R/diagMatrix.R

In Matrix: Sparse and Dense Matrix Classes and Methods

## Methods for "diagonalMatrix" and its subclasses, currently "[dl]diMatrix"

## ~~~~ COERCIONS TO ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

setAs("Matrix", "diagonalMatrix", ..M2diag)
setAs("matrix", "diagonalMatrix", ..M2diag)

## MJ: no longer needed ... replacement above
if(FALSE) {
setAs("matrix", "diagonalMatrix",
      function(from) {
	  d <- dim(from)
	  if(d[1] != (n <- d[2])) stop("non-square matrix")
	  if(any(from[row(from) != col(from)] != 0))
	      stop("matrix with non-zero off-diagonals cannot be coerced to \"diagonalMatrix\"")
	  x <- diag(from); names(x) <- NULL # don't want them in 'x' slot
	  if(is.logical(x)) {
	      cl <- "ldiMatrix"
	      uni <- allTrue(x) ## uni := {is it unit-diagonal ?}
	  } else {
	      cl <- "ddiMatrix"
	      uni <- allTrue(x == 1)
	      storage.mode(x) <- "double"
	  } ## TODO: complex
	  new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
	      x = if(uni) x[FALSE] else x, Dimnames = .M.DN(from))
      })

## ``generic'' coercion to  diagonalMatrix : build on  isDiagonal() and diag()
setAs("Matrix", "diagonalMatrix",
      function(from) {
	  d <- dim(from)
	  if(d[1] != (n <- d[2])) stop("non-square matrix")
	  if(!isDiagonal(from)) stop("matrix is not diagonal")
	  ## else:
	  x <- diag(from); names(x) <- NULL # don't want them in 'x' slot
	  if(is.logical(x)) {
	      cl <- "ldiMatrix"
	      uni <- allTrue(x)
	  } else {
	      cl <- "ddiMatrix"
	      uni <- allTrue(x == 1)
	      storage.mode(x) <- "double"
	  } ## TODO: complex
	  new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
	      x = if(uni) x[FALSE] else x, Dimnames = from@Dimnames)
      })
} ## MJ


## ~~~~ COERCIONS FROM ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

..diag2dsparse <- function(from)
    .Call(R_diagonal_as_sparse, from, "dtT", "U", TRUE)
..diag2lsparse <- function(from)
    .Call(R_diagonal_as_sparse, from, "ltT", "U", TRUE)
..diag2nsparse <- function(from)
    .Call(R_diagonal_as_sparse, from, "ntT", "U", TRUE)

..diag2tC <- function(from)
    .Call(R_diagonal_as_sparse, from, ".tC", "U", TRUE)
..diag2tR <- function(from)
    .Call(R_diagonal_as_sparse, from, ".tR", "U", TRUE)
..diag2tT <- function(from)
    .Call(R_diagonal_as_sparse, from, ".tT", "U", TRUE)
..diag2sC <- function(from)
    .Call(R_diagonal_as_sparse, from, ".sC", "U", TRUE)
..diag2sR <- function(from)
    .Call(R_diagonal_as_sparse, from, ".sR", "U", TRUE)
..diag2sT <- function(from)
    .Call(R_diagonal_as_sparse, from, ".sT", "U", TRUE)
..diag2gC <- function(from)
    .Call(R_diagonal_as_sparse, from, ".gC", "U", TRUE)
..diag2gR <- function(from)
    .Call(R_diagonal_as_sparse, from, ".gR", "U", TRUE)
..diag2gT <- function(from)
    .Call(R_diagonal_as_sparse, from, ".gT", "U", TRUE)

## .diag2[ts]T() are exported ...
.diag2tT <- function(from, uplo = "U", kind = ".", drop0 = TRUE)
    .Call(R_diagonal_as_sparse, from,
          `substr<-`(".tT", 1L, 1L, kind), uplo, drop0)
.diag2sT <- function(from, uplo = "U", kind = ".", drop0 = TRUE)
    .Call(R_diagonal_as_sparse, from,
          `substr<-`(".sT", 1L, 1L, kind), uplo, drop0)

## For group methods
.diag2tT.smart <- function(from, x, uplo = "U", kind = ".", drop0 = TRUE) {
    .Call(R_diagonal_as_sparse, from,
          `substr<-`(".sT", 1L, 1L, kind),
          if(is(x, "triangularMatrix")) x@uplo else uplo,
          drop0)
}
.diag2T.smart <- function(from, x, uplo = "U", kind = ".", drop0 = TRUE) {
    symmetric <- extends(cld <- getClassDef(class(x)), "symmetricMatrix")
    .Call(R_diagonal_as_sparse, from,
          `substr<-`(if(symmetric) ".sT" else ".tT", 1L, 1L, kind),
          if(symmetric || extends(cld, "triangularMatrix")) x@uplo else uplo,
          drop0)
}

..diag2tp  <- function(from) .diag2dense(from, ".tp", "U")
..diag2tr  <- function(from) .diag2dense(from, ".tr", "U")
..diag2dtr <- function(from) .diag2dense(from, "dtr", "U")
..diag2ltr <- function(from) .diag2dense(from, "ltr", "U")
..diag2ntr <- function(from) .diag2dense(from, "ntr", "U")
..diag2dsy <- function(from) .diag2dense(from, "dsy", "U")
..diag2lsy <- function(from) .diag2dense(from, "lsy", "U")
..diag2nsy <- function(from) .diag2dense(from, "nsy", "U")
..diag2dge <- function(from) .diag2dense(from, "dge", NULL)
..diag2lge <- function(from) .diag2dense(from, "lge", NULL)
..diag2nge <- function(from) .diag2dense(from, "nge", NULL)

setAs("diagonalMatrix",          "dMatrix", ..diag2d)
setAs("diagonalMatrix",          "lMatrix", ..diag2l)
setAs("diagonalMatrix",          "nMatrix", ..diag2nsparse)

setAs("diagonalMatrix",    "dsparseMatrix", ..diag2dsparse)
setAs("diagonalMatrix",    "lsparseMatrix", ..diag2lsparse)
setAs("diagonalMatrix",    "nsparseMatrix", ..diag2nsparse)

setAs("diagonalMatrix",    "CsparseMatrix", ..diag2tC)
setAs("diagonalMatrix",    "RsparseMatrix", ..diag2tR)
setAs("diagonalMatrix",    "TsparseMatrix", ..diag2tT)

setAs("diagonalMatrix", "triangularMatrix", ..diag2tC)
setAs("diagonalMatrix",  "symmetricMatrix", ..diag2sC)
setAs("diagonalMatrix",    "generalMatrix", ..diag2gC)

setAs("diagonalMatrix",      "denseMatrix", ..diag2tr)
setAs("diagonalMatrix",   "unpackedMatrix", ..diag2tr)
setAs("diagonalMatrix",     "packedMatrix", ..diag2tp)
setAs("diagonalMatrix",     "ddenseMatrix", ..diag2dtr)
setAs("diagonalMatrix",     "ldenseMatrix", ..diag2ltr)
setAs("diagonalMatrix",     "ndenseMatrix", ..diag2ntr)
setAs("diagonalMatrix",           "matrix", .diag2m)
setAs("diagonalMatrix",           "vector", .diag2v)

setMethod("as.vector", signature(x = "diagonalMatrix"),
          function(x, mode) as.vector(.diag2v(x), mode))

setMethod("as.numeric", signature(x = "diagonalMatrix"),
          function(x, ...) as.double(.diag2v(x)))
setMethod("as.numeric", signature(x = "ddiMatrix"),
          function(x, ...) .diag2v(x))

setMethod("as.logical", signature(x = "diagonalMatrix"),
          function(x, ...) as.logical(.diag2v(x)))
setMethod("as.logical", signature(x = "ldiMatrix"),
          function(x, ...) .diag2v(x))

## DEPRECATED IN 1.5-0; see ./zzz.R
if(FALSE) {
.kinds <- c("d", "l")
for (.kind in .kinds) {
    ## ddi->[^d]di and similar
    for (.otherkind in .kinds[.kinds != .kind])
        setAs(paste0(     .kind, "diMatrix"),
              paste0(.otherkind, "diMatrix"),
              get(paste0("..diag2", .otherkind),
                  mode = "function", inherits = FALSE))
    ## ddi->d[tsg][CRT] and similar
    for (.x in c("t", "s", "g"))
        for (.y in c("C", "R", "T"))
            setAs(paste0(.kind, "diMatrix"),
                  paste0(.kind, .x, .y, "Matrix"),
                  get(paste0("..diag2", .x, .y),
                      mode = "function", inherits = FALSE))
    ## ddi->d(tr|sy|ge) and similar
    for (.xy in c("tr", "sy", "ge"))
        setAs(paste0(.kind, "diMatrix"),
              paste0(.kind, .xy, "Matrix"),
              get(paste0("..diag2", .kind, .xy),
                  mode = "function", inherits = FALSE))
}
rm(.kinds, .kind, .otherkind, .x, .y, .xy)
} ## DEPRECATED IN 1.5-0; see ./zzz.R

rm(..diag2dsparse, ..diag2lsparse, ..diag2nsparse,
   ..diag2tC, ..diag2tR, ..diag2tT,
   ..diag2sC, ..diag2sR, ..diag2sT,
   ..diag2gC, ..diag2gR, ..diag2gT,
   ..diag2tp, ..diag2tr,
   ..diag2dtr, ..diag2ltr, ..diag2ntr,
   ..diag2dsy, ..diag2lsy, ..diag2nsy,
   ..diag2dge, ..diag2lge, ..diag2nge)

## MJ: no longer needed ... replacement above
if(FALSE) {
.diag2tT <- function(from, uplo = "U", kind = .M.kind(from), drop0 = TRUE) {
    ## to triangular Tsparse
    x <- from@x
    i <- if(from@diag == "U")
	      integer(0L)
	  else if(drop0 & any0(x)) {
	      ii <- which(isN0(x))
	      x <- x[ii]
	      ii - 1L
	  }
	  else
	      seq_len(from@Dim[1]) - 1L
    new(paste0(kind, "tTMatrix"),
	diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,
	uplo = uplo,
	x = x, # <- ok for diag = "U" and "N" (!)
	i = i, j = i)
}

.diag2sT <- function(from, uplo = "U", kind = .M.kind(from)) {
    ## to symmetric Tsparse
    n <- from@Dim[1]
    i <- seq_len(n) - 1L
    new(paste0(kind, "sTMatrix"),
	Dim = from@Dim, Dimnames = from@Dimnames,
	i = i, j = i, uplo = uplo,
	x = if(from@diag == "N") from@x else ## "U"-diag
	rep.int(switch(kind,
		       "d" = 1.,
		       "l" =,
		       "n" = TRUE,
		       ## otherwise
		       stop(gettextf("%s kind not yet implemented",
				     sQuote(kind)), domain=NA)),
		n))
}

## diagonal -> triangular,  upper / lower depending on "partner" 'x':
diag2tT.u <- function(d, x, kind = .M.kind(d), drop0 = TRUE)
    .diag2tT(d, uplo = if(is(x,"triangularMatrix")) x@uplo else "U", kind, drop0)

## diagonal -> sparse {triangular OR symmetric} (upper / lower) depending on "partner":
diag2Tsmart <- function(d, x, kind = .M.kind(d)) {
    clx <- getClassDef(class(x))
    if(extends(clx, "symmetricMatrix"))
	.diag2sT(d, uplo = x@uplo, kind)
    else
	.diag2tT(d, uplo = if(extends(clx,"triangularMatrix")) x@uplo else "U", kind)
}

## In order to evade method dispatch ambiguity warnings,
## and because we can save a .M.kind() call, we use this explicit
## "hack"  instead of signature  x = "diagonalMatrix" :
##
## ddi*:
di2tT <- function(from) .diag2tT(from, "U", "d")
setAs("ddiMatrix", "triangularMatrix", di2tT)
##_no_longer_ setAs("ddiMatrix", "sparseMatrix", di2tT)
## needed too (otherwise <dense> -> Tsparse is taken):
setAs("ddiMatrix", "TsparseMatrix", di2tT)
setAs("ddiMatrix", "dsparseMatrix", di2tT)
ddi2Csp <- function(from) .T2Cmat(.diag2tT(from, "U", "d"), isTri=TRUE) #-> dtC*
setAs("ddiMatrix", "dtCMatrix",     ddi2Csp)
setAs("ddiMatrix", "CsparseMatrix", ddi2Csp)
## Such that  as(Matrix(0, d,d), "dgCMatrix")  continues working:
setAs("ddiMatrix", "dgCMatrix", function(from) .dtC2g(ddi2Csp(from)))

setAs("ddiMatrix", "symmetricMatrix", function(from) .diag2sT(from, "U", "d"))
##
## ldi*:
ldi2tT <- function(from) .diag2tT(from, "U", "l")
setAs("ldiMatrix", "triangularMatrix", ldi2tT)
##_no_longer_ setAs("ldiMatrix", "sparseMatrix", di2tT)
## needed too (otherwise <dense> -> Tsparse is taken):
setAs("ldiMatrix", "TsparseMatrix", ldi2tT)
setAs("ldiMatrix", "lsparseMatrix", ldi2tT)
setAs("ldiMatrix", "CsparseMatrix",
      function(from) .T2Cmat(.diag2tT(from, "U", "l"), isTri=TRUE))
setAs("ldiMatrix", "symmetricMatrix", function(from) .diag2sT(from, "U", "l"))
rm(ldi2tT)

setAs("diagonalMatrix", "nMatrix",
      di2nMat <- function(from) {
	  i <- if(from@diag == "U") integer(0) else which(isN0(from@x)) - 1L
	  new("ntTMatrix", i = i, j = i, diag = from@diag,
	      Dim = from@Dim, Dimnames = from@Dimnames)
      })
setAs("diagonalMatrix", "nsparseMatrix", function(from) as(from, "nMatrix"))

##' A version of diag(x,n) which *does* preserve the mode of x, where diag() "fails"
mkDiag <- function(x, n) {
    y <- matrix(as0(mod=mode(x)), n,n)
    if (n > 0) y[1L + 0:(n - 1L) * (n + 1)] <- x
    y
}
## NB: diag(x,n) is really faster for n >= 20, and even more for large n
## --> using diag() where possible, ==> .ddi2mat()

.diag2mat <- function(from)
    ## want "ldiMatrix" -> <logical> "matrix"  (but integer -> <double> for now)
    mkDiag(if(from@diag == "U") as1(from@x) else from@x, n = from@Dim[1])

.ddi2mat <- function(from)
    `dimnames<-`(base::diag(if(from@diag == "U") as1(from@x) else from@x, nrow = from@Dim[1]),
                 from@Dimnames)

setAs("ddiMatrix", "matrix", .ddi2mat)
## the non-ddi diagonalMatrix -- only "ldiMatrix" currently:
setAs("diagonalMatrix", "matrix", .diag2mat)

setAs("diagonalMatrix", "generalMatrix", # prefer sparse:
      function(from) as(as(from, "CsparseMatrix"), "generalMatrix"))

setAs("diagonalMatrix", "denseMatrix",
      function(from) as(as(from, "CsparseMatrix"), "denseMatrix"))

setAs("ddiMatrix", "dgeMatrix", function(from) ..2dge(from))

setAs("ddiMatrix", "ddenseMatrix", #-> "dtr"
      function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
setAs("ldiMatrix", "ldenseMatrix", #-> "ltr"
      function(from) as(as(from, "triangularMatrix"),"denseMatrix"))
} ## MJ


## ~~~~ CONSTRUCTORS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

## diagonalMatrix constructor, allowing either or both of 'n' and 'x' to be
## missing ... like base::diag() but _not_ also extracting diagonal entries
Diagonal <- function(n, x = NULL, names = FALSE) {
    nx <- length(x)
    if(missing(n))
        n <- nx
    else if(!is.numeric(n) || length(n) != 1L || is.na(n) || n < 0L)
        stop("'n' must be a non-negative integer")
    if(is.double(n) && n >= .Machine$integer.max + 1)
        stop("dimensions cannot exceed 2^31-1")
    n <- as.integer(n) # discarding attributes
    if(is.null(x)) {
        r <- new("ddiMatrix")
        r@diag <- "U"
        if(n > 0L) {
            r@Dim <- c(n, n)
            if(is.character(names) && length(names) == n)
                r@Dimnames <- list(names, names)
        }
        return(r)
    }
    if(is.object(x))
        stop(gettextf("'x' has unsupported class \"%s\"", class(x)[1L]),
             domain = NA)
    names.x <- names(x) # keeping for later
    r <- new(switch(typeof(x),
                    ## discarding attributes, incl. 'dim' and 'names'
                    logical = { x <- as.logical(x); "ldiMatrix" },
                    integer =,
                    double = { x <- as.double(x); "ddiMatrix" },
                    stop(gettextf("'x' has unsupported type \"%s\"", typeof(x)),
                         domain = NA)))
    if(n == 0L)
        return(r)
    if(nx != 1L)
        r@x <-
            if(nx == n)
                x
            else if(nx > 0L)
                rep_len(x, n)
            else stop("attempt to recycle 'x' of length 0 to length 'n' (n > 0)")
    else if(is.na(x) || x != 1)
        r@x <- rep.int(x, n)
    else r@diag <- "U"
    r@Dim <- c(n, n)
    if(is.character(names)) {
        if(length(names) == n)
            r@Dimnames <- list(names, names)
    } else if(isTRUE(names) && !is.null(names.x)) {
        names.x <- rep_len(names.x, n) # we know length(names.x) > 0L
        r@Dimnames <- list(names.x, names.x)
    }
    r
}

.sparseDiagonal <- function(n, x = NULL, uplo = "U", shape = "t", unitri = TRUE,
                            kind, cols) {
    if(missing(n))
        n <- length(x)
    else if(!is.numeric(n) || length(n) != 1L || is.na(n) || n < 0L)
        stop("'n' must be a non-negative integer")
    if(is.double(n) && n >= .Machine$integer.max + 1)
        stop("dimensions cannot exceed 2^31-1")
    n <- nj <- as.integer(n) # stripping attributes

    if(!(missing(shape) ||
         (is.character(shape) && length(shape) == 1L && !is.na(shape) &&
          any(shape == c("g", "t", "s")))))
        stop("'shape' must be one of \"g\", \"t\", \"s\"")

    if(!((m.kind <- missing(kind)) ||
         (is.character(kind) && length(kind) == 1L && !is.na(kind) &&
          any(kind == c("d", "l", "n")))))
        stop("'kind' must be one of \"d\", \"l\", \"n\"")

    if(m.kind || kind != "n") {
        if(is.null(x))
           x <- if(m.kind) { kind <- "d"; 1 } else switch(kind, d = 1, l = TRUE)
        else if(is.object(x))
            stop(gettextf("'x' has unsupported class \"%s\"",
                          class(x)[1L]),
                 domain = NA)
        else {
            kind. <- switch(typeof(x),
                            ## discarding attributes, incl. 'dim' in array case
                            logical = { x <- as.logical(x); "l" },
                            integer =,
                            double = { x <- as.double(x); "d" },
                            stop(gettextf("'x' has unsupported type \"%s\"",
                                          typeof(x)),
                                 domain = NA))
            if(m.kind)
                kind <- kind.
            else if(kind != kind.) {
                warning(gettextf("mismatch between typeof(x)=\"%s\" and kind=\"%s\"; using kind=\"%s\"",
                                 typeof(x), kind, kind.),
                        domain = NA)
                kind <- kind.
            }
        }
    }

    if(!(m.cols <- missing(cols))) {
        if(!is.numeric(cols))
            stop("'cols' must be numeric")
        else if((nj <- length(cols)) > 0L &&
                (n == 0L || anyNA(rj <- range(cols)) ||
                 rj[1L] < 0L || rj[2L] >= n))
            stop("'cols' has elements not in seq(0, length.out = n)")
        else {
            cols <- as.integer(cols)
            shape <- "g"
        }
    }

    r <- new(paste0(kind, shape, "CMatrix"))
    r@Dim <- c(n, nj)
    if(shape != "g") {
        if(!missing(uplo)) {
            if(is.character(uplo) && length(uplo) == 1L && !is.na(uplo) &&
               any(uplo == c("U", "L")))
                r@uplo <- uplo
            else stop("'uplo' must be \"U\" or \"L\"")
        }
        if(shape == "t" && unitri &&
           (kind == "n" || (!anyNA(x) && all(if(kind == "l") x else x == 1)))) {
            r@diag <- "U"
            r@p <- integer(nj + 1)
            return(r)
        }
    }
    if(nj > 0L) {
        r@p <- 0:nj
        r@i <- if(m.cols) 0:(nj - 1L) else cols
        if(kind != "n") {
            x <-
                if((nx <- length(x)) == n)
                    x
                else if(nx > 0L)
                    rep_len(x, n)
                else stop("attempt to recycle 'x' of length 0 to length 'n' (n > 0)")
            r@x <- if(m.cols) x else x[1L + cols]
        }
    }
    r
}

## NB: .triDiagonal() would be misleading; it suggests tridiagonal _banded_
.trDiagonal <- function(n, x = NULL, uplo = "U", unitri = TRUE, kind)
    .sparseDiagonal(n, x, uplo, shape = "t", unitri = unitri, kind = kind)

## Package 'spdep' had a (relatively slow) version of this: as_dsCMatrix_I()
.symDiagonal <- function(n, x = NULL, uplo = "U", kind)
    .sparseDiagonal(n, x, uplo, shape = "s", kind = kind)

if(FALSE) {
## This is modified from a post of Bert Gunter to R-help on 1 Sep 2005.
## Bert's code built on a post by Andy Liaw who was probably influenced
## by earlier posts, notably one by Scott Chasalow on S-news on 16 Jan
## 2002, giving his own version written in Dec 1995.
.bdiag <- function(lst) {
    ## block-diagonal matrix [a dgTMatrix] from list of matrices
    stopifnot(is.list(lst), length(lst) >= 1)
    dims <- vapply(lst, dim, 1L, USE.NAMES=FALSE)
    ## make sure we had all matrices:
    if(!(is.matrix(dims) && nrow(dims) == 2))
	stop("some arguments are not matrices")
    csdim <- rbind(rep.int(0L, 2),
                   apply(dims, 1, cumsum))
    r <- new("dgTMatrix")
    r@Dim <- as.integer(csdim[nrow(csdim),])
    add1 <- matrix(1:0, 2,2)
    for(i in seq_along(lst)) {
	indx <- apply(csdim[i:(i+1),] + add1, 2, function(n) n[1]:n[2])
	if(is.null(dim(indx))) ## non-square matrix
	    r[indx[[1]],indx[[2]]] <- lst[[i]]
	else ## square matrix
	    r[indx[,1], indx[,2]] <- lst[[i]]
    }
    r
}
} else {
## expand(<mer>) needed something like bdiag() for lower triangular
## TsparseMatrix, hence Doug Bates provided a much more efficient
## implementation for those, here extended and generalized:
.bdiag <- function(lst) {
    if(!is.list(lst))
        stop("'lst' must be a list")
    if((n <- length(lst)) == 0L)
        return(new("dgTMatrix"))
    if(n == 1L)
        return(.CR2T(asCspN(lst[[1L]])))

### FIXME? this is _slow_ when 'lst' is list of 75000 3-by-3 dense matrices
    lst <- unname(lapply(lst, function(x) .CR2T(asCspN(x))))

    ## NB: class(.CR2T(.)) is always "[dln][gts]TMatrix"
    cl <- vapply(lst, class, "")
    kind  <- substr(cl, 1L, 1L) # "d", "l", or "n"
    shape <- substr(cl, 2L, 2L) # "g", "t", or "s"

    if(!(any(kind == (kind. <- "d")) || any(kind == (kind. <- "l"))))
        kind. <- "n"
    else if(any(z <- kind == "n"))
        lst[z] <- lapply(lst[z], .sparse2kind, kind.)

    shape. <-
        if(all(symmetric <- shape == "s"))
            "s"
        else if(all(shape == "t"))
            "t"
        else "g"

    if(shape. != "g") {
        uplo <- vapply(lst, slot, "", "uplo") # "U" or "L"
        if(shape. == "s")
            uplo. <-
                if(all(z <- uplo == "U"))
                    "U"
                else if(!any(z))
                    "L"
                else {
                    uplo.. <- if(2 * sum(z) >= n) { z <- !z; "U" } else "L"
                    lst[z] <- lapply(lst[z],
                                     function(x) .Call(R_sparse_transpose, x))
                    uplo..
                }
        else if(any(uplo != (uplo. <- uplo[1L])))
            shape. <- "g"
    }

    i_off <- c(0L, cumsum(vapply(lst, function(x) x@Dim[1L], 0L)))
    j_off <- c(0L, cumsum(vapply(lst, function(x) x@Dim[2L], 0L)))

    r <- new(paste0(kind., shape., "TMatrix"))
    r@Dim <- r@Dim <- c(i_off[n + 1L], j_off[n + 1L])
    if(shape. == "g")
        lst[symmetric] <- lapply(lst[symmetric], .sparse2g)
    else r@uplo <- uplo.
    r@i <- unlist(lapply(seq_len(n), function(k) i_off[k] + lst[[k]]@i),
                  FALSE, FALSE)
    r@j <- unlist(lapply(seq_len(n), function(k) j_off[k] + lst[[k]]@j),
                  FALSE, FALSE)
    if(kind. != "n")
        r@x <- unlist(lapply(lst, slot, "x"), FALSE, FALSE)
    r
}
}

bdiag <- function(...) {
    if((n <- ...length()) == 0L)
        new("dgCMatrix")
    else if(n > 1L)
        .T2C(.bdiag(list(...)))
    else if(!is.list(x <- ..1))
        as(x, "CsparseMatrix")
    else if(length(x) == 1L)
        as(x[[1L]], "CsparseMatrix")
    else .T2C(.bdiag(x))
}


## ~~~~ METHODS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 .diag.x <- function(m) if(m@diag != "N") rep.int(as1(m@x), m@Dim[1L]) else m@x
..diag.x <- function(m)                   rep.int(as1(m@x), m@Dim[1L])

setMethod("diag", signature(x = "diagonalMatrix"),
          function(x, nrow, ncol, names = TRUE) {
              r <- .diag.x(x)
              if(names &&
                 !any(vapply(dn <- x@Dimnames, is.null, NA)) &&
                 {
                     i <- seq_len(min(x@Dim))
                     identical(nms <- dn[[1L]][i], dn[[2L]][i])
                 })
                  names(r) <- nms
              r
          })

setMethod("diag<-", signature(x = "diagonalMatrix"),
          function(x, value) {
              n <- x@Dim[1L]
              nv <- length(value)
              if(nv != 1L && nv != n)
                  stop("replacement diagonal has wrong length")
              x@x <-
                  if(is.logical(x@x))
                      switch(typeof(value),
                             logical = rep_len(value, n),
                             integer =,
                             double =
                                 {
                                     x <- ..diag2d(x)
                                     rep_len(as.double(x), n)
                                 },
                             stop(gettextf("replacement diagonal has incompatible type \"%s\"", typeof(value)),
                                  domain = NA))
                  else
                      switch(typeof(value),
                             logical =,
                             integer =,
                             double = rep_len(as.double(value), n),
                             stop(gettextf("replacement diagonal has incompatible type \"%s\"", typeof(value)),
                                  domain = NA))
              x@diag <- "N"
              x
          })

setMethod("t", signature(x = "diagonalMatrix"),
          function(x) { x@Dimnames <- x@Dimnames[2:1]; x })

setMethod("band", signature(x = "diagonalMatrix"),
          function(x, k1, k2, ...)
              if(k1 <= 0L && k2 >= 0L) x else .setZero(x))

setMethod("triu", signature(x = "diagonalMatrix"),
          function(x, k = 0, ...)
              if(k <= 0L) x else .setZero(x))

setMethod("tril", signature(x = "diagonalMatrix"),
          function(x, k = 0, ...)
              if(k >= 0L) x else .setZero(x))

setMethod("forceSymmetric", signature(x = "diagonalMatrix", uplo = "character"),
          function(x, uplo) .diag2sparse(x, ".sC", uplo = uplo))

setMethod("forceSymmetric", signature(x = "diagonalMatrix", uplo = "missing"),
          function(x, uplo) .diag2sparse(x, ".sC", uplo = "U"))

setMethod("symmpart", signature(x = "diagonalMatrix"),
          function(x) forceSymmetric(..diag2d(x)))

setMethod("skewpart", signature(x = "diagonalMatrix"),
          function(x) symmetrizeDimnames(.setZero(x, "d")))

setMethod("isSymmetric", signature(object = "diagonalMatrix"),
          function(object, checkDN = TRUE, ...) {
              if(checkDN) {
                  ca <- function(check.attributes = TRUE, ...) check.attributes
                  if(ca(...) && !isSymmetricDN(object@Dimnames))
                      return(FALSE)
              }
              TRUE
          })

setMethod("isTriangular", signature(object = "diagonalMatrix"),
          function(object, upper = NA, ...)
              if(is.na(upper)) `attr<-`(TRUE, "kind", "U") else TRUE)

setMethod("isDiagonal", signature(object = "diagonalMatrix"),
          function(object) TRUE)

subDiag <- function(x, i, j, ..., drop) {
    x <- .diag2sparse(x, ".gC") ## was ->TsparseMatrix but C* is faster now
    x <- if(missing(i))
	x[, j, drop=drop]
    else if(missing(j))
	if(nargs() == 4L) x[i, , drop=drop] else x[i, drop=drop]
    else
	x[i,j, drop=drop]
    if(isS4(x) && isDiagonal(x)) as(x, "diagonalMatrix") else x
}

setMethod("[", signature(x = "diagonalMatrix", i = "index",
			 j = "index", drop = "logical"), subDiag)
setMethod("[", signature(x = "diagonalMatrix", i = "index",
			 j = "missing", drop = "logical"),
	  function(x, i, j, ..., drop) {
	      na <- nargs()
	      Matrix.msg("diag[i,m,l] : nargs()=", na, .M.level = 2)
	      if(na == 4L)
		   subDiag(x, i=i, , drop=drop)
	      else subDiag(x, i=i,   drop=drop)
	  })
setMethod("[", signature(x = "diagonalMatrix", i = "missing",
			 j = "index", drop = "logical"),
	  function(x, i, j, ..., drop) subDiag(x, j=j, drop=drop))

## When you assign to a diagonalMatrix, the result should be
## diagonal or sparse ---
replDiag <- function(x, i, j, ..., value) {
## FIXME: if   (i == j)  &&  isSymmetric(value) then -- want symmetricMatrix result! -- or diagMatrix
    x <- .diag2sparse(x, ".gC") # was ->TsparseMatrix till 2012-07
    if(missing(i))
	x[, j] <- value
    else if(missing(j)) { ##  x[i , ] <- v  *OR*   x[i] <- v
        na <- nargs()
##         message("diagnosing replDiag() -- nargs()= ", na)
	if(na == 4L)
            x[i, ] <- value
	else if(na == 3L)
            x[i] <- value
	else stop(gettextf("Internal bug: nargs()=%d; please report",
			   na), domain=NA)
    } else
	x[i,j] <- value
    ## TODO: the following is a bit expensive; have cases above e.g. [i,] where
    ## ----- we could check *much* faster :
    if(isDiagonal(x))
        .M2diag(x, check = FALSE)
    else if(isSymmetric(x))
        forceSymmetric(x)
    else if(!(it <- isTriangular(x)))
        x
    else if(attr(it, "kind") == "U")
        triu(x)
    else tril(x)
}

setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
				j = "index", value = "replValue"), replDiag)

setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index",
				j = "missing", value = "replValue"),
		 function(x,i,j, ..., value) {
                     ## message("before replDiag() -- nargs()= ", nargs())
                     if(nargs() == 3L)
                         replDiag(x, i=i, value=value)
                     else ## nargs() == 4 :
                         replDiag(x, i=i, , value=value)
                 })

setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
				j = "index", value = "replValue"),
		 function(x,i,j, ..., value) replDiag(x, j=j, value=value))

## x[] <- value :
setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
				j = "missing", value = "ANY"),
		 function(x,i,j, ..., value)
	     {
	      if(all0(value)) { # be faster
		  r <- new(paste0(.M.kind(x), "tTMatrix")) # of all "0"
		  r@Dim <- x@Dim
		  r@Dimnames <- x@Dimnames
		  r
	      } else { ## typically non-sense: assigning to full sparseMatrix
		  x[TRUE] <- value
		  x
	      }
	  })


setReplaceMethod("[", signature(x = "diagonalMatrix",
                                i = "matrix", # 2-col.matrix
				j = "missing", value = "replValue"),
		 function(x,i,j, ..., value) {
		     if(ncol(i) == 2L) {
			 if(all((ii <- i[,1L]) == i[,2L])) { # replace in diagonal only
			     if(x@diag == "U") {
				 one <- as1(x@x)
				 if(any(value != one | is.na(value))) {
				     x@diag <- "N"
				     x@x <- rep.int(one, x@Dim[1L])
				 } else return(x)
			     }
			     x@x[ii] <- value
			     x
			 } else { ## no longer diagonal, but remain sparse:
###  FIXME:  use  uplo="U" or uplo="L"  (or *not* "triangularMatrix") depending on LE <- i <= j
###          all(LE) //  all(!LE) // remaining cases
			     x <- .diag2sparse(x, ".tC") # was ->TsparseMatrix
			     x[i] <- value
			     x
			 }
		     }
		     else { # behave as "base R": use as if vector
			 x <- as(x, "matrix")
			 x[i] <- value
			 Matrix(x)
		     }
		 })


## value = "sparseMatrix":
setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
				value = "sparseMatrix"),
		 function (x, i, j, ..., value)
		 callGeneric(x=x, , j=j, value = as(value, "sparseVector")))
setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
				value = "sparseMatrix"),
		 function (x, i, j, ..., value)
		 callGeneric(x=x, i=i, , value = as(value, "sparseVector")))
setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
				value = "sparseMatrix"),
		 function (x, i, j, ..., value)
		 callGeneric(x=x, i=i, j=j, value = as(value, "sparseVector")))

## value = "sparseVector":
setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing", j = "index",
				value = "sparseVector"),
		 replDiag)
setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "missing",
				value = "sparseVector"),
		 replDiag)
setReplaceMethod("[", signature(x = "diagonalMatrix", i = "index", j = "index",
				value = "sparseVector"),
		 replDiag)

## FIXME: Many of these products are not handling 'Dimnames' appropriately ...

.prod.diag.missing <- function(x, boolArith) {
    if(boolArith) {
        if(!is.logical(x@x))
            x <- ..diag2l(x)
    } else {
        if(!is.double(x@x))
            x <- ..diag2d(x)
        if(x@diag == "N")
            x@x <- x@x * x@x
    }
    x
}

setMethod( "crossprod", signature(x = "diagonalMatrix", y = "missing"),
          function(x, y = NULL, boolArith = NA, ...) {
              r <- .prod.diag.missing(x, boolArith = isTRUE(boolArith))
              r@Dimnames <- r@Dimnames[c(2L, 2L)]
              r
          })

setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "missing"),
          function(x, y = NULL, boolArith = NA, ...) {
              r <- .prod.diag.missing(x, boolArith = isTRUE(boolArith))
              r@Dimnames <- r@Dimnames[c(1L, 1L)]
              r
          })

.prod.diag.diag <- function(x, y, boolArith) {
    if(boolArith) {
        if(x@diag == "N") {
            if(!is.logical(x@x))
                x <- ..diag2l(x)
            if(y@diag == "N")
                x@x <- x@x & y@x
            x
        } else if(is.logical(y@x))
            y
        else ..diag2l(y)
    } else {
        if(x@diag == "N") {
            if(!is.double(x@x))
                x <- ..diag2d(x)
            if(y@diag == "N")
                x@x <- x@x * y@x
            x
        } else if(is.double(y@x))
            y
        else ..diag2d(y)
    }
}

setMethod("%*%", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.diag.diag(x, y, boolArith = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, y@Dimnames, type = 1L)
              r
          })

setMethod("%&%", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.diag.diag(x, y, boolArith = TRUE)
              r@Dimnames <- mmultDimnames(x@Dimnames, y@Dimnames, type = 1L)
              r
          })

setMethod( "crossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 2L)
              r <- .prod.diag.diag(x, y, boolArith = isTRUE(boolArith))
              r@Dimnames <- mmultDimnames(x@Dimnames, y@Dimnames, type = 2L)
              r
          })

setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 3L)
              r <- .prod.diag.diag(x, y, boolArith = isTRUE(boolArith))
              r@Dimnames <- mmultDimnames(x@Dimnames, y@Dimnames, type = 3L)
              r
          })

.prod.diag.m <- function(x, y, boolArith, trans) {
    ## MJ: .m2ge() avoids a copy when argument is unreferenced,
    ##     so it is more efficient than Matrix() here
    if(boolArith) {
        kind <- "n"
        op <- `&`
    } else {
        kind <- "d"
        op <- `*`
    }
    .m2ge(if(x@diag == "N")
              op(x@x, if(trans) t(y) else y)
          else if(trans)
              t(y)
          else y,
          kind)
}

setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),
	  function(x, y) {
              mmultDim(x@Dim, dim(y), type = 1L)
              r <- .prod.diag.m(x, y, boolArith = FALSE, trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 1L)
              r
          })

setMethod("%&%", signature(x = "diagonalMatrix", y = "matrix"),
	  function(x, y) {
              mmultDim(x@Dim, dim(y), type = 1L)
              r <- .prod.diag.m(x, y, boolArith = TRUE, trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 1L)
              r
          })

setMethod( "crossprod", signature(x = "diagonalMatrix", y = "matrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, dim(y), type = 2L)
              r <- .prod.diag.m(x, y, boolArith = isTRUE(boolArith),
                                trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 2L)
              r
          })

setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "matrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, dim(y), type = 3L)
              r <- .prod.diag.m(x, y, boolArith = isTRUE(boolArith),
                                trans = TRUE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 3L)
              r
          })

.prod.m.diag <- function(x, y, boolArith, trans) {
    ## MJ: .m2ge() avoids a copy when argument is unreferenced,
    ##     so it is more efficient than Matrix() here
    if(boolArith) {
        kind <- "n"
        op <- `&`
    } else {
        kind <- "d"
        op <- `*`
    }
    .m2ge(if(y@diag == "N")
              op(if(trans) t(x) else x,
                 rep(y@x, each = dim(x)[1L + trans]))
          else if(trans)
              t(x)
          else x,
          kind)
}

setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(dim(x), y@Dim, type = 1L)
              r <- .prod.m.diag(x, y, boolArith = FALSE, trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 1L)
              r
          })

setMethod("%&%", signature(x = "matrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(dim(x), y@Dim, type = 1L)
              r <- .prod.m.diag(x, y, boolArith = TRUE, trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 1L)
              r
          })

setMethod( "crossprod", signature(x = "matrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(dim(x), y@Dim, type = 2L)
              r <- .prod.m.diag(x, y, boolArith = isTRUE(boolArith),
                                trans = TRUE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 2L)
              r
          })

setMethod("tcrossprod", signature(x = "matrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(dim(x), y@Dim, type = 3L)
              r <- .prod.m.diag(x, y, boolArith = isTRUE(boolArith),
                                trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 3L)
              r
          })

## FIXME: <unit diagonalMatrix> %*% <symmetricMatrix> should not be symmetric,
##        because the inherited 'rownames' and 'colnames' could differ ...

.prod.diag.dense <- function(x, y, boolArith, trans) {
    if(boolArith) {
        y <- ..dense2n(y)
        op <- `&`
        one <- TRUE
    } else {
        if(!is.double(y@x))
            y <- ..dense2d(y)
        op <- `*`
        one <- 1
    }
    if(x@diag == "N") {
        y@x <-
            if(!.hasSlot(y, "uplo")) {
                ## y=[nd]geMatrix
                if(trans)
                    y <- t(y)
                y@factors <- list()
                op(x@x, y@x)
            } else if(.hasSlot(y, "diag")) {
                ## y=[nd]t[rp]Matrix
                if(trans)
                    y <- t(y)
                if(y@diag != "N")
                    diag(y) <- one
                if(length(y@x) == (n <- y@Dim[1L])^2)
                    op(x@x, y@x)
                else if(y@uplo == "U")
                    op(x@x[sequence.default(1:n, rep.int(1L, n))], y@x)
                else
                    op(x@x[sequence.default(n:1,            1:n)], y@x)
            } else {
                ## y=[nd]s[yp]Matrix
                y <- .dense2g(y)
                y@factors <- list()
                op(x@x, y@x)
            }
        y
    } else if(trans)
        t(y)
    else y
}

setMethod("%*%", signature(x = "diagonalMatrix", y = "denseMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.diag.dense(x, y, boolArith = FALSE, trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 1L)
              r
          })

setMethod("%&%", signature(x = "diagonalMatrix", y = "denseMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.diag.dense(x, y, boolArith = TRUE, trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 1L)
              r
          })

setMethod( "crossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 2L)
              r <- .prod.diag.dense(x, y, boolArith = isTRUE(boolArith),
                                    trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 2L)
              r
          })

setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 3L)
              r <- .prod.diag.dense(x, y, boolArith = isTRUE(boolArith),
                                    trans = TRUE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 3L)
              r
          })

.prod.dense.diag <- function(x, y, boolArith, trans) {
    if(boolArith) {
        x <- ..dense2n(x)
        op <- `&`
        one <- TRUE
    } else {
        if(!is.double(x@x))
            x <- ..dense2d(x)
        op <- `*`
        one <- 1
    }
    if(y@diag == "N") {
        x@x <-
            if(!.hasSlot(x, "uplo")) {
                ## x=[nd]geMatrix
                if(trans)
                    x <- t(x)
                x@factors <- list()
                op(x@x, rep(y@x, each = x@Dim[1L]))
            } else if(.hasSlot(x, "diag")) {
                ## x=[nd]t[rp]Matrix
                if(trans)
                    x <- t(x)
                if(x@diag != "N")
                    diag(x) <- one
                if(length(x@x) == (n <- x@Dim[1L])^2)
                    op(x@x, rep(y@x, each = x@Dim[1L]))
                else if(x@uplo == "U")
                    op(x@x, rep.int(y@x, 1:n))
                else
                    op(x@x, rep.int(y@x, n:1))
            } else {
                ## x=[nd]s[yp]Matrix
                x <- .dense2g(x)
                x@factors <- list()
                op(x@x, rep(y@x, each = x@Dim[1L]))
            }
        x
    } else if(trans)
        t(x)
    else x
}

setMethod("%*%", signature(x = "denseMatrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.dense.diag(x, y, boolArith = FALSE, trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 1L)
              r
          })

setMethod("%&%", signature(x = "denseMatrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.dense.diag(x, y, boolArith = TRUE, trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 1L)
              r
          })

setMethod( "crossprod", signature(x = "denseMatrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 2L)
              r <- .prod.dense.diag(x, y, boolArith = isTRUE(boolArith),
                                    trans = TRUE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 2L)
              r
          })

setMethod("tcrossprod", signature(x = "denseMatrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 3L)
              r <- .prod.dense.diag(x, y, boolArith = isTRUE(boolArith),
                                    trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 3L)
              r
          })

.prod.diag.Csparse <- function(x, y, boolArith, trans) {
    if(x@diag == "N") {
        y <- .sparse2kind(y, if(boolArith) "l" else "d", drop0 = FALSE)
        if(!.hasSlot(y, "uplo")) {
            ## y=[ld]gCMatrix
            if(trans)
                y <- t(y)
            y@factors <- list()
        } else if(.hasSlot(y, "diag")) {
            ## y=[ld]tCMatrix
            if(trans)
                y <- t(y)
            if(y@diag != "N")
                y <- ..diagU2N(y)
        } else {
            ## y=[ld]sCMatrix
            y <- .sparse2g(y)
            y@factors <- list()
        }
        op <- if(boolArith) `&` else `*`
        y@x <- op(x@x[y@i + 1L], y@x)
        if(boolArith) .sparse2kind(y, "n", drop0 = TRUE) else y
    } else
        (if(trans) t else identity)(
            if(boolArith)
                .sparse2kind(y, "n", drop0 = TRUE)
            else .sparse2kind(y, "d", drop0 = FALSE))
}

setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.diag.Csparse(x, y, boolArith = FALSE, trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 1L)
              r
          })

setMethod("%&%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.diag.Csparse(x, y, boolArith = TRUE, trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 1L)
              r
          })

setMethod( "crossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 2L)
              r <- .prod.diag.Csparse(x, y, boolArith = isTRUE(boolArith),
                                      trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 2L)
              r
          })

setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 3L)
              r <- .prod.diag.Csparse(x, y, boolArith = isTRUE(boolArith),
                                      trans = TRUE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 3L)
              r
          })

.prod.Csparse.diag <- function(x, y, boolArith, trans) {
    if(y@diag == "N") {
        x <- .sparse2kind(x, if(boolArith) "l" else "d", drop0 = FALSE)
        if(!.hasSlot(x, "uplo")) {
            ## x=[ld]gCMatrix
            if(trans)
                x <- t(x)
            x@factors <- list()
        } else if(.hasSlot(x, "diag")) {
            ## x=[ld]tCMatrix
            if(trans)
                x <- t(x)
            if(x@diag != "N")
                x <- ..diagU2N(x)
        } else {
            ## x=[ld]sCMatrix
            x <- .sparse2g(x)
            x@factors <- list()
        }
        dp <- if((n <- length(p <- x@p)) > 1L) p[-1L] - p[-n] else integer(0L)
        x@x <- (if(boolArith) `&` else `*`)(x@x, rep.int(y@x, dp))
        if(boolArith) .sparse2kind(x, "n", drop0 = TRUE) else x
    } else
        (if(trans) t else identity)(
            if(boolArith)
                .sparse2kind(x, "n", drop0 = TRUE)
            else .sparse2kind(x, "d", drop0 = FALSE))
}

setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.Csparse.diag(x, y, boolArith = FALSE, trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 1L)
              r
          })

setMethod("%&%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.Csparse.diag(x, y, boolArith = TRUE, trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 1L)
              r
          })

setMethod( "crossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 2L)
              r <- .prod.Csparse.diag(x, y, boolArith = isTRUE(boolArith),
                                      trans = TRUE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 2L)
              r
          })

setMethod("tcrossprod", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 3L)
              r <- .prod.Csparse.diag(x, y, boolArith = isTRUE(boolArith),
                                      trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 3L)
              r
          })

.prod.diag.Rsparse <- function(x, y, boolArith, trans) {
    if(x@diag == "N") {
        y <- .sparse2kind(y, if(boolArith) "l" else "d", drop0 = FALSE)
        if(!.hasSlot(y, "uplo")) {
            ## y=[ld]gRMatrix
            if(trans)
                y <- t(y)
            y@factors <- list()
        } else if(.hasSlot(y, "diag")) {
            ## y=[ld]tRMatrix
            if(trans)
                y <- t(y)
            if(y@diag != "N")
                y <- ..diagU2N(y)
        } else {
            ## y=[ld]sRMatrix
            y <- .sparse2g(y)
            y@factors <- list()
        }
        dp <- if((n <- length(p <- x@p)) > 1L) p[-1L] - p[-n] else integer(0L)
        y@x <- (if(boolArith) `&` else `*`)(rep.int(x@x, dp), y@x)
        if(boolArith) .sparse2kind(y, "n", drop0 = TRUE) else y
    } else
        (if(trans) t else identity)(
            if(boolArith)
                .sparse2kind(y, "n", drop0 = TRUE)
            else .sparse2kind(y, "d", drop0 = FALSE))
}

setMethod("%*%", signature(x = "diagonalMatrix", y = "RsparseMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.diag.Rsparse(x, y, boolArith = FALSE, trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 1L)
              r
          })

setMethod("%&%", signature(x = "diagonalMatrix", y = "RsparseMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.diag.Rsparse(x, y, boolArith = TRUE, trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 1L)
              r
          })

setMethod( "crossprod", signature(x = "diagonalMatrix", y = "RsparseMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 2L)
              r <- .prod.diag.Rsparse(x, y, boolArith = isTRUE(boolArith),
                                      trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 2L)
              r
          })

setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "RsparseMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 3L)
              r <- .prod.diag.Rsparse(x, y, boolArith = isTRUE(boolArith),
                                      trans = TRUE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 3L)
              r
          })

.prod.Rsparse.diag <- function(x, y, boolArith, trans) {
    if(y@diag == "N") {
        x <- .sparse2kind(x, if(boolArith) "l" else "d", drop0 = FALSE)
        if(!.hasSlot(x, "uplo")) {
            ## x=[ld]gRMatrix
            if(trans)
                x <- t(x)
            x@factors <- list()
        } else if(.hasSlot(x, "diag")) {
            ## x=[ld]tRMatrix
            if(trans)
                x <- t(x)
            if(x@diag != "N")
                x <- ..diagU2N(x)
        } else {
            ## x=[ld]sRMatrix
            x <- .sparse2g(x)
            x@factors <- list()
        }
        op <- if(boolArith) `&` else `*`
        x@x <- op(x@x, y@x[x@j + 1L])
        if(boolArith) .sparse2kind(x, "n", drop0 = TRUE) else x
    } else
        (if(trans) t else identity)(
            if(boolArith)
                .sparse2kind(x, "n", drop0 = TRUE)
            else .sparse2kind(x, "d", drop0 = FALSE))
}

setMethod("%*%", signature(x = "RsparseMatrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.Rsparse.diag(x, y, boolArith = FALSE, trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 1L)
              r
          })

setMethod("%&%", signature(x = "RsparseMatrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.Rsparse.diag(x, y, boolArith = TRUE, trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 1L)
              r
          })

setMethod( "crossprod", signature(x = "RsparseMatrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 2L)
              r <- .prod.Rsparse.diag(x, y, boolArith = isTRUE(boolArith),
                                      trans = TRUE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 2L)
              r
          })

setMethod("tcrossprod", signature(x = "RsparseMatrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 3L)
              r <- .prod.Rsparse.diag(x, y, boolArith = isTRUE(boolArith),
                                      trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 3L)
              r
          })

.prod.diag.Tsparse <- function(x, y, boolArith, trans) {
    if(x@diag == "N") {
        y <- .sparse2kind(y, if(boolArith) "l" else "d", drop0 = FALSE)
        if(!.hasSlot(y, "uplo")) {
            ## y=[ld]gTMatrix
            if(trans)
                y <- t(y)
            y@factors <- list()
        } else if(.hasSlot(y, "diag")) {
            ## y=[ld]tTMatrix
            if(trans)
                y <- t(y)
            if(y@diag != "N")
                y <- ..diagU2N(y)
        } else {
            ## y=[ld]sTMatrix
            y <- .sparse2g(y)
            y@factors <- list()
        }
        op <- if(boolArith) `&` else `*`
        y@x <- op(x@x[y@i + 1L], y@x)
        if(boolArith) .sparse2kind(y, "n", drop0 = TRUE) else y
    } else
        (if(trans) t else identity)(
            if(boolArith)
                .sparse2kind(y, "n", drop0 = TRUE)
            else .sparse2kind(y, "d", drop0 = FALSE))
}

setMethod("%*%", signature(x = "diagonalMatrix", y = "TsparseMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.diag.Tsparse(x, y, boolArith = FALSE, trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 1L)
              r
          })

setMethod("%&%", signature(x = "diagonalMatrix", y = "TsparseMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.diag.Tsparse(x, y, boolArith = TRUE, trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 1L)
              r
          })

setMethod( "crossprod", signature(x = "diagonalMatrix", y = "TsparseMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 2L)
              r <- .prod.diag.Tsparse(x, y, boolArith = isTRUE(boolArith),
                                      trans = FALSE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 2L)
              r
          })

setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "TsparseMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 3L)
              r <- .prod.diag.Tsparse(x, y, boolArith = isTRUE(boolArith),
                                      trans = TRUE)
              r@Dimnames <- mmultDimnames(x@Dimnames, dimnames(y), type = 3L)
              r
          })

.prod.Tsparse.diag <- function(x, y, boolArith, trans) {
    if(y@diag == "N") {
        x <- .sparse2kind(x, if(boolArith) "l" else "d", drop0 = FALSE)
        if(!.hasSlot(x, "uplo")) {
            ## x=[ld]gTMatrix
            if(trans)
                x <- t(x)
            x@factors <- list()
        } else if(.hasSlot(x, "diag")) {
            ## x=[ld]tTMatrix
            if(trans)
                x <- t(x)
            if(x@diag != "N")
                x <- ..diagU2N(x)
        } else {
            ## x=[ld]sTMatrix
            x <- .sparse2g(x)
            x@factors <- list()
        }
        op <- if(boolArith) `&` else `*`
        x@x <- op(x@x, y@x[x@j + 1L])
        if(boolArith) .sparse2kind(x, "n", drop0 = TRUE) else x
    } else
        (if(trans) t else identity)(
            if(boolArith)
                .sparse2kind(x, "n", drop0 = TRUE)
            else .sparse2kind(x, "d", drop0 = FALSE))
}

setMethod("%*%", signature(x = "TsparseMatrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.Tsparse.diag(x, y, boolArith = FALSE, trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 1L)
              r
          })

setMethod("%&%", signature(x = "TsparseMatrix", y = "diagonalMatrix"),
	  function(x, y) {
              mmultDim(x@Dim, y@Dim, type = 1L)
              r <- .prod.Tsparse.diag(x, y, boolArith = TRUE, trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 1L)
              r
          })

setMethod( "crossprod", signature(x = "TsparseMatrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 2L)
              r <- .prod.Tsparse.diag(x, y, boolArith = isTRUE(boolArith),
                                      trans = TRUE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 2L)
              r
          })

setMethod("tcrossprod", signature(x = "TsparseMatrix", y = "diagonalMatrix"),
	  function(x, y = NULL, boolArith = NA, ...) {
              mmultDim(x@Dim, y@Dim, type = 3L)
              r <- .prod.Tsparse.diag(x, y, boolArith = isTRUE(boolArith),
                                      trans = FALSE)
              r@Dimnames <- mmultDimnames(dimnames(x), y@Dimnames, type = 3L)
              r
          })



###---------------- <Ops> (<Arith>, <Logic>, <Compare> ) ----------------------

## Use as S4 method for several signatures ==>  using callGeneric()
diagOdiag <- function(e1,e2) {
    ## result should also be diagonal _ if possible _
    r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"
    ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
    r00 <- callGeneric(if(is.numeric(e1@x)) 0 else FALSE,
		       if(is.numeric(e2@x)) 0 else FALSE)
    if(is0(r00)) { ##  r00 == 0 or FALSE --- result *is* diagonal
	if(is.numeric(r)) { # "double" *or* "integer"
            if(!is.double(r))
                r <- as.double(r)
            if(is.double(e2@x)) {
		e2@x <- r
                e2@diag <- "N"
                return(e2)
            }
	    if(!is.double(e1@x))
		## e.g. e1, e2 are logical;
		e1 <- ..diag2d(e1)
	}
	else if(is.logical(r))
	    e1 <- ..diag2l(e1)
	else stop(gettextf("intermediate 'r' is of type %s",
			   typeof(r)), domain=NA)
	e1@x <- r
        e1@diag <- "N"
	e1
    }
    else { ## result not diagonal, but at least symmetric:
        ## e.g., m == m
	isNum <- (is.numeric(r) || is.numeric(r00))
	isLog <- (is.logical(r) || is.logical(r00))
        Matrix.msg("exploding <diag> o <diag> into dense matrix", .M.level = 2)
	d <- e1@Dim
	n <- d[1L]
	stopifnot(length(r) == n)
	if(isNum && !is.double(r))
            r <- as.double(r)
	## faster (?) than  m <- matrix(r00,n,n); diag(m) <- r ; as.vector(m)
        xx <- rbind(r, matrix(r00,n,n), deparse.level=0L)[seq_len(n*n)]
	newcl <-
	    paste0(if(isNum) "d" else if(isLog) {
		if(!anyNA(r) && !anyNA(r00)) "n" else "l"
	    } else stop("not yet implemented .. please report"), "syMatrix")

	new(newcl, Dim = e1@Dim, Dimnames = e1@Dimnames, x = xx)
    }
}

### This would be *the* way, but we get tons of "ambiguous method dispatch"
## we use this hack instead of signature  x = "diagonalMatrix" :
diCls <- names(getClass("diagonalMatrix")@subclasses)
if(FALSE) {
setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),
          diagOdiag)
} else { ## These are just for method disambiguation:
    for(c1 in diCls)
	for(c2 in diCls)
	    setMethod("Ops", signature(e1 = c1, e2 = c2), diagOdiag)
}

## diagonal  o  triangular  |-->  triangular
## diagonal  o  symmetric   |-->  symmetric
##    {also when other is sparse: do these "here" --
##     before conversion to sparse, since that loses "diagonality"}
diagOtri <- function(e1,e2) {
    ## result must be triangular
    r <- callGeneric(d1 <- .diag.x(e1), diag(e2)) # error if not "compatible"
    ## Check what happens with non-diagonals, i.e. (0 o 0), (FALSE o 0), ...:
    e1.0 <- if(is.numeric(d1)) 0 else FALSE
    r00 <- callGeneric(e1.0, if(.n2 <- is.numeric(e2[0L])) 0 else FALSE)
    if(is0(r00)) { ##  r00 == 0 or FALSE --- result *is* triangular
        diag(e2) <- r
        ## check what happens "in the triangle"
        e2.2 <- if(.n2) 2 else TRUE
        if(!callGeneric(e1.0, e2.2) == e2.2) { # values "in triangle" can change:
            n <- dim(e2)[1L]
            it <- indTri(n, upper = (e2@uplo == "U"))
            e2[it] <- callGeneric(e1.0, e2[it])
        }
        e2
    }
    else { ## result not triangular ---> general
        rr <- as(e2, "generalMatrix")
        diag(rr) <- r
        rr
    }
}


setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "triangularMatrix"),
          diagOtri)
## For the reverse,  Ops == "Arith" | "Compare" | "Logic"
##   'Arith'  :=  '"+"', '"-"', '"*"', '"^"', '"%%"', '"%/%"', '"/"'
setMethod("Arith", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
          function(e1,e2)
      { ## this must only trigger for *dense* e1
	  switch(.Generic,
		 "+" = .Call(dtrMatrix_addDiag,
                             unpack(..dense2d(e1)),   .diag.x(e2)),
		 "-" = .Call(dtrMatrix_addDiag,
                             unpack(..dense2d(e1)), - .diag.x(e2)),
		 "*" = {
		     n <- e2@Dim[1L]
		     d2 <- if(e2@diag == "U") { # unit-diagonal
			 d <- rep.int(as1(e2@x), n)
			 e2@x <- d
			 e2@diag <- "N"
			 d
		     } else e2@x
		     e2@x <- diag(e1) * d2
		     e2
		 },
		 "^" = { ## will be dense ( as  <ANY> ^ 0 == 1 ):
		     e1 ^ .diag2dense(e2, ".ge")
		 },
		 ## otherwise:
		 callGeneric(e1, .diag2T.smart(e2, e1)))
})

## Compare --> 'swap' (e.g.   e1 < e2   <==>  e2 > e1 ):
setMethod("Compare", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
	  .Cmp.swap)
## '&' and "|'  are commutative:
setMethod("Logic", signature(e1 = "triangularMatrix", e2 = "diagonalMatrix"),
          function(e1, e2) callGeneric(e2, e1))

## For almost everything else, diag* shall be treated "as sparse" :
## These are cheap implementations via coercion

## For disambiguation --- define this for "sparseMatrix" , then for "ANY";
## and because we can save an .M.kind() call, we use this explicit
## "hack" for all diagonalMatrix *subclasses* instead of just "diagonalMatrix" :
##
## ddi*:
setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "sparseMatrix"),
	  function(e1,e2) callGeneric(.diag2T.smart(e1, e2, kind = "d"), e2))
setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ddiMatrix"),
	  function(e1,e2) callGeneric(e1, .diag2T.smart(e2, e1, kind = "d")))
## ldi*
setMethod("Ops", signature(e1 = "ldiMatrix", e2 = "sparseMatrix"),
	  function(e1,e2) callGeneric(.diag2T.smart(e1, e2, kind = "l"), e2))
setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "ldiMatrix"),
	  function(e1,e2) callGeneric(e1, .diag2T.smart(e2, e1, kind = "l")))

## Ops:	 Arith	--> numeric : "dMatrix"
##	 Compare --> logical
##	 Logic	 --> logical: "lMatrix"

## Other = "numeric" : stay diagonal if possible
## ddi*: Arith: result numeric, potentially ddiMatrix
for(arg2 in c("numeric","logical"))
setMethod("Arith", signature(e1 = "ddiMatrix", e2 = arg2),
	  function(e1,e2) {
	      n <- e1@Dim[1L]
	      if(length(e2) == 0L)
		  return(if(n) numeric() else e1)
	      f0 <- callGeneric(0, e2)
	      if(all0(f0)) { # remain diagonal
		  if(e1@diag == "U") {
		      if(any((r <- callGeneric(1, e2)) != 1)) {
			  e1@diag <- "N"
			  e1@x[seq_len(n)] <- r # possibly recycling r
		      } ## else: result = e1  (is "U" diag)
		  } else if(n) {
		      L1 <- (le <- length(e2)) == 1L
		      r <- callGeneric(e1@x, e2)
		      ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
		      e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
		  }
		  e1
	      } else
		  callGeneric(.diag2tT.smart(e1, e2, kind = "d"), e2)
	  })

for(arg1 in c("numeric","logical"))
setMethod("Arith", signature(e1 = arg1, e2 = "ddiMatrix"),
	  function(e1,e2) {
	      n <- e2@Dim[1L]
	      if(length(e1) == 0L)
		  return(if(n) numeric() else e2)
	      f0 <- callGeneric(e1, 0)
	      if(all0(f0)) { # remain diagonal
		  if(e2@diag == "U") {
		      if(any((r <- callGeneric(e1, 1)) != 1)) {
			  e2@diag <- "N"
			  e2@x[seq_len(n)] <- r # possibly recycling r
		      } ## else: result = e2  (is "U" diag)
		  } else {
		      L1 <- (le <- length(e1)) == 1L
		      r <- callGeneric(e1, e2@x)
		      ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
		      e2@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
		  }
		  e2
	      } else
		  callGeneric(e1, .diag2tT.smart(e2, e1, kind = "d"))
	  })

## ldi* Arith --> result numeric, potentially ddiMatrix
for(arg2 in c("numeric","logical"))
setMethod("Arith", signature(e1 = "ldiMatrix", e2 = arg2),
	  function(e1,e2) {
	      n <- e1@Dim[1L]
	      if(length(e2) == 0L)
		  return(if(n) numeric()
			 else copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE))
	      f0 <- callGeneric(0, e2)
	      if(all0(f0)) { # remain diagonal
		  E <- copyClass(e1, "ddiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE)
		  ## storage.mode(E@x) <- "double"
		  if(e1@diag == "U") {
		      if(any((r <- callGeneric(1, e2)) != 1)) {
			  E@diag <- "N"
			  E@x[seq_len(n)] <- r # possibly recycling r
		      } ## else: result = E  (is "U" diag)
		  } else if(n) {
		      L1 <- (le <- length(e2)) == 1L
		      r <- callGeneric(e1@x, e2)
		      ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
		      E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
		  }
		  E
	      } else
		  callGeneric(.diag2tT.smart(e1, e2, kind = "l"), e2)
	  })

for(arg1 in c("numeric","logical"))
setMethod("Arith", signature(e1 = arg1, e2 = "ldiMatrix"),
	  function(e1,e2) {
	      n <- e2@Dim[1L]
	      if(length(e1) == 0L)
		  return(if(n) numeric()
			 else copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE))
	      f0 <- callGeneric(e1, 0)
	      if(all0(f0)) { # remain diagonal
		  E <- copyClass(e2, "ddiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE)
		  ## storage.mode(E@x) <- "double"
		  if(e2@diag == "U") {
		      if(any((r <- callGeneric(e1, 1)) != 1)) {
			  E@diag <- "N"
			  E@x[seq_len(n)] <- r # possibly recycling r
		      } ## else: result = E  (is "U" diag)
		  } else if(n) {
		      L1 <- (le <- length(e1)) == 1L
		      r <- callGeneric(e1, e2@x)
		      ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
		      E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
		  }
		  E
	      } else
		  callGeneric(e1, .diag2tT.smart(e2, e1, kind = "l"))
	  })

## ddi*: for "Ops" without "Arith": <Compare> or <Logic> --> result logical, potentially ldi
##
## Note that  ("numeric", "ddiMatrix")  is simply swapped, e.g.,
if(FALSE) {
    selectMethod("<", c("numeric","lMatrix"))# Compare
    selectMethod("&", c("numeric","lMatrix"))# Logic
} ## so we don't need to define a method here :

for(arg2 in c("numeric","logical"))
setMethod("Ops", signature(e1 = "ddiMatrix", e2 = arg2),
	  function(e1,e2) {
	      n <- e1@Dim[1L]
	      if(length(e2) == 0L)
		  return(if(n) logical()
			 else copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE))
	      f0 <- callGeneric(0, e2)
	      if(all0(f0)) { # remain diagonal
		  E <- copyClass(e1, "ldiMatrix", c("diag", "Dim", "Dimnames"), check=FALSE)
		  ## storage.mode(E@x) <- "logical"
		  if(e1@diag == "U") {
		      if(any((r <- callGeneric(1, e2)) != 1)) {
			  E@diag <- "N"
			  E@x[seq_len(n)] <- r # possibly recycling r
		      } ## else: result = E  (is "U" diag)
		  } else if(n) {
		      L1 <- (le <- length(e2)) == 1L
		      r <- callGeneric(e1@x, e2)
		      ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
		      E@x[seq_len(n)] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
		  }
		  E
	      } else
		  callGeneric(.diag2tT.smart(e1, e2, kind = "d"), e2)
	  })

## ldi*: for "Ops" without "Arith": <Compare> or <Logic> --> result logical, potentially ldi
for(arg2 in c("numeric","logical"))
setMethod("Ops", signature(e1 = "ldiMatrix", e2 = arg2),
	  function(e1,e2) {
	      n <- e1@Dim[1L]
	      if(length(e2) == 0L)
                  return(if(n) logical() else e1)
	      f0 <- callGeneric(FALSE, e2)
	      if(all0(f0)) { # remain diagonal
		  if(e1@diag == "U") {
		      if(any((r <- callGeneric(TRUE, e2)) != 1)) {
			  e1@diag <- "N"
			  e1@x[seq_len(n)] <- r # possibly recycling r
		      } ## else: result = e1  (is "U" diag)
		  } else if(n) {
		      L1 <- (le <- length(e2)) == 1L
		      r <- callGeneric(e1@x, e2)
		      ## "future fixme": if we have idiMatrix, and r is 'integer', use idiMatrix
		      e1@x[] <- if(L1) r else r[1L + ((n+1)*(0:(n-1L))) %% le]
		  }
		  e1
	      } else
		  callGeneric(.diag2tT.smart(e1, e2, kind = "l"), e2)
	  })


## Not {"sparseMatrix", "numeric} :  {"denseMatrix", "matrix", ... }
for(other in c("ANY", "Matrix", "dMatrix")) {
    ## ddi*:
    setMethod("Ops", signature(e1 = "ddiMatrix", e2 = other),
	      function(e1,e2) callGeneric(.diag2T.smart(e1, e2, kind="d"), e2))
    setMethod("Ops", signature(e1 = other, e2 = "ddiMatrix"),
	      function(e1,e2) callGeneric(e1, .diag2T.smart(e2, e1, kind="d")))
    ## ldi*:
    setMethod("Ops", signature(e1 = "ldiMatrix", e2 = other),
	      function(e1,e2) callGeneric(.diag2T.smart(e1, e2, kind="l"), e2))
    setMethod("Ops", signature(e1 = other, e2 = "ldiMatrix"),
	      function(e1,e2) callGeneric(e1, .diag2T.smart(e2, e1, kind="l")))
}

## Direct subclasses of "denseMatrix": currently ddenseMatrix, ldense... :
if(FALSE) # now also contains "geMatrix"
dense.subCl <- local({ dM.scl <- getClass("denseMatrix")@subclasses
		       names(dM.scl)[vapply(dM.scl, slot, 0, "distance") == 1] })
dense.subCl <- paste0(c("d","l","n"), "denseMatrix")
for(DI in diCls) {
    dMeth <- if(extends(DI, "dMatrix"))
	function(e1,e2) callGeneric(.diag2T.smart(e1, e2, kind = "d"), e2)
    else # "lMatrix", the only other kind for now
	function(e1,e2) callGeneric(.diag2T.smart(e1, e2, kind = "l"), e2)
    for(c2 in c(dense.subCl, "Matrix")) {
	for(Fun in c("*", "&")) {
	    setMethod(Fun, signature(e1 = DI, e2 = c2),
		      function(e1,e2) callGeneric(e1, Diagonal(x = diag(e2))))
	    setMethod(Fun, signature(e1 = c2, e2 = DI),
		      function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
	}
	setMethod("^", signature(e1 = c2, e2 = DI),
		  function(e1,e2) callGeneric(Diagonal(x = diag(e1)), e2))
	for(Fun in c("%%", "%/%", "/")) ## 0 <op> 0 |--> NaN  for these.
	    setMethod(Fun, signature(e1 = DI, e2 = c2), dMeth)
    }
}

## Group methods "Math", "Math2" in			--> ./Math.R

### "Summary" : "max"   "min"   "range" "prod"  "sum"   "any"   "all"
### ----------   the last 4: separately here
for(cl in diCls) {
setMethod("any", cl,
	  function (x, ..., na.rm) {
	      if(any(x@Dim == 0)) FALSE
	      else if(x@diag == "U") TRUE else any(x@x, ..., na.rm = na.rm)
	  })
setMethod("all",  cl, function (x, ..., na.rm) {
    n <- x@Dim[1L]
    if(n >= 2) FALSE
    else if(n == 0 || x@diag == "U") TRUE
    else all(x@x, ..., na.rm = na.rm)
})
setMethod("prod", cl, function (x, ..., na.rm) {
    n <- x@Dim[1L]
    if(n >= 2) 0
    else if(n == 0 || x@diag == "U") 1
    else ## n == 1, diag = "N" :
	prod(x@x, ..., na.rm = na.rm)
})

setMethod("sum", cl,
	  function(x, ..., na.rm) {
	      r <- sum(x@x, ..., na.rm = na.rm)# double or integer, correctly
	      if(x@diag == "U" && !is.na(r)) r + x@Dim[1L] else r
	  })
}

## The remaining ones are  max, min, range :

setMethod("Summary", "ddiMatrix",
	  function(x, ..., na.rm) {
	      if(any(x@Dim == 0)) callGeneric(numeric(0), ..., na.rm=na.rm)
	      else if(x@diag == "U")
		  callGeneric(x@x, 0, 1, ..., na.rm=na.rm)
	      else callGeneric(x@x, 0, ..., na.rm=na.rm)
	  })
setMethod("Summary", "ldiMatrix",
	  function(x, ..., na.rm) {
	      if(any(x@Dim == 0)) callGeneric(logical(0), ..., na.rm=na.rm)
	      else if(x@diag == "U")
		  callGeneric(x@x, FALSE, TRUE, ..., na.rm=na.rm)
	      else callGeneric(x@x, FALSE, ..., na.rm=na.rm)
	  })



## similar to prTriang() in ./Auxiliaries.R :
prDiag <-
    function(x, digits = getOption("digits"), justify = "none", right = TRUE)
{
    cf <- array(".", dim = x@Dim, dimnames = x@Dimnames)
    cf[row(cf) == col(cf)] <-
	vapply(diag(x), format, "", digits = digits, justify = justify)
    print(cf, quote = FALSE, right = right)
    invisible(x)
}

## somewhat consistent with "print" for sparseMatrix :
setMethod("print", signature(x = "diagonalMatrix"), prDiag)

setMethod("show", signature(object = "diagonalMatrix"),
	  function(object) {
	      d <- dim(object)
	      cl <- class(object)
	      cat(sprintf('%d x %d diagonal matrix of class "%s"',
			  d[1L], d[2L], cl))
	      if(d[1L] < 50) {
		  cat("\n")
		  prDiag(object)
	      } else {
		  cat(", with diagonal entries\n")
		  show(diag(object))
		  invisible(object)
	      }
	  })

rm(arg1, arg2, other, DI, Fun, cl, c1, c2,
   dense.subCl, diCls)# not used elsewhere

setMethod("summary", signature(object = "diagonalMatrix"),
	  function(object, ...) {
	      d <- dim(object)
	      r <- summary(object@x, ...)
	      attr(r, "header") <-
		  sprintf('%d x %d diagonal Matrix of class "%s"',
			  d[1L], d[2L], class(object))
	      ## use ole' S3 technology for such a simple case
	      class(r) <- c("diagSummary", class(r))
	      r
	  })

print.diagSummary <- function (x, ...) {
    cat(attr(x, "header"),"\n")
    class(x) <- class(x)[-1]
    print(x, ...)
    invisible(x)
}