R version 2.6.2 Patched (2008-03-10 r44737)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> ## For both 'Extract' ("[") and 'Replace' ("[<-") Method testing
> 
> library(Matrix)
Loading required package: lattice

Attaching package: 'Matrix'


	The following object(s) are masked from package:stats :

	 xtabs 

> 
> source(system.file("test-tools.R", package = "Matrix"))# identical3() etc
> 
> options(verbose = TRUE)# to show message()s
> 
> ### 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]        # ditto; 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 columns
7 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 7th
1 x 4 Matrix of class "dgeMatrix"
     [,1] [,2] [,3] [,4]
[1,]    7   14   21   28
> m[integer(0),] #-> 0 x 4 Matrix
0 x 4 Matrix of class "dgeMatrix"
     [,1] [,2] [,3] [,4]
> m[2:4, numeric(0)] #-> 3 x 0 Matrix
3 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)
keeping Tsparse matrix *symmetric* in sub-assignment
> 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 lines
17 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.mat(x.x) # as.mat() *drops* (NULL,NULL) dimnames
> 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 ; A
4 x 3 sparse Matrix of class "dgCMatrix"
          
[1,] . 1 .
[2,] . 1 .
[3,] . . .
[4,] . . .
> B <- A;              B[c(1,2,1), 2] <- 1:3; B; B. <- B
4 x 3 sparse Matrix of class "dgCMatrix"
          
[1,] . 3 .
[2,] . 2 .
[3,] . . .
[4,] . . .
> B.[3,] <- rbind(4:2)
> diag(B.) <- 10 * diag(B.)
> C <- B.; C[,2] <- C[,2];  C[1,] <- C[1,]; C[2:3,2:1] <- C[2:3,2:1]
> 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})),
+ 	  identical(C, drop0(B.)))
> 
> 
> ## 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#sparseMatrix
    dMatrix#dMatrix
 
2: Ambiguous method selection for "==", target "dgTMatrix#numeric" (the first of the signatures shown will be used)
    dMatrix#numeric
    sparseMatrix#numeric
 
> 
> m0 <- Diagonal(5)
> stopifnot(identical(m0[2,], m0[,2]),
+ 	  identical(m0[,1], c(1,0,0,0,0)))
> ### Diagonal -- Sparse:
> (m1 <- as(m0, "sparseMatrix"))  # dtTMatrix
5 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,] . . . . 1
> 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
> 
> (uTr <- new("dtTMatrix", Dim = c(3L,3L), diag="U"))
3 x 3 sparse Matrix of class "dtTMatrix"
          
[1,] 1 . .
[2,] . 1 .
[3,] . . 1
> uTr[1,] <- 0
> assert.EQ.mat(uTr, cbind(0, rbind(0,diag(2))))
> 
> 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 ;M
5 x 5 diagonal matrix of class "ddiMatrix"
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    .    .    .    .
[2,]    .    1    .    .    .
[3,]    .    .    0    .    .
[4,]    .    .    .    1    .
[5,]    .    .    .    .    1
> 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 ;M
5 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 ;M
5 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)))
> 
> 
> ## "Vector indices" -------------------
> D <- Diagonal(6)
> M <- as(D,"dgeMatrix")
> m <- as(D,"matrix")
> s <- as(D,"TsparseMatrix")
> S <- as(s,"CsparseMatrix")
> i <- c(3,1,6); v <- c(10,15,20)
> ## (logical,value) which both are recycled:
> L <- c(TRUE, rep(FALSE,8)) ; z <- c(50,99)
> 
> ## vector subassignment, both with integer & logical
> ## these now work correctly {though not very efficiently; hence warnings}
> m[i] <- v # the role model: only first column is affected
> M[i] <- v; assert.EQ.mat(M,m) # dge
> D[i] <- v; assert.EQ.mat(D,m) # ddi -> dtT -> dgT
diagnosing replTmat(x,i,j,v): nargs()= 3; missing(i,j)= (0,1).
'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix
> s[i] <- v; assert.EQ.mat(s,m) # dtT -> dgT
diagnosing replTmat(x,i,j,v): nargs()= 3; missing(i,j)= (0,1).
'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix
> S[i] <- v; assert.EQ.mat(S,m); S # dtC -> dtT -> dgT -> dgC
diagnosing replTmat(x,i,j,v): nargs()= 3; missing(i,j)= (0,1).
'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix
6 x 6 sparse Matrix of class "dgCMatrix"
                 
[1,] 15 . . . . .
[2,]  . 1 . . . .
[3,] 10 . 1 . . .
[4,]  . . . 1 . .
[5,]  . . . . 1 .
[6,] 20 . . . . 1
> ## logical
> m[L] <- z
> M[L] <- z; assert.EQ.mat(M,m)
> D[L] <- z; assert.EQ.mat(D,m)
diagnosing replTmat(x,i,j,v): nargs()= 3; missing(i,j)= (0,1).
> s[L] <- z; assert.EQ.mat(s,m)
diagnosing replTmat(x,i,j,v): nargs()= 3; missing(i,j)= (0,1).
> S[L] <- z; assert.EQ.mat(S,m) ; S
diagnosing replTmat(x,i,j,v): nargs()= 3; missing(i,j)= (0,1).
6 x 6 sparse Matrix of class "dgCMatrix"
                    
[1,] 50  . . 50  . .
[2,]  .  1 .  .  . .
[3,] 10  . 1  .  . .
[4,]  . 99 .  1 99 .
[5,]  .  . .  .  1 .
[6,] 20  . .  .  . 1
> 
> ## indexing [i]  vs  [i,] --- now ok
> stopifnot(identical4(m[i], M[i], D[i], s[i]), identical(s[i],S[i]))
> stopifnot(identical4(m[L], M[L], D[L], s[L]), identical(s[L],S[L]))
> assert.EQ.mat(D[i,], m[i,])
> assert.EQ.mat(M[i,], m[i,])
> assert.EQ.mat(s[i,], m[i,])
> assert.EQ.mat(S[i,], m[i,])
> 
> assert.EQ.mat(D[,i], m[,i])
> assert.EQ.mat(M[,i], m[,i])
> assert.EQ.mat(s[,i], m[,i])
> assert.EQ.mat(S[,i], m[,i])
> 
> 
> ## --- 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
> mt
5 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
> mt
5 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 2:3
5 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#sparseMatrix
    dMatrix#dMatrix
 
> 
> mt[c(2,4), ] <- 0; stopifnot(as(mt[c(2,4), ],"matrix") == 0)
> mt[2:3, 4:7] <- 33
> validObject(mt)
[1] TRUE
> mt
5 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 zeros
5 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
> mc
5 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 .   .
> 
> S <- as(Diagonal(5),"sparseMatrix")
> 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",
+           is(S, "triangularMatrix"))
> 
> ## triangular assignment
> ## the slick (but inefficient in case of sparse!) way to assign sub-diagonals:
> ## equivalent to tmp <- `diag<-`(S[,-1], -2:1); S[,-1] <- tmp
> ## which dispatches to (x="TsparseMatrix", i="missing",j="index", value="replValue")
> diag(S[,-1]) <- -2:1 # used to give a wrong warning
> S <- as(S,"triangularMatrix")
> assert.EQ.mat(S, local({s <- diag(5); diag(s[,-1]) <- -2:1; s}))
> 
> trH[c(1:2,4), c(2:3,5)] <- 0 # gave an *error* upto Jan.2008
> trH[ lower.tri(trH) ] <- 0   # ditto, because of callNextMethod()
.TM.repl.i.2col(): drop 'matrix' case ...
diagnosing replTmat(x,i,j,v): nargs()= 3; missing(i,j)= (0,1).
'sub-optimal sparse 'x[i] <- v' assignment: Coercing class dtTMatrix to dgTMatrix
> 
> m <- Matrix(0+1:28, nrow = 4)
> m[-3,c(2,4:5,7)] <- m[ 3, 1:4] <- m[1:3, 6] <- 0
> mT <- as(m, "dgTMatrix")
> stopifnot(identical(mT[lower.tri(mT)],
+                     m [lower.tri(m) ]))
<sparse>[ <logic> ] : .M.sub.i.logical() maybe inefficient
> lM <- upper.tri(mT, diag=TRUE)
> mT[lM] <- 0
.TM.repl.i.2col(): drop 'matrix' case ...
diagnosing replTmat(x,i,j,v): nargs()= 3; missing(i,j)= (0,1).
>  m[lM] <- 0
> assert.EQ.mat(mT, as(m,"matrix"))
> mT[lM] <- -1:0
.TM.repl.i.2col(): drop 'matrix' case ...
diagnosing replTmat(x,i,j,v): nargs()= 3; missing(i,j)= (0,1).
>  m[lM] <- -1:0
> assert.EQ.mat(mT, as(m,"matrix"))
> (mT <- drop0(mT))
4 x 7 sparse Matrix of class "dgCMatrix"
                         
[1,] -1  .  . -1 -1 -1 -1
[2,]  2 -1 -1  .  .  .  .
[3,]  .  .  . -1 -1 -1 -1
[4,]  4  . 12  .  .  .  .
> 
> 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 .     .     .     0.200 .    
 [2,] 0.500 .     .     .     0.167 .    
 [3,] 0.333 0.250 0.200 0.167 0.143 0.125
 [4,] 0.250 .     .     .     0.125 .    
 [5,] 0.200 0.167 0.143 0.125 0.111 0.100
 [6,] 0.167 .     .     .     0.100 .    
 [7,] 0.143 .     .     .     0.091 .    
 [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] TRUE
Warning message:
Ambiguous method selection for "kronecker", target "dtTMatrix#dsTMatrix" (the first of the signatures shown will be used)
    TsparseMatrix#TsparseMatrix
    dsparseMatrix#dsparseMatrix
 
> 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)
keeping Tsparse matrix *symmetric* in sub-assignment
> 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
keeping Tsparse matrix *symmetric* in sub-assignment
> 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#numeric
    sparseMatrix#numeric
 
> 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#dMatrix
    numeric#sparseMatrix
 
> (ge <- m. >= mc) # contains "=" -> result is dense
5 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., drop0(ne1)))
> 
> (M3 <- Matrix(upper.tri(matrix(, 3, 3)))) # ltC; indexing used to fail
3 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")
+ 	  )
> 
> M <- Diagonal(4); M[1,2] <- 2
> M. <- as(M, "CsparseMatrix")
> (R <- as(M., "RsparseMatrix"))
4 x 4 sparse Matrix of class "dtRMatrix"
            
[1,] 1 2 . .
[2,] . 1 . .
[3,] . . 1 .
[4,] . . . 1
> stopifnot(is(M, "triangularMatrix"),
+           is(M.,"triangularMatrix"),
+           is(R, "triangularMatrix"))
> stopifnot(dim(M[2:3, FALSE]) == c(2,0),
+           dim(R[2:3, FALSE]) == c(2,0),
+           identical(M [2:3,TRUE], M [2:3,]),
+           identical(M.[2:3,TRUE], M.[2:3,]),
+           identical(R [2:3,TRUE], R [2:3,]),
+           dim(R[FALSE, FALSE]) == c(0,0))
> 
> cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons''
Time elapsed:  16.321 0.164 18.032 0 0 
>