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R : Copyright 2006, The R Foundation for Statistical ComputingVersion 2.3.1 Patched (2006-08-13 r38879)ISBN 3-900051-07-0R 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.> #### For both 'Extract' ("[") and 'Replace' ("[<-") Method testing>> library(Matrix)Loading required package: lattice>> source(system.file("test-tools.R", package = "Matrix"))# identical3() etc>> ### Dense Matrices>> m <- Matrix(1:28, nrow = 7)Warning message:integer matrices not yet implemented in 'Matrix'; using 'double' ones' in: Matrix(1:28, nrow = 7)> validObject(m) ; m@x <- as.double(m@x) ; validObject(m)[1] TRUE[1] TRUE> stopifnot(identical(m, m[]),+ identical(m[2, 3], 16), # simple number+ identical(m[2, 3:4], c(16,23))) # simple numeric of length 2>> m[2, 3:4, drop=FALSE] # sub matrix of class 'dgeMatrix'1 x 2 Matrix of class "dgeMatrix"[,1] [,2][1,] 16 23> m[-(4:7), 3:4] # dito; the upper right corner of 'm'3 x 2 Matrix of class "dgeMatrix"[,1] [,2][1,] 15 22[2,] 16 23[3,] 17 24>> ## rows or columns only:> m[1,] # first row, as simple numeric vector[1] 1 8 15 22> m[,2] # 2nd column[1] 8 9 10 11 12 13 14> m[,1:2] # sub matrix of first two columns7 x 2 Matrix of class "dgeMatrix"[,1] [,2][1,] 1 8[2,] 2 9[3,] 3 10[4,] 4 11[5,] 5 12[6,] 6 13[7,] 7 14> m[-(1:6),, drop=FALSE] # not the first 6 rows, i.e. only the 7th1 x 4 Matrix of class "dgeMatrix"[,1] [,2] [,3] [,4][1,] 7 14 21 28> m[integer(0),] #-> 0 x 4 Matrix0 x 4 Matrix of class "dgeMatrix"[,1] [,2] [,3] [,4]> m[2:4, numeric(0)] #-> 3 x 0 Matrix3 x 0 Matrix of class "dgeMatrix"[1,][2,][3,]>> ## logical indexing> stopifnot(identical(m[2,3], m[(1:nrow(m)) == 2, (1:ncol(m)) == 3]),+ identical(m[2,], m[(1:nrow(m)) == 2, ]),+ identical(m[,3:4], m[, (1:4) >= 3]))>> ## dimnames indexing:> mn <- m> dimnames(mn) <- list(paste("r",letters[1:nrow(mn)],sep=""),+ LETTERS[1:ncol(mn)])> mn["rd", "D"][1] 25> stopifnot(identical(mn["rc", "D"], mn[3,4]), mn[3,4] == 24,+ identical(mn[, "A"], mn[,1]), mn[,1] == 1:7,+ identical(mn[c("re", "rb"), "B"], mn[c(5,2), 2])+ )>> mo <- m> m[2,3] <- 100> m[1:2, 4] <- 200> m[, 1] <- -1> m[1:3,]3 x 4 Matrix of class "dgeMatrix"[,1] [,2] [,3] [,4][1,] -1 8 15 200[2,] -1 9 100 200[3,] -1 10 17 24>> g10 <- m [ m > 10 ]> stopifnot(18 == length(g10))> ## needs R >= 2.3.0 [Buglet in R(<= 2.2.1)'s possibleExtends()]:> stopifnot(10 == length(m[ m <= 10 ]))>>> ### Sparse Matrices -------------------------------------->> m <- 1:800> set.seed(101) ; m[sample(800, 600)] <- 0> m <- Matrix(m, nrow = 40)> mm <- as(m, "matrix")> dimnames(mm) <- NULL ## << workaround: as(<sparse>, "matrix") has NULL dimnames> str(mC <- as(m, "dgCMatrix"))Formal class 'dgCMatrix' [package "Matrix"] with 6 slots..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 .....@ p : int [1:21] 0 8 22 28 37 41 50 63 71 81 .....@ Dim : int [1:2] 40 20..@ Dimnames:List of 2.. ..$ : NULL.. ..$ : NULL..@ x : num [1:200] 3 7 12 22 25 30 38 39 42 45 .....@ factors : list()> str(mT <- as(m, "dgTMatrix"))Formal class 'dgTMatrix' [package "Matrix"] with 6 slots..@ i : int [1:200] 2 6 11 21 24 29 37 38 1 4 .....@ j : int [1:200] 0 0 0 0 0 0 0 0 1 1 .....@ Dim : int [1:2] 40 20..@ Dimnames:List of 2.. ..$ : NULL.. ..$ : NULL..@ x : num [1:200] 3 7 12 22 25 30 38 39 42 45 .....@ factors : list()> stopifnot(identical(mT, as(mC, "dgTMatrix")),+ identical(mC, as(mT, "dgCMatrix")))>> mC[,1][1] 0 0 3 0 0 0 7 0 0 0 0 12 0 0 0 0 0 0 0 0 0 22 0 0 25[26] 0 0 0 0 30 0 0 0 0 0 0 0 38 39 0> mC[1:2,]2 x 20 sparse Matrix of class "dgCMatrix"[1,] . . . 121 . . 241 . . . . 441 . . 561 . 641 . . .[2,] . 42 . . . 202 . . . . . . 482 522 . . . . 722 .> mC[7, drop = FALSE]1 x 20 sparse Matrix of class "dgCMatrix"[1,] 7 . . . . . . 287 . . 407 . 487 527 . . . . 727 .> assert.EQ.mat(mC[1:2,], mm[1:2,])> stopifnot(all.equal(mC[,3], mm[,3]))> assert.EQ.mat(mC[7, , drop=FALSE], mm[7, , drop=FALSE])>> stopifnot(dim(mC[numeric(0), ]) == c(0,20), # used to give warnings+ dim(mC[, integer(0)]) == c(40,0),+ identical(mC[, integer(0)], mC[, FALSE]),+ identical(mC[7, drop = FALSE],+ mC[7,, drop = FALSE]))> validObject(print(mT[,c(2,4)]))40 x 2 sparse Matrix of class "dgTMatrix"[1,] . 121[2,] 42 .[3,] . .[4,] . .[5,] 45 .[6,] . .[7,] . .[8,] . 128[9,] . 129[10,] 50 .[11,] . .[12,] 52 132[13,] . 133[14,] . .[15,] 55 .[16,] . .[17,] . .[18,] . 138[19,] . .[20,] . .[21,] . 141[22,] . 142[23,] 63 .[24,] . .[25,] 65 .[26,] . .[27,] 67 .[28,] 68 .[29,] . .[30,] . .[31,] 71 .[32,] 72 .[33,] . .[34,] 74 .[35,] . .[36,] 76 .[37,] . .[38,] . .[39,] . 159[40,] 80 .[1] TRUE> stopifnot(all.equal(mT[2,], mm[2,]),+ ## row or column indexing in combination with t() :+ identical(mT[2,], t(mT)[,2]),+ identical(mT[-2,], t(t(mT)[,-2])),+ identical(mT[c(2,5),], t(t(mT)[,c(2,5)]))+ )> assert.EQ.mat(mT[4,, drop = FALSE], mm[4,, drop = FALSE])> stopifnot(identical3(mm[,1], mC[,1], mT[,1]),+ identical3(mm[3,], mC[3,], mT[3,]),+ identical3(mT[2,3], mC[2,3], 0),+ identical(mT[], mT),+ ## TODO: identical4() with m[c(3,7), 2:4] - fail because of 'dimnames'+ ## TODO: identical3() with as(mC[c(3,7), 2:4],"matrix"),+ ## fails because of 'dimnames'+ identical(mm[c(3,7), 2:4], as(mT[c(3,7), 2:4],"matrix"))+ )>> x.x <- crossprod(mC)> stopifnot(class(x.x) == "dsCMatrix",+ class(x.x. <- round(x.x / 10000)) == "dsCMatrix")> head(x.x.) # Note the *non*-structural 0's printed as "0"6 x 20 sparse Matrix of class "dgCMatrix"[1,] 1 0 . 1 . 1 1 3 . 3 2 1 6 1 . 2 4 6 5 1[2,] 0 6 2 1 3 5 7 5 12 14 14 9 11 16 12 13 17 19 19 10[3,] . 2 6 . 4 2 5 3 8 12 5 16 9 11 23 . . 6 7 7[4,] 1 1 . 17 . 8 10 13 8 6 18 18 29 35 14 8 25 10 19 21[5,] . 3 4 . 14 4 10 . . 29 8 9 19 11 11 . . 26 26 16[6,] 1 5 2 8 4 42 5 19 14 9 8 10 42 56 50 27 29 32 64 16> ## FIXME (once we require 2.4.x or higher):> ## tail(x.x., -2) # the last two lines>> lx.x <- as(x.x, "lsCMatrix") # FALSE only for "structural" 0> if(FALSE) { ## FIXME: needs coercion "lsCMatrix" to "lgTMatrix"+ lx.x[1:10, 1:10]+ lx.x[1:3, ]+ }>> ## --- negative indices ----------> mc <- mC[1:5, 1:7]> mt <- mT[1:5, 1:7]> ## sub matrix> assert.EQ.mat(mC[1:2, 0:3], mm[1:2, 0:3]) # test 0-index> stopifnot(identical(mc[-(3:5), 0:2], mC[1:2, 0:2]),+ identical(mt[-(3:5), 0:2], mT[1:2, 0:2]),+ identical(mC[2:3, 4], mm[2:3, 4]))> assert.EQ.mat(mC[1:2,], mm[1:2,])> ## sub vector> stopifnot(identical4(mc[-(1:4), ], mC[5, 1:7],+ mt[-(1:4), ], mT[5, 1:7]))> stopifnot(identical4(mc[-(1:4), -(2:4)], mC[5, c(1,5:7)],+ mt[-(1:4), -(2:4)], mT[5, c(1,5:7)]))>> ## mixing of negative and positive must give error> assertError(mT[-1:1,])>> ## Sub *Assignment* ---- now works (partially):> mt0 <- mt> mt[1, 4] <- -99> mt[2:3, 1:6] <- 0> mt5 x 7 sparse Matrix of class "dgTMatrix"[1,] . . . -99 . . 241[2,] . . . . . . .[3,] . . . . . . 243[4,] . . . . . . .[5,] . 45 . . . . .> m2 <- mt+mt> m2[1,4] <- -200> m2[c(1,3), c(5:6,2)] <- 1:6> stopifnot(m2[1,4] == -200,+ as.vector(m2[c(1,3), c(5:6,2)]) == 1:6)> mt[,3] <- 30> mt[2:3,] <- 250> mt[1:5 %% 2 == 1, 3] <- 0> mt[3:1, 1:7 > 5] <- 0> mt5 x 7 sparse Matrix of class "dgTMatrix"[1,] . . . -99 . . .[2,] 250 250 250 250 250 . .[3,] 250 250 . 250 250 . .[4,] . . 30 . . . .[5,] . 45 . . . . .>> tt <- as(mt,"matrix")> ii <- c(0,2,5)> jj <- c(2:3,5)> tt[ii, jj] <- 1:6 # 0 is just "dropped"> mt[ii, jj] <- 1:6> assert.EQ.mat(mt, tt)>> mt[1:5, 2:6]5 x 5 sparse Matrix of class "dgTMatrix"[1,] . . -99 . .[2,] 1 3 250 5 .[3,] 250 . 250 250 .[4,] . 30 . . .[5,] 2 4 . 6 .> as((mt0 - mt)[1:5,], "dsparseMatrix")# [1,5] and lines 2:35 x 7 sparse Matrix of class "dgCMatrix"[1,] . . . 220 . . 241[2,] -250 41 -3 -250 -5 202 .[3,] -247 -250 . -250 -250 . 243[4,] . . -30 . . . .[5,] . 43 -4 . -6 . .>> mt[c(2,4), ] <- 0; stopifnot(as(mt[c(2,4), ],"matrix") == 0)> mt[2:3, 4:7] <- 33> validObject(mt)[1] TRUE> mt5 x 7 sparse Matrix of class "dgTMatrix"[1,] . . . -99 . . .[2,] . . . 33 33 33 33[3,] 250 250 . 33 33 33 33[4,] . . . . . . .[5,] . 2 4 . 6 . .>> mc[1,4] <- -99 ; stopifnot(mc[1,4] == -99)> mc[1,4] <- 00 ; stopifnot(mc[1,4] == 00)> mc[1,4] <- -99 ; stopifnot(mc[1,4] == -99)> mc[1:2,4:3] <- 4:1; stopifnot(as.matrix(mc[1:2,4:3]) == 4:1)>> mc[-1, 3] <- -2:1 # 0 should not be entered; 'value' recycled> mt[-1, 3] <- -2:1> stopifnot(mc@x != 0, mt@x != 0,+ mc[-1,3] == -2:1, mt[-1,3] == -2:1) ##--> BUG -- fixed>> ev <- 1:5 %% 2 == 0> mc[ev, 3] <- 0:1> if(FALSE)## FIXME+ stopifnot(mc[ev, 3] == 0:1) ##-> BUG {very peculiar; the 2nd time it works ...}> validObject(mc)[1] TRUE> mc # now shows a non-structural zeros5 x 7 sparse Matrix of class "dgCMatrix"[1,] . . 2 4 . . 241[2,] . 42 -2 3 . 202 .[3,] 3 . -1 . . . 243[4,] . . 1 . . . .[5,] . 45 1 . . . .> mc[ii, jj] <- 1:6> mc[c(2,5), c(3,5)] <- 3.2> validObject(mc)[1] TRUE> (m. <- mc)5 x 7 sparse Matrix of class "dgCMatrix"[1,] . . 2.0 4 . . 241[2,] . 1 3.2 3 3.2 202 .[3,] 3 . -1.0 . . . 243[4,] . . 1.0 . . . .[5,] . 2 3.2 . 3.2 . .> if(FALSE)## FIXME:+ mc[4,] <- 0 # -> error -- another Bug>> H <- Hilbert(9)> Hc <- as(round(H, 3), "dsCMatrix")# a sparse matrix with no 0 ...> (trH <- tril(Hc[1:5, 1:5]))5 x 5 sparse Matrix of class "dtCMatrix"[1,] 1.000 . . . .[2,] 0.500 0.333 . . .[3,] 0.333 0.250 0.200 . .[4,] 0.250 0.200 0.167 0.143 .[5,] 0.200 0.167 0.143 0.125 0.111> stopifnot(is(trH, "triangularMatrix"), trH@uplo == "L")>> i <- c(1:2, 4, 6:7); j <- c(2:4,6)> H[i,j] <- 0> (H. <- round(as(H, "sparseMatrix"), 3)[ , 2:7])9 x 6 sparse Matrix of class "dgCMatrix"[1,] . . . 0.200 . 0.143[2,] . . . 0.167 . 0.125[3,] 0.250 0.200 0.167 0.143 0.125 0.111[4,] . . . 0.125 . 0.100[5,] 0.167 0.143 0.125 0.111 0.100 0.091[6,] . . . 0.100 . 0.083[7,] . . . 0.091 . 0.077[8,] 0.111 0.100 0.091 0.083 0.077 0.071[9,] 0.100 0.091 0.083 0.077 0.071 0.067> Hc. <- Hc> Hc.[i,j] <- 0 ## now "works", but setting "non-structural" 0s> stopifnot(as.matrix(Hc.[i,j]) == 0)> Hc.[, 1:6]9 x 6 sparse Matrix of class "dgCMatrix"[1,] 1.000 0.000 0.000 0.000 0.200 0.000[2,] 0.500 0.000 0.000 0.000 0.167 0.000[3,] 0.333 0.250 0.200 0.167 0.143 0.125[4,] 0.250 0.000 0.000 0.000 0.125 0.000[5,] 0.200 0.167 0.143 0.125 0.111 0.100[6,] 0.167 0.000 0.000 0.000 0.100 0.000[7,] 0.143 0.000 0.000 0.000 0.091 0.000[8,] 0.125 0.111 0.100 0.091 0.083 0.077[9,] 0.111 0.100 0.091 0.083 0.077 0.071>> cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons''Time elapsed: 22.532 0.256 24.283 0 0>