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#### Toplevel ``virtual'' class "Matrix"### Virtual coercions -- via smart "helpers" (-> ./Auxiliaries.R)setAs("Matrix", "sparseMatrix", function(from) as(from, "CsparseMatrix"))setAs("Matrix", "CsparseMatrix", function(from) as_Csparse(from))setAs("Matrix", "denseMatrix", function(from) as_dense(from))## Maybe TODO:## setAs("Matrix", "nMatrix", function(from) ....)## Most of these work; this is a last resort:setAs(from = "Matrix", to = "matrix", # do *not* call base::as.matrix() here:function(from) .bail.out.2("coerce", class(from), class(to)))setAs(from = "matrix", to = "Matrix", function(from) Matrix(from))## ## probably not needed eventually:## setAs(from = "ddenseMatrix", to = "matrix",## function(from) {## if(length(d <- dim(from)) != 2) stop("dim(.) has not length 2")## array(from@x, dim = d, dimnames = dimnames(from))## })## should propagate to all subclasses:setMethod("as.matrix", signature(x = "Matrix"), function(x) as(x, "matrix"))## for 'Matrix' objects, as.array() should be equivalent:setMethod("as.array", signature(x = "Matrix"), function(x) as(x, "matrix"))## head and tail apply to all Matrix objects for which subscripting is allowed:setMethod("head", signature(x = "Matrix"), utils::head.matrix)setMethod("tail", signature(x = "Matrix"), utils::tail.matrix)setMethod("drop", signature(x = "Matrix"),function(x) if(all(dim(x) != 1)) x else drop(as(x, "matrix")))## slow "fall back" method {subclasses should have faster ones}:setMethod("as.vector", signature(x = "Matrix", mode = "missing"),function(x) as.vector(as(x, "matrix")))## mainly need these for "dMatrix" or "lMatrix" respectively, but why not general:setMethod("as.numeric", signature(x = "Matrix"),function(x, ...) as.numeric(as.vector(x)))setMethod("as.logical", signature(x = "Matrix"),function(x, ...) as.logical(as.vector(x)))setMethod("cov2cor", signature(V = "Matrix"),function(V) { ## was as(cov2cor(as(V, "matrix")), "dpoMatrix"))r <- Vp <- (d <- dim(V))[1]if(p != d[2]) stop("'V' is not a square matrix")Is <- sqrt(1/diag(V)) # diag( 1/sigma_i )if(any(!is.finite(Is)))warning("diag(.) had 0 or NA entries; non-finite result is doubtful")Is <- Diagonal(x = Is)r <- Is %*% V %*% Isr[cbind(1L:p,1L:p)] <- 1 # exact in diagonalas(forceSymmetric(r), "dpoMatrix")})## "base" has an isSymmetric() S3-generic since R 2.3.0setMethod("isSymmetric", signature(object = "symmetricMatrix"),function(object, ...) TRUE)setMethod("isSymmetric", signature(object = "triangularMatrix"),## TRUE iff diagonal:function(object, ...) isDiagonal(object))setMethod("isTriangular", signature(object = "matrix"), isTriMat)setMethod("isDiagonal", signature(object = "matrix"), .is.diagonal)## The "catch all" methods -- far from optimal:setMethod("symmpart", signature(x = "Matrix"),function(x) as((x + t(x))/2, "symmetricMatrix"))setMethod("skewpart", signature(x = "Matrix"),function(x) (x - t(x))/2)## FIXME: do this (similarly as for "ddense.." in CsetMethod("symmpart", signature(x = "matrix"), function(x) (x + t(x))/2)setMethod("skewpart", signature(x = "matrix"), function(x) (x - t(x))/2)setMethod("dim", signature(x = "Matrix"),function(x) x@Dim, valueClass = "integer")setMethod("length", "Matrix", function(x) prod(dim(x)))setMethod("dimnames", signature(x = "Matrix"), function(x) x@Dimnames)## not exported but used more than once for "dimnames<-" method :## -- or do only once for all "Matrix" classes ??dimnamesGets <- function (x, value) {d <- dim(x)if (!is.list(value) || length(value) != 2 ||!(is.null(v1 <- value[[1]]) || length(v1) == d[1]) ||!(is.null(v2 <- value[[2]]) || length(v2) == d[2]))stop(sprintf("invalid dimnames given for '%s' object", class(x)))x@Dimnames <- list(if(!is.null(v1)) as.character(v1),if(!is.null(v2)) as.character(v2))x}setMethod("dimnames<-", signature(x = "Matrix", value = "list"),dimnamesGets)setMethod("unname", signature("Matrix", force="missing"),function(obj) { obj@Dimnames <- list(NULL,NULL); obj})setMethod("all", signature(x = "Matrix"),function(x, ..., na.rm)callGeneric(as(x, "lMatrix"), ..., na.rm=na.rm))setMethod("any", signature(x = "Matrix"),function(x, ..., na.rm)callGeneric(as(x, "lMatrix"), ..., na.rm=na.rm))## NOTE: "&" and "|" are now in group "Logic" c "Ops" --> ./Ops.R## "!" is in ./not.RMatrix <- function (data = NA, nrow = 1, ncol = 1, byrow = FALSE,dimnames = NULL, sparse = NULL, forceCheck = FALSE){sparseDefault <- function(m) prod(dim(m)) > 2*sum(isN0(as(m, "matrix")))i.M <- is(data, "Matrix")if(!i.M && inherits(data, "table")) # special treatmentclass(data) <- "matrix" # "matrix" first for S4 dispatchif(is.null(sparse1 <- sparse) && (i.M || is(data, "matrix")))sparse <- sparseDefault(data)sM <- FALSEdoDN <- TRUEif (i.M) {if(!missing(nrow) || !missing(ncol)|| !missing(byrow))warning("'nrow', 'ncol', etc, are disregarded when 'data' is \"Matrix\" already")sM <- is(data,"sparseMatrix")if(!forceCheck && ((sparse && sM) || (!sparse && !sM)))return(data)## else : convert dense <-> sparse -> at end}else if (!is.matrix(data)) { ## cut & paste from "base::matrix" :if (missing(nrow))nrow <- ceiling(length(data)/ncol)else if (missing(ncol))ncol <- ceiling(length(data)/nrow)if(length(data) == 1 && is0(data) && !identical(sparse, FALSE)) {## Matrix(0, ...) : always sparse unless "sparse = FALSE":if(is.null(sparse)) sparse1 <- sparse <- TRUEi.M <- sM <- TRUEisSym <- nrow == ncol## will be sparse: do NOT construct full matrix!data <- new(paste(if(is.numeric(data)) "d" elseif(is.logical(data)) "l" elsestop("invalid 'data'"),if(isSym) "s" else "g", "CMatrix", sep=''),p = rep.int(0L, ncol+1L),Dim = as.integer(c(nrow,ncol)),Dimnames = if(is.null(dimnames)) list(NULL,NULL)else dimnames)} else { ## normal case - using .Internal() to avoid more copyingif(getRversion() >= "2.7.0")data <- .Internal(matrix(data, nrow, ncol, byrow, dimnames))else {data <- .Internal(matrix(data, nrow, ncol, byrow))dimnames(data) <- dimnames}if(is.null(sparse))sparse <- sparseDefault(data)}doDN <- FALSE} else if(!missing(nrow) || !missing(ncol)|| !missing(byrow))warning("'nrow', 'ncol', etc, are disregarded for matrix 'data'")## 'data' is now a "matrix" or "Matrix"if (doDN && !is.null(dimnames))dimnames(data) <- dimnames## check for symmetric / triangular / diagonal :isSym <- isSymmetric(data)if((isTri <- !isSym))isTri <- isTriangular(data)isDiag <- isSym # cannot be diagonal if it isn't symmetricif(isDiag)isDiag <- !isTRUE(sparse1) && isDiagonal(data)## try to coerce ``via'' virtual classesif(isDiag) { ## diagonal is preferred to sparse !data <- as(data, "diagonalMatrix")isSym <- FALSE} else if(sparse && !sM)data <- as(data, "sparseMatrix")else if(!sparse) {if(i.M) { ## data is 'Matrix'if(!is(data, "denseMatrix"))data <- as(data, "denseMatrix")} else { ## data is "matrix" (and result "dense" -> go via "general"ctype <- typeof(data)if (ctype == "complex")stop("complex matrices not yet implemented in Matrix package")if (ctype == "integer") ## integer Matrices not yet implementedstorage.mode(data) <- "double"data <- new(paste(.M.kind(data), "geMatrix", sep=''),Dim = dim(data),Dimnames = .M.DN(data),x = c(data))}}if(isTri && !is(data, "triangularMatrix")) {data <- if(attr(isTri,"kind") == "L") tril(data) else triu(data)#was as(data, "triangularMatrix")} else if(isSym && !is(data, "symmetricMatrix"))data <- forceSymmetric(data) #was as(data, "symmetricMatrix")data}## Methods for operations where one argument is numeric## Using as.matrix() and rbind()## in order to get dimnames from names {at least potentially}:setMethod("%*%", signature(x = "Matrix", y = "numeric"),function(x, y) callGeneric(x, as.matrix(y)))setMethod("%*%", signature(x = "numeric", y = "Matrix"),function(x, y) callGeneric(matrix(x, nrow = 1, byrow=TRUE), y))setMethod("%*%", signature(x = "Matrix", y = "matrix"),function(x, y) callGeneric(x, Matrix(y)))setMethod("%*%", signature(x = "matrix", y = "Matrix"),function(x, y) callGeneric(Matrix(x), y))setMethod("crossprod", signature(x = "Matrix", y = "numeric"),function(x, y = NULL) callGeneric(x, as.matrix(y)))setMethod("crossprod", signature(x = "numeric", y = "Matrix"),function(x, y = NULL) callGeneric(as.matrix(x), y))setMethod("crossprod", signature(x = "Matrix", y = "matrix"),function(x, y = NULL) callGeneric(x, Matrix(y)))setMethod("crossprod", signature(x = "matrix", y = "Matrix"),function(x, y = NULL) callGeneric(Matrix(x), y))## The as.matrix() promotion seems illogical to MM,## but is according to help(tcrossprod, package = "base") :setMethod("tcrossprod", signature(x = "Matrix", y = "numeric"),function(x, y = NULL) callGeneric(x, as.matrix(y)))setMethod("tcrossprod", signature(x = "numeric", y = "Matrix"),function(x, y = NULL) callGeneric(as.matrix(x), y))setMethod("tcrossprod", signature(x = "Matrix", y = "matrix"),function(x, y = NULL) callGeneric(x, Matrix(y)))setMethod("tcrossprod", signature(x = "matrix", y = "Matrix"),function(x, y = NULL) callGeneric(Matrix(x), y))## maybe not 100% optimal, but elegant:setMethod("solve", signature(a = "Matrix", b = "missing"),function(a, b, ...) solve(a, Diagonal(nrow(a))))setMethod("solve", signature(a = "Matrix", b = "numeric"),function(a, b, ...) callGeneric(a, Matrix(b)))setMethod("solve", signature(a = "Matrix", b = "matrix"),function(a, b, ...) callGeneric(a, Matrix(b)))setMethod("solve", signature(a = "matrix", b = "Matrix"),function(a, b, ...) callGeneric(Matrix(a), b))## when no sub-class method is found, bail outsetMethod("solve", signature(a = "Matrix", b = "Matrix"),function(a, b, ...) .bail.out.2("solve", class(a), class(b)))## bail-out methods in order to get better error messagessetMethod("%*%", signature(x = "Matrix", y = "Matrix"),function (x, y)stop(gettextf('not-yet-implemented method for <%s> %%*%% <%s>',class(x), class(y))))setMethod("crossprod", signature(x = "Matrix", y = "ANY"),function (x, y = NULL) .bail.out.2(.Generic, class(x), class(y)))setMethod("crossprod", signature(x = "ANY", y = "Matrix"),function (x, y = NULL) .bail.out.2(.Generic, class(x), class(y)))setMethod("tcrossprod", signature(x = "Matrix", y = "ANY"),function (x, y = NULL) .bail.out.2(.Generic, class(x), class(y)))setMethod("tcrossprod", signature(x = "ANY", y = "Matrix"),function (x, y = NULL) .bail.out.2(.Generic, class(x), class(y)))## cheap fallbackssetMethod("crossprod", signature(x = "Matrix", y = "Matrix"),function(x, y = NULL) t(x) %*% y)setMethod("tcrossprod", signature(x = "Matrix", y = "Matrix"),function(x, y = NULL) x %*% t(y))## There are special sparse methods; this is a "fall back":setMethod("kronecker", signature(X = "Matrix", Y = "ANY",FUN = "ANY", make.dimnames = "ANY"),function(X, Y, FUN, make.dimnames, ...) {if(is(X, "sparseMatrix"))warning("using slow kronecker() method")X <- as(X, "matrix") ; Matrix(callGeneric()) })setMethod("kronecker", signature(X = "ANY", Y = "Matrix",FUN = "ANY", make.dimnames = "ANY"),function(X, Y, FUN, make.dimnames, ...) {if(is(Y, "sparseMatrix"))warning("using slow kronecker() method")Y <- as(Y, "matrix") ; Matrix(callGeneric()) })## FIXME: All of these should never be calledsetMethod("chol", signature(x = "Matrix"),function(x, pivot = FALSE, ...) .bail.out.1(.Generic, class(x)))setMethod("determinant", signature(x = "Matrix"),function(x, logarithm = TRUE, ...) .bail.out.1(.Generic, class(x)))setMethod("diag", signature(x = "Matrix"),function(x, nrow, ncol) .bail.out.1(.Generic, class(x)))setMethod("t", signature(x = "Matrix"),function(x) .bail.out.1(.Generic, class(x)))setMethod("norm", signature(x = "Matrix", type = "character"),function(x, type, ...) .bail.out.1(.Generic, class(x)))setMethod("rcond", signature(x = "Matrix", norm = "character"),function(x, norm, ...) .bail.out.1(.Generic, class(x)))## for all :setMethod("norm", signature(x = "ANY", type = "missing"),function(x, type, ...) norm(x, type = "O", ...))setMethod("rcond", signature(x = "ANY", norm = "missing"),function(x, norm, ...) rcond(x, norm = "O", ...))## MM: More or less "Cut & paste" from## --- diff.default() from R/src/library/base/R/diff.R :setMethod("diff", signature(x = "Matrix"),function(x, lag = 1, differences = 1, ...) {if (length(lag) > 1 || length(differences) > 1 ||lag < 1 || differences < 1)stop("'lag' and 'differences' must be integers >= 1")xlen <- nrow(x)if (lag * differences >= xlen)return(x[,FALSE][0]) # empty of proper modei1 <- -1:-lagfor (i in 1:differences)x <- x[i1, , drop = FALSE] -x[-nrow(x):-(nrow(x)-lag+1), , drop = FALSE]x})setMethod("image", "Matrix",function(x, ...) { # coercing to sparse is not inefficient,## since we need 'i' and 'j' for levelplot()x <- as(as(x, "sparseMatrix"), "dMatrix")callGeneric()})## Group Methods##-> see ./Ops.R## ~~~~~## For all non-dMatrix objects, and note that "all" and "any" have their ownsetMethod("Summary", signature(x = "Matrix", na.rm = "ANY"),function(x, ..., na.rm)callGeneric(as(x,"dMatrix"), ..., na.rm = na.rm))### --------------------------------------------------------------------------###### Subsetting "[" and### SubAssign "[<-" : The "missing" cases can be dealt with here, "at the top":## Using "index" for indices should allow## integer (numeric), logical, or character (names!) indices :## "x[]":setMethod("[", signature(x = "Matrix",i = "missing", j = "missing", drop = "ANY"),function (x, i, j, ..., drop) x)## missing 'drop' --> 'drop = TRUE'## -----------## select rows __ or __ vector indexing:setMethod("[", signature(x = "Matrix", i = "index", j = "missing",drop = "missing"),function(x,i,j, ..., drop) {if(nargs() == 2) { ## e.g. M[0] , M[TRUE], M[1:2]if(any(as.logical(i)) || prod(dim(x)) == 0)## FIXME: for *large sparse*, use sparseVector !as.vector(x)[i]else ## save memory (for large sparse M):as.vector(x[1,1])[FALSE]} else {callGeneric(x, i=i, , drop=TRUE)## ^^}})## select columnssetMethod("[", signature(x = "Matrix", i = "missing", j = "index",drop = "missing"),function(x,i,j, ..., drop) callGeneric(x, j=j, drop= TRUE))setMethod("[", signature(x = "Matrix", i = "index", j = "index",drop = "missing"),function(x,i,j, ..., drop) callGeneric(x, i=i, j=j, drop= TRUE))## bail out if any of (i,j,drop) is "non-sense"setMethod("[", signature(x = "Matrix", i = "ANY", j = "ANY", drop = "ANY"),function(x,i,j, ..., drop)stop("invalid or not-yet-implemented 'Matrix' subsetting"))## logical indexing, such as M[ M >= 7 ] *BUT* also M[ M[,1] >= 3,],## The following is *both* for M [ <logical> ]## and also for M [ <logical> , ].M.sub.i.logical <- function (x, i, j, ..., drop){nA <- nargs()if(nA == 2) { ## M [ M >= 7 ]## FIXME: when both 'x' and 'i' are sparse, this can be very inefficientif(is(x, "sparseMatrix"))message("<sparse>[ <logic> ] : .M.sub.i.logical() maybe inefficient")toC <- geClass(x)if(canCoerce(x, toC)) as(x, toC)@x[as.vector(i)]else as(as(as(x, "generalMatrix"), "denseMatrix"), toC)@x[as.vector(i)]## -> error when lengths don't match} else if(nA == 3) { ## M [ M[,1, drop=FALSE] >= 7, ]stop("not-yet-implemented 'Matrix' subsetting") ## FIXME} else stop("nargs() = ", nA,". Extraneous illegal arguments inside '[ .. ]' (i.logical)?")}setMethod("[", signature(x = "Matrix", i = "lMatrix", j = "missing",drop = "ANY"),.M.sub.i.logical)setMethod("[", signature(x = "Matrix", i = "logical", j = "missing",drop = "ANY"),.M.sub.i.logical)subset.ij <- function(x, ij) {m <- nrow(ij)if(m > 3) {cld <- getClassDef(class(x))sym.x <- extends(cld, "symmetricMatrix")if(sym.x) {W <- if(x@uplo == "U") # stored only [i,j] with i <= jij[,1] > ij[,2] else ij[,1] < ij[,2]if(any(W))ij[W,] <- ij[W, 2:1]}if(extends(cld, "sparseMatrix")) {## do something smarter:nr <- nrow(x)if(!extends(cld, "CsparseMatrix")) {x <- as(x, "CsparseMatrix") # simpler; our standardcld <- getClassDef(class(x))}tri.x <- extends(cld, "triangularMatrix")if(tri.x) {## need these for the 'x' slot in any caseif (x@diag == "U") x <- .Call(Csparse_diagU2N, x)## slightly more efficient than non0.i() or non0ind():ij.x <- .Call(compressed_non_0_ij, x, isC=TRUE)} else { ## symmetric / general : for symmetric, only "existing"bij.x <- non0.i(x, cld)}mi <- match(encodeInd(ij.x, nr),encodeInd(ij -1L, nr), nomatch=0)mmi <- mi != 0## Result:ans <- vector(mode = .type.kind[.M.kindC(cld)], length = m)## those that are *not* zero:ans[mi[mmi]] <-if(extends(cld, "nsparseMatrix")) TRUE else x@x[mmi]ans} else { ## non-sparse : dense##---- NEVER happens: 'denseMatrix' has its own setMethod(.) !message("m[ <ij-matrix> ]: inefficiently indexing single elements")i1 <- ij[,1]i2 <- ij[,2]## very inefficient for large munlist(lapply(seq_len(m), function(j) x[i1[j], i2[j]]))}} else { # 1 <= m <= 3i1 <- ij[,1]i2 <- ij[,2]unlist(lapply(seq_len(m), function(j) x[i1[j], i2[j]]))}}## A[ ij ] where ij is (i,j) 2-column matrix -- but also when that is logical mat!.M.sub.i.2col <- function (x, i, j, ..., drop){nA <- nargs()if(nA == 2) { ## M [ cbind(ii,jj) ] or M [ <logical matrix> ]if(!is.integer(nc <- ncol(i)))stop(".M.sub.i.2col(): 'i' has no integer column number;\n","should never happen; please report")if(is.logical(i))return(.M.sub.i.logical(x, i=i)) # call with 2 args!else if(!is.numeric(i) || nc != 2)stop("such indexing must be by logical or 2-column numeric matrix")m <- nrow(i)if(m == 0) return(vector(mode = .type.kind[.M.kind(x)]))## elsesubset.ij(x, i)} else stop("nargs() = ", nA,". Extraneous illegal arguments inside '[ .. ]' (i.2col)?")}setMethod("[", signature(x = "Matrix", i = "matrix", j = "missing"),# drop="ANY".M.sub.i.2col)### "[<-" : -----------------## x[] <- value :setReplaceMethod("[", signature(x = "Matrix", i = "missing", j = "missing",value = "ANY"),## double/logical/...function (x, value) {## Fails for 'nMatrix' ... FIXME : make sure have method therex@x <- rep(value, length = length(x@x))validObject(x)# check if type and lengths above matchx})## A[ ij ] <- value, where ij is (i,j) 2-column matrix :## ----------------## The cheap general method --- FIXME: provide special ones; done for Tsparse..## NOTE: need '...' below such that setMethod() does## not use .local() such that nargs() will work correctly:.M.repl.i.2col <- function (x, i, j, ..., value){nA <- nargs()if(nA == 3) { ## M [ cbind(ii,jj) ] <- value or M [ Lmat ] <- valueif(!is.integer(nc <- ncol(i)))stop(".M.repl.i.2col(): 'i' has no integer column number;\n","should never happen; please report")else if(!is.numeric(i) || nc != 2)stop("such indexing must be by logical or 2-column numeric matrix")if(is.logical(i)) {message(".M.repl.i.2col(): drop 'matrix' case ...")## c(i) : drop "matrix" to logical vectorreturn( callGeneric(x, i=c(i), value=value) )}if(!is.integer(i)) storage.mode(i) <- "integer"if(any(i < 0))stop("negative values are not allowed in a matrix subscript")if(any(is.na(i)))stop("NAs are not allowed in subscripted assignments")if(any(i0 <- (i == 0))) # remove themi <- i[ - which(i0, arr.ind = TRUE)[,"row"], ]## now have integer i >= 1m <- nrow(i)## mod.x <- .type.kind[.M.kind(x)]if(length(value) > 0 && m %% length(value) != 0)warning("number of items to replace is not a multiple of replacement length")## recycle:value <- rep(value, length = m)i1 <- i[,1]i2 <- i[,2]if(m > 2)message("m[ <ij-matrix> ] <- v: inefficiently treating single elements")## inefficient -- FIXME -- (also loses "symmetry" unnecessarily)for(k in seq_len(m))x[i1[k], i2[k]] <- value[k]x} else stop("nargs() = ", nA,". Extraneous illegal arguments inside '[ .. ]' ?")}setReplaceMethod("[", signature(x = "Matrix", i = "matrix", j = "missing",value = "replValue"),.M.repl.i.2col)setReplaceMethod("[", signature(x = "Matrix", i = "missing", j = "ANY",value = "Matrix"),function (x, i, j, ..., value)callGeneric(x=x, , j=j, value = as.vector(value)))setReplaceMethod("[", signature(x = "Matrix", i = "ANY", j = "missing",value = "Matrix"),function (x, i, j, ..., value)callGeneric(x=x, i=i, , value = as.vector(value)))setReplaceMethod("[", signature(x = "Matrix", i = "ANY", j = "ANY",value = "Matrix"),function (x, i, j, ..., value)callGeneric(x=x, i=i, j=j, value = as.vector(value)))setReplaceMethod("[", signature(x = "Matrix", i = "missing", j = "ANY",value = "matrix"),function (x, i, j, ..., value)callGeneric(x=x, , j=j, value = c(value)))setReplaceMethod("[", signature(x = "Matrix", i = "ANY", j = "missing",value = "matrix"),function (x, i, j, ..., value)callGeneric(x=x, i=i, , value = c(value)))setReplaceMethod("[", signature(x = "Matrix", i = "ANY", j = "ANY",value = "matrix"),function (x, i, j, value)callGeneric(x=x, i=i, j=j, value = c(value)))## (ANY,ANY,ANY) is used when no `real method' is implemented :setReplaceMethod("[", signature(x = "Matrix", i = "ANY", j = "ANY",value = "ANY"),function (x, i, j, value) {if(!is.atomic(value))stop(sprintf("RHS 'value' (class %s) matches 'ANY', but must match matrix class %s",class(value),class(x)))else stop("not-yet-implemented 'Matrix[<-' method")})