Random Sparse Matrix — rsparsematrix • Matrix

Generate a random sparse matrix efficiently. The default has rounded gaussian non-zero entries, and rand.x = NULL generates random pattern matrices, i.e. inheriting from nsparseMatrix.

rsparsematrix(nrow, ncol, density, nnz = round(density * maxE),
              symmetric = FALSE,
              rand.x = function(n) signif(rnorm(n), 2), ...)

Arguments

nrow, ncol: number of rows and columns, i.e., the matrix dimension (dim).
density: optional number in \([0,1]\), the density is the proportion of non-zero entries among all matrix entries. If specified it determines the default for nnz, otherwise nnz needs to be specified.
nnz: number of non-zero entries, for a sparse matrix typically considerably smaller than nrow*ncol. Must be specified if density is not.
symmetric: logical indicating if result should be a matrix of class symmetricMatrix. Note that in the symmetric case, nnz denotes the number of non zero entries of the upper (or lower) part of the matrix, including the diagonal.
rand.x: NULL or the random number generator for the x slot, a function such that rand.x(n) generates a numeric vector of length n. Typical examples are rand.x = rnorm, or rand.x = runif; the default is nice for didactical purposes.
...: optionally further arguments passed to sparseMatrix(), notably repr.

Details

The algorithm first samples “encoded” \((i,j)\)s without replacement, via one dimensional indices, if not symmetric sample.int(nrow*ncol, nnz), then—if rand.x is not NULL—gets x <- rand.x(nnz) and calls sparseMatrix(i=i, j=j, x=x, ..). When rand.x=NULL, sparseMatrix(i=i, j=j, ..) will return a pattern matrix (i.e., inheriting from nsparseMatrix).

Value

a sparseMatrix, say M of dimension (nrow, ncol), i.e., with dim(M) == c(nrow, ncol), if symmetric is not true, with nzM <- nnzero(M) fulfilling nzM <= nnz and typically, nzM == nnz.

Author

Martin Maechler

Examples

set.seed(17)# to be reproducible
M <- rsparsematrix(8, 12, nnz = 30) # small example, not very sparse
M
#> 8 x 12 sparse Matrix of class "dgCMatrix"
#>                                                                          
#> [1,] -0.710  .     .     .     0.54  .     .     -0.62 .    .    -1.2 .  
#> [2,]  .      .     .     .     .     0.12 -0.720  .    .   -0.96  .   .  
#> [3,]  .      .     1.20 -0.83 -0.23  .     .      .    .    .     .   .  
#> [4,]  0.052  .    -0.45  .     .     .     .      1.80 .    .     .   .  
#> [5,] -0.780  .     0.25  .     2.40 -0.60  .      .    .    .     .   .  
#> [6,] -0.880  .     0.26 -3.60  .     .     0.074  .    .    .     .   1.7
#> [7,]  .      .     .     .     1.20  0.38  .      .    .   -0.33  .   .  
#> [8,] -0.990 -0.21  .     .     .     .    -1.400  0.32 1.9  .     .   .  
M1 <- rsparsematrix(1000, 20,  nnz = 123,  rand.x = runif)
summary(M1)
#> 1000 x 20 sparse Matrix of class "dgCMatrix", with 123 entries
#>       i  j           x
#> 1    30  1 0.121030300
#> 2   256  1 0.171285824
#> 3   471  1 0.658082934
#> 4   490  1 0.672053193
#> 5   515  1 0.563469009
#> 6   799  1 0.754721688
#> 7   914  1 0.214298567
#> 8   112  2 0.230193013
#> 9   146  2 0.520770952
#> 10  238  2 0.895551263
#> 11  460  2 0.747560311
#> 12  494  2 0.338654988
#> 13  669  2 0.633221050
#> 14  753  2 0.029495869
#> 15   26  3 0.857548872
#> 16  103  3 0.877821950
#> 17  123  3 0.373133136
#> 18  163  3 0.365224795
#> 19  395  3 0.244816811
#> 20  425  3 0.474136304
#> 21  697  3 0.463969983
#> 22  858  3 0.272504956
#> 23  875  3 0.840738221
#> 24  157  4 0.277547142
#> 25  317  4 0.394847750
#> 26  400  4 0.991649291
#> 27  510  4 0.362585672
#> 28  514  4 0.520276636
#> 29  634  4 0.808294520
#> 30  850  4 0.007048685
#> 31  934  4 0.536796092
#> 32   30  5 0.166392594
#> 33  263  5 0.306517981
#> 34  301  5 0.834864402
#> 35  884  5 0.772908976
#> 36  967  5 0.792207911
#> 37  268  6 0.697779252
#> 38  290  6 0.080128319
#> 39  434  6 0.307286057
#> 40  535  6 0.539794671
#> 41  759  6 0.651017611
#> 42  866  6 0.069991217
#> 43  167  7 0.720624894
#> 44  394  7 0.798488620
#> 45  502  7 0.837568737
#> 46  580  7 0.182004452
#> 47  705  7 0.289417504
#> 48  723  7 0.114946217
#> 49  216  8 0.780055751
#> 50  409  8 0.961610656
#> 51  631  8 0.188212461
#> 52  361  9 0.849970878
#> 53  411  9 0.110761594
#> 54  482  9 0.918999826
#> 55  564  9 0.106341774
#> 56  634  9 0.966994960
#> 57  817  9 0.080746639
#> 58  842  9 0.936882774
#> 59  940  9 0.723470934
#> 60  989  9 0.964498797
#> 61   47 10 0.359321831
#> 62  405 10 0.023504461
#> 63  507 10 0.112909265
#> 64  717 10 0.748889274
#> 65  734 10 0.642421125
#> 66  329 11 0.111511966
#> 67  438 11 0.498936020
#> 68  492 11 0.691674638
#> 69  570 11 0.246009281
#> 70  748 11 0.161394011
#> 71  753 11 0.872274340
#> 72  783 11 0.100716683
#> 73  977 11 0.462361495
#> 74  355 12 0.807811439
#> 75  645 12 0.652533316
#> 76  672 12 0.437335808
#> 77  697 12 0.308880390
#> 78  864 12 0.614445118
#> 79  949 12 0.469374262
#> 80  167 13 0.640432993
#> 81  318 13 0.598486273
#> 82  382 13 0.373182097
#> 83  400 13 0.973641726
#> 84  547 13 0.338046568
#> 85  601 13 0.117673368
#> 86  729 13 0.159017836
#> 87  996 13 0.350850822
#> 88  307 14 0.998227660
#> 89  385 14 0.323179815
#> 90  453 14 0.351955581
#> 91  526 14 0.706791886
#> 92  680 14 0.538912676
#> 93  916 14 0.176190115
#> 94  926 14 0.276029720
#> 95   11 15 0.118834062
#> 96  161 15 0.343942903
#> 97  211 15 0.850774512
#> 98  323 15 0.133445217
#> 99  478 15 0.788471288
#> 100 597 15 0.145946067
#> 101 608 15 0.197623800
#> 102 886 15 0.862795090
#> 103 275 16 0.714235556
#> 104 510 16 0.019910095
#> 105 527 16 0.639534228
#> 106 695 16 0.428969391
#> 107 765 16 0.905435610
#> 108 103 17 0.899292917
#> 109 736 17 0.150202421
#> 110 101 18 0.505359340
#> 111 513 18 0.784202072
#> 112 739 18 0.770542073
#> 113 941 18 0.728378107
#> 114 225 19 0.216264430
#> 115 558 19 0.311900054
#> 116 680 19 0.807296937
#> 117 948 19 0.314206922
#> 118 154 20 0.226125864
#> 119 341 20 0.942557140
#> 120 637 20 0.635889334
#> 121 650 20 0.914174104
#> 122 767 20 0.673403587
#> 123 952 20 0.392104291

## a random *symmetric* Matrix
(S9 <- rsparsematrix(9, 9, nnz = 10, symmetric=TRUE)) # dsCMatrix
#> 9 x 9 sparse Matrix of class "dsCMatrix"
#>                                                    
#>  [1,] -0.038  .    .    1.50 0.17  .     0.96 .   .
#>  [2,]  .      .    .    .    .     .    -0.48 .   .
#>  [3,]  .      .    .    .    .     .     .    1.3 .
#>  [4,]  1.500  .    .    .    .    -0.48  .    .   .
#>  [5,]  0.170  .    .    .    .     .     .    2.4 .
#>  [6,]  .      .    .   -0.48 .     .    -0.48 .   .
#>  [7,]  0.960 -0.48 .    .    .    -0.48 -0.33 .   .
#>  [8,]  .      .    1.3  .    2.40  .     .    .   .
#>  [9,]  .      .    .    .    .     .     .    .   .
nnzero(S9)# ~ 20: as 'nnz' only counts one "triangle"
#> [1] 18

## a random patter*n* aka boolean Matrix (no 'x' slot):
(n7 <- rsparsematrix(5, 12, nnz = 10, rand.x = NULL))
#> 5 x 12 sparse Matrix of class "ngCMatrix"
#>                             
#> [1,] . . . . . . . . . . . .
#> [2,] . . . . . . . . | . . .
#> [3,] . . | . . . | . . . . .
#> [4,] | . . . . . . | . | . .
#> [5,] . | . . . | . . . | . |

## a [T]riplet representation sparseMatrix:
T2 <- rsparsematrix(40, 12, nnz = 99, repr = "T")
head(T2)
#> 6 x 12 sparse Matrix of class "dgTMatrix"
#>                                                              
#> [1,] 1.8  .    -2.8  .    . -0.77 . -1.20 . .     .      0.27
#> [2,] .   -0.71  .    .    .  .    .  .    . 0.96  .     -0.32
#> [3,] .    .     .    .    .  .    .  .    . .    -0.051  .   
#> [4,] .    .     .    .    .  .    .  0.17 . .    -0.027  .   
#> [5,] .    .     .    .    .  .    .  .    . .    -1.400 -0.94
#> [6,] .    .     .   -0.26 .  .    .  .    . .     .      .