DelayedMatrixStats ports the matrixStats API to work with DelayedMatrix objects from the DelayedArray package. It provides high-performing functions operating on rows and columns of DelayedMatrix objects, including all subclasses such as RleArray (from the DelayedArray package) and HDF5Array (from the HDF5Array) as well as supporting all types of seeds, such as matrix (from the base package) and Matrix (from the Matrix package).
The DelayedArray package allows developers to store array-like data using in-memory or on-disk representations (e.g., in HDF5 files) and provides a common and familiar array-like interface for interacting with these data.
The DelayedMatrixStats package is designed to make life easier for Bioconductor developers wanting to use DelayedArray by providing a rich set of column-wise and row-wise summary functions.
We briefly demonstrate and explain these two features using a simple example. We’ll simulate some (unrealistic) RNA-seq read counts data from 10,000 genes and 20 samples and store it on disk as a HDF5Array:
library(DelayedArray)
x <- do.call(cbind, lapply(1:20, function(j) {
rpois(n = 10000, lambda = sample(20:40, 10000, replace = TRUE))
}))
colnames(x) <- paste0("S", 1:20)
x <- realize(x, "HDF5Array")
x
#> DelayedMatrix object of 10000 x 20 integers:
#> S1 S2 S3 S4 ... S17 S18 S19 S20
#> [1,] 45 21 24 45 . 27 31 20 21
#> [2,] 19 24 35 21 . 20 16 39 37
#> [3,] 34 30 25 24 . 35 10 30 30
#> [4,] 18 17 34 34 . 26 28 45 23
#> [5,] 29 30 30 21 . 35 21 35 32
#> ... . . . . . . . . .
#> [9996,] 20 35 22 18 . 42 20 20 20
#> [9997,] 36 34 16 26 . 27 22 14 29
#> [9998,] 40 29 52 29 . 13 32 40 26
#> [9999,] 22 26 30 38 . 37 25 27 43
#> [10000,] 37 37 34 22 . 37 33 32 21Suppose you wish to compute the standard deviation of the read counts for each gene.
You might think to use apply() like in the following:
system.time(row_sds <- apply(x, 1, sd))
#> user system elapsed
#> 116.266 2.631 119.520
head(row_sds)
#> [1] 8.870412 9.124288 8.928959 9.150784 9.173187 6.167828This works, but takes quite a while.
Or perhaps you already know that the matrixStats package
provides a rowSds() function:
matrixStats::rowSds(x)
#> Error in rowVars(x, rows = rows, cols = cols, na.rm = na.rm, center = center, : Argument 'x' must be a matrix or a vector.Unfortunately (and perhaps unsurprisingly) this doesn’t work. matrixStats is designed for use on in-memory matrix objects. Well, why don’t we just first realize our data in-memory and then use matrixStats
system.time(row_sds <- matrixStats::rowSds(as.matrix(x)))
#> user system elapsed
#> 0.015 0.000 0.015
head(row_sds)
#> [1] 8.870412 9.124288 8.928959 9.150784 9.173187 6.167828This works and is many times faster than the apply()-based approach! However,
it rather defeats the purpose of using a HDF5Array for storing the
data since we have to bring all the data into memory at once to compute the
result.
Instead, we can use DelayedMatrixStats::rowSds(), which has the speed
benefits of matrixStats::rowSds()1 but without having to load the
entire data into memory at once2:
library(DelayedMatrixStats)
system.time(row_sds <- rowSds(x))
#> user system elapsed
#> 0.178 0.006 0.184
head(row_sds)
#> [1] 8.870412 9.124288 8.928959 9.150784 9.173187 6.167828Finally, by using DelayedMatrixStats we can use the same code,
(colMedians(x)) regardless of whether the input is an ordinary matrix or a
DelayedMatrix. This is useful for packages wishing to support both types of
objects, e.g., packages wanting to retain backward compatibility or during a
transition period from matrix-based to DelayeMatrix-based objects.
The initial release of DelayedMatrixStats supports the complete set of column-wise and row-wise matrixStats API3. Please see the matrixStats vignette (available online) for a summary these methods. The following table documents the API coverage and availability of ‘seed-aware’ methods in the current version of DelayedMatrixStats.
| Method | Block processing | base::matrix optimized | Matrix::Matrix optimized | DelayedArray::RleArray (SolidRleArraySeed) optimized | DelayedArray::RleArray (ChunkedRleArraySeed) optimized | HDF5Array::HDF5Matrix optimized | base::data.frame optimized | S4Vectors::DataFrame optimized |
|---|---|---|---|---|---|---|---|---|
colAlls() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colAnyMissings() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colAnyNAs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colAnys() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colAvgsPerRowSet() |
❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colCollapse() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colCounts() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colCummaxs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colCummins() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colCumprods() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colCumsums() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colDiffs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colIQRDiffs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colIQRs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colLogSumExps() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colMadDiffs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colMads() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colMaxs() |
❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colMeans2() |
✔ | ✔ | ✔ | ✔ | ❌ | ❌ | ❌ | ❌ |
colMedians() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colMins() |
❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colOrderStats() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colProds() |
✔ | ✔ | ❌ | ✔ | ❌ | ❌ | ❌ | ❌ |
colQuantiles() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colRanges() |
❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colRanks() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colSdDiffs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colSds() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colSums2() |
✔ | ✔ | ✔ | ✔ | ❌ | ❌ | ❌ | ❌ |
colTabulates() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colVarDiffs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colVars() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colWeightedMads() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colWeightedMeans() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colWeightedMedians() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colWeightedSds() |
❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
colWeightedVars() |
❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowAlls() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowAnyMissings() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowAnyNAs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowAnys() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowAvgsPerColSet() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowCollapse() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowCounts() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowCummaxs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowCummins() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowCumprods() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowCumsums() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowDiffs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowIQRDiffs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowIQRs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowLogSumExps() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowMadDiffs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowMads() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowMaxs() |
❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowMeans2() |
✔ | ✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowMedians() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowMins() |
❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowOrderStats() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowProds() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowQuantiles() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowRanges() |
❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowRanks() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowSdDiffs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowSds() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowSums2() |
✔ | ✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowTabulates() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowVarDiffs() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowVars() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowWeightedMads() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowWeightedMeans() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowWeightedMedians() |
✔ | ✔ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowWeightedSds() |
❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
rowWeightedVars() |
❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
As well as offering a familiar API, DelayedMatrixStats provides ‘seed-aware’ methods that are optimized for specific types of DelayedMatrix objects.
To illustrate this idea, we will compare two ways of computing the column sums of a DelayedMatrix object:
force_block_processing argumentWe will demonstrate this by computing the column sums matrices with 20,000 rows and 600 columns where the data have different structure and are stored in DelayedMatrix objects with different types of seed:
We use the microbenchmark package to measure running time and the profmem package to measure the total memory allocations of each method.
In each case, the ‘seed-aware’ method is many times faster and allocates substantially lower total memory.
library(DelayedMatrixStats)
library(Matrix)
library(microbenchmark)
library(profmem)
set.seed(666)
# -----------------------------------------------------------------------------
# Dense with values in (0, 1)
# Fast, memory-efficient column sums of DelayedMatrix with ordinary matrix seed
#
# Generate some data
dense_matrix <- matrix(runif(20000 * 600),
nrow = 20000,
ncol = 600)
# Benchmark
dm_matrix <- DelayedArray(dense_matrix)
class(seed(dm_matrix))
#> [1] "matrix"
dm_matrix
#> DelayedMatrix object of 20000 x 600 doubles:
#> [,1] [,2] [,3] ... [,599] [,600]
#> [1,] 0.7743685 0.6601787 0.4098798 . 0.89118118 0.05776471
#> [2,] 0.1972242 0.8436035 0.9198450 . 0.31799523 0.63099417
#> [3,] 0.9780138 0.2017589 0.4696158 . 0.31783791 0.02830454
#> [4,] 0.2013274 0.8797239 0.6474768 . 0.55217184 0.09678816
#> [5,] 0.3612444 0.8158778 0.5928599 . 0.08530977 0.39224147
#> ... . . . . . .
#> [19996,] 0.19490291 0.07763570 0.56391725 . 0.09703424 0.62659353
#> [19997,] 0.61182993 0.01910121 0.04046034 . 0.59708388 0.88389731
#> [19998,] 0.12932744 0.21155070 0.19344085 . 0.51682032 0.13378223
#> [19999,] 0.18985573 0.41716539 0.35110782 . 0.62939661 0.94601427
#> [20000,] 0.87889047 0.25308041 0.54666920 . 0.81630322 0.73272217
microbenchmark(
block_processing = colSums2(dm_matrix, force_block_processing = TRUE),
seed_aware = colSums2(dm_matrix),
times = 10)
#> Unit: milliseconds
#> expr min lq mean median uq max
#> block_processing 396.49635 438.70959 473.31929 459.15869 476.7210 646.58449
#> seed_aware 15.45444 16.04262 16.85022 16.69319 17.1094 19.69856
#> neval cld
#> 10 b
#> 10 a
total(profmem(colSums2(dm_matrix, force_block_processing = TRUE)))
#> [1] 389690208
total(profmem(colSums2(dm_matrix)))
#> [1] 171760
# -----------------------------------------------------------------------------
# Sparse (60% zero) with values in (0, 1)
# Fast, memory-efficient column sums of DelayedMatrix with ordinary matrix seed
#
# Generate some data
sparse_matrix <- dense_matrix
zero_idx <- sample(length(sparse_matrix), 0.6 * length(sparse_matrix))
sparse_matrix[zero_idx] <- 0
# Benchmark
dm_dgCMatrix <- DelayedArray(Matrix(sparse_matrix, sparse = TRUE))
class(seed(dm_dgCMatrix))
#> [1] "dgCMatrix"
#> attr(,"package")
#> [1] "Matrix"
dm_dgCMatrix
#> DelayedMatrix object of 20000 x 600 doubles:
#> [,1] [,2] [,3] ... [,599] [,600]
#> [1,] 0.7743685 0.0000000 0.4098798 . 0.8911812 0.0000000
#> [2,] 0.0000000 0.0000000 0.9198450 . 0.3179952 0.6309942
#> [3,] 0.9780138 0.0000000 0.4696158 . 0.0000000 0.0000000
#> [4,] 0.0000000 0.8797239 0.0000000 . 0.0000000 0.0000000
#> [5,] 0.0000000 0.0000000 0.5928599 . 0.0000000 0.3922415
#> ... . . . . . .
#> [19996,] 0.1949029 0.0000000 0.5639173 . 0.09703424 0.62659353
#> [19997,] 0.6118299 0.0000000 0.0000000 . 0.00000000 0.88389731
#> [19998,] 0.0000000 0.0000000 0.1934408 . 0.51682032 0.00000000
#> [19999,] 0.0000000 0.0000000 0.0000000 . 0.62939661 0.94601427
#> [20000,] 0.8788905 0.0000000 0.0000000 . 0.81630322 0.00000000
microbenchmark(
block_processing = colSums2(dm_dgCMatrix, force_block_processing = TRUE),
seed_aware = colSums2(dm_dgCMatrix),
times = 10)
#> Unit: milliseconds
#> expr min lq mean median uq
#> block_processing 648.24739 672.45284 734.55810 732.49228 756.79118
#> seed_aware 15.45374 17.15742 17.71539 17.73988 18.62781
#> max neval cld
#> 930.90152 10 b
#> 18.85939 10 a
total(profmem(colSums2(dm_dgCMatrix, force_block_processing = TRUE)))
#> [1] 445529384
total(profmem(colSums2(dm_dgCMatrix)))
#> [1] 14992
# -----------------------------------------------------------------------------
# Dense with values in {0, 100} featuring runs of identical values
# Fast, memory-efficient column sums of DelayedMatrix with Rle-based seed
#
# Generate some data
runs <- rep(sample(100, 500000, replace = TRUE), rpois(500000, 100))
runs <- runs[seq_len(20000 * 600)]
runs_matrix <- matrix(runs,
nrow = 20000,
ncol = 600)
# Benchmark
dm_rle <- RleArray(Rle(runs),
dim = c(20000, 600))
class(seed(dm_rle))
#> [1] "SolidRleArraySeed"
#> attr(,"package")
#> [1] "DelayedArray"
dm_rle
#> RleMatrix object of 20000 x 600 integers:
#> [,1] [,2] [,3] [,4] ... [,597] [,598] [,599] [,600]
#> [1,] 72 75 47 89 . 46 45 91 99
#> [2,] 72 75 47 89 . 46 45 91 99
#> [3,] 72 75 47 89 . 46 45 91 99
#> [4,] 72 75 47 89 . 46 45 91 99
#> [5,] 72 75 47 89 . 46 45 91 99
#> ... . . . . . . . . .
#> [19996,] 75 47 89 86 . 45 60 99 50
#> [19997,] 75 47 89 86 . 45 60 99 50
#> [19998,] 75 47 89 86 . 45 60 99 50
#> [19999,] 75 47 89 86 . 45 60 99 50
#> [20000,] 75 47 89 86 . 45 91 99 50
microbenchmark(
block_processing = colSums2(dm_rle, force_block_processing = TRUE),
seed_aware = colSums2(dm_rle),
times = 10)
#> Unit: milliseconds
#> expr min lq mean median uq
#> block_processing 1443.10276 1455.550194 1493.81394 1494.059675 1502.131174
#> seed_aware 6.03291 7.623312 27.13669 8.513302 9.738147
#> max neval cld
#> 1604.5774 10 b
#> 181.8261 10 a
total(profmem(colSums2(dm_rle, force_block_processing = TRUE)))
#> [1] 436703944
total(profmem(colSums2(dm_rle)))
#> [1] 47968The development of ‘seed-aware’ methods is ongoing work (see the Roadmap), and for now only a few methods and seed-types have a ‘seed-aware’ method.
An extensive set of benchmarks is under development at http://peterhickey.org/BenchmarkingDelayedMatrixStats/.
A key feature of a DelayedArray is the ability to register ‘delayed
operations’. For example, let’s compute sin(dm_matrix):
system.time(sin_dm_matrix <- sin(dm_matrix))
#> user system elapsed
#> 0.002 0.000 0.002This instantaneous because the operation is not actually performed, rather
it is registered and only performed when the object is realized. All methods
in DelayedMatrixStats will correctly realise these delayed
operations before computing the final result. For example, let’s compute
colSums2(sin_dm_matrix) and compare check we get the correct answer:
all.equal(colSums2(sin_dm_matrix), colSums(sin(as.matrix(dm_matrix))))
#> [1] TRUEThe initial version of DelayedMatrixStats provides complete coverage of the matrixStats column-wise and row-wise API4, allowing package developers to use these functions with DelayedMatrix objects as well as with ordinary matrix objects. This should simplify package development and assist authors to support to their software for large datasets stored in disk-backed data structures such as HDF5Array. Such large datasets are increasingly common with the rise of single-cell genomics.
Future releases of DelayedMatrixStats will improve the
performance of these methods, specifically by developing additional ‘seed-aware’
methods. The plan is to prioritise commonly used methods (e.g.,
colMeans2()/rowMeans2(), colSums2()/rowSums2(), etc.) and the
development of ‘seed-aware’ methods for the HDF5Matrix class. To do so, we
will leverage the beachmat package. Proof-of-concept code
has shown that this can greatly increase the performance when analysing such
disk-backed data.
Importantly, all package developers using methods from DelayedMatrixStats will immediately gain from performance improvements to these low-level routines. By using DelayedMatrixStats, package developers will be able to focus on higher level programming tasks and address important scientific questions and technological challenges in high-throughput biology.