--- pkg/R/diagMatrix.R 2006/07/22 17:59:53 1331 +++ pkg/R/diagMatrix.R 2007/08/15 13:33:19 2052 @@ -1,38 +1,90 @@ +#### 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) + ## Allow Diagonal(4) and Diagonal(x=1:5) if(missing(n)) - n <- length(x) + n <- length(x) else { - stopifnot(length(n) == 1, n == as.integer(n), n >= 0) - n <- as.integer(n) + 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") + 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 { - cl <- "ddiMatrix" - x <- as.numeric(x) - } - new(cl, Dim = c(n,n), diag = "N", x = x) + 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) } } -setAs("diagonalMatrix", "triangularMatrix", - function(from) { - n <- from@Dim[1] - i <- seq(length = n) - x <- from@x - new(if(is.numeric(x)) "dtTMatrix" else "ltTMatrix", - diag = from@diag, Dim = from@Dim, Dimnames = from@Dimnames, - x = x, i = i, j = i) - }) +### 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),])) + add1 <- matrix(1:0, 2,2) + 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) { + i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L + 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) +} + +diag2sT <- function(from) { # to symmetric Tsparse + i <- if(from@diag == "U") integer(0) else seq_len(from@Dim[1]) - 1L + new(paste(.M.kind(from), "sTMatrix", sep=''), + Dim = from@Dim, Dimnames = from@Dimnames, + x = from@x, i = i, j = i) +} + +setAs("diagonalMatrix", "triangularMatrix", diag2tT) +setAs("diagonalMatrix", "sparseMatrix", diag2tT) +## needed too (otherwise -> Tsparse is taken): +setAs("diagonalMatrix", "TsparseMatrix", diag2tT) +## is better than this: +## setAs("diagonalMatrix", "sparseMatrix", +## function(from) +## as(from, if(is(from, "dMatrix")) "dgCMatrix" else "lgCMatrix")) +setAs("diagonalMatrix", "CsparseMatrix", + function(from) as(diag2tT(from), "CsparseMatrix")) + +setAs("diagonalMatrix", "symmetricMatrix", diag2sT) setAs("diagonalMatrix", "matrix", function(from) { @@ -42,42 +94,54 @@ nrow = n, ncol = n) }) -setAs("diagonalMatrix", "generalMatrix", - function(from) { - x <- as(from, "matrix") - as(x, - if(is.logical(x)) "lgeMatrix" -## Not yet: -## else if(is.complex(x)) "zgeMatrix" -## else if(is.integer(x)) "igeMatrix" - else "dgeMatrix") - }) +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(length = n) - 1:1 - new("dgTMatrix", i = i, j = i, - x = if(from@diag == "U") rep(1,n) else from@x, + 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, "dgTMatrix"), "dgCMatrix")) + function(from) as(as(from, "sparseMatrix"), "dgCMatrix")) setAs("ldiMatrix", "lgTMatrix", function(from) { + .Deprecated("as(, \"sparseMatrix\")") n <- from@Dim[1] - i <- (if(from@diag == "U") seq(length = n) else which(from@x)) - 1:1 - new("lgTMatrix", i = i, j = i, + 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")) -setAs("diagonalMatrix", "sparseMatrix", - function(from) - as(from, if(is(from, "dMatrix")) "dgCMatrix" else "lgCMatrix")) +if(FALSE) # now have faster "ddense" -> "dge" setAs("ddiMatrix", "dgeMatrix", function(from) as(as(from, "matrix"), "dgeMatrix")) @@ -95,7 +159,7 @@ 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) }) @@ -120,6 +184,55 @@ x = if(uni) x[FALSE] else x) }) + +setMethod("diag", signature(x = "diagonalMatrix"), + 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(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, drop) subDiag(x, i=i, drop=drop)) +setMethod("[", signature(x = "diagonalMatrix", i = "missing", + j = "index", drop = "logical"), + function(x, 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 +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 }) @@ -130,42 +243,43 @@ setMethod("isSymmetric", signature(object = "diagonalMatrix"), function(object) TRUE) -setMethod("diag", signature(x = "diagonalMatrix"), - function(x = 1, nrow, ncol = n) { - if(x@diag == "U") - rep.int(if(is.logical(x@x)) TRUE else 1, x@Dim[1]) - else x@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 -}) +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) ## Basic Matrix Multiplication {many more to add} - -## FIXME: extend this for 'ldi', i.e. do "diagonalMatrix" +## --------------------- +## 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") x@x <- x@x * y@x - return(x) + 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 = "ddiMatrix", y = "ddiMatrix"), +setMethod("%*%", signature(x = "diagonalMatrix", y = "diagonalMatrix"), diagdiagprod, valueClass = "ddiMatrix") -formals(diagdiagprod) <- alist(x=, y=NULL) -setMethod("crossprod", signature(x = "ddiMatrix", y = "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("tcrossprod", signature(x = "ddiMatrix", y = "ddiMatrix"), +setMethod("crossprod", signature(x = "diagonalMatrix", y = "missing"), + diagdiagprod, valueClass = "ddiMatrix") +setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "missing"), diagdiagprod, valueClass = "ddiMatrix") @@ -178,10 +292,12 @@ } setMethod("%*%", signature(x = "diagonalMatrix", y = "matrix"), - diagmatprod) + diagmatprod) formals(diagmatprod) <- alist(x=, y=NULL) setMethod("crossprod", signature(x = "diagonalMatrix", y = "matrix"), - diagmatprod) + diagmatprod) +setMethod("tcrossprod", signature(x = "diagonalMatrix", y = "matrix"), + diagmatprod) diagdgeprod <- function(x, y) { dx <- dim(x) @@ -199,21 +315,21 @@ 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.int(y@x, dx[1]), "Matrix") - }) + 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.int(y@x, dx[1]) - x - }) + 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} @@ -228,32 +344,108 @@ ## function(x, y = NULL) { ## }) +setMethod("crossprod", signature(x = "diagonalMatrix", y = "sparseMatrix"), + function(x, y = NULL) { x <- as(x, "sparseMatrix"); callGeneric() }) -### ---------------- diagonal o sparse ----------------------------- +setMethod("crossprod", signature(x = "sparseMatrix", y = "diagonalMatrix"), + function(x, y = NULL) { y <- as(y, "sparseMatrix"); callGeneric() }) -## These are cheap implementations via coercion +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() }) -## FIXME?: In theory, this can be done *FASTER*, in some cases, via tapply1() +## 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("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("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) -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() }) +### ---------------- 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 +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"))) + ## similar to prTriang() in ./Auxiliaries.R : @@ -268,5 +460,10 @@ } setMethod("show", signature(object = "diagonalMatrix"), - function(object) prDiag(object)) - + 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) + })