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[matrix] View of /pkg/R/diagMatrix.R
 [matrix] / pkg / R / diagMatrix.R

# View of /pkg/R/diagMatrix.R

Tue Dec 26 15:57:06 2006 UTC (12 years, 8 months ago) by maechler
File size: 13895 byte(s)
`more "[<-" fixes; validity of triangular sparse`
```#### All methods for "diagonalMatrix" and its subclasses,
####  currently "ddiMatrix", "ldiMatrix"

## Purpose: Constructor of diagonal matrices -- ~= diag() ,
##          but *not* diag() extractor!
Diagonal <- function(n, x = NULL)
{
## Allow  Diagonal(4)  and	Diagonal(x=1:5)
if(missing(n))
n <- length(x)
else {
stopifnot(length(n) == 1, n == as.integer(n), n >= 0)
n <- as.integer(n)
}

if(missing(x)) ## unit diagonal matrix
new("ddiMatrix", Dim = c(n,n), diag = "U")
else {
stopifnot(length(x) == n)
if(is.logical(x))
cl <- "ldiMatrix"
else if(is.numeric(x)) {
cl <- "ddiMatrix"
x <- as.numeric(x)
}
else if(is.complex(x)) {
cl <- "zdiMatrix"  # will not yet work
} else stop("'x' has invalid data type")
new(cl, Dim = c(n,n), diag = "N", x = x)
}
}

### 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 most probably was influenced
### by earlier posts, notably one by Scott Chasalow on S-news, 16 Jan 2002
### who posted his bdiag() function written in December 1995.

bdiag <- function(...) {
if(nargs() == 0) return(new("dgCMatrix"))
## else :
mlist <- if (nargs() == 1) as.list(...) else list(...)
dims <- sapply(mlist, dim)
## make sure we had all matrices:
if(!(is.matrix(dims) && nrow(dims) == 2))
stop("some arguments are not matrices")
csdim <- rbind(rep.int(0:0, 2),
apply(sapply(mlist, dim), 1, cumsum))
ret <- new("dgTMatrix", Dim = as.integer(csdim[nrow(csdim),]))
for(i in seq_along(mlist)) {
indx <- apply(csdim[i:(i+1),] + add1, 2, function(n) n[1]:n[2])
if(is.null(dim(indx))) ## non-square matrix
ret[indx[[1]],indx[[2]]] <- mlist[[i]]
else ## square matrix
ret[indx[,1],indx[,2]] <- mlist[[i]]
}
## slightly debatable if we really should return Csparse.. :
as(ret, "CsparseMatrix")
}

diag2T <- function(from) {
i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1:1
new(paste(.M.kind(from), "tTMatrix", sep=''),
diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,
x = from@x, # <- ok for diag = "U" and "N" (!)
i = i, j = i)
}

setAs("diagonalMatrix", "triangularMatrix", diag2T)
setAs("diagonalMatrix", "sparseMatrix", diag2T)
## is better than this:
## setAs("diagonalMatrix", "sparseMatrix",
##       function(from)
## 	  as(from, if(is(from, "dMatrix")) "dgCMatrix" else "lgCMatrix"))
setAs("diagonalMatrix", "CsparseMatrix",
function(from) as(diag2T(from), "CsparseMatrix"))

setAs("diagonalMatrix", "matrix",
function(from) {
n <- from@Dim[1]
diag(x = if(from@diag == "U") { if(is.numeric(from@x)) 1. else TRUE
} else from@x,
nrow = n, ncol = n)
})

setAs("diagonalMatrix", "generalMatrix", # prefer sparse:
function(from) as(from, paste(.M.kind(from), "gCMatrix", sep='')))

.diag.x <- function(m) {
if(m@diag == "U")
rep.int(if(is.numeric(m@x)) 1. else TRUE,
m@Dim[1])
else m@x
}

.diag.2N <- function(m) {
if(m@diag == "U") m@diag <- "N"
m
}

## given the above, the following  4  coercions should be all unneeded;
## we prefer triangular to general:
setAs("ddiMatrix", "dgTMatrix",
function(from) {
.Deprecated("as(, \"sparseMatrix\")")
n <- from@Dim[1]
i <- seq_len(n) - 1:1
new("dgTMatrix", i = i, j = i, x = .diag.x(from),
Dim = c(n,n), Dimnames = from@Dimnames) })

setAs("ddiMatrix", "dgCMatrix",
function(from) as(as(from, "sparseMatrix"), "dgCMatrix"))

setAs("ldiMatrix", "lgTMatrix",
function(from) {
.Deprecated("as(, \"sparseMatrix\")")
n <- from@Dim[1]
if(from@diag == "U") { # unit-diagonal
x <- rep.int(TRUE, n)
i <- seq_len(n) - 1:1
} else { # "normal"
nz <- nz.NA(from@x, na. = TRUE)
x <- from@x[nz]
i <- which(nz) - 1:1
}
new("lgTMatrix", i = i, j = i, x = x,
Dim = c(n,n), Dimnames = from@Dimnames) })

setAs("ldiMatrix", "lgCMatrix",
function(from) as(as(from, "lgTMatrix"), "lgCMatrix"))

if(FALSE) # now have faster  "ddense" -> "dge"
setAs("ddiMatrix", "dgeMatrix",
function(from) as(as(from, "matrix"), "dgeMatrix"))

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("has non-zero off-diagonal entries")
x <- diag(from)
if(is.logical(x)) {
cl <- "ldiMatrix"
uni <- all(x)
} else {
cl <- "ddiMatrix"
uni <- all(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)
})

## ``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)
if(is.logical(x)) {
cl <- "ldiMatrix"
uni <- all(x)
} else {
cl <- "ddiMatrix"
uni <- all(x == 1)
storage.mode(x) <- "double"
}
new(cl, Dim = c(n,n), diag = if(uni) "U" else "N",
x = if(uni) x[FALSE] else x)
})

setMethod("diag", signature(x = "diagonalMatrix"),
function(x = 1, nrow, ncol = n) .diag.x(x))

## When you assign to a diagonalMatrix, the result should be
## diagonal or sparse ---
## FIXME: this now fails because the "denseMatrix" methods come first in dispatch

replDiag <- function(x, i, j, value) {
x <- as(x, "sparseMatrix")
if(missing(i))
x[, j] <- value
else if(missing(j))
x[i, ] <- value
else
x[i,j] <- value
if(isDiagonal(x)) as(x, "diagonalMatrix") else 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, value) replDiag(x, i=i, value=value))
setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
j = "index", value = "replValue"),
function(x, j, value) replDiag(x, j=j, value=value))

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

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

setMethod("chol", signature(x = "ddiMatrix"),# pivot = "ANY"
function(x, pivot) {
if(any(x@x < 0)) stop("chol() is undefined for diagonal matrix with negative entries")
x@x <- sqrt(x@x)
x
})
## chol(L) is L for logical diagonal:
setMethod("chol", signature(x = "ldiMatrix"), function(x, pivot) x)

setMethod("!", "ldiMatrix", function(e1) {
if(e1@diag == "N")
e1@x <- !e1@x
else { ## "U"
e1@diag <- "N"
e1@x <- rep.int(FALSE, e1@Dim[1])
}
x
})

## Basic Matrix Multiplication {many more to add}
##       ---------------------
## Note that "ldi" logical are treated as numeric
diagdiagprod <- function(x, y) {
if(any(dim(x) != dim(y))) stop("non-matching dimensions")
if(x@diag != "U") {
if(y@diag != "U") {
nx <- x@x * y@x
if(is.numeric(nx) && !is.numeric(x@x))
x <- as(x, "dMatrix")
x@x <- as.numeric(nx)
}
return(x)
} else ## x is unit diagonal
return(y)
}

setMethod("%*%", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
diagdiagprod, valueClass = "ddiMatrix")

formals(diagdiagprod) <- alist(x=, y=x)
setMethod("crossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
diagdiagprod, valueClass = "ddiMatrix")
setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "diagonalMatrix"),
diagdiagprod, valueClass = "ddiMatrix")
setMethod("crossprod", signature(x = "diagonalMatrix", y = "missing"),
diagdiagprod, valueClass = "ddiMatrix")
setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "missing"),
diagdiagprod, valueClass = "ddiMatrix")

diagmatprod <- function(x, y) {
dx <- dim(x)
dy <- dim(y)
if(dx[2] != dy[1]) stop("non-matching dimensions")
n <- dx[1]
as(if(x@diag == "U") y else x@x * y, "Matrix")
}

setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"),
diagmatprod)
formals(diagmatprod) <- alist(x=, y=NULL)
setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"),
diagmatprod)
setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "matrix"),
diagmatprod)

diagdgeprod <- function(x, y) {
dx <- dim(x)
dy <- dim(y)
if(dx[2] != dy[1]) stop("non-matching dimensions")
if(x@diag != "U")
y@x <- x@x * y@x
y
}
setMethod("%*%", signature(x = "diagonalMatrix", y = "dgeMatrix"),
diagdgeprod, valueClass = "dgeMatrix")
formals(diagdgeprod) <- alist(x=, y=NULL)
setMethod("crossprod", signature(x = "diagonalMatrix", y = "dgeMatrix"),
diagdgeprod, valueClass = "dgeMatrix")

setMethod("%*%", signature(x = "matrix", y = "diagonalMatrix"),
function(x, y) {
dx <- dim(x)
dy <- dim(y)
if(dx[2] != dy[1]) stop("non-matching dimensions")
as(if(y@diag == "U") x else x * rep(y@x, each = dx[1]), "Matrix")
})

setMethod("%*%", signature(x = "dgeMatrix", y = "diagonalMatrix"),
function(x, y) {
dx <- dim(x)
dy <- dim(y)
if(dx[2] != dy[1]) stop("non-matching dimensions")
if(y@diag == "N")
x@x <- x@x * rep(y@x, each = dx[1])
x
})

## crossprod {more of these}

## tcrossprod --- all are not yet there: do the dense ones here:

## FIXME:
## setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "denseMatrix"),
## 	  function(x, y = NULL) {
##           })

## setMethod("tcrossprod", signature(x = "denseMatrix", y = "diagonalMatrix"),
## 	  function(x, y = NULL) {
##           })

### ---------------- diagonal  o  sparse  -----------------------------

## Use function for several signatures, in order to evade
## ambiguous dispatch for "ddi", since there's also Arith(ddense., ddense.)
diagOdiag <- function(e1,e2) { # result should also be diagonal
r <- callGeneric(.diag.x(e1), .diag.x(e2)) # error if not "compatible"
if(is.numeric(r)) {
if(is.numeric(e2@x)) {
e2@x <- r; return(.diag.2N(e2)) }
if(!is.numeric(e1@x))
## e.g. e1, e2 are logical;
e1 <- as(e1, "dMatrix")
}
else if(is.logical(r))
e1 <- as(e1, "lMatrix")
else stop("intermediate 'r' is of type", typeof(r))
e1@x <- r
.diag.2N(e1)
}

setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "diagonalMatrix"),
diagOdiag)
## These two are just for method disambiguation:
setMethod("Ops", signature(e1 = "ddiMatrix", e2 = "diagonalMatrix"),
diagOdiag)
setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "ddiMatrix"),
diagOdiag)

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

## for disambiguation
setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "sparseMatrix"),
function(e1,e2) callGeneric(as(e1, "sparseMatrix"), e2))
setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "diagonalMatrix"),
function(e1,e2) callGeneric(e1, as(e2, "sparseMatrix")))
## in general:
setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "ANY"),
function(e1,e2) callGeneric(as(e1,"sparseMatrix"), e2))
setMethod("Ops", signature(e1 = "ANY", e2 = "diagonalMatrix"),
function(e1,e2) callGeneric(e1, as(e2,"sparseMatrix")))

## FIXME?: In theory, this can be done *FASTER*, in some cases, via tapply1()
setMethod("%*%", signature(x = "diagonalMatrix", y = "sparseMatrix"),
function(x, y) as(x, "sparseMatrix") %*% y)
## NB: The previous is *not* triggering for  "ddi" o "dgC" (= distance 3)
##     since there's a "ddense" o "Csparse" at dist. 2 => triggers first.
## ==> do this:
setMethod("%*%", signature(x = "diagonalMatrix", y = "CsparseMatrix"),
function(x, y) as(x, "CsparseMatrix") %*% y)
## NB: this is *not* needed for Tsparse & Rsparse
## TODO: Write tests in ./tests/ which ensure that many "ops" with diagonal*
##       do indeed work by going throug sparse (and *not* ddense)!

setMethod("%*%", signature(x = "sparseMatrix", y = "diagonalMatrix"),
function(x, y) x %*% as(y, "sparseMatrix"))

setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
function(x, y = NULL) { x <- as(x, "sparseMatrix"); callGeneric() })

setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
function(x, y = NULL) { y <- as(y, "sparseMatrix"); callGeneric() })

setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
function(x, y = NULL) { x <- as(x, "sparseMatrix"); callGeneric() })

setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
function(x, y = NULL) { y <- as(y, "sparseMatrix"); callGeneric() })

## 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)] <-
sapply(diag(x), format, digits = digits, justify = justify)
print(cf, quote = FALSE, right = right)
invisible(x)
}

setMethod("show", signature(object = "diagonalMatrix"),
function(object) {
d <- dim(object)
cl <- class(object)
cat(sprintf('%d x %d diagonal matrix of class "%s"\n',
d[1], d[2], cl))
prDiag(object)
})
```