# R/diagMatrix.R In Matrix: Sparse and Dense Matrix Classes and Methods

#### Documented in bdiagDiagonal.sparseDiagonal.symDiagonal.trDiagonal

```## 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),])
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,
unpack(..dense2d(e1)),   .diag.x(e2)),
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, ...)
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, ...) {