Contents

1 Introduction

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.

2 Install and load the package

if (!requireNamespace("BiocManager", quietly=TRUE))
    install.packages("BiocManager")
BiocManager::install("SparseArray")
library(SparseArray)

3 SVT_SparseArray objects

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.

3.1 Construction

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 SVT_SparseMatrix> of type "integer" (nzcount=8):
##      [,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   80
a <- 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 SVT_SparseArray> of type "integer" (nzcount=15):
## ,,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  150

Alternatively, 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   80
as.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  150

3.2 Accessors

The standard array accessors are supported:

dim(svt2)
## [1] 5 4 3
length(svt2)
## [1] 60
dimnames(svt2) <- list(NULL, letters[1:4], LETTERS[1:3])
svt2
## <5 x 4 x 3 SVT_SparseArray> of type "integer" (nzcount=15):
## ,,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   0 150

Some additional accessors defined in the S4Arrays / SparseArray framework:

type(svt1)
## [1] "integer"
type(svt1) <- "double"
svt1
## <6 x 4 SVT_SparseMatrix> of type "double" (nzcount=8):
##      [,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   80
is_sparse(svt1)
## [1] TRUE

Other 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] 0.6666667

See ?SparseArray for more information and additional examples.

3.3 Subsetting and subassignment

svt2[5:3, , "C"]
## <3 x 4 SVT_SparseMatrix> of type "integer" (nzcount=3):
##        a   b   c   d
## [1,]   0   0   0 150
## [2,]   0   0   0 140
## [3,]   0   0   0 130

Like 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.

3.4 Summarization methods (whole array)

The following summarization methods are provided at the moment: anyNA(), any, all, min, max, range, sum, prod, mean, var, sd.

anyNA(svt2)
## [1] TRUE
range(svt2, na.rm=TRUE)
## [1]   0 150
mean(svt2, na.rm=TRUE)
## [1] 20.33898
var(svt2, na.rm=TRUE)
## [1] 1717.124

See ?SparseArray_summarization for more information and additional examples.

3.5 Operations from the ‘Ops’, ‘Math’, ‘Math2’, and ‘Complex’ groups

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 SVT_SparseMatrix> of type "double" (nzcount=8):
##       [,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  48.0

See ?SparseArray_Ops, ?SparseArray_Math, and ?SparseArray_Complex, for more information and additional examples.

3.6 Other operations on SVT_SparseArray objects

More operations will be added in the future e.g. is.na(), is.infinite(), is.nan(), etc…

3.7 Generate a random SVT_SparseArray object

Two convenience functions are provided for this:

randomSparseArray(c(5, 6, 2), density=0.5)
## <5 x 6 x 2 SVT_SparseArray> of type "double" (nzcount=30):
## ,,1
##       [,1]  [,2]  [,3]  [,4]  [,5]  [,6]
## [1,]  0.00  0.00  0.00  0.00 -0.80  0.00
## [2,]  0.00  0.00  0.75 -0.47 -0.38  0.00
## [3,]  0.53  0.34  0.00  0.00 -0.12  0.00
## [4,] -0.34  0.00  0.00  0.00 -0.18  0.00
## [5,]  0.00 -1.10  0.45 -0.77  0.00  1.50
## 
## ,,2
##        [,1]   [,2]   [,3]   [,4]   [,5]   [,6]
## [1,] -0.460 -1.300 -0.260 -1.100  0.000 -0.580
## [2,] -0.270  0.000  0.000  0.000  0.000  0.000
## [3,] -1.700 -0.390  1.400  0.000  0.000 -0.024
## [4,] -0.720 -0.230 -0.270  0.098  0.000 -0.320
## [5,]  0.000  0.000  0.000  0.500  1.400  0.000
poissonSparseArray(c(5, 6, 2), density=0.5)
## <5 x 6 x 2 SVT_SparseArray> of type "integer" (nzcount=40):
## ,,1
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    2    0    2    0    2
## [2,]    1    2    1    1    1    1
## [3,]    1    0    1    0    0    0
## [4,]    1    0    2    1    1    0
## [5,]    1    2    3    3    3    1
## 
## ,,2
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    2    1    2    1    1
## [2,]    0    1    1    1    2    0
## [3,]    0    1    2    1    1    0
## [4,]    0    0    0    0    1    0
## [5,]    0    1    0    1    2    0

See ?randomSparseArray for more information and additional examples.

4 SVT_SparseMatrix objects

4.1 Transposition

t(svt1)
## <4 x 6 SVT_SparseMatrix> of type "double" (nzcount=8):
##      [,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   80

Note that multidimensional transposition is supported via aperm():

aperm(svt2)
## <3 x 4 x 5 SVT_SparseArray> of type "double" (nzcount=16):
## ,,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   0 150

See ?SparseArray_aperm for more information and additional examples.

4.2 Combine multidimensional objects along a given dimension

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 SVT_SparseMatrix> of type "double" (nzcount=13):
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]   10    0    0    0    1    0
## [2,]   20   30    0    0    1    1
## [3,]    0    0   50    0    0    1
## [4,]    0   40   60    0    0    0
## [5,]    0    0   70    0    1    0
## [6,]    0    0    0   80    0    0

Note 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 SVT_SparseArray> of type "integer" (nzcount=76):
## ,,1
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    0    0    0    1    1
## [2,]    0    0    0    0    0    0
## [3,]    0    0    0    0    1    2
## [4,]    0    2    1    0    1    0
## [5,]    0    1    1    1    1    1
## 
## ...
## 
## ,,11
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    0    0    0    0    0    0
## [2,]    0    0    0    0    0    0
## [3,]    0    0    0    0    0    0
## [4,]    0    0    0    0    0    1
## [5,]    0    0    0    0    0    0
svt5a <- 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 SVT_SparseArray> of type "integer" (nzcount=76):
## ,,1
##       [,1]  [,2]  [,3]  [,4] ...  [,8]  [,9] [,10] [,11]
## [1,]     1     0     1     0   .     0     0     0     0
## [2,]     0     1     0     0   .     0     0     2     0
## [3,]     0     0     0     0   .     1     0     0     0
## [4,]     0     1     1     0   .     0     0     0     0
## [5,]     0     0     0     0   .     2     1     0     0
## 
## ...
## 
## ,,6
##       [,1]  [,2]  [,3]  [,4] ...  [,8]  [,9] [,10] [,11]
## [1,]     1     2     0     0   .     0     0     1     0
## [2,]     0     1     1     0   .     0     0     0     0
## [3,]     2     0     1     1   .     0     1     2     0
## [4,]     0     1     1     0   .     1     0     0     1
## [5,]     1     2     0     0   .     0     1     0     0

See ?SparseArray_abind for more information and additional examples.

4.3 Matrix multiplication and cross-product

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  102  102
## b  210  103
## c  110  104
## d  111  105
## e  112  106

They also support crossprod() and tcrossprod():

crossprod(svt3)
##      [,1] [,2]
## [1,]    3    1
## [2,]    1    2

See ?SparseMatrix_mult for more information and additional examples.

4.4 matrixStats methods

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    2.5

Note 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 250
colVars(svt2, dims=2)
##        A        B        C 
## 732.6316 857.6316      NaN
colAnyNAs(svt2)
##       A     B     C
## a FALSE FALSE  TRUE
## b FALSE FALSE FALSE
## c FALSE FALSE FALSE
## d FALSE FALSE FALSE
colAnyNAs(svt2, dims=2)
##     A     B     C 
## FALSE FALSE  TRUE

See ?matrixStats_methods for more information and additional examples.

4.5 rowsum() method

A 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   0 110 115

See ?rowsum_methods for more information and additional examples.

4.6 Read/write a sparse matrix from/to a CSV file

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 SVT_SparseMatrix> of type "integer" (nzcount=17):
##     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   0 112 117

See ?readSparseCSV for more information and additional examples.

5 Comparison with dgCMatrix objects

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:

See ?SVT_SparseArray for more information.

6 Learn more

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

7 Session information

sessionInfo()
## R Under development (unstable) (2024-01-16 r85808)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 22.04.3 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
## 
## 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                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## 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_1.3.4     S4Arrays_1.3.3        IRanges_2.37.1       
##  [4] abind_1.4-5           S4Vectors_0.41.3      MatrixGenerics_1.15.0
##  [7] matrixStats_1.2.0     BiocGenerics_0.49.1   Matrix_1.6-5         
## [10] BiocStyle_2.31.0     
## 
## loaded via a namespace (and not attached):
##  [1] crayon_1.5.2        cli_3.6.2           knitr_1.45         
##  [4] rlang_1.1.3         xfun_0.42           jsonlite_1.8.8     
##  [7] htmltools_0.5.7     sass_0.4.8          rmarkdown_2.25     
## [10] grid_4.4.0          evaluate_0.23       jquerylib_0.1.4    
## [13] fastmap_1.1.1       yaml_2.3.8          lifecycle_1.0.4    
## [16] bookdown_0.37       BiocManager_1.30.22 compiler_4.4.0     
## [19] XVector_0.43.1      lattice_0.22-5      digest_0.6.34      
## [22] R6_2.5.1            bslib_0.6.1         tools_4.4.0        
## [25] zlibbioc_1.49.0     cachem_1.0.8