R Under development (unstable) (2024-10-17 r87242 ucrt) -- "Unsuffered Consequences" Copyright (C) 2024 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > #### Testing cbind() & rbind() -- based on cbind2() & rbind2() > ## (where using 'cBind()' and 'rBind()' in Matrix) > > ## for R_DEFAULT_PACKAGES=NULL : > library(utils) > > library(Matrix) > > source(system.file("test-tools.R", package = "Matrix"))# identical3() etc Loading required package: tools > > ### --- Dense Matrices --- > > m1 <- m2 <- m <- matrix(1:12, 3,4) > dimnames(m2) <- list(LETTERS[1:3], + letters[1:4]) > dimnames(m1) <- list(NULL,letters[1:4]) > M <- Matrix(m) > M1 <- Matrix(m1) > M2 <- Matrix(m2) > > stopifnot( + identical3(cbind ( M, 10*M), + show(cbind2( M, 10*M)), + Matrix(cbind ( m, 10*m))) + , + identical3(cbind (M1, 100+M1), + show(cbind2(M1, 100+M1)), + Matrix(cbind (m1, 100+m1))) + , + identical3(cbind (M1, 10*M2), + show(cbind2(M1, 10*M2)), + Matrix(cbind (m1, 10*m2))) + , + identical3(cbind (M2, M1+M2), + show(cbind2(M2, M1+M2)), + Matrix(cbind (m2, m1+m2))) + , + identical(colnames(show(cbind(M1, MM = -1))), + c(colnames(M1), "MM")) + , + identical3(rbind ( M, 10*M), + show(rbind2( M, 10*M)), + Matrix(rbind ( m, 10*m))) + , + identical3(rbind (M2, M1+M2), + show(rbind2(M2, M1+M2)), + Matrix(rbind (m2, m1+m2))) + , + Qidentical(show (rbind(R1 = 10:11, M1)), + Matrix(rbind(R1 = 10:11, m1)), strictClass=FALSE) + , TRUE) 3 x 8 Matrix of class "dgeMatrix" [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 1 4 7 10 10 40 70 100 [2,] 2 5 8 11 20 50 80 110 [3,] 3 6 9 12 30 60 90 120 3 x 8 Matrix of class "dgeMatrix" a b c d a b c d [1,] 1 4 7 10 101 104 107 110 [2,] 2 5 8 11 102 105 108 111 [3,] 3 6 9 12 103 106 109 112 3 x 8 Matrix of class "dgeMatrix" a b c d a b c d A 1 4 7 10 10 40 70 100 B 2 5 8 11 20 50 80 110 C 3 6 9 12 30 60 90 120 3 x 8 Matrix of class "dgeMatrix" a b c d a b c d A 1 4 7 10 2 8 14 20 B 2 5 8 11 4 10 16 22 C 3 6 9 12 6 12 18 24 3 x 5 Matrix of class "dgeMatrix" a b c d MM [1,] 1 4 7 10 -1 [2,] 2 5 8 11 -1 [3,] 3 6 9 12 -1 6 x 4 Matrix of class "dgeMatrix" [,1] [,2] [,3] [,4] [1,] 1 4 7 10 [2,] 2 5 8 11 [3,] 3 6 9 12 [4,] 10 40 70 100 [5,] 20 50 80 110 [6,] 30 60 90 120 6 x 4 Matrix of class "dgeMatrix" a b c d A 1 4 7 10 B 2 5 8 11 C 3 6 9 12 2 8 14 20 4 10 16 22 6 12 18 24 4 x 4 Matrix of class "dgeMatrix" a b c d R1 10 11 10 11 1 4 7 10 2 5 8 11 3 6 9 12 > > identical.or.eq <- function(x,y, tol=0, ...) { + if(identical(x,y, ...)) + TRUE + else if(isTRUE(aeq <- all.equal(x,y, tolerance = tol))) + structure(TRUE, comment = "not identical") + else aeq + } > identicalShow <- function(x,y, ...) + if(!isTRUE(id <- identical.or.eq(x, y, ...))) cat(id,"\n") > > ## Checking deparse.level { <==> example at end of ?cbind }: > checkRN <- function(dd, B = rbind) { + FN <- function(deparse.level) + rownames(B(1:4, c=2,"a+"=10, dd, deparse.level=deparse.level)) + rn <- c("1:4", "c", "a+", "dd", "") + isMatr <- (length(dim(dd)) == 2) + id <- if(isMatr) 5 else 4 + identicalShow(rn[c(5,2:3, 5)], FN(deparse.level= 0)) # middle two names + identicalShow(rn[c(5,2:3,id)], FN(deparse.level= 1)) # last shown if vector + identicalShow(rn[c(1,2:3,id)], FN(deparse.level= 2)) # first shown; (last if vec.) + } > checkRN(10) # <==> ?cbind's ex > checkRN(1:4) > checkRN( rbind(c(0:1,0,0))) > checkRN(Matrix(rbind(c(0:1,0,0)))) ## in R <= 3.4.1, from methods:::rbind bug : > ## Modes: character, NULL Lengths: 4, 0 target is character, current is NULL > checkRN(10 , rbind) > checkRN(1:4, rbind) > checkRN( rbind(c(0:1,0,0)), rbind) > checkRN(Matrix(rbind(c(0:1,0,0))), rbind) > > cbind(0, Matrix(0+0:1, 1,2), 3:2)# FIXME? should warn - as with matrix() 1 x 4 Matrix of class "dgeMatrix" [,1] [,2] [,3] [,4] [1,] 0 0 1 3 Warning message: In cbind.Matrix(x, y, deparse.level = 0L) : number of rows of result is not a multiple of vector length > as(rbind(0, Matrix(0+0:1, 1,2), 3:2), + "sparseMatrix") 3 x 2 sparse Matrix of class "dgCMatrix" [1,] . . [2,] . 1 [3,] 3 2 > cbind(M2, 10*M2[nrow(M2):1 ,])# keeps the rownames from the first 3 x 8 Matrix of class "dgeMatrix" a b c d a b c d A 1 4 7 10 30 60 90 120 B 2 5 8 11 20 50 80 110 C 3 6 9 12 10 40 70 100 > > (im <- cbind(I = 100, M)) 3 x 5 Matrix of class "dgeMatrix" I [1,] 100 1 4 7 10 [2,] 100 2 5 8 11 [3,] 100 3 6 9 12 > str(im) Formal class 'dgeMatrix' [package "Matrix"] with 4 slots ..@ Dim : int [1:2] 3 5 ..@ Dimnames:List of 2 .. ..$ : NULL .. ..$ : chr [1:5] "I" "" "" "" ... ..@ x : num [1:15] 100 100 100 1 2 3 4 5 6 7 ... ..@ factors : list() > (mi <- cbind(M2, I = 1000)) 3 x 5 Matrix of class "dgeMatrix" a b c d I A 1 4 7 10 1000 B 2 5 8 11 1000 C 3 6 9 12 1000 > str(mi) Formal class 'dgeMatrix' [package "Matrix"] with 4 slots ..@ Dim : int [1:2] 3 5 ..@ Dimnames:List of 2 .. ..$ : chr [1:3] "A" "B" "C" .. ..$ : chr [1:5] "a" "b" "c" "d" ... ..@ x : num [1:15] 1 2 3 4 5 6 7 8 9 10 ... ..@ factors : list() > (m1m <- cbind(M,I=100,M2)) 3 x 9 Matrix of class "dgeMatrix" I a b c d A 1 4 7 10 100 1 4 7 10 B 2 5 8 11 100 2 5 8 11 C 3 6 9 12 100 3 6 9 12 > showProc.time() Time (user system elapsed): 0.14 0.02 0.15 > > ## lgeMatrix -- rbind2() had bug (in C code): > is.lge <- function(M) isValid(M, "lgeMatrix") > stopifnot(exprs = { + is.lge(rbind(M2 > 0, M2 < 0)) # had Error in rbind2(): + ## REAL() can only be applied to a 'numeric', not a 'logical' + is.lge(rbind(M2 < 0, M2 > 0)) # ditto + is.lge(rbind(Matrix(1:6 %% 3 != 0, 2,3), FALSE)) + is.lge(L <- rbind(Matrix(TRUE, 2,3), TRUE)) + all(L) + is.lge(rbind(Matrix(TRUE, 2,3), FALSE)) + }) > > ### --- Diagonal / Sparse - had bugs > > D4 <- Diagonal(4) > (D4T <- as(D4, "TsparseMatrix")) 4 x 4 sparse Matrix of class "dtTMatrix" (unitriangular) [1,] I . . . [2,] . I . . [3,] . . I . [4,] . . . I > D4C <- as(D4T, "CsparseMatrix") > c1 <- Matrix(0+0:3, 4, sparse=TRUE) ; r1 <- t(c1); r1 1 x 4 sparse Matrix of class "dgCMatrix" [1,] . 1 2 3 > > d4 <- rbind(Diagonal(4), 0:3) > m4 <- cbind(Diagonal(x=-1:2), 0:3) > c4. <- cbind(Diagonal(4), c1) > c.4 <- cbind(c1, Diagonal(4)) > r4. <- rbind(Diagonal(4), r1) > r.4 <- rbind(r1, Diagonal(4)) > assert.EQ.mat(d4, rbind(diag(4), 0:3)) > assert.EQ.mat(m4, cbind(diag(-1:2), 0:3)) > stopifnot(identical(Matrix(cbind(diag(3),0)), cbind2(Diagonal(3),0)), + is(d4, "sparseMatrix"), is(m4, "sparseMatrix"), + identical(.tCRT(d4), cbind(Diagonal(4), 0:3)), + identical(.tCRT(m4), rbind(Diagonal(x=-1:2), 0:3))) > showProc.time() Time (user system elapsed): 0.06 0 0.06 > > ### --- Sparse Matrices --- > > identical4(cbind(diag(4), diag(4)), + cbind(D4C, D4C), + cbind(D4T, D4C), + cbind(D4C, D4T)) [1] FALSE > nr <- 4 > nc <- 6 > m. <- matrix(rep_len(c(0, 2:-1), nr * nc), nr, nc) > M <- Matrix(m.) > (mC <- as(M, "CsparseMatrix")) 4 x 6 sparse Matrix of class "dgCMatrix" [1,] . -1 . 1 2 . [2,] 2 . -1 . 1 2 [3,] 1 2 . -1 . 1 [4,] . 1 2 . -1 . > (mT <- as(M, "TsparseMatrix")) 4 x 6 sparse Matrix of class "dgTMatrix" [1,] . -1 . 1 2 . [2,] 2 . -1 . 1 2 [3,] 1 2 . -1 . 1 [4,] . 1 2 . -1 . > stopifnot(identical(mT, as(mC, "TsparseMatrix")), + identical(mC, as(mT, "CsparseMatrix"))) > > for(v in list(0, 2, 1:0)) + for(fnam in c("cbind", "rbind")) { + cat(fnam,"(m, v=", deparse(v),"), class(m) :") + FUN <- get(fnam) + for(m in list(M, mC, mT)) { + cat("", class(m),"") + assert.EQ.mat(FUN(v, m), FUN(v, m.)) ; cat(",") + assert.EQ.mat(FUN(m, v), FUN(m., v)) ; cat(".") + } + cat("\n") + } cbind (m, v= 0 ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. rbind (m, v= 0 ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. cbind (m, v= 2 ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. rbind (m, v= 2 ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. cbind (m, v= 1:0 ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. rbind (m, v= 1:0 ), class(m) : dgeMatrix ,. dgCMatrix ,. dgTMatrix ,. > showProc.time() Time (user system elapsed): 0.08 0 0.36 > > cbind(0, mC); cbind(mC, 0) 4 x 7 sparse Matrix of class "dgCMatrix" [1,] . . -1 . 1 2 . [2,] . 2 . -1 . 1 2 [3,] . 1 2 . -1 . 1 [4,] . . 1 2 . -1 . 4 x 7 sparse Matrix of class "dgCMatrix" [1,] . -1 . 1 2 . . [2,] 2 . -1 . 1 2 . [3,] 1 2 . -1 . 1 . [4,] . 1 2 . -1 . . > cbind(0, mT); cbind(mT, 2) 4 x 7 sparse Matrix of class "dgTMatrix" [1,] . . -1 . 1 2 . [2,] . 2 . -1 . 1 2 [3,] . 1 2 . -1 . 1 [4,] . . 1 2 . -1 . 4 x 7 sparse Matrix of class "dgTMatrix" [1,] . -1 . 1 2 . 2 [2,] 2 . -1 . 1 2 2 [3,] 1 2 . -1 . 1 2 [4,] . 1 2 . -1 . 2 > cbind(diag(nr), mT) 4 x 10 sparse Matrix of class "dgTMatrix" [1,] 1 . . . . -1 . 1 2 . [2,] . 1 . . 2 . -1 . 1 2 [3,] . . 1 . 1 2 . -1 . 1 [4,] . . . 1 . 1 2 . -1 . > stopifnot(identical(t(cbind(diag(nr), mT)), + rbind(diag(nr), t(mT)))) > (cc <- cbind(mC, 0,7,0, diag(nr), 0)) 4 x 14 sparse Matrix of class "dgCMatrix" [1,] . -1 . 1 2 . . 7 . 1 . . . . [2,] 2 . -1 . 1 2 . 7 . . 1 . . . [3,] 1 2 . -1 . 1 . 7 . . . 1 . . [4,] . 1 2 . -1 . . 7 . . . . 1 . > stopifnot(identical3(cc, + as(cbind(mT, 0, 7, 0, diag(nr), 0), "CsparseMatrix"), + as(cbind( M, 0, 7, 0, diag(nr), 0), "CsparseMatrix"))) > > cbind(mC, 1, 100*mC, 0, 0:2) 4 x 15 sparse Matrix of class "dgCMatrix" [1,] . -1 . 1 2 . 1 . -100 . 100 200 . . . [2,] 2 . -1 . 1 2 1 200 . -100 . 100 200 . 1 [3,] 1 2 . -1 . 1 1 100 200 . -100 . 100 . 2 [4,] . 1 2 . -1 . 1 . 100 200 . -100 . . . > cbind(mT, 1, 0, mT+10*mT, 0, 0:2) 4 x 16 sparse Matrix of class "dgCMatrix" [1,] . -1 . 1 2 . 1 . . -11 . 11 22 . . . [2,] 2 . -1 . 1 2 1 . 22 . -11 . 11 22 . 1 [3,] 1 2 . -1 . 1 1 . 11 22 . -11 . 11 . 2 [4,] . 1 2 . -1 . 1 . . 11 22 . -11 . . . > one <- 1 > zero <- 0 > dimnames(mC) <- dimnames(mT) <- list(LETTERS[1:4], letters[1:6]) > op <- options(sparse.colnames = TRUE)# show colnames in print : > cbind(mC, one, 100*mC, zero, 0:2) 4 x 15 sparse Matrix of class "dgCMatrix" a b c d e f one a b c d e f zero A . -1 . 1 2 . 1 . -100 . 100 200 . . . B 2 . -1 . 1 2 1 200 . -100 . 100 200 . 1 C 1 2 . -1 . 1 1 100 200 . -100 . 100 . 2 D . 1 2 . -1 . 1 . 100 200 . -100 . . . > cbind(mC, one, 100*mC, zero, 0:2, deparse.level=0)# no "zero", "one" 4 x 15 sparse Matrix of class "dgCMatrix" a b c d e f a b c d e f A . -1 . 1 2 . 1 . -100 . 100 200 . . . B 2 . -1 . 1 2 1 200 . -100 . 100 200 . 1 C 1 2 . -1 . 1 1 100 200 . -100 . 100 . 2 D . 1 2 . -1 . 1 . 100 200 . -100 . . . > cbind(mC, one, 100*mC, zero, 0:2, deparse.level=2)# even "0:2" 4 x 15 sparse Matrix of class "dgCMatrix" a b c d e f one a b c d e f zero 0:2 A . -1 . 1 2 . 1 . -100 . 100 200 . . . B 2 . -1 . 1 2 1 200 . -100 . 100 200 . 1 C 1 2 . -1 . 1 1 100 200 . -100 . 100 . 2 D . 1 2 . -1 . 1 . 100 200 . -100 . . . > cbind(mT, one, zero, mT+10*mT, zero, 0:2) 4 x 16 sparse Matrix of class "dgCMatrix" a b c d e f one zero a b c d e f zero A . -1 . 1 2 . 1 . . -11 . 11 22 . . . B 2 . -1 . 1 2 1 . 22 . -11 . 11 22 . 1 C 1 2 . -1 . 1 1 . 11 22 . -11 . 11 . 2 D . 1 2 . -1 . 1 . . 11 22 . -11 . . . > > > ## logical (sparse) - should remain logical : > L5 <- Diagonal(n = 5, x = TRUE) > v5 <- rep(x = c(FALSE,TRUE), length.out = ncol(L5)) > stopifnot(is(show(rbind(L5,v5)), "lsparseMatrix"), + is(show(cbind(v5,L5)), "lsparseMatrix"), + is(rbind(L5, 2* v5), "dsparseMatrix"), + is(cbind(2* v5, L5), "dsparseMatrix")) 6 x 5 sparse Matrix of class "lgRMatrix" [,1] [,2] [,3] [,4] [,5] | . . . . . | . . . . . | . . . . . | . . . . . | v5 . | . | . 5 x 6 sparse Matrix of class "lgCMatrix" v5 [1,] . | . . . . [2,] | . | . . . [3,] . . . | . . [4,] | . . . | . [5,] . . . . . | > > ## print() / show() of non-structural zeros: > (m <- Matrix(c(0, 0, 2:0), 3, 5)) 3 x 5 sparse Matrix of class "dgCMatrix" [,1] [,2] [,3] [,4] [,5] [1,] . 1 . . 2 [2,] . . 2 . 1 [3,] 2 . 1 . . > (m2 <- cbind(m,m)) 3 x 10 sparse Matrix of class "dgCMatrix" [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,] . 1 . . 2 . 1 . . 2 [2,] . . 2 . 1 . . 2 . 1 [3,] 2 . 1 . . 2 . 1 . . > (m4 <- rbind(m2,m2)) 6 x 10 sparse Matrix of class "dgCMatrix" [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,] . 1 . . 2 . 1 . . 2 [2,] . . 2 . 1 . . 2 . 1 [3,] 2 . 1 . . 2 . 1 . . [4,] . 1 . . 2 . 1 . . 2 [5,] . . 2 . 1 . . 2 . 1 [6,] 2 . 1 . . 2 . 1 . . > diag(m4) [1] 0 0 1 0 1 2 > for(i in 1:6) { + m4[i, i ] <- i + m4[i,i+1] <- 0 + } > m4 ## now show some non-structural zeros: 6 x 10 sparse Matrix of class "dgCMatrix" [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,] 1 . . . 2 . 1 . . 2 [2,] . 2 . . 1 . . 2 . 1 [3,] 2 . 3 . . 2 . 1 . . [4,] . 1 . 4 . . 1 . . 2 [5,] . . 2 . 5 . . 2 . 1 [6,] 2 . 1 . . 6 . 1 . . > > ## Mixture of dense and sparse/diagonal -- used to fail, even in 1.0-0 > D5 <- Diagonal(x = 10*(1:5)) > (D5.1 <- cbind2(D5, 1)) 5 x 6 sparse Matrix of class "dgCMatrix" [,1] [,2] [,3] [,4] [,5] [,6] [1,] 10 . . . . 1 [2,] . 20 . . . 1 [3,] . . 30 . . 1 [4,] . . . 40 . 1 [5,] . . . . 50 1 > ## "FIXME" in newer versions of R, do not need Matrix() here: > s42 <- Matrix(z42 <- cbind2(rep(0:1,4), rep(1:0,4)), + sparse=TRUE) > (C86 <- rbind(1, 0, D5.1, 0)) 8 x 6 sparse Matrix of class "dgCMatrix" [,1] [,2] [,3] [,4] [,5] [,6] [1,] 1 1 1 1 1 1 [2,] . . . . . . [3,] 10 . . . . 1 [4,] . 20 . . . 1 [5,] . . 30 . . 1 [6,] . . . 40 . 1 [7,] . . . . 50 1 [8,] . . . . . . > stopifnotValid(D5.1, "dgCMatrix") > stopifnotValid(print(rbind2(Matrix(1:10, 2,5), D5)), "dgRMatrix") 7 x 5 sparse Matrix of class "dgRMatrix" [,1] [,2] [,3] [,4] [,5] [1,] 1 3 5 7 9 [2,] 2 4 6 8 10 [3,] 10 . . . . [4,] . 20 . . . [5,] . . 30 . . [6,] . . . 40 . [7,] . . . . 50 > stopifnotValid(print(cbind2(Matrix(10:1, 5,2), D5.1)), "dgCMatrix") 5 x 8 sparse Matrix of class "dgCMatrix" [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 10 5 10 . . . . 1 [2,] 9 4 . 20 . . . 1 [3,] 8 3 . . 30 . . 1 [4,] 7 2 . . . 40 . 1 [5,] 6 1 . . . . 50 1 > stopifnotValid(zz <- cbind2(z42, C86), "dgCMatrix") > stopifnot(identical(zz, cbind2(s42, C86))) > > ## Using "nMatrix" > (m1 <- sparseMatrix(1:3, 1:3)) # ngCMatrix 3 x 3 sparse Matrix of class "ngCMatrix" [,1] [,2] [,3] [1,] | . . [2,] . | . [3,] . . | > m2 <- sparseMatrix(1:3, 1:3, x = 1:3) > stopifnotValid(c12 <- cbind(m1,m2), "dgCMatrix") # was "ngC.." because of cholmod_horzcat ! > stopifnotValid(c21 <- cbind(m2,m1), "dgCMatrix") # ditto > stopifnotValid(r12 <- rbind(m1,m2), "dgCMatrix") # was "ngC.." because of cholmod_vertcat ! > stopifnotValid(r21 <- rbind(m2,m1), "dgCMatrix") # ditto > d1 <- as(m1, "denseMatrix") > d2 <- as(m2, "denseMatrix") > stopifnotValid(cbind2(d2,d1), "dgeMatrix") > stopifnotValid(cbind2(d1,d2), "dgeMatrix")## gave an error in Matrix 1.1-5 > stopifnotValid(rbind2(d2,d1), "dgeMatrix") > stopifnotValid(rbind2(d1,d2), "dgeMatrix")## gave an error in Matrix 1.1-5 > > ## rbind2() / cbind2() mixing sparse/dense: used to "fail", > ## ------------------- then (in 'devel', ~ 2015-03): completely wrong > S <- .sparseDiagonal(2) > s <- diag(2) > S9 <- rbind(S,0,0,S,0,NaN,0,0,0,2)## r/cbind2() failed to determine 'sparse' in Matrix <= 1.2-2 > s9 <- rbind(s,0,0,s,0,NaN,0,0,0,2) > assert.EQ.mat(S9, s9) > D <- Matrix(1:6, 3,2); d <- as(D, "matrix") > T9 <- t(S9); t9 <- t(s9); T <- t(D); t <- t(d) > stopifnot(identical(rbind (s9,d), rbind2(s9,d)), + identical(rbind2(D,S9), t(cbind2(T,T9))), + identical(rbind2(S9,D), t(cbind2(T9,T)))) > assert.EQ.mat(rbind2(S9,D), rbind2(s9,d)) > assert.EQ.mat(rbind2(D,S9), rbind2(d,s9)) > ## now with cbind2() -- no problem! > stopifnot(identical(cbind (t9,t), cbind2(t9,t))) > assert.EQ.mat(cbind2(T9,T), cbind2(t9,t)) > assert.EQ.mat(cbind2(T,T9), cbind2(t,t9)) > > > > options(op) > showProc.time() Time (user system elapsed): 0.22 0.01 0.24 > > proc.time() user system elapsed 1.84 0.18 2.31