __unfinished__ -->
# }
# NOT RUN {
R0 <- chol(mm, pivot=FALSE)
R1 <- chol(mm, pivot=TRUE )
stopifnot(all.equal(t(R1), re[[1]]$L),
all.equal(t(R0), re[[2]]$L),
identical(as(1:5, "pMatrix"), re[[2]]$P), # no pivoting
TRUE)
# }
# NOT RUN {
<!-- %% --> ../TODO : .diag.dsC() should be renamed, documented, tested,... -->
# }
# NOT RUN {
<!-- %dont -->
# }
# NOT RUN {
# Version of the underlying SuiteSparse library by Tim Davis :
.SuiteSparse_version()
# }
```

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