SparseArray 1.4.8
SparseArray is an infrastructure package that provides an array-like container for efficient in-memory representation of multidimensional sparse data in R.
The package defines the SparseArray virtual class and two concrete subclasses: COO_SparseArray and SVT_SparseArray. Each subclass uses its own internal representation of the nonzero multidimensional data, the “COO layout” and the “SVT layout”, respectively.
Note that the SparseArray virtual class could easily be extended by other S4 classes that intent to implement alternative internal representations of the nonzero multidimensional data.
This vignette focuses on the SVT_SparseArray container.
if (!require("BiocManager", quietly=TRUE))
install.packages("BiocManager")
BiocManager::install("SparseArray")library(SparseArray)The SVT_SparseArray container provides an efficient representation of the nonzero multidimensional data via a novel layout called the “SVT layout”.
Note that SVT_SparseArray objects mimic as much as possible the behavior of ordinary matrix and array objects in base R. In particular, they suppport most of the “standard matrix and array API” defined in base R and in the matrixStats package from CRAN.
SVT_SparseArray objects can be constructed in many ways. A common way is to coerce an ordinary matrix or array to SVT_SparseArray:
m <- matrix(0L, nrow=6, ncol=4)
m[c(1:2, 8, 10, 15:17, 24)] <- (1:8)*10L
svt1 <- as(m, "SVT_SparseArray")
svt1## <6 x 4 SparseMatrix> of type "integer" [nzcount=8 (33%)]:
## [,1] [,2] [,3] [,4]
## [1,] 10 0 0 0
## [2,] 20 30 0 0
## [3,] 0 0 50 0
## [4,] 0 40 60 0
## [5,] 0 0 70 0
## [6,] 0 0 0 80a <- array(0L, 5:3)
a[c(1:2, 8, 10, 15:17, 20, 24, 40, 56:60)] <- (1:15)*10L
svt2 <- as(a, "SVT_SparseArray")
svt2## <5 x 4 x 3 SparseArray> of type "integer" [nzcount=15 (25%)]:
## ,,1
## [,1] [,2] [,3] [,4]
## [1,] 10 0 0 60
## [2,] 20 0 0 70
## [3,] 0 30 0 0
## [4,] 0 0 0 0
## [5,] 0 40 50 80
##
## ,,2
## [,1] [,2] [,3] [,4]
## [1,] 0 0 0 0
## [2,] 0 0 0 0
## [3,] 0 0 0 0
## [4,] 90 0 0 0
## [5,] 0 0 0 100
##
## ,,3
## [,1] [,2] [,3] [,4]
## [1,] 0 0 0 110
## [2,] 0 0 0 120
## [3,] 0 0 0 130
## [4,] 0 0 0 140
## [5,] 0 0 0 150Alternatively, the ordinary matrix or array can be passed to the
SVT_SparseArray constructor function:
svt1 <- SVT_SparseArray(m)
svt2 <- SVT_SparseArray(a)Note that coercing an ordinary matrix or array to SparseArray is also supported and will produce the same results:
svt1 <- as(m, "SparseArray")
svt2 <- as(a, "SparseArray")This is because, for most use cases, the SVT_SparseArray representation is more efficient than the COO_SparseArray representation, so the former is usually preferred over the latter.
For the same reason, the SparseArray constructor function will also
give the preference to the SVT_SparseArray representation:
svt1 <- SparseArray(m)
svt2 <- SparseArray(a)This is actually the most convenient way to turn an ordinary matrix or array into an SVT_SparseArray object.
Coercion back to ordinary matrix or array is supported:
as.array(svt1) # same as as.matrix(svt1)## [,1] [,2] [,3] [,4]
## [1,] 10 0 0 0
## [2,] 20 30 0 0
## [3,] 0 0 50 0
## [4,] 0 40 60 0
## [5,] 0 0 70 0
## [6,] 0 0 0 80as.array(svt2)## , , 1
##
## [,1] [,2] [,3] [,4]
## [1,] 10 0 0 60
## [2,] 20 0 0 70
## [3,] 0 30 0 0
## [4,] 0 0 0 0
## [5,] 0 40 50 80
##
## , , 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0 0 0 0
## [2,] 0 0 0 0
## [3,] 0 0 0 0
## [4,] 90 0 0 0
## [5,] 0 0 0 100
##
## , , 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0 0 0 110
## [2,] 0 0 0 120
## [3,] 0 0 0 130
## [4,] 0 0 0 140
## [5,] 0 0 0 150The standard array accessors are supported:
dim(svt2)## [1] 5 4 3length(svt2)## [1] 60dimnames(svt2) <- list(NULL, letters[1:4], LETTERS[1:3])
svt2## <5 x 4 x 3 SparseArray> of type "integer" [nzcount=15 (25%)]:
## ,,A
## a b c d
## [1,] 10 0 0 60
## [2,] 20 0 0 70
## [3,] 0 30 0 0
## [4,] 0 0 0 0
## [5,] 0 40 50 80
##
## ,,B
## a b c d
## [1,] 0 0 0 0
## [2,] 0 0 0 0
## [3,] 0 0 0 0
## [4,] 90 0 0 0
## [5,] 0 0 0 100
##
## ,,C
## a b c d
## [1,] 0 0 0 110
## [2,] 0 0 0 120
## [3,] 0 0 0 130
## [4,] 0 0 0 140
## [5,] 0 0 0 150Some additional accessors defined in the S4Arrays / SparseArray framework:
type(svt1)## [1] "integer"type(svt1) <- "double"
svt1## <6 x 4 SparseMatrix> of type "double" [nzcount=8 (33%)]:
## [,1] [,2] [,3] [,4]
## [1,] 10 0 0 0
## [2,] 20 30 0 0
## [3,] 0 0 50 0
## [4,] 0 40 60 0
## [5,] 0 0 70 0
## [6,] 0 0 0 80is_sparse(svt1)## [1] TRUEOther accessors/extractors specific to sparse arrays:
## Get the number of nonzero array elements in 'svt1':
nzcount(svt1)## [1] 8## Extract the "linear indices" of the nonzero array elements in 'svt1':
nzwhich(svt1)## [1] 1 2 8 10 15 16 17 24## Extract the "array indices" (a.k.a. "array coordinates") of the
## nonzero array elements in 'svt1':
nzwhich(svt1, arr.ind=TRUE)## [,1] [,2]
## [1,] 1 1
## [2,] 2 1
## [3,] 2 2
## [4,] 4 2
## [5,] 3 3
## [6,] 4 3
## [7,] 5 3
## [8,] 6 4## Extract the values of the nonzero array elements in 'svt1' and return
## them in a vector "parallel" to 'nzwhich(svt1)':
#nzvals(svt1) # NOT READY YET!
sparsity(svt1)## [1] 0.6666667See ?SparseArray for more information and additional examples.
svt2[5:3, , "C"]## <3 x 4 SparseMatrix> of type "integer" [nzcount=3 (25%)]:
## a b c d
## [1,] 0 0 0 150
## [2,] 0 0 0 140
## [3,] 0 0 0 130Like with ordinary arrays in base R, assigning values of type "double" to
an SVT_SparseArray object of type "integer" will automatically change the
type of the object to "double":
type(svt2)## [1] "integer"svt2[5, 1, 3] <- NaN
type(svt2)## [1] "double"See ?SparseArray_subsetting for more information and additional examples.
The following summarization methods are provided at the moment: anyNA(),
any, all, min, max, range, sum, prod, mean, var, sd.
anyNA(svt2)## [1] TRUErange(svt2, na.rm=TRUE)## [1] 0 150mean(svt2, na.rm=TRUE)## [1] 20.33898var(svt2, na.rm=TRUE)## [1] 1717.124See ?SparseArray_summarization for more information and additional examples.
SVT_SparseArray objects support operations from the ‘Ops’, ‘Math’, Math2,
and ‘Complex’ groups, with some restrictions.
See ?S4groupGeneric in the methods package for more
information about these group generics.
signif((svt1^1.5 + svt1) %% 100 - 0.6 * svt1, digits=2)## <6 x 4 SparseMatrix> of type "double" [nzcount=8 (33%)]:
## [,1] [,2] [,3] [,4]
## [1,] 36.0 0.0 0.0 0.0
## [2,] -2.6 76.0 0.0 0.0
## [3,] 0.0 0.0 -26.0 0.0
## [4,] 0.0 69.0 -11.0 0.0
## [5,] 0.0 0.0 14.0 0.0
## [6,] 0.0 0.0 0.0 48.0See ?SparseArray_Ops, ?SparseArray_Math, and ?SparseArray_Complex,
for more information and additional examples.
More operations will be added in the future e.g. is.na(), is.infinite(),
is.nan(), etc…
Two convenience functions are provided for this:
randomSparseArray(c(5, 6, 2), density=0.5)## <5 x 6 x 2 SparseArray> of type "double" [nzcount=30 (50%)]:
## ,,1
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.64 0.00 0.00 0.00 0.00 0.22
## [2,] 0.00 2.30 1.00 0.00 0.00 -0.20
## [3,] -0.13 -0.53 0.00 0.00 0.00 0.53
## [4,] -1.40 1.80 0.00 -0.88 0.61 0.00
## [5,] 0.00 0.74 0.18 0.13 0.00 0.00
##
## ,,2
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.00 0.00 0.00 0.00 0.00 -0.49
## [2,] 0.00 -1.30 0.00 1.10 -1.30 0.00
## [3,] 0.51 0.00 0.21 0.50 0.96 -1.20
## [4,] 0.00 0.24 0.00 0.00 0.97 -0.35
## [5,] -1.90 0.00 0.00 0.00 -3.10 -1.00poissonSparseArray(c(5, 6, 2), density=0.5)## <5 x 6 x 2 SparseArray> of type "integer" [nzcount=28 (47%)]:
## ,,1
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0 0 1 2 1 4
## [2,] 0 0 0 0 0 2
## [3,] 0 1 0 0 3 0
## [4,] 0 1 0 0 0 1
## [5,] 0 1 1 2 2 0
##
## ,,2
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1 0 1 2 1 0
## [2,] 0 2 1 0 0 1
## [3,] 1 0 1 2 1 1
## [4,] 0 0 0 0 0 0
## [5,] 1 0 0 0 1 1See ?randomSparseArray for more information and additional examples.
t(svt1)## <4 x 6 SparseMatrix> of type "double" [nzcount=8 (33%)]:
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 10 20 0 0 0 0
## [2,] 0 30 0 40 0 0
## [3,] 0 0 50 60 70 0
## [4,] 0 0 0 0 0 80Note that multidimensional transposition is supported via aperm():
aperm(svt2)## <3 x 4 x 5 SparseArray> of type "double" [nzcount=16 (27%)]:
## ,,1
## a b c d
## A 10 0 0 60
## B 0 0 0 0
## C 0 0 0 110
##
## ,,2
## a b c d
## A 20 0 0 70
## B 0 0 0 0
## C 0 0 0 120
##
## ,,3
## a b c d
## A 0 30 0 0
## B 0 0 0 0
## C 0 0 0 130
##
## ,,4
## a b c d
## A 0 0 0 0
## B 90 0 0 0
## C 0 0 0 140
##
## ,,5
## a b c d
## A 0 40 50 80
## B 0 0 0 100
## C NaN 0 0 150See ?SparseArray_aperm for more information and additional examples.
Like ordinary matrices in base R, SVT_SparseMatrix objects can be
combined by rows or columns, with rbind() or cbind():
svt3 <- poissonSparseMatrix(6, 2, density=0.5)
cbind(svt1, svt3)## <6 x 6 SparseMatrix> of type "double" [nzcount=13 (36%)]:
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 10 0 0 0 1 1
## [2,] 20 30 0 0 0 0
## [3,] 0 0 50 0 0 1
## [4,] 0 40 60 0 1 0
## [5,] 0 0 70 0 0 0
## [6,] 0 0 0 80 2 0Note that multidimensional objects can be combined along any dimension
with abind():
svt4a <- poissonSparseArray(c(5, 6, 2), density=0.4)
svt4b <- poissonSparseArray(c(5, 6, 5), density=0.2)
svt4c <- poissonSparseArray(c(5, 6, 4), density=0.2)
abind(svt4a, svt4b, svt4c)## <5 x 6 x 11 SparseArray> of type "integer" [nzcount=77 (23%)]:
## ,,1
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1 1 2 1 0 0
## [2,] 0 0 1 0 2 1
## [3,] 0 1 0 2 0 1
## [4,] 0 1 0 3 1 1
## [5,] 0 0 0 1 0 0
##
## ...
##
## ,,11
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0
## [3,] 0 1 0 0 1 1
## [4,] 0 0 0 1 1 0
## [5,] 0 0 0 0 0 0svt5a <- aperm(svt4a, c(1, 3:2))
svt5b <- aperm(svt4b, c(1, 3:2))
svt5c <- aperm(svt4c, c(1, 3:2))
abind(svt5a, svt5b, svt5c, along=2)## <5 x 11 x 6 SparseArray> of type "integer" [nzcount=77 (23%)]:
## ,,1
## [,1] [,2] [,3] [,4] ... [,8] [,9] [,10] [,11]
## [1,] 1 0 0 0 . 0 0 0 0
## [2,] 0 0 0 1 . 0 0 0 0
## [3,] 0 0 0 0 . 0 0 1 0
## [4,] 0 0 0 0 . 0 0 1 0
## [5,] 0 1 0 0 . 0 0 0 0
##
## ...
##
## ,,6
## [,1] [,2] [,3] [,4] ... [,8] [,9] [,10] [,11]
## [1,] 0 0 1 0 . 1 0 0 0
## [2,] 1 1 0 0 . 1 0 0 0
## [3,] 1 1 1 0 . 0 0 0 1
## [4,] 1 0 0 0 . 0 0 0 0
## [5,] 0 0 0 0 . 0 0 0 0See ?SparseArray_abind for more information and additional examples.
Like ordinary matrices in base R, SVT_SparseMatrix objects can be
multiplied with the %*% operator:
m6 <- matrix(0L, nrow=5, ncol=6, dimnames=list(letters[1:5], LETTERS[1:6]))
m6[c(2, 6, 12:17, 22:30)] <- 101:117
svt6 <- SparseArray(m6)
svt6 %*% svt3## [,1] [,2]
## a 333 0
## b 437 204
## c 230 104
## d 232 105
## e 234 106They also support crossprod() and tcrossprod():
crossprod(svt3)## [,1] [,2]
## [1,] 6 1
## [2,] 1 2See ?SparseMatrix_mult for more information and additional examples.
The SparseArray package provides memory-efficient col/row summarization methods for SVT_SparseMatrix objects:
colVars(svt6)## A B C D E F
## 2040.2 2080.8 2185.3 3467.0 2443.3 2.5Note that multidimensional objects are supported:
colVars(svt2)## A B C
## a 80 1620 NaN
## b 380 0 0
## c 500 0 0
## d 1520 2000 250colVars(svt2, dims=2)## A B C
## 732.6316 857.6316 NaNcolAnyNAs(svt2)## A B C
## a FALSE FALSE TRUE
## b FALSE FALSE FALSE
## c FALSE FALSE FALSE
## d FALSE FALSE FALSEcolAnyNAs(svt2, dims=2)## A B C
## FALSE FALSE TRUESee ?matrixStats_methods for more information and additional examples.
rowsum() methodA rowsum() method is provided:
rowsum(svt6, group=c(1:3, 2:1))## A B C D E F
## 1 0 102 106 107 112 230
## 2 101 0 208 108 220 230
## 3 0 0 104 0 110 115See ?rowsum_methods for more information and additional examples.
Use writeSparseCSV() to write a sparse matrix to a CSV file:
csv_file <- tempfile()
writeSparseCSV(m6, csv_file)Use readSparseCSV() to read the file. This will import the data as
an SVT_SparseMatrix object:
readSparseCSV(csv_file)## <5 x 6 SparseMatrix> of type "integer" [nzcount=17 (57%)]:
## A B C D E F
## a 0 102 0 107 0 113
## b 101 0 103 108 109 114
## c 0 0 104 0 110 115
## d 0 0 105 0 111 116
## e 0 0 106 0 112 117See ?readSparseCSV for more information and additional examples.
The nonzero data of a SVT_SparseArray object is stored in a Sparse Vector Tree. This internal data representation is referred to as the “SVT layout”. It is similar to the “CSC layout” (compressed, sparse, column-oriented format) used by CsparseMatrix derivatives from the Matrix package, like dgCMatrix or lgCMatrix objects, but with the following improvements:
The “SVT layout” supports sparse arrays of arbitrary dimensions.
With the “SVT layout”, the sparse data can be of any type.
Whereas CsparseMatrix derivatives only support sparse data of
type "double" or "logical" at the moment.
The “SVT layout” imposes no limit on the number of nonzero array elements that can be stored. With dgCMatrix/lgCMatrix objects, this number must be < 2^31.
Overall, the “SVT layout” allows more efficient operations on SVT_SparseArray objects.
See ?SVT_SparseArray for more information.
Please consult the individual man pages in the SparseArray
package to learn more about SVT_SparseArray objects and about the
package. A good starting point is the man page for SparseArray
objects: ?SparseArray
sessionInfo()## R version 4.4.0 (2024-04-24)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 22.04.4 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.19-bioc/R/lib/libRblas.so
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
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## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB LC_COLLATE=C
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
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## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
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## time zone: America/New_York
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats4 stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] SparseArray_1.4.8 S4Arrays_1.4.1 IRanges_2.38.0
## [4] abind_1.4-5 S4Vectors_0.42.0 MatrixGenerics_1.16.0
## [7] matrixStats_1.3.0 BiocGenerics_0.50.0 Matrix_1.7-0
## [10] BiocStyle_2.32.0
##
## loaded via a namespace (and not attached):
## [1] crayon_1.5.2 cli_3.6.2 knitr_1.46
## [4] rlang_1.1.3 xfun_0.44 jsonlite_1.8.8
## [7] htmltools_0.5.8.1 sass_0.4.9 rmarkdown_2.27
## [10] grid_4.4.0 evaluate_0.23 jquerylib_0.1.4
## [13] fastmap_1.2.0 yaml_2.3.8 lifecycle_1.0.4
## [16] bookdown_0.39 BiocManager_1.30.23 compiler_4.4.0
## [19] XVector_0.44.0 lattice_0.22-6 digest_0.6.35
## [22] R6_2.5.1 bslib_0.7.0 tools_4.4.0
## [25] zlibbioc_1.50.0 cachem_1.1.0