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 [matrix] / pkg / Matrix / R / diagMatrix.R

# View of /pkg/Matrix/R/diagMatrix.R

Mon Mar 17 22:20:29 2008 UTC (11 years, 7 months ago) by maechler
Original Path: pkg/R/diagMatrix.R
File size: 18918 byte(s)
`more methods for subclasses, against "ambiguity" warnings`
```#### 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 {
lx <- length(x)
stopifnot(lx == 1 || lx == n) # but keep 'x' short for now
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 = if(lx == 1) rep.int(x,n) else 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(0L, 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")
}

.diag2tT <- function(from, uplo = "U", kind = .M.kind(from)) {
## to triangular Tsparse
i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L
new(paste(kind, "tTMatrix", sep=''),
diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames,
uplo = uplo,
x = from@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(paste(kind, "sTMatrix", sep=''),
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("'", kind,"' kind not yet implemented")), n))
}

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

## 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*:
diag2tT <- function(from) .diag2tT(from, "U", "d")
setAs("ddiMatrix", "triangularMatrix", diag2tT)
setAs("ddiMatrix", "sparseMatrix", diag2tT)
## needed too (otherwise <dense> -> Tsparse is taken):
setAs("ddiMatrix", "TsparseMatrix", diag2tT)
setAs("ddiMatrix", "CsparseMatrix",
function(from) as(.diag2tT(from, "U", "d"), "CsparseMatrix"))
setAs("ddiMatrix", "symmetricMatrix",
function(from) .diag2sT(from, "U", "d"))
##
## ldi*:
diag2tT <- function(from) .diag2tT(from, "U", "l")
setAs("ldiMatrix", "triangularMatrix", diag2tT)
setAs("ldiMatrix", "sparseMatrix", diag2tT)
## needed too (otherwise <dense> -> Tsparse is taken):
setAs("ldiMatrix", "TsparseMatrix", diag2tT)
setAs("ldiMatrix", "CsparseMatrix",
function(from) as(.diag2tT(from, "U", "l"), "CsparseMatrix"))
setAs("ldiMatrix", "symmetricMatrix",
function(from) .diag2sT(from, "U", "l"))

setAs("diagonalMatrix", "nMatrix",
function(from) {
n <- from@Dim[1]
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", "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)
})

setMethod("as.vector", signature(x = "diagonalMatrix", mode="missing"),
function(x, mode) {
n <- x@Dim[1]
mod <- mode(x@x)
r <- vector(mod, length = n^2)
if(n)
r[1 + 0:(n - 1) * (n + 1)] <-
if(x@diag == "U")
switch(mod, "integer"= 1L,
"numeric"= 1, "logical"= TRUE)
else x@x
r
})

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

.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
}

if(FALSE) {
## 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) - 1L
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) - 1L
} else { # "normal"
nz <- nz.NA(from@x, na. = TRUE)
x <- from@x[nz]
i <- which(nz) - 1L
}
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)
})

## In order to evade method dispatch ambiguity warnings,
## we use this hack instead of signature  x = "diagonalMatrix" :
diCls <- names(getClass("diagonalMatrix")@subclasses)
for(cls in diCls) {
setMethod("diag", signature(x = cls),
function(x = 1, nrow, ncol) .diag.x(x))
}

subDiag <- function(x, i, j, ..., drop) {
x <- as(x, "sparseMatrix")
x <- if(missing(i))
x[, j, drop=drop]
else if(missing(j))
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) 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 ---
## FIXME: this now fails because the "denseMatrix" methods come first in dispatch
## Only(?) current bug:  x[i] <- value  is wrong when  i is *vector*
replDiag <- function(x, i, j, ..., value) {
x <- as(x, "sparseMatrix")
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 == 4)
x[i, ] <- value
else if(na == 3)
x[i] <- value
else stop("Internal bug: nargs()=",na,"; please report")
} 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,j, ..., value) {
## message("before replDiag() -- nargs()= ", nargs())
if(nargs() == 3)
replDiag(x, i=i, value=value)
else ## nargs() == 4 :
replDiag(x, i=i, , value=value)
})

setReplaceMethod("[", signature(x = "diagonalMatrix", i = "matrix", # 2-col.matrix
j = "missing", value = "replValue"),
function(x,i,j, ..., value) {
if(ncol(i) == 2) {
if(all((ii <- i[,1]) == i[,2])) { # replace in diagonal only
x@x[ii] <- value
x
} else { ## no longer diagonal, but remain sparse:
x <- as(x, "sparseMatrix")
x[i] <- value
x
}
}
else { # behave as "base R": use as if vector
x <- as(x, "matrix")
x[i] <- value
Matrix(x)
}
})

setReplaceMethod("[", signature(x = "diagonalMatrix", i = "missing",
j = "index", value = "replValue"),
function(x,i,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("symmpart", signature(x = "diagonalMatrix"), function(x) x)
setMethod("skewpart", signature(x = "diagonalMatrix"), setZero)

setMethod("chol", signature(x = "ddiMatrix"),
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)

## 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) {
##           })

setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
function(x, y = NULL) crossprod(as(x, "sparseMatrix"), y))

setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
function(x, y = NULL) crossprod(x, as(y, "sparseMatrix")))

setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"),
function(x, y = NULL) tcrossprod(as(x, "sparseMatrix"), y))

setMethod("tcrossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"),
function(x, y = NULL) tcrossprod(x, as(y, "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)
setMethod("%*%", signature(x = "CsparseMatrix", y = "diagonalMatrix"),
function(x, y) x %*% as(y, "CsparseMatrix"))
## 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 through sparse (and *not* ddense)!

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

setMethod("solve", signature(a = "diagonalMatrix", b = "missing"),
function(a, b, ...) {
a@x <- 1/ a@x
a@Dimnames <- a@Dimnames[2:1]
a
})

solveDiag <- function(a, b, ...) {
if((n <- a@Dim[1]) != nrow(b))
stop("incompatible matrix dimensions")
## trivially invert a 'in place' and multiply:
a@x <- 1/ a@x
a@Dimnames <- a@Dimnames[2:1]
a %*% b
}
setMethod("solve", signature(a = "diagonalMatrix", b = "matrix"),
solveDiag)
setMethod("solve", signature(a = "diagonalMatrix", b = "Matrix"),
solveDiag)

## Schur()  ---> ./eigen.R

### ---------------- 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)

## FIXME:    diagonal  o  triangular  |-->  triangular
## -----     diagonal  o  symmetric   |-->  symmetric
##    {also when other is sparse: do these "here" --
##     before conversion to sparse, since that loses "diagonality"}

## 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" :
setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "sparseMatrix"),
function(e1,e2) callGeneric(diag2tT.u(e1,e2), e2))
setMethod("Ops", signature(e1 = "sparseMatrix", e2 = "diagonalMatrix"),
function(e1,e2) callGeneric(e1, diag2tT.u(e2,e1)))
## in general:
setMethod("Ops", signature(e1 = "diagonalMatrix", e2 = "ANY"),
function(e1,e2) callGeneric(diag2tT.u(e1,e2), e2))
setMethod("Ops", signature(e1 = "ANY", e2 = "diagonalMatrix"),
function(e1,e2) callGeneric(e1, diag2tT.u(e2,e1)))

## 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)
})
```