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R version 2.5.1 beta (2007-06-13 r41947)Copyright (C) 2007 The R Foundation for Statistical ComputingISBN 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 +0, nrow = 7)> validObject(m)[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>> m. <- as.matrix(m)>> ## m[ cbind(i,j) ] indexing:> ij <- cbind(1:6, 2:3)> stopifnot(identical(m[ij], m.[ij]))>> ## testing operations on logical Matrices rather more than indexing:> g10 <- m [ m > 10 ]> stopifnot(18 == length(g10))> stopifnot(10 == length(m[ m <= 10 ]))> sel <- (20 < m) & (m < 150)> sel.<- (20 < m.)& (m.< 150)> nsel <-(20 >= m) | (m >= 150)> (ssel <- as(sel, "sparseMatrix"))7 x 4 sparse Matrix of class "lgCMatrix"[1,] . . . .[2,] . . | .[3,] . . . |[4,] . . . |[5,] . . . |[6,] . . . |[7,] . . | |> stopifnot(is(sel, "lMatrix"), is(ssel, "lsparseMatrix"),+ identical3(as.mat(sel.), as.mat(sel), as.mat(ssel)),+ identical3(!sel, !ssel, nsel), # !<sparse> is typically dense+ identical3(m[ sel], m[ ssel], as.matrix(m)[as.matrix( ssel)]),+ identical3(m[!sel], m[!ssel], as.matrix(m)[as.matrix(!ssel)])+ )>> ## more 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,])>> ## *repeated* (aka 'duplicated') indices - did not work at all ...> i <- rep(8:10,2)> j <- c(2:4, 4:3)> assert.EQ.mat(mC[i,], mm[i,])> assert.EQ.mat(mC[,j], mm[,j])> assert.EQ.mat(mC[i, 2:1], mm[i, 2:1])> assert.EQ.mat(mC[c(4,1,2:1), j], mm[c(4,1,2:1), j])> assert.EQ.mat(mC[i,j], mm[i,j])> set.seed(7)> for(n in 1:50) {+ i <- sample(sample(nrow(mC), 7), 20, replace = TRUE)+ j <- sample(sample(ncol(mC), 6), 17, replace = TRUE)+ assert.EQ.mat(mC[i,j], mm[i,j])+ }>> ##---- Symmetric indexing of symmetric Matrix ----------> m. <- mC; m.[, c(2, 7:12)] <- 0> validObject(S <- crossprod(add.simpleDimnames(m.) %% 100))[1] TRUE> ss <- as(S, "matrix")> T <- as(S, "TsparseMatrix")> ## non-repeated indices:> i <- c(7:5, 2:4);assert.EQ.mat(T[i,i], ss[i,i])> N <- nrow(T)> set.seed(11)> for(n in 1:50) {+ i <- sample(N, max(2, sample(N,1)), replace = FALSE)+ validObject(Tii <- T[i,i])+ stopifnot(is(Tii, "dsTMatrix"), # remained symmetric Tsparse+ identical(t(Tii), t(T)[i,i]))+ assert.EQ.mat(Tii, ss[i,i])+ }>> ## repeated ones ``the challenge'' (to do smartly):> j <- c(4, 4, 9, 12, 9, 4, 17, 3, 18, 4, 12, 18, 4, 9)> assert.EQ.mat(T[j,j], ss[j,j])> ## and another two sets (a, A) & (a., A.) :> a <- matrix(0, 6,6)> a[upper.tri(a)] <- (utr <- c(2, 0,-1, 0,0,5, 7,0,0,0, 0,0,-2,0,8))> ta <- t(a); ta[upper.tri(a)] <- utr; a <- t(ta)> diag(a) <- c(0,3,0,4,6,0)> A <- as(Matrix(a), "TsparseMatrix")> A. <- A> diag(A.) <- 10 * (1:6)> a. <- as(A., "matrix")> ## More testing {this was not working for a long time..}> set.seed(1)> for(n in 1:100) {+ i <- sample(1:nrow(A), 3+2*rpois(1, lam=3), replace=TRUE)+ Aii <- A[i,i]+ A.ii <- A.[i,i]+ stopifnot(class(Aii) == class(A),+ class(A.ii) == class(A.))+ assert.EQ.mat(Aii , a [i,i])+ assert.EQ.mat(A.ii, a.[i,i])+ assert.EQ.mat(T[i,i], ss[i,i])+ }>>> stopifnot(all.equal(mC[,3], mm[,3]),+ identical(mC[ij], mm[ij]))> 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)]))[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),+ identical4( mm[c(3,7), 2:4], as.mat( m[c(3,7), 2:4]),+ as.mat(mT[c(3,7), 2:4]), as.mat(mC[c(3,7), 2:4]))+ )>> x.x <- crossprod(mC)> stopifnot(class(x.x) == "dsCMatrix",+ class(x.x. <- round(x.x / 10000)) == "dsCMatrix",+ identical(x.x[cbind(2:6, 2:6)],+ diag(x.x [2:6, 2:6])))> 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> tail(x.x., -3) # all but the first three lines17 x 20 sparse Matrix of class "dgCMatrix"[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[7,] 1 7 5 10 10 5 87 14 9 31 77 47 79 43 28 17 67 110 36 121[8,] 3 5 3 13 . 19 14 70 10 24 37 13 59 62 34 19 58 21 64 44[9,] . 12 8 8 . 14 9 10 116 41 58 33 33 72 78 43 69 72 75 25[10,] 3 14 12 6 29 9 31 24 41 167 69 56 99 44 70 24 105 82 85 32[11,] 2 14 5 18 8 8 77 37 58 69 267 80 86 139 49 105 194 119 122 129[12,] 1 9 16 18 9 10 47 13 33 56 80 194 70 77 81 . 90 32 . 106[13,] 6 11 9 29 19 42 79 59 33 99 86 70 324 157 55 . 69 142 144 155[14,] 1 16 11 35 11 56 43 62 72 44 139 77 157 375 123 102 145 39 196 81[15,] . 12 23 14 11 50 28 34 78 70 49 81 55 123 368 71 112 41 41 86[16,] 2 13 . 8 . 27 17 19 43 24 105 . . 102 71 233 124 44 139 .[17,] 4 17 . 25 . 29 67 58 69 105 194 90 69 145 112 124 523 141 245 100[18,] 6 19 6 10 26 32 110 21 72 82 119 32 142 39 41 44 141 497 104 111[19,] 5 19 7 19 26 64 36 64 75 85 122 . 144 196 41 139 245 104 542 55[20,] 1 10 7 21 16 16 121 44 25 32 129 106 155 81 86 . 100 111 55 541>> lx.x <- as(x.x, "lsCMatrix") # FALSE only for "structural" 0> (l10 <- lx.x[1:10, 1:10])# "lsC"10 x 10 sparse Matrix of class "lsCMatrix"[1,] | | . | . | | | . |[2,] | | | | | | | | | |[3,] . | | . | | | | | |[4,] | | . | . | | | | |[5,] . | | . | | | . . |[6,] | | | | | | | | | |[7,] | | | | | | | | | |[8,] | | | | . | | | | |[9,] . | | | . | | | | |[10,] | | | | | | | | | |> (l3 <- lx.x[1:3, ])3 x 20 sparse Matrix of class "lgCMatrix"[1,] | | . | . | | | . | | | | | . | | | | |[2,] | | | | | | | | | | | | | | | | | | | |[3,] . | | . | | | | | | | | | | | . . | | |> m.x <- as(x.x, "matrix")> stopifnot(class(l10) == "lsCMatrix", # symmetric indexing -> symmetric !+ identical(as.mat(lx.x), m.x != 0),+ identical(as.logical(lx.x), as.logical(m.x)),+ identical(as.mat(l10), m.x[1:10, 1:10] != 0),+ identical(as.mat(l3 ), m.x[1:3, ] != 0)+ )>> ##-- Sub*assignment* with repeated / duplicated index:> A <- Matrix(0,4,3) ; A[c(1,2,1), 2] <- 1 ; A4 x 3 sparse Matrix of class "dgCMatrix"[1,] . 1 .[2,] . 1 .[3,] . . .[4,] . . .> B <- A; B[c(1,2,1), 2] <- 1:3; B4 x 3 sparse Matrix of class "dgCMatrix"[1,] . 3 .[2,] . 2 .[3,] . . .[4,] . . .> stopifnot(identical(unname(as.matrix(A)),+ local({a <- matrix(0,4,3); a[c(1,2,1), 2] <- 1 ; a})),+ identical(unname(as.matrix(B)),+ local({a <- matrix(0,4,3); a[c(1,2,1), 2] <- 1:3; a})))>>> ## used to fail> n <- 5 ## or much larger> sm <- new("dsTMatrix", i=as.integer(1),j=as.integer(1),+ Dim=as.integer(c(n,n)), x = 1)> (cm <- as(sm, "CsparseMatrix"))5 x 5 sparse Matrix of class "dsCMatrix"[1,] . . . . .[2,] . 1 . . .[3,] . . . . .[4,] . . . . .[5,] . . . . .> sm[2,][1] 0 1 0 0 0> stopifnot(sm[2,] == c(0:1, rep.int(0,ncol(sm)-2)),+ sm[2,] == cm[2,],+ sm[,3] == sm[3,],+ all(sm[,-(1:3)] == t(sm[-(1:3),])), # all(<lge.>)+ all(sm[,-(1:3)] == 0)+ )Warning messages:1: Ambiguous method selection for "==", target "dgTMatrix#dgTMatrix" (the first of the signatures shown will be used)sparseMatrix#sparseMatrixdMatrix#dMatrixin: .findInheritedMethods(classes, fdef, mtable)2: Ambiguous method selection for "==", target "dgTMatrix#numeric" (the first of the signatures shown will be used)dMatrix#numericsparseMatrix#numericin: .findInheritedMethods(classes, fdef, mtable)>> ### Diagonal -- Sparse:> m0 <- Diagonal(5)> (m1 <- as(m0, "sparseMatrix")) # dtTMatrix5 x 5 sparse Matrix of class "dtTMatrix"[1,] 1 . . . .[2,] . 1 . . .[3,] . . 1 . .[4,] . . . 1 .[5,] . . . . 1> (m2 <- as(m0, "CsparseMatrix")) # dtCMatrix (with an irrelevant warning)5 x 5 sparse Matrix of class "dtCMatrix"[1,] 1 . . . .[2,] . 1 . . .[3,] . . 1 . .[4,] . . . 1 .[5,] . . . . 1Warning message:Ambiguous method selection for "coerce", target "ddiMatrix#CsparseMatrix" (the first of the signatures shown will be used)diagonalMatrix#CsparseMatrixddenseMatrix#CsparseMatrixin: .findInheritedMethods(signature, fdef, mtable = allmethods, table = mlist,> m1g <- as(m1, "generalMatrix")> stopifnot(is(m1g, "dgTMatrix"))> assert.EQ.mat(m2[1:3,], diag(5)[1:3,])> assert.EQ.mat(m2[,c(4,1)], diag(5)[,c(4,1)])> stopifnot(identical(m2[1:3,], as(m1[1:3,], "CsparseMatrix")),+ identical(Matrix:::uniqTsparse(m1[, c(4,2)]),+ Matrix:::uniqTsparse(as(m2[, c(4,2)], "TsparseMatrix")))+ )## failed in 0.9975-11>> M <- m0; M[1,] <- 0> stopifnot(identical(M, Diagonal(x=c(0, rep(1,4)))))> M <- m0; M[,3] <- 3 ; M ; stopifnot(is(M, "sparseMatrix"), M[,3] == 3)5 x 5 sparse Matrix of class "dgTMatrix"[1,] 1 . 3 . .[2,] . 1 3 . .[3,] . . 3 . .[4,] . . 3 1 .[5,] . . 3 . 1> validObject(M)[1] TRUE> M <- m0; M[1:3, 3] <- 0 ;M5 x 5 diagonal matrix of class "ddiMatrix"[,1] [,2] [,3] [,4] [,5][1,] 1 . . . .[2,] . 1 . . .[3,] . . 0 . .[4,] . . . 1 .[5,] . . . . 1Warning message:Ambiguous method selection for "diag", target "ddiMatrix" (the first of the signatures shown will be used)diagonalMatrixddenseMatrixin: .findInheritedMethods(classes, fdef, mtable)> T <- m0; T[1:3, 3] <- 10> stopifnot(identical(M, Diagonal(x=c(1,1, 0, 1,1))),+ is(T, "triangularMatrix"), identical(T[,3], c(10,10,10,0,0)))>> M <- m1; M[1,] <- 0 ; M ; assert.EQ.mat(M, diag(c(0,rep(1,4))), tol=0)5 x 5 sparse Matrix of class "dtTMatrix"[1,] . . . . .[2,] . 1 . . .[3,] . . 1 . .[4,] . . . 1 .[5,] . . . . 1> M <- m1; M[,3] <- 3 ; stopifnot(is(M,"sparseMatrix"), M[,3] == 3)> validObject(M)[1] TRUE> M <- m1; M[1:3, 3] <- 0 ;M5 x 5 sparse Matrix of class "dtTMatrix"[1,] 1 . . . .[2,] . 1 . . .[3,] . . . . .[4,] . . . 1 .[5,] . . . . 1> assert.EQ.mat(M, diag(c(1,1, 0, 1,1)), tol=0)> T <- m1; T[1:3, 3] <- 10; validObject(T)[1] TRUE> stopifnot(is(T, "dtTMatrix"), identical(T[,3], c(10,10,10,0,0)))>> M <- m2; M[1,] <- 0 ; M ; assert.EQ.mat(M, diag(c(0,rep(1,4))), tol=0)5 x 5 sparse Matrix of class "dtCMatrix"[1,] . . . . .[2,] . 1 . . .[3,] . . 1 . .[4,] . . . 1 .[5,] . . . . 1> M <- m2; M[,3] <- 3 ; stopifnot(is(M,"sparseMatrix"), M[,3] == 3)> validObject(M)[1] TRUE> M <- m2; M[1:3, 3] <- 0 ;M5 x 5 sparse Matrix of class "dtCMatrix"[1,] 1 . . . .[2,] . 1 . . .[3,] . . . . .[4,] . . . 1 .[5,] . . . . 1> assert.EQ.mat(M, diag(c(1,1, 0, 1,1)), tol=0)> T <- m2; T[1:3, 3] <- 10; validObject(T)[1] TRUE> stopifnot(is(T, "dtCMatrix"), identical(T[,3], c(10,10,10,0,0)))>>> ## --- 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 . .Warning message:Ambiguous method selection for "-", target "dgTMatrix#dgTMatrix" (the first of the signatures shown will be used)sparseMatrix#sparseMatrixdMatrix#dMatrixin: .findInheritedMethods(classes, fdef, mtable)>> 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) ## failed earlier>> mc0 <- mc> mt0 <- as(mc0, "TsparseMatrix")> m0 <- as(mc0, "matrix")> set.seed(1)> for(i in 1:50) {+ mc <- mc0; mt <- mt0 ; m <- m0+ ev <- 1:5 %% 2 == round(runif(1))# 0 or 1+ j <- sample(ncol(mc), 1 + round(runif(1)))+ nv <- rpois(sum(ev) * length(j), lambda = 1)+ mc[ev, j] <- nv+ m[ev, j] <- nv+ mt[ev, j] <- nv+ if(i %% 10 == 1) print(mc[ev,j, drop = FALSE])+ stopifnot(as.vector(mc[ev, j]) == nv, ## failed earlier...+ as.vector(mt[ev, j]) == nv)+ validObject(mc) ; assert.EQ.mat(mc, m)+ validObject(mt) ; assert.EQ.mat(mt, m)+ }[1,] 2[2,] .[1,] 2[2,] 1[1,] 1 .[2,] . .[3,] 1 .[1,] 1[2,] 1[3,] 1[1,] .[2,] 3[3,] 1>> mc # no longer has non-structural zeros5 x 7 sparse Matrix of class "dgCMatrix"[1,] . . 2 4 . . 241[2,] 1 42 -2 3 . 1 .[3,] 3 . -1 . . . 243[4,] 1 . . . . 1 .[5,] . 45 1 . . . .> mc[ii, jj] <- 1:6> mc[c(2,5), c(3,5)] <- 3.2> validObject(mc)[1] TRUE> m. <- mc> mc[4,] <- 0> mc5 x 7 sparse Matrix of class "dgCMatrix"[1,] . . 2.0 4 . . 241[2,] 1 1 3.2 3 3.2 1 .[3,] 3 . -1.0 . . . 243[4,] . . . . . . .[5,] . 2 3.2 . 3.2 . .>> 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>> ## an example that failed for a long time> sy3 <- new("dsyMatrix", Dim = as.integer(c(2, 2)), x = c(14, -1, 2, -7))> validObject(dm <- kronecker(Diagonal(2), sy3))# now sparse with new kronecker[1] TRUEWarning message:Ambiguous method selection for "kronecker", target "dtTMatrix#dsTMatrix" (the first of the signatures shown will be used)TsparseMatrix#TsparseMatrixdsparseMatrix#dsparseMatrixin: .findInheritedMethods(classes, fdef, mtable)> dm <- Matrix(as.matrix(dm))# -> "dsyMatrix"> (s2 <- as(dm, "sparseMatrix"))4 x 4 sparse Matrix of class "dsCMatrix"[1,] 14 2 . .[2,] 2 -7 . .[3,] . . 14 2[4,] . . 2 -7> validObject(st <- as(s2, "TsparseMatrix"))[1] TRUE> stopifnot(is(s2, "symmetricMatrix"),+ is(st, "symmetricMatrix"))> validObject(s.32 <- st[1:3,1:2]) ## 3 x 2 - and *not* dsTMatrix[1] TRUE> validObject(s2.32 <- s2[1:3,1:2])[1] TRUE> I <- c(1,4:3)> stopifnot(is(s2.32, "generalMatrix"),+ is(s.32, "generalMatrix"),+ identical(as.mat(s.32), as.mat(s2.32)),+ identical3(dm[1:3,-1], asD(s2[1:3,-1]), asD(st[1:3,-1])),+ identical4(2, dm[4,3], s2[4,3], st[4,3]),+ identical3(diag(dm), diag(s2), diag(st)),+ is((cI <- s2[I,I]), "dsCMatrix"),+ is((tI <- st[I,I]), "dsTMatrix"),+ identical4(as.mat(dm)[I,I], as.mat(dm[I,I]), as.mat(tI), as.mat(cI))+ )>> ## now sub-assign and check for consistency> ## symmetric subassign should keep symmetry> st[I,I] <- 0; validObject(st); stopifnot(is(st,"symmetricMatrix"))[1] TRUE> s2[I,I] <- 0; validObject(s2); stopifnot(is(s2,"symmetricMatrix"))[1] TRUE> ##> m <- as.mat(st)> m[2:1,2:1] <- 4:1> st[2:1,2:1] <- 4:1> s2[2:1,2:1] <- 4:1> stopifnot(identical(m, as.mat(st)),+ 1:4 == as.vector(s2[1:2,1:2]),+ identical(m, as.mat(s2)))>> ## now a slightly different situation for 's2' (had bug)> s2 <- as(dm, "sparseMatrix")> s2[I,I] <- 0; diag(s2)[2:3] <- -(1:2)> stopifnot(is(s2,"symmetricMatrix"), diag(s2) == c(0:-2,0))> t2 <- as(s2, "TsparseMatrix")> m <- as.mat(s2)> s2[2:1,2:1] <- 4:1> t2[2:1,2:1] <- 4:1> m[2:1,2:1] <- 4:1> assert.EQ.mat(t2, m)> assert.EQ.mat(s2, m)> ## and the same (for a different s2 !)> s2[2:1,2:1] <- 4:1> t2[2:1,2:1] <- 4:1> assert.EQ.mat(t2, m)# ok> assert.EQ.mat(s2, m)# failed in 0.9975-8>>> ## m[cbind(i,j)] <- value:> m.[ cbind(3:5, 1:3) ] <- 1:3> stopifnot(m.[3,1] == 1, m.[4,2] == 2)> x.x[ cbind(2:6, 2:6)] <- 12:16> validObject(x.x)[1] TRUE> stopifnot(class(x.x) == "dsCMatrix",+ 12:16 == as.mat(x.x)[cbind(2:6, 2:6)])> (ne1 <- (mc - m.) != 0)5 x 7 sparse Matrix of class "lgCMatrix"[1,] . . . . . . .[2,] . . . . . . .[3,] | . . . . . .[4,] | | . . . | .[5,] . . | . . . .Warning message:Ambiguous method selection for "!=", target "dgCMatrix#numeric" (the first of the signatures shown will be used)dMatrix#numericsparseMatrix#numericin: .findInheritedMethods(classes, fdef, mtable)> stopifnot(identical(ne1, 0 != abs(mc - m.)))Warning message:Ambiguous method selection for "!=", target "numeric#dgCMatrix" (the first of the signatures shown will be used)numeric#dMatrixnumeric#sparseMatrixin: .findInheritedMethods(classes, fdef, mtable)> (ge <- m. >= mc) # contains "=" -> result is dense5 x 7 Matrix of class "lgeMatrix"[,1] [,2] [,3] [,4] [,5] [,6] [,7][1,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE[2,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE[3,] FALSE TRUE TRUE TRUE TRUE TRUE TRUE[4,] TRUE TRUE TRUE TRUE TRUE TRUE TRUE[5,] TRUE TRUE FALSE TRUE TRUE TRUE TRUE> ne. <- mc != m. # was wrong (+ warning)> stopifnot(identical(!(m. < mc), m. >= mc),+ identical(m. < mc, as(!ge, "sparseMatrix")),+ identical(ne., Matrix:::drop0(ne1)))>> (M3 <- Matrix(upper.tri(matrix(, 3, 3)))) # ltC; indexing used to fail3 x 3 sparse Matrix of class "ltCMatrix"[1,] . | |[2,] . . |[3,] . . .> T3 <- as(M3, "TsparseMatrix")> stopifnot(identical(drop(M3), M3),+ identical4(drop(M3[,2, drop = FALSE]), M3[,2, drop = TRUE],+ drop(T3[,2, drop = FALSE]), T3[,2, drop = TRUE]),+ is(T3, "triangularMatrix"),+ !is(T3[,2, drop=FALSE], "triangularMatrix")+ )>> cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons''Time elapsed: 10.299 0.184 11.314 0 0>