R/Auxiliaries.R

In bedatadriven/renjin-matrix: Sparse and Dense Matrix Classes and Methods

#### "Namespace private" Auxiliaries  such as method functions
#### (called from more than one place --> need to be defined early)

## Need to consider NAs ;  "== 0" even works for logical & complex:
## Note that "!x" is faster than "x == 0", but does not (yet!) work for complex
## if we did these in C, would gain a factor 2 (or so):
is0  <- function(x) !is.na(x) & x == 0
isN0 <- function(x)  is.na(x) | x != 0
is1  <- function(x) !is.na(x) & x   # also == "isTRUE componentwise"

##
##allFalse <- function(x) !any(x) && !any(is.na(x))## ~= all0, but allFalse(NULL) = TRUE w/warning
##all0 <- function(x) !any(is.na(x)) && all(!x) ## ~= allFalse
allFalse <-
all0 <- function(x) if(is.atomic(x)) .Call(R_all0, x) else !any(x) && !any(is.na(x))

##anyFalse <- function(x) isTRUE(any(!x))		 ## ~= any0
## any0 <- function(x) isTRUE(any(x == 0))	      ## ~= anyFalse
anyFalse <-
any0 <- function(x) if(is.atomic(x)) .Call(R_any0, x) else isTRUE(any(!x))

## These work "identically" for  1 ('==' TRUE)  and 0 ('==' FALSE)
##	(but give a warning for "double"  1 or 0)
## TODO: C versions of these would be faster
allTrue  <- function(x) all(x) && !anyNA(x)


## Note that mode(<integer>) = "numeric" -- as0(), as1() return "double"
## which is good *AS LONG AS* we do not really have i..Matrix integer matrices
as1 <- function(x, mod=mode(x))
    switch(mod, "integer"= 1L, "double"=, "numeric"= 1, "logical"= TRUE,
	   "complex"= 1+0i, stop(gettextf("invalid 'mod': %s", mod), domain = NA))
as0 <- function(x, mod=mode(x))
    switch(mod, "integer"= 0L, "double"=, "numeric"= 0, "logical"= FALSE,
	   "complex"= 0+0i, stop(gettextf("invalid 'mod': %s", mod), domain = NA))

##' Should the matrix/Matrix  x  or a combination of x and y   be treated as  'sparse' ?
## sparseDefault <- function(x, y=NULL) {
##     if(is.null(y))
##         prod(dim(x)) > 2*sum(isN0(as(x, "matrix")))
##     else ## nrow / ncol ... differentiate  this would be for  rbind / cbind --> ./bind2.R
##         (nnzero(x) + nnzero(y)) * 2 < (nrow(x)+nrow(y)) * nc
## }
sparseDefault <- function(x) prod(dim(x)) > 2*sum(isN0(as(x, "matrix")))


## NB:  .fixupDimnames() needs to be defined in ./AllClass.R

.M.DN <- function(x) dimnames(x) %||% list(NULL,NULL)

.has.DN <- ## has non-trivial Dimnames slot?
    function(x) !identical(list(NULL,NULL), x@Dimnames)

## This is exported now ( -> ../man/is.null.DN.Rd ):
is.null.DN <- function(dn) {
    is.null(dn) || {
	if(!is.null(names(dn))) names(dn) <- NULL
	ch0 <- character(0)
	identical(dn, list(NULL,NULL)) ||
	identical(dn, list(ch0, NULL)) ||
	identical(dn, list(NULL, ch0)) ||
	identical(dn, list(ch0, ch0))
    }
}

##' return 'x' unless it is NULL where you'd use 'orElse'
`%||%` <- function(x, orElse) if(!is.null(x)) x else orElse

##  not %in%  :
`%nin%` <- function (x, table) is.na(match(x, table))

##' @title Check identical(i, 0:n) {or identical(i, 1:n) when Ostart is false}
##' @param i an integer vector, to be compared with 0:n or 1:n
##' @param n an integer number
##' @param Ostart logical indicating if comparison with 0:n or 1:n should be made
##' @return TRUE or FALSE
##' @author Martin Maechler
isSeq <- function(i, n, Ostart = TRUE) {
    ## FIXME: Port to C, use simple .Call() which is much faster notably in FALSE cases
    ##        and then *export* (and hence document)
    identical(i, if(Ostart) 0L:n else seq_len(n))
}


.bail.out.1 <- function(fun, cl) {
    stop(gettextf('not-yet-implemented method for %s(<%s>).\n ->>  Ask the package authors to implement the missing feature.', fun, cl),
	 call. = FALSE, domain=NA)
}
.bail.out.2 <- function(fun, cl1, cl2) {
    stop(gettextf('not-yet-implemented method for %s(<%s>, <%s>).\n ->>  Ask the package authors to implement the missing feature.',
		  fun, cl1, cl2), call. = FALSE, domain=NA)
}

Matrix.msg <- function(..., .M.level = 1) {
    if(!is.null(v <- getOption("Matrix.verbose")) && v >= .M.level)
        message(...)
}

## TODO: faster via C, either R's  R_data_class() [which needs to become API !]
##       or even direct  getAttrib(x, R_ClassSymbol); ..
##' class - single string, no "package" attribute,..
.class0 <- function(x)  as.vector(class(x))

## we can set this to FALSE and possibly measure speedup:
.copyClass.check <- TRUE

## This should be done in C and be exported by 'methods':  [FIXME - ask JMC ]
copyClass <- function(x, newCl, sNames =
		      intersect(slotNames(newCl), slotNames(x)),
                      check = .copyClass.check)
{
    r <- new(newCl)
    ## Equivalent of
    ##   for(n in sNames) slot(r, n, check=check) <- slot(x, n)  :
    if(check) for(n in sNames) slot(r, n) <- slot(x, n)
    else for(n in sNames) # don't check, be fast
	## .Call("R_set_slot", r, n, slot(x,n), PACKAGE = "methods")
	## "ugly", but not using .Call(*, "methods")
	attr(r, n) <- attr(x, n)
    r
}

##' Return the (maybe super-)class of class 'cl'   from "Matrix", returning  character(0) if there is none.
##'
##' @title The Matrix (Super-) Class of a Class
##' @param cl string, class name
##' @param cld its class definition
##' @param ...Matrix if TRUE, the result must be of pattern "[dlniz]..Matrix"
##'     where the first letter "[dlniz]" denotes the content kind.
##' @param dropVirtual
##' @param ... other arguments are passed to .selectSuperClasses()
##' @return a character string
##' @author Martin Maechler, Date: 24 Mar 2009
MatrixClass <- function(cl, cld = getClassDef(cl),
			...Matrix = TRUE, dropVirtual = TRUE, ...)
{
    ## stopifnot(is.character(cl))
    ## Hmm, packageSlot(cl)  *can* be misleading --> use  cld@package  first:
    if(is.null(pkg <- cld@package)) {
	if(is.null(pkg <- packageSlot(cl))) return(character())
	## else we use 'pkg'
    }
    if(identical(pkg, "Matrix") &&
       (!...Matrix || (cl != "indMatrix" && identical(1L, grep("^[dlniz]..Matrix$", cl)))))
	cl
    else { ## possibly recursively
	r <- .selectSuperClasses(cld@contains, dropVirtual = dropVirtual,
				 namesOnly = TRUE, ...)
	if(length(r))
	    Recall(r[1], ...Matrix = ...Matrix, dropVirtual = dropVirtual)
	else r
    }
}

attrSlotNames <- function(m, factors = TRUE) {
    ## slotnames of Matrix objects which are *not* directly content related
    sn <- slotNames(m); sn[sn %nin% c("x","i","j","p", if(!factors) "factors")]
}

##' @param m
##' @return the slots of 'm' which are "attributes" of some kind.
attrSlots <- function(m, factors = TRUE) sapply(attrSlotNames(m, factors=factors),
			 function(sn) slot(m, sn), simplify = FALSE)

##' @return { NULL | TRUE | character | list(.) }
attr.all_Mat <- function(target, current,
			 check.attributes = TRUE, factorsCheck = FALSE, ...) {
    msg <- if(check.attributes)
	all.equal(attrSlots(target,  factors=factorsCheck),
		  attrSlots(current, factors=factorsCheck),
		  check.attributes = TRUE, ...) ## else NULL
    if((c1 <- class(target)) != (c2 <- class(current)))
	## list(): so we can easily check for this
	list(c(if(!isTRUE(msg)) msg, paste0("class(target) is ", c1, ", current is ", c2)))
    else msg
}

##' @return combination for  all.equal() functions in ./Matrix.R & ./sparseMatrix.R
.a.e.comb <- function(msg, r) {
    if((is.null(msg) || isTRUE(msg)) & (r.ok <- isTRUE(r))) TRUE
    else c(if(!isTRUE(msg)) msg, if(!r.ok) r)
}


## chol() via "dpoMatrix"
## This will only be called for *dense* matrices
cholMat <- function(x, pivot = FALSE, ...) {
    packed <- .isPacked(x)
    nmCh <- if(packed) "pCholesky" else "Cholesky"
    if(!is.null(ch <- x@factors[[nmCh]]))
	return(ch) ## use the cache
    px <- as(x, if(packed) "dppMatrix" else "dpoMatrix")
    if (isTRUE(validObject(px, test=TRUE))) ## 'pivot' is not used for dpoMatrix
	.set.factors(x, nmCh, chol(px, pivot, ...))
    else stop("'x' is not positive definite -- chol() undefined.")
}


invPerm.R <- function(p) { p[p] <- seq_along(p) ; p }
## how much faster would this be in C? -- less than a factor of two?
invPerm <- function(p, zero.p = FALSE, zero.res = FALSE)
    .Call(inv_permutation, p, zero.p, zero.res)



##  sign( <permutation> ) == determinant( <pMatrix>)

signPerm <- function(p)
{
    ## Purpose: sign(<permutation>) via the cycles
    ## ----------------------------------------------------------------------
    ## Arguments: a permutation of 1:n
    ## ----------------------------------------------------------------------
    ## Author: Peter Dalgaard, 14 Apr 2008 // speedup: Martin Maechler 2008-04-16

    n <- length(p)
    x <- integer(n)
    ii <- seq_len(n)
    for (i in ii) {
	z <- ii[!x][1]             # index of first unmarked x[] entry
	if (is.na(z)) break
	repeat { ## mark x[] <- i  for those in i-th cycle
	    x[z] <- i
	    z <- p[z]
	    if (x[z]) break
	}
    }
    ## Now, table(x) gives the cycle lengths,
    ## where  split(seq_len(n), x)  would give the cycles list
    ## tabulate(x, i - 1L) is quite a bit faster than the equivalent
    ## table(x)
    clen <- tabulate(x, i - 1L)
    ## The sign is -1 (<==>  permutation is odd)  iff
    ## the cycle factorization contains an odd number of even-length cycles:
    1L - (sum(clen %% 2 == 0) %% 2L)*2L
}


detSparseLU <- function(x, logarithm = TRUE, ...) {
    ## Purpose: Compute determinant() from  lu.x = lu(x)
    ## ----------------------------------------------------------------------
    ## Author: Martin Maechler, Date: 15 Apr 2008

    if(any(x@Dim == 0)) return(mkDet(numeric(0)))
    ll <- lu(x, errSing = FALSE)
    ##          ^^^^^^^^^^^^^^^ no error in case of singularity
    if(identical(NA, ll)) { ## LU-decomposition failed with singularity
	return(mkDet(ldet = if(anyNA(x)) NaN else -Inf,
		     logarithm=logarithm, sig = 1L))
    }
    ## else
    stopifnot(all(c("L","U") %in% slotNames(ll))) # ensure we have *sparse* LU
    r <- mkDet(diag(ll@U), logarithm)
    ## Det(x) == Det(P L U Q) == Det(P) * 1 * Det(U) * Det(Q); where Det(P), Det(Q) in {-1,1}
    r$sign <- r$sign * signPerm(ll@p + 1L) * signPerm(ll@q + 1L)
    r
}


## Log(Determinant) from diagonal ... used several times

mkDet <- function(d, logarithm = TRUE, ldet = sum(log(abs(d))),
                  sig = -1L+2L*as.integer(prod(sign(d)) >= 0))
{		# sig: -1 or +1 (not 0 !)
    modulus <- if (logarithm) ldet else exp(ldet)
    attr(modulus, "logarithm") <- logarithm
    val <- list(modulus = modulus, sign = sig)
    class(val) <- "det"
    val
}

dimCheck <- function(a, b) {
    da <- dim(a)
    db <- dim(b)
    if(any(da != db))
	stop(gettextf("Matrices must have same dimensions in %s",
		      deparse(sys.call(sys.parent()))),
	     call. = FALSE, domain=NA)
    da
}

mmultCheck <- function(a, b, kind = 1L) {
    ## Check matching matrix dimensions and return that matching dim
    ## 1)    %*%    : [n x m] , [m x k]
    ## 2)  crossprod: [m x n] , [m x k]
    ## 3) tcrossprod: [n x m] , [k x m]
    ## switch(kind,
    ##    { ## %*%  (kind = 1)
    ##        ca <- dim(a)[2L]
    ##        rb <- dim(b)[1L]
    ##    },
    ##    { ## crossprod   (kind = 2)
    ##        ca <- dim(a)[1L]
    ##        rb <- dim(b)[1L]
    ##    },
    ##    { ## tcrossprod  (kind = 3)
    ##        ca <- dim(a)[2L]
    ##        rb <- dim(b)[2L]
    ##    })
    ca <- dim(a)[1L + (kind %% 2L)]
    rb <- dim(b)[1L + (kind  > 2)]
    if(ca != rb)
	stop(gettextf("non-conformable matrix dimensions in %s",
		      deparse(sys.call(sys.parent()))),
	     call. = FALSE, domain=NA)
    ca
}

##' Constructs "sensical" dimnames for something like  a + b ;
##' assume dimCheck() has happened before
##'
##' NOTA BENE:   R's  ?Arithmetic  says
##' ---------
##'>  For arrays (and an array result) the dimensions and dimnames are taken from
##'>  first argument if it is an array, otherwise the second.
##' but that's not quite correct:
##' The dimnames are taken from second *if* the first are NULL.
##'
##' @title Construct dimnames for  a  o  b
##' @param a matrix
##' @param b matrix
##' @param useFirst logical indicating if dimnames(a), the first, is taken, unless NULL
##' @param check logical indicating if a warning should be signalled for mismatches
##' @return a \code{\link{list}} of length two with dimnames
##' @author Martin Maechler
dimNamesCheck <- function(a, b, useFirst = TRUE, check = FALSE) {
    nullDN <- list(NULL,NULL)
    h.a <- !identical(nullDN, dna <- dimnames(a))
    h.b <- !identical(nullDN, dnb <- dimnames(b))
    if(h.a || h.b) {
        if(useFirst) {
            if(!h.a) dnb else dna
        } else {
            if (!h.b) dna
            else if(!h.a) dnb
            else { ## both have non-trivial dimnames
                r <- dna # "default" result
                for(j in 1:2) if(!is.null(dn <- dnb[[j]])) {
                    if(is.null(r[[j]]))
                        r[[j]] <- dn
                    else if(check && !identical(r[[j]], dn))
                        warning(gettextf("dimnames [%d] mismatch in %s", j,
                                         deparse(sys.call(sys.parent()))),
                                call. = FALSE, domain=NA)
                }
                r
            }
        }
    }
    else
	nullDN
}

##' @title Symmetrize dimnames(.)
##' @param x a square matrix
##' @param col logical indicating if the column names should be taken when
##' both are non-NULL.
##' @param names logical indicating if the names(dimnames(.)) should be
##' symmetrized and kept *if* they differ.
##' @return a matrix like \code{x}, say \code{r}, with dimnames fulfilling
##' 		dr <- dimnames(r); identical(dr[1], dr[2])
##' @author Martin Maechler
symmetrizeDimnames <- function(x, col=TRUE, names=TRUE) {
    dimnames(x) <- symmDN(dimnames(x), col=col, names=names)
    x
}

symmDN <- function(dn, col=TRUE, names=TRUE) {
    if(is.null(dn) || identical(dn[1L], dn[2L]))
	return(dn)
    J <-
        if(col) {
            if(is.null(dn[[2L]])) 1L else 2L
        } else { ## !col : row
            if(is.null(dn[[1L]])) 2L else 1L
        }

    if(!is.null(n <- names(dn))) {
	if(length(n) != 2)
	    stop("names(dimnames(<matrix>)) must be NULL or of length two")
	if(n[1L] != n[2L])
	    names(dn) <- if(names) n[c(J,J)] # else NULL
    }
    dn[c(J,J)]
}

rowCheck <- function(a, b) {
    da <- dim(a)
    db <- dim(b)
    if(da[1] != db[1])
	stop(gettextf("Matrices must have same number of rows in %s",
		      deparse(sys.call(sys.parent()))),
	     call. = FALSE, domain=NA)
    ## return the common nrow()
    da[1]
}

colCheck <- function(a, b) {
    da <- dim(a)
    db <- dim(b)
    if(da[2] != db[2])
	stop(gettextf("Matrices must have same number of columns in %s",
		      deparse(sys.call(sys.parent()))),
	     call. = FALSE, domain=NA)
    ## return the common ncol()
    da[2]
}

## is.na(<nsparse>) is FALSE everywhere.  Consequently, this function
## just gives an "all-FALSE" nCsparseMatrix of same form as x
##'
##' @title all FALSE nCsparseMatrix "as x"
##' @param x Matrix
##' @return n.CsparseMatrix "as \code{x}"
##' @author Martin Maechler
is.na_nsp <- function(x) {
    d <- x@Dim
    dn <- x@Dimnames
    ## step-wise construction ==> no validity check for speedup
    r <- new(if(d[1] == d[2] && identical(dn[[1]], dn[[2]]))
	     "nsCMatrix" else "ngCMatrix")
    r@Dim <- d
    r@Dimnames <- dn
    r@p <- rep.int(0L, d[2]+1L)
    r
}

allTrueMat <- function(x, sym = (d[1] == d[2] && identical(dn[[1]], dn[[2]])),
		       packed=TRUE)
{
    d <- x@Dim
    dn <- x@Dimnames
    r <- new("ngeMatrix", Dim=d, Dimnames=dn, x = rep.int(TRUE, prod(d)))
    if(sym) as(r, if(packed) "nspMatrix" else "nsyMatrix")
    else r
}
allTrueMatrix <- function(x) allTrueMat(x)



## Note: !isPacked(.)  i.e. `full' still contains
## ----  "*sy" and "*tr" which have "undefined" lower or upper part
isPacked <- function(x)
{
    ## Is 'x' a packed (dense) matrix ?
    is(x, "denseMatrix") &&
    ## unneeded(!): any("x" == slotNames(x)) &&
    length(x@x) < prod(x@Dim)
}
##" Is 'x' a packed (dense) matrix -- "no-check" version
.isPacked <- function(x) length(x@x) < prod(x@Dim)

emptyColnames <- function(x, msg.if.not.empty = FALSE)
{
    ## Useful for compact printing of (parts) of sparse matrices
    ## possibly	 dimnames(x) "==" NULL :
    dn <- dimnames(x)
    nc <- ncol(x)
    if(msg.if.not.empty && is.list(dn) && length(dn) >= 2 &&
       is.character(cn <- dn[[2]]) && any(cn != "")) {
	lc <- length(cn)
	message(if(lc > 3)
		gettextf("   [[ suppressing %d column names %s ... ]]", nc,
			 paste(sQuote(cn[1:3]), collapse = ", "))
		else
		gettextf("   [[ suppressing %d column names %s ]]", nc,
			 paste(sQuote(cn[1:lc]), collapse = ", ")),
		domain=NA)
    }
    dimnames(x) <- list(dn[[1]], character(nc))
    x
}



## The i-th unit vector  e[1:n] with e[j] = \delta_{i,j}
## .E.i.log <- function(i,n)  i == (1:n)
## .E.i <- function(i,n)
##     r <- numeric(n)
##     r[i] <- 1.
##     r
## }

idiag <- function(n, p=n)
{
    ## Purpose: diag() returning  *integer*
    ## --------------------------------------------------------
    ## Author: Martin Maechler, Date:  8 Dec 2007, 23:13
    r <- matrix(0L, n,p)
    if ((m <- min(n, p)) > 0)
	r[1 + 0:(m - 1) * (n + 1)] <- 1L
    r
}

ldiag <- function(n, p=n)
{
    ## Purpose: diag() returning  *logical*
    r <- matrix(FALSE, n,p)
    if ((m <- min(n, p)) > 0)
	r[1 + 0:(m - 1) * (n + 1)] <- TRUE
    r
}

## The indices of the diagonal entries of an  n x n matrix,  n >= 1
## i.e. indDiag(n) === which(diag(n) == 1)
indDiag <- function(n) cumsum(c(1L, rep.int(n+1L, n-1)))

### TODO:  write in C and port to base (or 'utils') R
### -----
### "Theory" behind this: /u/maechler/R/MM/MISC/lower-tri-w.o-matrix.R
## NB: also have "abIndex" version:  abIindTri() --> ./abIndex.R
indTri <- function(n, upper = TRUE, diag = FALSE) {
    ## Indices of (strict) upper/lower triangular part
    ## == which(upper.tri(diag(n), diag=diag) or
    ##	  which(lower.tri(diag(n), diag=diag) -- but
    ## much more efficiently for largish 'n'
    stopifnot(length(n) == 1, n == (n. <- as.integer(n)), (n <- n.) >= 0)
    if(n <= 2) {
        if(n == 0) return(integer(0))
        if(n == 1) return(if(diag) 1L else integer(0))
        ## else n == 2
        v <- if(upper) 3L else 2L
	return(if(diag) c(1L, v, 4L) else v)
    }

    ## n >= 3 [also for n == 2 && diag (==TRUE)] :

    ## First, compute the 'diff(.)' of the result [fast, using integers]
    n. <- if(diag) n else n - 1L
    n1 <- n. - 1L
    ## all '1' but a few
    r <- rep.int(1L, choose(n.+1, 2) - 1)
    tt <- if(diag) 2L else 3L
    r[cumsum(if(upper) 1:n1 else n.:2)] <- if(upper) n:tt else tt:n
    ## now have differences; revert to "original":
    cumsum(c(if(diag) 1L else if(upper) n+1L else 2L, r))
}


prTriang <- function(x, digits = getOption("digits"),
                     maxp = getOption("max.print"),
		     justify = "none", right = TRUE)
{
    ## modeled along stats:::print.dist
    upper <- x@uplo == "U"

    m <- as(x, "matrix")
    cf <- format(m, digits = digits, justify = justify)
    cf[if(upper) row(cf) > col(cf)
	else	 row(cf) < col(cf)] <- "."
    print(cf, quote = FALSE, right = right, max = maxp)
    invisible(x)
}

prMatrix <- function(x, digits = getOption("digits"),
                     maxp = getOption("max.print")) {
    d <- dim(x)
    cl <- class(x) ## cld <- getClassDef(cl)
    tri <- extends(cl, "triangularMatrix")
    xtra <- if(tri && x@diag == "U") " (unitriangular)" else ""
    cat(sprintf('%d x %d Matrix of class "%s"%s\n',
		d[1], d[2], cl, xtra))
    if(prod(d) <= maxp) {
	if(tri)
	    prTriang(x, digits = digits, maxp = maxp)
	else
	    print(as(x, "matrix"), digits = digits, max = maxp)
    }
    else { ## d[1] > maxp / d[2] >= nr :
	m <- as(x, "matrix")
	nr <- maxp %/% d[2]
	n2 <- ceiling(nr / 2)
	print(head(m, max(1, n2)))
	cat("\n ..........\n\n")
	print(tail(m, max(1, nr - n2)))
	cat("\n ..........\n\n")

    }
    ## DEBUG: cat("str(.):\n") ; str(x)
    invisible(x)# as print() S3 methods do
}

nonFALSE <- function(x) {
    ## typically used for lMatrices:  (TRUE,NA,FALSE) |-> (TRUE,TRUE,FALSE)
    if(any(ix <- is.na(x))) x[ix] <- TRUE
    x
}

nz.NA <- function(x, na.value) {
    ## Non-Zeros of x
    ## na.value: TRUE: NA's give TRUE, they are not 0
    ##             NA: NA's are not known ==> result := NA
    ##          FALSE: NA's give FALSE, could be 0
    stopifnot(is.logical(na.value), length(na.value) == 1)
    if(is.na(na.value)) x != 0
    else  if(na.value)	isN0(x)
    else		x != 0 & !is.na(x)
}

### This assumes that e.g. the i-slot in Csparse is *not* over-allocated:
nnzSparse <- function(x, cl = class(x), cld = getClassDef(cl))
{
    ## Purpose: number of *stored* / structural non-zeros {NA's counted too}
    ## ----------------------------------------------------------------------
    ## Arguments: x sparseMatrix
    ## ----------------------------------------------------------------------
    ## Author: Martin Maechler, 18 Apr 2008
    if(extends(cld, "CsparseMatrix") || extends(cld, "TsparseMatrix"))
	length(x@i)
    else if(extends(cld, "RsparseMatrix"))
	length(x@j)
    else if(extends(cld, "indMatrix"))	# is "sparse" too
	x@Dim[1]
    else stop(gettext("'x' must be \"sparseMatrix\""), domain=NA)
}


## For sparseness handling, return a
## 2-column (i,j) matrix of 0-based indices of non-zero entries:

non0.i <- function(M, cM = class(M), uniqT=TRUE) {
    if(extends(cM, "TsparseMatrix")) {
	if(uniqT && is_not_uniqT(M))
	    .Call(compressed_non_0_ij, as(M,"CsparseMatrix"), TRUE)
	else cbind(M@i, M@j)
    } else if(extends(cM, "indMatrix")) {
	cbind(seq_len(nrow(M)), M@perm) - 1L
    } else { ## C* or R*
	.Call(compressed_non_0_ij, M, extends(cM, "CsparseMatrix"))
    }
}

non0ind <- function(x, cld = getClassDef(class(x)),
		    uniqT = TRUE, xtendSymm = TRUE, check.Udiag = TRUE)
{
    if(is.numeric(x))
	return(if((n <- length(x))) {
	    if(is.matrix(x)) arrayInd(seq_len(n)[isN0(x)], dim(x)) - 1L
	    else (0:(n-1))[isN0(x)]
	} else integer(0))
    ## else
    stopifnot(extends(cld, "sparseMatrix"))

    ij <- non0.i(x, cld, uniqT=uniqT)
    if(xtendSymm && extends(cld, "symmetricMatrix")) { # also get "other" triangle
	notdiag <- ij[,1] != ij[,2]# but not the diagonals again
	rbind(ij, ij[notdiag, 2:1], deparse.level=0)
    }
    else if(check.Udiag && extends(cld, "triangularMatrix")) { # check for "U" diag
	if(x@diag == "U") {
	    i <- seq_len(dim(x)[1]) - 1L
	    rbind(ij, cbind(i,i, deparse.level=0), deparse.level=0)
	} else ij
    }
    else
	ij
}

if(FALSE) { ## -- now have  .Call(m_encodeInd, ...) etc :

## nr= nrow: since  i in {0,1,.., nrow-1}  these are 1L "decimal" encodings:
## Further, these map to and from the usual "Fortran-indexing" (but 0-based)
encodeInd  <- function(ij, di) {
    stopifnot(length(di) == 2)
    nr <- di[1L]
    ## __ care against integer overflow __
    if(prod(di) >= .Machine$integer.max) nr <- as.double(nr)
    ij[,1] + ij[,2] * nr
}
encodeInd2 <- function(i,j, di) {
    stopifnot(length(di) == 2)
    nr <- di[1L]
    ## __ care against integer overflow __
    if(prod(di) >= .Machine$integer.max) nr <- as.double(nr)
    i +  j * nr
}
} else {
##' Encode Matrix index (i,j)  |-->  i + j * nrow   {i,j : 0-origin}
##'
##' @param ij 2-column integer matrix
##' @param dim dim(.), i.e. length 2 integer vector
##' @param checkBnds logical indicating  0 <= ij[,k] < di[k]  need to be checked.
##'
##' @return encoded index; integer if prod(dim) is small; double otherwise
encodeInd <- function(ij, dim, orig1=FALSE, checkBnds=TRUE)
    .Call(m_encodeInd, ij, dim, orig1, checkBnds)
## --> in ../src/Mutils.c :  m_encodeInd(ij, di, orig_1, chk_bnds)
##                           ~~~~~~~~~~~

##' Here, 1-based indices (i,j) are default:
encodeInd2 <- function(i, j, dim, orig1=TRUE, checkBnds=TRUE)
    .Call(m_encodeInd2, i,j, dim, orig1, checkBnds)

}

##' Decode "encoded" (i,j) indices back to  cbind(i,j)
##' This is the inverse of encodeInd(.)
##'
##' @title Decode "Encoded" (i,j) Indices
##' @param code integer in 0:((n x m - 1)  <==> encodeInd(.) result
##' @param nr the number of rows
##' @return
##' @author Martin Maechler
decodeInd <- function(code, nr) cbind(as.integer(code %% nr),
				      as.integer(code %/% nr), deparse.level=0L)

complementInd <- function(ij, dim, orig1=FALSE, checkBnds=FALSE)
{
    ## Purpose: Compute the complement of the 2-column 0-based ij-matrix
    ##		but as 1-based indices
    n <- prod(dim)
    if(n == 0) return(integer(0))
    seq_len(n)[-(1L + .Call(m_encodeInd, ij, dim, orig1, checkBnds))]
}

unionInd <- function(ij1, ij2) unique(rbind(ij1, ij2))

intersectInd <- function(ij1, ij2, di, orig1=FALSE, checkBnds=FALSE) {
    ## from 2-column (i,j) matrices where i in {0,.., nrow-1},
    ## return only the *common* entries
    decodeInd(intersect(.Call(m_encodeInd, ij1, di, orig1, checkBnds),
			.Call(m_encodeInd, ij2, di, orig1, checkBnds)), nr=di[1])
}

WhichintersectInd <- function(ij1, ij2, di, orig1=FALSE, checkBnds=FALSE) {
    ## from 2-column (i,j) matrices where i \in {0,.., nrow-1},
    ## find *where*  common entries are in ij1 & ij2
    m1 <- match(.Call(m_encodeInd, ij1, di, orig1, checkBnds),
                .Call(m_encodeInd, ij2, di, orig1, checkBnds))
    ni <- !is.na(m1)
    list(which(ni), m1[ni])
}


### There is a test on this in ../tests/dgTMatrix.R !

uniqTsparse <- function(x, class.x = c(class(x))) {
    ## Purpose: produce a *unique* triplet representation:
    ##		by having (i,j) sorted and unique
    ## -----------------------------------------------------------
    ## The following is not quite efficient {but easy to program,
    ## and as() are based on C code  (all of them?)
    ##
    ## FIXME: Do it fast for the case where 'x' is already 'uniq'
    if(extends(class.x, "TsparseMatrix")) {
	tri <- extends(class.x, "triangularMatrix")
	.Call(Csparse_to_Tsparse, .Call(Tsparse_to_Csparse, x, tri), tri)
    } else
	stop(gettextf("not yet implemented for class %s", dQuote(class.x)),
	     domain = NA)
}

## Note: maybe, using
## ----    xj <- .Call(Matrix_expand_pointers, x@p)
## would be slightly more efficient than as( <dgC> , "dgTMatrix")
## but really efficient would be to use only one .Call(.) for uniq(.) !

drop0 <- function(x, tol = 0, is.Csparse = NA) {
    .Call(Csparse_drop,
	  if(isTRUE(is.Csparse) || is.na(is.Csparse) && is(x, "CsparseMatrix"))
	      x else as(x, "CsparseMatrix"),
	  tol)
}


uniq <- function(x) {
    if(is(x, "TsparseMatrix")) uniqTsparse(x) else
    if(is(x, "sparseMatrix")) drop0(x) else x
}

asTuniq <- function(x) {
    if(is(x, "TsparseMatrix")) uniqTsparse(x) else as(x,"TsparseMatrix")
}

## is 'x' a uniq Tsparse Matrix ?
is_not_uniqT <- function(x, di = dim(x))
    is.unsorted(x@j) || anyDuplicatedT(x, di)

## is 'x' a TsparseMatrix with duplicated entries (to be *added* for uniq):
is_duplicatedT <- # <- keep old name for a while, as ../inst/test-tools-Matrix.R has used it
anyDuplicatedT <- function(x, di = dim(x))
    anyDuplicated(.Call(m_encodeInd2, x@i, x@j, di, FALSE, FALSE))


t_geMatrix <- function(x) {
    x@x <- as.vector(t(array(x@x, dim = x@Dim))) # no dimnames here
    x@Dim <- x@Dim[2:1]
    x@Dimnames <- x@Dimnames[2:1]
    x@factors <- list() ## FIXME -- do better, e.g., for "LU"?
    x
}

## t( [dl]trMatrix ) and  t( [dl]syMatrix ) :
t_trMatrix <- function(x) {
    x@x <- as.vector(t(as(x, "matrix")))
    x@Dim <- x@Dim[2:1]
    x@Dimnames <- x@Dimnames[2:1]
    x@uplo <- if (x@uplo == "U") "L" else "U"
    # and keep x@diag
    x
}

fixupDense <- function(m, from, cldm = getClassDef(class(m))) {
    if(extends(cldm, "triangularMatrix")) {
	m@uplo <- from@uplo
	m@diag <- from@diag
    } else if(extends(cldm, "symmetricMatrix")) {
	m@uplo <- from@uplo
    }
    m
}

##' @title Transform {vectors, matrix, Matrix, ...} to  dgeMatrix
##' @export
..2dge <- function(from) .Call(dup_mMatrix_as_dgeMatrix, from)

## -> ./ldenseMatrix.R :
l2d_Matrix <- function(from, cl = MatrixClass(class(from)), cld = getClassDef(cl)) {
    ## stopifnot(is(from, "lMatrix"))
    fixupDense(new(sub("^l", "d", cl),
		   x = as.double(from@x),
		   Dim = from@Dim, Dimnames = from@Dimnames),
	       from, cld)
    ## FIXME: treat 'factors' smartly {not for triangular!}
}

## -> ./ndenseMatrix.R :
n2d_Matrix <- function(from, cl = MatrixClass(class(from)), cld = getClassDef(cl)) {
    ## stopifnot(is(from, "nMatrix"))
    fixupDense(new(sub("^n", "d", cl), x = as.double(from@x),
		   Dim = from@Dim, Dimnames = from@Dimnames),
	       from, cld)
    ## FIXME: treat 'factors' smartly {not for triangular!}
}
n2l_Matrix <- function(from, cl = MatrixClass(class(from)), cld = getClassDef(cl)) {
    fixupDense(new(sub("^n", "l", cl),
		   x = from@x, Dim = from@Dim, Dimnames = from@Dimnames),
	       from, cld)
    ## FIXME: treat 'factors' smartly {not for triangular!}
}
## -> ./ddenseMatrix.R :
d2l_Matrix <- function(from, cl = MatrixClass(class(from)), cld = getClassDef(cl)) {
    fixupDense(new(sub("^d", "l", cl), x = as.logical(from@x),
                   Dim = from@Dim, Dimnames = from@Dimnames),
	       from, cld)
    ## FIXME: treat 'factors' smartly {not for triangular!}
}

n2l_spMatrix <- function(from) {
    ## stopifnot(is(from, "nMatrix"))
    new(sub("^n", "l", MatrixClass(class(from))),
        ##x = as.double(from@x),
        Dim = from@Dim, Dimnames = from@Dimnames)
}

tT2gT <- function(x, cl = class(x), toClass, cld = getClassDef(cl)) {
    ## coerce *tTMatrix to *gTMatrix {triangular -> general}
    d <- x@Dim
    if(uDiag <- x@diag == "U")	     # unit diagonal, need to add '1's
        uDiag <- (n <- d[1]) > 0
    if(missing(toClass)) {
        do.n <- extends(cld, "nMatrix")
        toKind <- if(do.n) "n" else substr(MatrixClass(cl), 1,1) # "d" | "l"|"i"|"z"
        toClass <- paste0(toKind, "gTMatrix")
    } else {
        do.n <- extends(toClass, "nMatrix")
        toKind <- if(do.n) "n" else substr(toClass, 1,1)
    }

    if(do.n) ## no 'x' slot
	new(toClass, # == "ngTMatrix"
            Dim = d, Dimnames = x@Dimnames,
	    i = c(x@i, if(uDiag) 0:(n-1)),
	    j = c(x@j, if(uDiag) 0:(n-1)))
    else
	new(toClass, Dim = d, Dimnames = x@Dimnames,
	    i = c(x@i, if(uDiag) 0:(n-1)),
	    j = c(x@j, if(uDiag) 0:(n-1)),
	    x = c(x@x, if(uDiag) rep.int(if(toKind == "l") TRUE else 1, n)))
}
## __TODO__
## Hack for the above, possibly considerably faster:
## Just *modify* the 'x' object , using attr(x, "class') <- toClass


## Fast very special one ../src/Tsparse.c -- as_cholmod_triplet() in ../src/chm_common.c
## 'x' *must* inherit from TsparseMatrix!
.gT2tC <- function(x, uplo, diag="N") .Call(Tsparse_to_tCsparse, x, uplo, diag)
## Ditto in ../src/Csparse.c :
.gC2tC <- function(x, uplo, diag="N") .Call(Csparse_to_tCsparse, x, uplo, diag)
.gC2tT <- function(x, uplo, diag="N") .Call(Csparse_to_tTsparse, x, uplo, diag)

gT2tT <- function(x, uplo, diag, toClass,
		  do.n = extends(toClass, "nMatrix"))
{
    ## coerce *gTMatrix to *tTMatrix {general -> triangular}
    i <- x@i
    j <- x@j
    sel <-
	if(uplo == "U") {
	    if(diag == "U") i < j else i <= j
	} else {
	    if(diag == "U") i > j else i >= j
	}
    i <- i[sel]
    j <- j[sel]
    if(do.n) ## no 'x' slot
	new("ntTMatrix", i = i, j = j, uplo = uplo, diag = diag,
	    Dim = x@Dim, Dimnames = x@Dimnames)
    else
	new(toClass, i = i, j = j, uplo = uplo, diag = diag,
	    x = x@x[sel], Dim = x@Dim, Dimnames = x@Dimnames)
}

check.gT2tT <- function(from, toClass, do.n = extends(toClass, "nMatrix")) {
    if(isTr <- isTriangular(from)) {
	gT2tT(from, uplo = attr(isTr, "kind") %||% "U",
	      diag = "N", ## improve: also test for unit diagonal
	      toClass = toClass, do.n = do.n)
    } else stop("not a triangular matrix")
}

gT2sT <- function(x, toClass, do.n = extends(toClass, "nMatrix")) {
    upper <- x@i <= x@j
    i <- x@i[upper]
    j <- x@j[upper]
    if(do.n) ## no 'x' slot
	new("nsTMatrix", Dim = x@Dim, Dimnames = x@Dimnames,
	    i = i, j = j, uplo = "U")
    else
	new(toClass, Dim = x@Dim, Dimnames = x@Dimnames,
	    i = i, j = j, x = x@x[upper], uplo = "U")
}

check.gT2sT <- function(x, toClass, do.n = extends(toClass, "nMatrix"))
{
    if(isSymmetric(x))
        gT2sT(x, toClass, do.n)
    else
	stop("not a symmetric matrix; consider forceSymmetric() or symmpart()")
}


if(FALSE)# unused
l2d_meth <- function(x) {
    cl <- MatrixClass(class(x))
    as(callGeneric(as(x, sub("^l", "d", cl))), cl)
}

## return "d" or "l" or "n" or "z"
.M.kind <- function(x, clx = class(x)) {
    ## 'clx': class() *or* class definition of x
    if(is.matrix(x) || is.atomic(x)) { ## 'old style' matrix or vector
	if     (is.numeric(x)) "d" ## also for integer: see .V.kind(), .M.kindC()
	else if(is.logical(x)) "l" ## FIXME ? "n" if no NA ??
	else if(is.complex(x)) "z"
	else stop(gettextf("not yet implemented for matrix with typeof %s",
			   typeof(x)), domain = NA)
    }
    else .M.kindC(clx)
}

## the same as .M.kind, but also knows "i"
.V.kind <- function(x, clx = class(x)) {
    ## 'clx': class() *or* class definition of x
    if(is.matrix(x) || is.atomic(x)) { ## 'old style' matrix or vector
	if     (is.integer(x)) "i"
	else if(is.numeric(x)) "d"
	else if(is.logical(x)) "l" ## FIXME ? "n" if no NA ??
	else if(is.complex(x)) "z"
	else stop(gettextf("not yet implemented for matrix with typeof %s",
			   typeof(x)), domain = NA)
    }
    else .M.kindC(clx)
}

.M.kindC <- function(clx, ex = extends(clx)) { ## 'clx': class() *or* classdefinition
    if(is.character(clx))		# < speedup: get it once
	clx <- getClassDef(clx)
    if(any(ex == "sparseVector")) {
	## must work for class *extending* "dsparseVector" ==> cannot use  (clx@className) !
	if     (any(ex == "dsparseVector")) "d"
	else if(any(ex == "nsparseVector")) "n"
	else if(any(ex == "lsparseVector")) "l"
	else if(any(ex == "zsparseVector")) "z"
	else if(any(ex == "isparseVector")) "i"
	else stop(gettextf(" not yet implemented for %s", clx@className),
		  domain = NA)
    }
    else if(any(ex == "dMatrix")) "d"
    else if(any(ex == "nMatrix")) "n"
    else if(any(ex == "lMatrix")) "l"
    else if(any(ex == "indMatrix")) "n" # permutation -> pattern
    else if(any(ex == "zMatrix")) "z"
    else if(any(ex == "iMatrix")) "i"
    else stop(gettextf(" not yet implemented for %s", clx@className),
	      domain = NA)
}

## typically used as .type.kind[.M.kind(x)]:
.type.kind <- c("d" = "double",
		"i" = "integer",
		"l" = "logical",
		"n" = "logical",
		"z" = "complex")
## the reverse, a "version of" .M.kind(.):
.kind.type <- setNames(names(.type.kind), as.vector(.type.kind))

.M.shape <- function(x, clx = class(x)) {
    ## 'clx': class() *or* class definition of x
    if(is.matrix(x)) { ## 'old style matrix'
	if     (isDiagonal  (x)) "d"
	else if(isTriangular(x)) "t"
	else if(isSymmetric (x)) "s"
	else "g" # general
    }
    else {
	if(is.character(clx)) # < speedup: get it once
	    clx <- getClassDef(clx)
        ex <- extends(clx)
	if(     any(ex == "diagonalMatrix"))  "d"
	else if(any(ex == "triangularMatrix"))"t"
	else if(any(ex == "symmetricMatrix")) "s"
	else "g"
    }
}

## a faster simpler version [for sparse matrices, i.e., never diagonal]
.M.shapeC <- function(x, clx = class(x)) {
    if(is.character(clx)) # < speedup: get it once
	clx <- getClassDef(clx)
    if	   (extends(clx, "triangularMatrix")) "t"
    else if(extends(clx, "symmetricMatrix"))  "s" else "g"
}


class2 <- function(cl, kind = "l", do.sub = TRUE) {
    ## Find "corresponding" class; since pos.def. matrices have no pendant:
    cl <- MatrixClass(cl)
    if(cl %in% c("dpoMatrix","corMatrix"))
	paste0(kind, "syMatrix")
    else if(cl == "dppMatrix")
	paste0(kind, "spMatrix")
    else if(do.sub) sub("^[a-z]", kind, cl)
    else cl
}

## see also as_smartClass() below
geClass <- function(x) {
    if     (is(x, "dMatrix")) "dgeMatrix"
    else if(is(x, "lMatrix")) "lgeMatrix"
    else if(is(x, "nMatrix") || is(x, "indMatrix")) "ngeMatrix"
    else if(is(x, "zMatrix")) "zgeMatrix"
    else stop(gettextf("general Matrix class not yet implemented for %s",
		       dQuote(class(x))), domain = NA)
}

.dense.prefixes <- c("d" = "tr", ## map diagonal to triangular
                     "t" = "tr",
                     "s" = "sy",
                     "g" = "ge")

.sparse.prefixes <- c("d" = "t", ## map diagonal to triangular
                      "t" = "t",
                      "s" = "s",
                      "g" = "g")

as_M.kind <- function(x, clx) {
    if(is.character(clx)) # < speedup: get it once
	clx <- getClassDef(clx)
    if(is(x, clx)) x else as(x, paste0(.M.kindC(clx), "Matrix"))
}

## Used, e.g. after subsetting: Try to use specific class -- if feasible :
as_dense <- function(x, cld = if(isS4(x)) getClassDef(class(x))) {
    as(x, paste0(.M.kind(x, cld), .dense.prefixes[.M.shape(x, cld)], "Matrix"))
}

## This is "general" but slower than the next definition
if(FALSE)
.sp.class <- function(x) { ## find and return the "sparseness class"
    if(!is.character(x)) x <- class(x)
    for(cl in paste0(c("C","T","R"), "sparseMatrix"))
	if(extends(x, cl))
	    return(cl)
    ## else (should rarely happen)
    NA_character_
}

.sp.class <- function(x) { ## find and return the "sparseness class"
    x <- if(!is.character(x)) MatrixClass(class(x)) else MatrixClass(x)
    if(any((ch <- substr(x,3,3)) == c("C","T","R")))
        return(paste0(ch, "sparseMatrix"))
    ## else
    NA_character_
}


### Goal: Eventually get rid of these --- want to foster coercions
### ----  *to* virtual classes whenever possible, e.g. as(*, "CsparseMatrix")
## 2007-12: better goal: use them only for "matrix" [maybe speed them up later]

## Here, getting the class definition and passing it, should be faster
as_Csparse <- function(x, cld = if(isS4(x)) getClassDef(class(x))) {
    as(x, paste0(.M.kind(x, cld),
		 .sparse.prefixes[.M.shape(x, cld)], "CMatrix"))
}

if(FALSE) # replaced by .Call(dense_to_Csparse, *) which is perfect for "matrix"
as_Csparse2 <- function(x, cld = if(isS4(x)) getClassDef(class(x))) {
    ## Csparse + U2N when needed
    sh <- .M.shape(x, cld)
    x <- as(x, paste0(.M.kind(x, cld), .sparse.prefixes[sh], "CMatrix"))
    if(sh == "t") .Call(Csparse_diagU2N, x) else x
}

## *do* use this where applicable
as_Csp2 <- function(x) {
    ## Csparse + U2N when needed
    x <- as(x, "CsparseMatrix")
    if(is(x, "triangularMatrix")) .Call(Csparse_diagU2N, x) else x
}

## 'cl'   : class() *or* class definition of from
as_gCsimpl2 <- function(from, cl = class(from))
    as(from, paste0(.M.kind(from, cl), "gCMatrix"))
## to be used directly in setAs(.) needs one-argument-only  (from) :
as_gCsimpl <- function(from) as(from, paste0(.M.kind(from), "gCMatrix"))

## slightly smarter:
as_Sp <- function(from, shape, cl = class(from)) {
    if(is.character(cl)) cl <- getClassDef(cl)
    as(from, paste0(.M.kind(from, cl),
		    shape,
		    if(extends(cl, "TsparseMatrix")) "TMatrix" else "CMatrix"))
}
## These are used in ./sparseMatrix.R:
as_gSparse <- function(from) as_Sp(from, "g", getClassDef(class(from)))
as_sSparse <- function(from) as_Sp(from, "s", getClassDef(class(from)))
as_tSparse <- function(from) as_Sp(from, "t", getClassDef(class(from)))

as_geSimpl2 <- function(from, cl = class(from))
    as(from, paste0(.M.kind(from, cl), "geMatrix"))
## to be used directly in setAs(.) needs one-argument-only  (from) :
as_geSimpl <- function(from) as(from, paste0(.M.kind(from), "geMatrix"))

## Smarter, (but sometimes too smart!) compared to geClass() above:
as_smartClass <- function(x, cl, cld = getClassDef(cl)) {
    if(missing(cl)) return(as_geSimpl(x))
    ## else
    if(extends(cld, "diagonalMatrix")  && isDiagonal(x))
        ## diagonal* result:
	as(x, cl)
    else if(extends(cld, "symmetricMatrix") &&  isSymmetric(x)) {
        ## symmetric* result:
        kind <- .M.kind(x, cld)
	as(x, class2(cl, kind, do.sub= kind != "d"))
    } else if(extends(cld, "triangularMatrix") && isTriangular(x))
	as(x, cl)
    else ## revert to
	as_geSimpl2(x, cld)
}

as_CspClass <- function(x, cl) {
    ## NOTE: diagonal is *not* sparse:
    cld <- getClassDef(cl)
    ##(extends(cld, "diagonalMatrix") && isDiagonal(x)) ||
    if (extends(cld, "symmetricMatrix") && isSymmetric(x))
        forceSymmetric(as(x,"CsparseMatrix"))
    else if (extends(cld, "triangularMatrix") && isTriangular(x))
	as(x, cl)
    else if(is(x, "CsparseMatrix")) x
    else as(x, paste0(.M.kind(x, cld), "gCMatrix"))
}

asTri <- function(from, newclass) {
    ## TODO: also check for unit-diagonal: 'diag = "U"'
    isTri <- isTriangular(from)
    if(isTri)
 	new(newclass, x = from@x, Dim = from@Dim,
	    Dimnames = from@Dimnames, uplo = attr(isTri, "kind"))
    else stop("not a triangular matrix")
}

mat2tri <- function(from, sparse=NA) {
    isTri <- isTriangular(from)
    if(isTri) {
	d <- dim(from)
	if(is.na(sparse))
	    sparse <- prod(d) > 2*sum(isN0(from)) ## <==> sparseDefault() in Matrix()
	if(sparse)
	    as(as(from, "sparseMatrix"), "triangularMatrix")
	else
	    new(paste0(.M.kind(from),"trMatrix"), x = base::as.vector(from),
                Dim = d, Dimnames = .M.DN(from), uplo = attr(isTri, "kind"))
    }
    else stop("not a triangular matrix")
}


try_as <- function(x, classes, tryAnyway = FALSE) {
    if(!tryAnyway && !is(x, "Matrix"))
	return(x)
    ## else
    ok <- canCoerce(x, classes[1])
    while(!ok && length(classes <- classes[-1])) {
	ok <- canCoerce(x, classes[1])
    }
    if(ok) as(x, classes[1]) else x
}


## For *dense* matrices
isTriMat <- function(object, upper = NA, ...) {
    ## pretest: is it square?
    d <- dim(object)
    if(d[1] != d[2]) return(FALSE)
    TRUE.U <- structure(TRUE, kind = "U")
    if(d[1] == 0) return(TRUE.U)
    ## else slower test
    TRUE.L <- structure(TRUE, kind = "L")
    if(!is.matrix(object))
	object <- as(object,"matrix")
    if(is.na(upper)) {
	if(all0(object[lower.tri(object)]))
	    TRUE.U
	else if(all0(object[upper.tri(object)]))
	    TRUE.L
	else FALSE
    } else if(upper)
	if(all0(object[lower.tri(object)])) TRUE.U else FALSE
    else ## upper is FALSE
	if(all0(object[upper.tri(object)])) TRUE.L else FALSE
}

## For Tsparse matrices:
isTriT <- function(object, upper = NA, ...) {
    ## pretest: is it square?
    d <- dim(object)
    if(d[1] != d[2]) return(FALSE)
    ## else
    TRUE.U <- structure(TRUE, kind = "U")
    if(d[1] == 0) return(TRUE.U)
    TRUE.L <- structure(TRUE, kind = "L")
    if(is.na(upper)) {
	if(all(object@i <= object@j))
	    TRUE.U
	else if(all(object@i >= object@j))
	    TRUE.L
	else FALSE
    } else if(upper) {
	if(all(object@i <= object@j)) TRUE.U else FALSE
    } else { ## 'lower'
	if(all(object@i >= object@j)) TRUE.L else FALSE
    }
}

## For Csparse matrices
isTriC <- function(object, upper = NA, ...) {
    ## pretest: is it square?
    d <- dim(object)
    if(d[1] != d[2]) return(FALSE)
    ## else
    TRUE.U <- structure(TRUE, kind = "U")
    if((n <- d[1]) == 0) return(TRUE.U)
    TRUE.L <- structure(TRUE, kind = "L")
    ## Need this, since 'i' slot of symmetric looks like triangular :
    if(is(object, "symmetricMatrix")) # triangular only iff diagonal :
        return(if(length(oi <- object@i) == n && isSeq(oi, n-1L)
                  && isSeq(object@p, n))
               structure(TRUE, kind = object@uplo) else FALSE)
    ## else
    ni <- 1:n
    ## the row indices split according to column:
    ilist <- split(object@i, factor(rep.int(ni, diff(object@p)), levels= ni))
    lil <- lengths(ilist, use.names = FALSE)
    if(any(lil == 0)) {
	pos <- lil > 0
	if(!any(pos)) ## matrix of all 0's
	    return(TRUE.U)
	ilist <- ilist[pos]
	ni <- ni[pos]
    }
    ni0 <- ni - 1L # '0-based ni'
    if(is.na(upper)) {
	if(all(sapply(ilist, max, USE.NAMES = FALSE) <= ni0))
	    TRUE.U
	else if(all(sapply(ilist, min, USE.NAMES = FALSE) >= ni0))
	    TRUE.L
	else FALSE
    } else if(upper) {
	if(all(sapply(ilist, max, USE.NAMES = FALSE) <= ni0))
	    TRUE.U else FALSE
    } else { ## 'lower'
	if(all(sapply(ilist, min, USE.NAMES = FALSE) >= ni0))
	    TRUE.L else FALSE
    }
}


## When the matrix is known to be [n x n] aka "square"
## (need "vector-indexing" work for 'M'):
.is.diagonal.sq.matrix <- function(M, n = dim(M)[1L])
    all0(M[rep_len(c(FALSE, rep.int(TRUE,n)), n^2)])

.is.diagonal <- function(object) {
    ## "matrix" or "denseMatrix" (but not "diagonalMatrix")
    d <- dim(object)
    if(d[1L] != (n <- d[2L])) FALSE
    else if(is.matrix(object)) .is.diagonal.sq.matrix(object, n)
    else ## "denseMatrix" -- packed or unpacked
        if(is(object, "generalMatrix")) # "dge", "lge", ...
	    .is.diagonal.sq.matrix(object@x, n)
        else { ## "dense" but not {diag, general}, i.e. triangular or symmetric:
            ## -> has 'uplo'  differentiate between packed and unpacked

### .......... FIXME ...............
	    ## packed <- isPacked(object)
	    ## if(object@uplo == "U") {
	    ## } else { ## uplo == "L"
	    ## }
### very cheap workaround
	    all0(as.matrix(object)[rep_len(c(FALSE, rep.int(TRUE,n)), n^2)])
        }
}


## Purpose: Transform a *unit diagonal* sparse triangular matrix
##	into one with explicit diagonal entries '1'

## for "dtC*", "ltC* ..: directly
xtC.diagU2N <- function(x) if(x@diag == "U") .Call(Csparse_diagU2N, x) else x

##' @title uni-diagonal to "regular" triangular Matrix
##'
##' NOTE:   class is *not* checked here! {speed}
##' @param x a dense unidiagonal (x@diag == "U") triangular Matrix
##'     ("ltrMatrix", "dtpMatrix", ...).
##' @param kind character indicating content kind: "d","l",..
##' @param isPacked logical indicating if 'x' is packed
##' @return Matrix "like" x, but with x@diag == "N" (and 1 or TRUE values "filled" in .@x)
##' @author Martin Maechler
.dense.diagU2N <- function(x, kind = .M.kind(x), isPacked = length(x@x) < n^2)
{
### FIXME: Move this to C ----- (possibly with an option of *not* copying)
    ## For denseMatrix, .@diag = "U"  means the 'x' slot can have wrong values
    ## which are documented to never be accessed
    n <- x@Dim[1]
    if(n > 0) {
	one <- if(kind == "d") 1. else TRUE
	if(isPacked) { ## { == isPacked(x)) } : dtp-, ltp-, or "ntpMatrix":
	    ## x@x is of length	 n*(n+1)/2
	    if(n == 1)
		x@x <- one
	    else {
		di <- if(x@uplo == "U") seq_len(n) else c(1L,n:2L)
		x@x[cumsum(di)] <- one
	    }
	} else {
	    ## okay: now have  'x' slot of length n x n
	    x@x[1L+ (0:(n-1L))*(n+1L)] <- one # even for "n..Matrix"
	}
    }
    x@diag <- "N"
    x
}

.diagU2N <- function(x, cl, checkDense = FALSE)
{
    ## fast "no-test" version --- we *KNOW* 'x' is 'triangularMatrix'
    if(extends(cl, "CsparseMatrix"))
	.Call(Csparse_diagU2N, x)
    else if(extends(cl, "TsparseMatrix"))
	.Call(Tsparse_diagU2N, x)
    else {
	kind <- .M.kind(x, cl)
        if(checkDense && extends(cl,"denseMatrix")) {
	    .dense.diagU2N(x, kind)
        }
        else { ## possibly dense, not [CT]sparseMatrix  ==>  Rsparse*
	    .Call(Tsparse_diagU2N,
		  as(as(x, paste0(kind, "Matrix")), "TsparseMatrix"))
	    ## leave it as T* - the caller can always coerce to C* if needed
        }
    }
} ## .diagU2N()

diagU2N <- function(x, cl = getClassDef(class(x)), checkDense = FALSE)
{
    if(extends(cl, "triangularMatrix") && x@diag == "U")
	.diagU2N(x, cl, checkDense=checkDense)
    else x
}

##' @title coerce triangular Matrix to uni-diagonal
##'
##' NOTE: class is *not* checked here! {speed}
##' @param x a dense triangular Matrix ("ltrMatrix", "dtpMatrix", ...).
##' @return Matrix "like" x, but with x@diag == "U"
.dense.diagN2U <- function(x)
{
    ## as we promise that the diagonal entries are not accessed when
    ##	diag = "U",   we don't even need to set them to one !!
    x@diag <- "U"
    x
}

diagN2U <- function(x, cl = getClassDef(class(x)), checkDense = FALSE)
{
    if(!(extends(cl, "triangularMatrix") && x@diag == "N"))
	return(x)
    if(checkDense && extends(cl,"denseMatrix")) {
	.dense.diagN2U(x)
    }
    else ## still possibly dense
	.Call(Csparse_diagN2U, as(x, "CsparseMatrix"))
}

.dgC.0.factors <- function(x)
    if(!length(x@factors)) x else { x@factors <- list() ; x }
.as.dgC.0.factors <- function(x) {
    if(!is(x, "dgCMatrix"))
	as(x, "dgCMatrix") # will not have 'factors'
    else ## dgCMatrix
	.dgC.0.factors(x)
}

.set.factors <- function(x, name, value, warn.no.slot=FALSE)
    .Call(R_set_factors, x, value, name, warn.no.slot)

### Fast, much simplified version of tapply()
tapply1 <- function (X, INDEX, FUN = NULL, ..., simplify = TRUE) {
    sapply(unname(split(X, INDEX)), FUN, ...,
	   simplify = simplify, USE.NAMES = FALSE)
}

## tapply.x <- function (X, n, INDEX, FUN = NULL, ..., simplify = TRUE) {
##     tapply1(X, factor(INDEX, 0:(n-1)), FUN = FUN, ..., simplify = simplify)
## }

### MM: Unfortunately, these are still pretty slow for large sparse ...

sparsapply <- function(x, MARGIN, FUN, sparseResult = TRUE, ...)
{
    ## Purpose: "Sparse Apply": better utility than tapply1() for colSums() etc :
    ##    NOTE: Only applicable sum()-like where the "zeros do not count"
    ## ----------------------------------------------------------------------
    ## Arguments: x: sparseMatrix;  others as in *apply()
    ## ----------------------------------------------------------------------
    ## Author: Martin Maechler, Date: 16 May 2007
    stopifnot(MARGIN %in% 1:2)
    xi <- if(MARGIN == 1) x@i else x@j
    ui <- unique(xi)
    n <- x@Dim[MARGIN]
    ## FIXME: Here we assume 'FUN' to return  'numeric' !
    r <- if(sparseResult) new("dsparseVector", length = n) else numeric(n)
    r[ui + 1L] <- sapply(ui, function(i) FUN(x@x[xi == i], ...))
    r
}

sp.colMeans <- function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE)
{
    nr <- nrow(x)
    if(na.rm) ## use less than nrow(.) in case of NAs
	nr <- nr - sparsapply(x, 2, function(u) sum(is.na(u)),
			      sparseResult=sparseResult)
    sparsapply(x, 2, sum, sparseResult=sparseResult, na.rm=na.rm) / nr
}

sp.rowMeans <- function(x, na.rm = FALSE, dims = 1, sparseResult = FALSE)
{
    nc <- ncol(x)
    if(na.rm) ## use less than ncol(.) in case of NAs
	nc <- nc - sparsapply(x, 1, function(u) sum(is.na(u)),
			      sparseResult=sparseResult)
    sparsapply(x, 1, sum, sparseResult=sparseResult, na.rm=na.rm) / nc
}

all0Matrix <- function(n,m) {
    ## an  all-0 matrix	 -- chose what Matrix() also gives -- "most efficiently"
    n <- as.integer(n)
    m <- as.integer(m)
    new(if(n == m) "dsCMatrix" else "dgCMatrix",
	Dim = c(n,m),
	p = rep.int(0L, m+1L))
}

.setZero <- function(x, newclass = if(d[1] == d[2]) "dsCMatrix" else "dgCMatrix") {
    ## all-0 matrix  from x  which must inherit from 'Matrix'
    d <- x@Dim
    new(newclass, Dim = d, Dimnames = x@Dimnames, p = rep.int(0L, d[2]+1L))
}

.M.vectorSub <- function(x,i) { ## e.g. M[0] , M[TRUE],  M[1:2]
    if(any(as.logical(i)) || prod(dim(x)) == 0)
	## FIXME: for *large sparse*, use sparseVector !
	as(x, "matrix")[i]
    else ## save memory (for large sparse M):
	as.vector(x[1,1])[FALSE]
}

##' Compute the three "parts" of two sets:
##' @param x arbitrary vector; possibly with duplicated values,
##' @param y (ditto)
##' @param uniqueCheck
##' @param check
##'
##' @return list(x.only = setdiff(x,y),
##'              y.only = setdiff(y,x),
##'	         int = intersect(x,y))
setparts <- function(x,y, uniqueCheck = TRUE, check = TRUE) {
    if(check) {
        x <- as.vector(x)
        y <- as.vector(y)
    }
    if(uniqueCheck) {
        x <- unique.default(x)
        y <- unique.default(y)
    }
    .setparts(x,y)
}
.setparts <- function(x,y) {
    n1 <- length(m1 <- match(x,y, 0L))
    n2 <- length(m2 <- match(y,x, 0L))
    ix <- seq_len(n1)[m1 == 0L]
    iy <- seq_len(n2)[m2 == 0L]
    list(x.only = x[ix], ix.only = ix, mx = m1,
         y.only = y[iy], iy.only = iy, my = m2,
         int = if(n1 < n2) y[m1] else x[m2])
}

##' @title Warn about extraneous arguments in the "..."  (of its caller).
##' A merger of my approach and the one in seq.default()
##' @author Martin Maechler, June 2012, May 2014
##' @param ...
##' @param which.call passed to sys.call().  A caller may use -2 if the message should
##' mention *its* caller
chk.s <- function(..., which.call = -1) {
    if(nx <- length(list(...)))
	warning(sprintf(ngettext(nx,
                                 "extra argument %s will be disregarded in\n %s",
                                 "extra arguments %s will be disregarded in\n %s"),
                        sub(")$", '', sub("^list\\(", '', deparse(list(...), control=c()))),
                        deparse(sys.call(which.call), control=c())),
                call. = FALSE, domain=NA)
}

##' *Only* to be used as function in
##'    setMethod.("Compare", ...., .Cmp.swap)  -->  ./Ops.R  & ./diagMatrix.R
.Cmp.swap <- function(e1,e2) {
    ## "swap RHS and LHS" and use the method below:
    switch(.Generic,
	   "==" =, "!=" = callGeneric(e2, e1),
	   "<"	= e2 >	e1,
	   "<=" = e2 >= e1,
	   ">"	= e2 <	e1,
	   ">=" = e2 <= e1)
}