SparseMatrix multiplication and cross-product
SparseMatrix-mult.RdLike ordinary matrices in base R, SparseMatrix derivatives can
be multiplied with the %*% operator. They also support
crossprod() and tcrossprod().
Value
The %*%, crossprod() and tcrossprod() methods
for SparseMatrix objects always return an ordinary matrix
of type() "double".
Note
Matrix multiplication and cross-product of SparseMatrix
derivatives are multithreaded.
See set_SparseArray_nthread for how to control the number
of threads.
See also
SparseMatrix objects.
S4Arrays::typein the S4Arrays package to get the type of the elements of an array-like object.Ordinary matrix objects in base R.
Examples
m1 <- matrix(0L, nrow=15, ncol=6)
m1[c(2, 6, 12:17, 22:33, 55, 59:62, 90)] <- 101:126
svt1 <- as(m1, "SVT_SparseMatrix")
set.seed(333)
svt2 <- poissonSparseMatrix(nrow=6, ncol=7, density=0.2)
svt1 %*% svt2
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 118 0 0 0 0 0 0
#> [2,] 119 0 101 0 0 0 101
#> [3,] 120 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0 0
#> [5,] 0 0 0 0 0 0 0
#> [6,] 0 0 102 0 0 0 102
#> [7,] 0 0 0 0 0 0 0
#> [8,] 0 0 0 0 0 0 0
#> [9,] 0 0 0 0 0 0 0
#> [10,] 0 0 121 0 0 0 0
#> [11,] 0 0 0 0 0 0 0
#> [12,] 0 0 103 0 0 0 103
#> [13,] 0 0 104 0 0 0 104
#> [14,] 0 0 227 0 0 0 105
#> [15,] 0 0 355 0 126 0 232
m1 %*% svt2
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 118 0 0 0 0 0 0
#> [2,] 119 0 101 0 0 0 101
#> [3,] 120 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0 0
#> [5,] 0 0 0 0 0 0 0
#> [6,] 0 0 102 0 0 0 102
#> [7,] 0 0 0 0 0 0 0
#> [8,] 0 0 0 0 0 0 0
#> [9,] 0 0 0 0 0 0 0
#> [10,] 0 0 121 0 0 0 0
#> [11,] 0 0 0 0 0 0 0
#> [12,] 0 0 103 0 0 0 103
#> [13,] 0 0 104 0 0 0 104
#> [14,] 0 0 227 0 0 0 105
#> [15,] 0 0 355 0 126 0 232
## Unary crossprod() and tcrossprod():
crossprod(svt1) # same as t(svt1) %*% svt1
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 64291 59192 12019 25848 12625 13356
#> [2,] 59192 138094 25478 42095 26768 14742
#> [3,] 12019 25478 42485 0 29507 0
#> [4,] 25848 42095 0 44654 0 15498
#> [5,] 12625 26768 29507 0 31001 0
#> [6,] 13356 14742 0 15498 0 15876
tcrossprod(svt1) # same as svt1 %*% t(svt1)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 40749 41098 14160 0 0 0 11663 11770 11877 11984 12091 12198
#> [2,] 41098 51651 14280 0 0 10302 11772 11880 11988 12096 12204 22715
#> [3,] 14160 14280 14400 0 0 0 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [5,] 0 0 0 0 0 0 0 0 0 0 0 0
#> [6,] 0 10302 0 0 0 10404 0 0 0 0 0 10506
#> [7,] 11663 11772 0 0 0 0 11881 11990 12099 12208 12317 12426
#> [8,] 11770 11880 0 0 0 0 11990 12100 12210 12320 12430 12540
#> [9,] 11877 11988 0 0 0 0 12099 12210 12321 12432 12543 12654
#> [10,] 11984 12096 0 0 0 0 12208 12320 12432 27185 12656 12768
#> [11,] 12091 12204 0 0 0 0 12317 12430 12543 12656 12769 12882
#> [12,] 12198 22715 0 0 0 10506 12426 12540 12654 12768 12882 23605
#> [13,] 12305 22924 0 0 0 10608 12535 12650 12765 12880 12995 23822
#> [14,] 12412 23133 0 0 0 10710 12644 12760 12876 27754 13108 24039
#> [15,] 12519 23342 0 0 0 10812 12753 12870 12987 27987 13221 24256
#> [,13] [,14] [,15]
#> [1,] 12305 12412 12519
#> [2,] 22924 23133 23342
#> [3,] 0 0 0
#> [4,] 0 0 0
#> [5,] 0 0 0
#> [6,] 10608 10710 10812
#> [7,] 12535 12644 12753
#> [8,] 12650 12760 12870
#> [9,] 12765 12876 12987
#> [10,] 12880 27754 27987
#> [11,] 12995 13108 13221
#> [12,] 23822 24039 24256
#> [13,] 24041 24260 24479
#> [14,] 24260 39365 39708
#> [15,] 24479 39708 55930
## Binary crossprod() and tcrossprod():
crossprod(svt1[1:6, ], svt2) # same as t(svt1[1:6, ]) %*% svt2
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 0 0 102 0 102 0 102
#> [2,] 0 0 107 0 0 0 107
#> [3,] 120 0 118 0 0 0 118
#> [4,] 0 0 0 0 0 0 0
#> [5,] 0 0 124 0 0 0 124
#> [6,] 0 0 0 0 0 0 0
tcrossprod(svt1, t(svt2)) # same as svt1 %*% svt2
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 118 0 0 0 0 0 0
#> [2,] 119 0 101 0 0 0 101
#> [3,] 120 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0 0
#> [5,] 0 0 0 0 0 0 0
#> [6,] 0 0 102 0 0 0 102
#> [7,] 0 0 0 0 0 0 0
#> [8,] 0 0 0 0 0 0 0
#> [9,] 0 0 0 0 0 0 0
#> [10,] 0 0 121 0 0 0 0
#> [11,] 0 0 0 0 0 0 0
#> [12,] 0 0 103 0 0 0 103
#> [13,] 0 0 104 0 0 0 104
#> [14,] 0 0 227 0 0 0 105
#> [15,] 0 0 355 0 126 0 232
## Sanity checks:
m12 <- m1 %*% as.matrix(svt2)
stopifnot(
identical(svt1 %*% svt2, m12),
identical(m1 %*% svt2, m12),
identical(crossprod(svt1), t(svt1) %*% svt1),
identical(tcrossprod(svt1), svt1 %*% t(svt1)),
identical(crossprod(svt1[1:6, ], svt2), t(svt1[1:6, ]) %*% svt2),
identical(tcrossprod(svt1, t(svt2)), m12)
)