'Arith' operations on SparseArray objects
SparseArray-Arith-methods.RdSparseArray derivatives support operations from the Arith
group, with some restrictions.
See ?S4groupGeneric in the methods package
for more information about the Arith group generic.
IMPORTANT NOTES:
Only SVT_SparseArray objects are supported at the moment. Support for COO_SparseArray objects might be added in the future.
SVT_SparseArray of
type()"complex"don't supportArithoperations at the moment.
Details
Two forms of 'Arith' operations are supported:
Between an SVT_SparseArray object
svtand an atomic vectory:svt op y y op svtThe
Arithoperations that support this form are:*,/,^,%%,%/%. Note that, except for*(for which bothsvt * yandy * svtare supported), atomic vectorymust be on the right e.g.svt ^ 3.Between two SVT_SparseArray objects
svt1andsvt2of same dimensions (a.k.a. conformable arrays):svt1 op svt2The
Arithoperations that support this form are:+,-,*.
Value
A SparseArray derivative of the same dimensions as the input object(s).
See also
S4groupGenericin the methods package.SparseArray objects.
Ordinary array objects in base R.
Examples
## ---------------------------------------------------------------------
## Basic examples
## ---------------------------------------------------------------------
svt1 <- SVT_SparseArray(dim=c(15, 6), type="integer")
svt1[cbind(1:15, 2)] <- 100:114
svt1[cbind(1:15, 5)] <- -(114:100)
svt1
#> <15 x 6 SparseMatrix> of type "integer" [nzcount=30 (33%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0 100 0 0 -114 0
#> [2,] 0 101 0 0 -113 0
#> [3,] 0 102 0 0 -112 0
#> [4,] 0 103 0 0 -111 0
#> [5,] 0 104 0 0 -110 0
#> ... . . . . . .
#> [11,] 0 110 0 0 -104 0
#> [12,] 0 111 0 0 -103 0
#> [13,] 0 112 0 0 -102 0
#> [14,] 0 113 0 0 -101 0
#> [15,] 0 114 0 0 -100 0
svt1 * -0.01
#> <15 x 6 SparseMatrix> of type "double" [nzcount=30 (33%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.00 -1.00 0.00 0.00 1.14 0.00
#> [2,] 0.00 -1.01 0.00 0.00 1.13 0.00
#> [3,] 0.00 -1.02 0.00 0.00 1.12 0.00
#> [4,] 0.00 -1.03 0.00 0.00 1.11 0.00
#> [5,] 0.00 -1.04 0.00 0.00 1.10 0.00
#> ... . . . . . .
#> [11,] 0.00 -1.10 0.00 0.00 1.04 0.00
#> [12,] 0.00 -1.11 0.00 0.00 1.03 0.00
#> [13,] 0.00 -1.12 0.00 0.00 1.02 0.00
#> [14,] 0.00 -1.13 0.00 0.00 1.01 0.00
#> [15,] 0.00 -1.14 0.00 0.00 1.00 0.00
svt1 * 10 # result is of type "double"
#> <15 x 6 SparseMatrix> of type "double" [nzcount=30 (33%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0 1000 0 0 -1140 0
#> [2,] 0 1010 0 0 -1130 0
#> [3,] 0 1020 0 0 -1120 0
#> [4,] 0 1030 0 0 -1110 0
#> [5,] 0 1040 0 0 -1100 0
#> ... . . . . . .
#> [11,] 0 1100 0 0 -1040 0
#> [12,] 0 1110 0 0 -1030 0
#> [13,] 0 1120 0 0 -1020 0
#> [14,] 0 1130 0 0 -1010 0
#> [15,] 0 1140 0 0 -1000 0
svt1 * 10L # result is of type "integer"
#> <15 x 6 SparseMatrix> of type "integer" [nzcount=30 (33%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0 1000 0 0 -1140 0
#> [2,] 0 1010 0 0 -1130 0
#> [3,] 0 1020 0 0 -1120 0
#> [4,] 0 1030 0 0 -1110 0
#> [5,] 0 1040 0 0 -1100 0
#> ... . . . . . .
#> [11,] 0 1100 0 0 -1040 0
#> [12,] 0 1110 0 0 -1030 0
#> [13,] 0 1120 0 0 -1020 0
#> [14,] 0 1130 0 0 -1010 0
#> [15,] 0 1140 0 0 -1000 0
svt1 * c(10, 5, 0.1) # right vector recycled along 1st dimension
#> <15 x 6 SparseMatrix> of type "double" [nzcount=30 (33%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.0 1000.0 0.0 0.0 -1140.0 0.0
#> [2,] 0.0 505.0 0.0 0.0 -565.0 0.0
#> [3,] 0.0 10.2 0.0 0.0 -11.2 0.0
#> [4,] 0.0 1030.0 0.0 0.0 -1110.0 0.0
#> [5,] 0.0 520.0 0.0 0.0 -550.0 0.0
#> ... . . . . . .
#> [11,] 0.0 550.0 0.0 0.0 -520.0 0.0
#> [12,] 0.0 11.1 0.0 0.0 -10.3 0.0
#> [13,] 0.0 1120.0 0.0 0.0 -1020.0 0.0
#> [14,] 0.0 565.0 0.0 0.0 -505.0 0.0
#> [15,] 0.0 11.4 0.0 0.0 -10.0 0.0
svt1 / 10L
#> <15 x 6 SparseMatrix> of type "double" [nzcount=30 (33%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.0 10.0 0.0 0.0 -11.4 0.0
#> [2,] 0.0 10.1 0.0 0.0 -11.3 0.0
#> [3,] 0.0 10.2 0.0 0.0 -11.2 0.0
#> [4,] 0.0 10.3 0.0 0.0 -11.1 0.0
#> [5,] 0.0 10.4 0.0 0.0 -11.0 0.0
#> ... . . . . . .
#> [11,] 0.0 11.0 0.0 0.0 -10.4 0.0
#> [12,] 0.0 11.1 0.0 0.0 -10.3 0.0
#> [13,] 0.0 11.2 0.0 0.0 -10.2 0.0
#> [14,] 0.0 11.3 0.0 0.0 -10.1 0.0
#> [15,] 0.0 11.4 0.0 0.0 -10.0 0.0
svt1 ^ 2
#> <15 x 6 SparseMatrix> of type "double" [nzcount=30 (33%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0 10000 0 0 12996 0
#> [2,] 0 10201 0 0 12769 0
#> [3,] 0 10404 0 0 12544 0
#> [4,] 0 10609 0 0 12321 0
#> [5,] 0 10816 0 0 12100 0
#> ... . . . . . .
#> [11,] 0 12100 0 0 10816 0
#> [12,] 0 12321 0 0 10609 0
#> [13,] 0 12544 0 0 10404 0
#> [14,] 0 12769 0 0 10201 0
#> [15,] 0 12996 0 0 10000 0
svt1 ^ (2:6)
#> <15 x 6 SparseMatrix> of type "double" [nzcount=30 (33%)]:
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 10000 0 0 12996
#> [2,] 0 1030301 0 0 -1442897
#> [3,] 0 108243216 0 0 157351936
#> [4,] 0 11592740743 0 0 -16850581551
#> [5,] 0 1265319018496 0 0 1771561000000
#> ... . . . . .
#> [11,] 0 12100 0 0 10816
#> [12,] 0 1367631 0 0 -1092727
#> [13,] 0 157351936 0 0 108243216
#> [14,] 0 18424351793 0 0 -10510100501
#> [15,] 0 2194972623936 0 0 1000000000000
#> [,6]
#> [1,] 0
#> [2,] 0
#> [3,] 0
#> [4,] 0
#> [5,] 0
#> ... .
#> [11,] 0
#> [12,] 0
#> [13,] 0
#> [14,] 0
#> [15,] 0
svt1 %% 5L
#> <15 x 6 SparseMatrix> of type "integer" [nzcount=24 (27%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0 0 0 0 1 0
#> [2,] 0 1 0 0 2 0
#> [3,] 0 2 0 0 3 0
#> [4,] 0 3 0 0 4 0
#> [5,] 0 4 0 0 0 0
#> ... . . . . . .
#> [11,] 0 0 0 0 1 0
#> [12,] 0 1 0 0 2 0
#> [13,] 0 2 0 0 3 0
#> [14,] 0 3 0 0 4 0
#> [15,] 0 4 0 0 0 0
svt1 %/% 5L
#> <15 x 6 SparseMatrix> of type "integer" [nzcount=30 (33%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0 20 0 0 -23 0
#> [2,] 0 20 0 0 -23 0
#> [3,] 0 20 0 0 -23 0
#> [4,] 0 20 0 0 -23 0
#> [5,] 0 20 0 0 -22 0
#> ... . . . . . .
#> [11,] 0 22 0 0 -21 0
#> [12,] 0 22 0 0 -21 0
#> [13,] 0 22 0 0 -21 0
#> [14,] 0 22 0 0 -21 0
#> [15,] 0 22 0 0 -20 0
svt2 <- SVT_SparseArray(dim=dim(svt1), type="double")
svt2[c(2, 6, 12:17, 22:33, 55, 59:62, 90)] <- runif(26)
svt2
#> <15 x 6 SparseMatrix> of type "double" [nzcount=26 (29%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.0000000 0.8143864 0.6549458 0.0000000 0.7607204 0.0000000
#> [2,] 0.6247395 0.5103984 0.7155539 0.0000000 0.6053032 0.0000000
#> [3,] 0.0000000 0.0000000 0.4122341 0.0000000 0.0000000 0.0000000
#> [4,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> ... . . . . . .
#> [11,] 0.0000000 0.1516054 0.0000000 0.0000000 0.0000000 0.0000000
#> [12,] 0.6009843 0.8188669 0.0000000 0.0000000 0.0000000 0.0000000
#> [13,] 0.4543698 0.1019313 0.0000000 0.0000000 0.0000000 0.0000000
#> [14,] 0.8167198 0.6939910 0.0000000 0.6505006 0.0000000 0.0000000
#> [15,] 0.5466602 0.1770074 0.0000000 0.3788358 0.0000000 0.6604255
svt1 + svt2
#> <15 x 6 SparseMatrix> of type "double" [nzcount=43 (48%)]:
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0000000 100.8143864 0.6549458 0.0000000 -113.2392796
#> [2,] 0.6247395 101.5103984 0.7155539 0.0000000 -112.3946968
#> [3,] 0.0000000 102.0000000 0.4122341 0.0000000 -112.0000000
#> [4,] 0.0000000 103.0000000 0.0000000 0.0000000 -111.0000000
#> [5,] 0.0000000 104.0000000 0.0000000 0.0000000 -110.0000000
#> ... . . . . .
#> [11,] 0.0000000 110.1516054 0.0000000 0.0000000 -104.0000000
#> [12,] 0.6009843 111.8188669 0.0000000 0.0000000 -103.0000000
#> [13,] 0.4543698 112.1019313 0.0000000 0.0000000 -102.0000000
#> [14,] 0.8167198 113.6939910 0.0000000 0.6505006 -101.0000000
#> [15,] 0.5466602 114.1770074 0.0000000 0.3788358 -100.0000000
#> [,6]
#> [1,] 0.0000000
#> [2,] 0.0000000
#> [3,] 0.0000000
#> [4,] 0.0000000
#> [5,] 0.0000000
#> ... .
#> [11,] 0.0000000
#> [12,] 0.0000000
#> [13,] 0.0000000
#> [14,] 0.0000000
#> [15,] 0.6604255
svt1 - svt2
#> <15 x 6 SparseMatrix> of type "double" [nzcount=43 (48%)]:
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0000000 99.1856136 -0.6549458 0.0000000 -114.7607204
#> [2,] -0.6247395 100.4896016 -0.7155539 0.0000000 -113.6053032
#> [3,] 0.0000000 102.0000000 -0.4122341 0.0000000 -112.0000000
#> [4,] 0.0000000 103.0000000 0.0000000 0.0000000 -111.0000000
#> [5,] 0.0000000 104.0000000 0.0000000 0.0000000 -110.0000000
#> ... . . . . .
#> [11,] 0.0000000 109.8483946 0.0000000 0.0000000 -104.0000000
#> [12,] -0.6009843 110.1811331 0.0000000 0.0000000 -103.0000000
#> [13,] -0.4543698 111.8980687 0.0000000 0.0000000 -102.0000000
#> [14,] -0.8167198 112.3060090 0.0000000 -0.6505006 -101.0000000
#> [15,] -0.5466602 113.8229926 0.0000000 -0.3788358 -100.0000000
#> [,6]
#> [1,] 0.0000000
#> [2,] 0.0000000
#> [3,] 0.0000000
#> [4,] 0.0000000
#> [5,] 0.0000000
#> ... .
#> [11,] 0.0000000
#> [12,] 0.0000000
#> [13,] 0.0000000
#> [14,] 0.0000000
#> [15,] -0.6604255
svt1 * svt2
#> <15 x 6 SparseMatrix> of type "double" [nzcount=13 (14%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.00000 81.43864 0.00000 0.00000 -86.72212 0.00000
#> [2,] 0.00000 51.55024 0.00000 0.00000 -68.39926 0.00000
#> [3,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [4,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> [5,] 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> ... . . . . . .
#> [11,] 0.00000 16.67660 0.00000 0.00000 0.00000 0.00000
#> [12,] 0.00000 90.89423 0.00000 0.00000 0.00000 0.00000
#> [13,] 0.00000 11.41630 0.00000 0.00000 0.00000 0.00000
#> [14,] 0.00000 78.42099 0.00000 0.00000 0.00000 0.00000
#> [15,] 0.00000 20.17884 0.00000 0.00000 0.00000 0.00000
svt2 * (0.1 * svt1 - svt2 ^ 2) + svt1 / sum(svt2)
#> <15 x 6 SparseMatrix> of type "double" [nzcount=43 (48%)]:
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.00000000 14.93088724 -0.28094156 0.00000000 -17.46538319
#> [2,] -0.24383548 12.42247816 -0.36637600 0.00000000 -15.34137798
#> [3,] 0.00000000 7.47368787 -0.07005381 0.00000000 -8.20640237
#> [4,] 0.00000000 7.54695932 0.00000000 0.00000000 -8.13313092
#> [5,] 0.00000000 7.62023077 0.00000000 0.00000000 -8.05985947
#> ... . . . . .
#> [11,] 0.00000000 9.72403482 0.00000000 0.00000000 -7.62023077
#> [12,] -0.21706475 16.67346812 0.00000000 0.00000000 -7.54695932
#> [13,] -0.09380551 9.34697342 0.00000000 0.00000000 -7.47368787
#> [14,] -0.54477754 15.78753011 0.00000000 -0.27525999 -7.40041642
#> [15,] -0.16336246 10.36528315 0.00000000 -0.05436923 -7.32714497
#> [,6]
#> [1,] 0.00000000
#> [2,] 0.00000000
#> [3,] 0.00000000
#> [4,] 0.00000000
#> [5,] 0.00000000
#> ... .
#> [11,] 0.00000000
#> [12,] 0.00000000
#> [13,] 0.00000000
#> [14,] 0.00000000
#> [15,] -0.28805240
## Sanity checks:
m1 <- as.matrix(svt1)
m2 <- as.matrix(svt2)
stopifnot(
identical(as.matrix(svt1 * -0.01), m1 * -0.01),
identical(as.matrix(svt1 * 10), m1 * 10),
identical(as.matrix(svt1 * 10L), m1 * 10L),
identical(as.matrix(svt1 / 10L), m1 / 10L),
identical(as.matrix(svt1 ^ 3.5), m1 ^ 3.5),
identical(as.matrix(svt1 %% 5L), m1 %% 5L),
identical(as.matrix(svt1 %/% 5L), m1 %/% 5L),
identical(as.matrix(svt1 + svt2), m1 + m2),
identical(as.matrix(svt1 - svt2), m1 - m2),
identical(as.matrix(svt1 * svt2), m1 * m2),
all.equal(as.matrix(svt2 * (0.1 * svt1 - svt2 ^ 2) + svt1 / sum(svt2)),
m2 * (0.1 * m1 - m2 ^ 2) + m1 / sum(m2))
)
## ---------------------------------------------------------------------
## An example combining operations from the 'Arith', 'Compare',
## and 'Logic' groups
## ---------------------------------------------------------------------
m3 <- matrix(0L, nrow=15, ncol=6)
m3[c(2, 6, 12:17, 22:33, 55, 59:62, 90)] <- 101:126
svt3 <- SparseArray(m3)
## Can be 5x or 10x faster than with a dgCMatrix object on a big
## SVT_SparseMatrix object!
svt4 <- (svt3^1.5 + svt3) %% 100 - 0.2 * svt3 > 0
svt4
#> <15 x 6 SparseMatrix> of type "logical" [nzcount=20 (22%)]:
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] FALSE FALSE TRUE FALSE FALSE FALSE
#> [2,] FALSE TRUE FALSE FALSE FALSE FALSE
#> [3,] FALSE FALSE TRUE FALSE FALSE FALSE
#> [4,] FALSE FALSE FALSE FALSE FALSE FALSE
#> [5,] FALSE FALSE FALSE FALSE FALSE FALSE
#> ... . . . . . .
#> [11,] FALSE FALSE FALSE FALSE FALSE FALSE
#> [12,] TRUE TRUE FALSE FALSE FALSE FALSE
#> [13,] TRUE TRUE FALSE FALSE FALSE FALSE
#> [14,] TRUE TRUE FALSE TRUE FALSE FALSE
#> [15,] TRUE TRUE FALSE TRUE FALSE TRUE
## Sanity check:
m4 <- (m3^1.5 + m3) %% 100 - 0.2 * m3 > 0
stopifnot(identical(as.matrix(svt4), m4))