The aim of this document is to measure the performance of
the r Biocpkg("HDF5Array")
package for normalization and PCA
(Principal Component Analysis) of on-disk single cell data, two
computationally intensive operations at the core of single cell analysis.
The benchmarks presented in the document were specifically designed to observe the impact of two critical parameters on performance:
Hopefully these benchmarks will also facilitate comparing performance
of single cell analysis workflows based on r Biocpkg("HDF5Array")
with workflows based on other tools like Seurat or Scanpy.
Let's install and load r Biocpkg("HDF5Array")
as well as the other
packages used in this vignette:
if (!require("BiocManager", quietly=TRUE)) install.packages("BiocManager") pkgs <- c("HDF5Array", "ExperimentHub", "DelayedMatrixStats", "RSpectra") BiocManager::install(pkgs)
Load the packages:
library(HDF5Array) library(ExperimentHub) library(DelayedMatrixStats) library(RSpectra)
## Needed for the make_timings_table() function. path <- system.file(package="HDF5Array", "scripts", "make_timings_table.R", mustWork=TRUE) source(path, verbose=FALSE)
The datasets that we will use for our benchmarks are subsets of the
1.3 Million Brain Cell Dataset from 10x Genomics. This is a sparse
27,998 x 1,306,127 matrix of counts, with one gene per row and one cell
per column. Around 7% of the matrix values are nonzero counts.
The dataset is available via the r Biocpkg("ExperimentHub")
package
in two forms:
As a sparse HDF5 file: This is the original HDF5 file provided by 10x Genomics. It uses the CSR/CSC/Yale representation to store the sparse data.
As a dense HDF5 file: The same data as the above but stored as a regular HDF5 dataset with (compressed) chunks of dimensions 100 x 100.
The two files are hosted on r Biocpkg("ExperimentHub")
under resource
ids EH1039
and EH1040
:
hub <- ExperimentHub() hub["EH1039"]$description # sparse representation hub["EH1040"]$description # dense representation
Let's download them to the local r Biocpkg("ExperimentHub")
cache
if they are not there yet:
## Note that this will be quick if the HDF5 files are already in the ## local ExperimentHub cache. Otherwise, it will take a while! brain_s_path <- hub[["EH1039"]] brain_D_path <- hub[["EH1040"]]
brain_s_path
and brain_D_path
are the paths to the downloaded files.
We use the TENxMatrix()
and HDF5Array()
constructors to bring the
sparse and dense datasets in R, as DelayedArray derivatives. Note that
this does not load the matrix data in memory.
## Use 'h5ls(brain_s_path)' to find out the group. brain_s <- TENxMatrix(brain_s_path, group="mm10")
brain_s
is a 27,998 x 1,306,127 TENxMatrix object:
class(brain_s) dim(brain_s) is_sparse(brain_s)
See ?TENxMatrix
in the r Biocpkg("HDF5Array")
package for more
information about TENxMatrix objects.
## Use 'h5ls(brain_D_path)' to find out the name of the dataset. brain_D <- HDF5Array(brain_D_path, name="counts")
brain_D
is a 27,998 x 1,306,127 HDF5Matrix object
that contains the same data as brain_s
:
class(brain_D) dim(brain_D) chunkdim(brain_D) is_sparse(brain_D)
See ?HDF5Matrix
in the r Biocpkg("HDF5Array")
package for more
information about HDF5Matrix objects.
Even though the data in brain_D_path
is stored in a dense format,
we can flag it as quantitatively sparse. This is done by calling
the HDF5Array()
constructor function with as.sparse=TRUE
:
brain_Ds <- HDF5Array(brain_D_path, name="counts", as.sparse=TRUE)
The only difference between brain_D
and brain_Ds
is that
the latter is now seen as a sparse object, and will be treated as such:
class(brain_Ds) dim(brain_Ds) chunkdim(brain_Ds) is_sparse(brain_Ds)
Concretely this means that, when blocks of data are loaded from the dense HDF5 file to memory during block-processed operations, they end up directly in an in-memory sparse representation without going thru an in-memory dense representation first. This is expected to reduce memory footprint and (hopefully) will help with overall performance.
Finally note that the dense HDF5 file does not contain the dimnames of the
matrix, so we manually add them to brain_s
and brain_Ds
:
dimnames(brain_Ds) <- dimnames(brain_D) <- dimnames(brain_s)
For our benchmarks below, we create subsets of the 1.3 Million Brain
Cell Dataset of increasing sizes: subsets with 12,500 cells, 25,000 cells,
50,000 cells, 100,000 cells, and 200,000 cells. Note that subsetting a
TENxMatrix or HDF5Matrix object with [
is a delayed operation so has
virtually no cost:
brain1_s <- brain_s[ , 1:12500] brain1_D <- brain_D[ , 1:12500] brain1_Ds <- brain_Ds[ , 1:12500] brain2_s <- brain_s[ , 1:25000] brain2_D <- brain_D[ , 1:25000] brain2_Ds <- brain_Ds[ , 1:25000] brain3_s <- brain_s[ , 1:50000] brain3_D <- brain_D[ , 1:50000] brain3_Ds <- brain_Ds[ , 1:50000] brain4_s <- brain_s[ , 1:100000] brain4_D <- brain_D[ , 1:100000] brain4_Ds <- brain_Ds[ , 1:100000] brain5_s <- brain_s[ , 1:200000] brain5_D <- brain_D[ , 1:200000] brain5_Ds <- brain_Ds[ , 1:200000]
We'll use the following code for normalization:
## Also selects the most variable genes (1000 by default). simple_normalize <- function(mat, num_var_genes=1000) { stopifnot(length(dim(mat)) == 2, !is.null(rownames(mat))) mat <- mat[rowSums(mat) > 0, ] col_sums <- colSums(mat) / 10000 mat <- t(t(mat) / col_sums) row_vars <- rowVars(mat) row_vars_order <- order(row_vars, decreasing=TRUE) variable_idx <- head(row_vars_order, n=num_var_genes) mat <- log1p(mat[variable_idx, ]) mat / rowSds(mat) }
and the following code for PCA:
simple_PCA <- function(mat, k=25) { stopifnot(length(dim(mat)) == 2) row_means <- rowMeans(mat) Ax <- function(x, args) (as.numeric(mat %*% x) - row_means * sum(x)) Atx <- function(x, args) (as.numeric(x %*% mat) - as.vector(row_means %*% x)) RSpectra::svds(Ax, Atrans=Atx, k=k, dim=dim(mat)) }
Note that the implementations of simple_normalize()
and simple_PCA()
are expected to work on any matrix-like object regardless of its exact
type/representation e.g. it can be an ordinary matrix, a SparseMatrix
object from the r Biocpkg("SparseArray")
package, a dgCMatrix object
from the r CRANpkg("Matrix")
package, a DelayedMatrix derivative
(TENxMatrix, HDF5Matrix, TileDBMatrix), etc...
However, when the input is a DelayedMatrix object or derivative, it's important to be aware that:
Summarization methods like sum()
, colSums()
, rowVars()
, or rowSds()
,
and matrix multiplication (%*%
), are block-processed operations.
The block size is 100 Mb by default. Increasing or decreasing the block size will typically increase or decrease the memory usage of block-processed operations. It will also impact performance, but sometimes in unexpected or counter-intuitive ways.
The block size can be controlled with DelayedArray::getAutoBlockSize()
and DelayedArray::setAutoBlockSize()
.
For our benchmarks below, we'll use the following block sizes:
| | NORMALIZATION | PCA | | -------------------- | ------------: | -----: | | TENxMatrix (sparse) | 250 Mb | 40 Mb | | HDF5Matrix (dense) | 16 Mb | 100 Mb | | HDF5Matrix as sparse | 250 Mb | 40 Mb |
While manually running our benchmarks below on a Linux or macOS system, we will also monitor memory usage at the command line in a terminal with:
(while true; do ps u -p <PID>; sleep 1; done) >ps.log 2>&1 &
where <PID>
is the process id of our R session. This will allow us
to measure the maximum amount of memory used by the calls
to simple_normalize()
or simple_PCA()
.
In this section we run simple_normalize()
on the three different
representations (TENxMatrix, HDF5Matrix, and "HDF5Matrix as sparse")
of the smaller test dataset only (27,998 x 12,500), and we report the
time of each run.
See the Comprehensive timings obtained on various machines section
below in this document for simple_normalize()
and simple_pca()
timings
obtained on various machines on all our test datasets and using four different
block sizes: 16 Mb, 40 Mb, 100 Mb, and 250 Mb.
dim(brain1_s) DelayedArray::setAutoBlockSize(250e6) # set block size to 250 Mb system.time(norm_brain1_s <- simple_normalize(brain1_s)) dim(norm_brain1_s)
dim(brain1_D) DelayedArray::setAutoBlockSize(16e6) # set block size to 16 Mb system.time(norm_brain1_D <- simple_normalize(brain1_D)) dim(norm_brain1_D)
dim(brain1_Ds) DelayedArray::setAutoBlockSize(250e6) # set block size to 250 Mb system.time(norm_brain1_Ds <- simple_normalize(brain1_Ds)) dim(norm_brain1_Ds)
Note that the normalized datasets obtained in the previous section
are DelayedMatrix objects that carry delayed operations. These operations
can be displayed with showtree()
e.g. for norm_brain1_s
:
class(norm_brain1_s) showtree(norm_brain1_s)
The other norm_brain1_*
objects carry similar operations.
Before we proceed with PCA, we're going to write the normalized datasets to new HDF5 files. This introduces an additional cost, but, on the other hand, it has the benefit of triggering on-disk realization of the object. This means that all the delayed operations carried by the object will get realized on-the-fly before the matrix data actually lands on the disk, making the new object (TENxMatrix or HDF5Matrix) more efficient for PCA or whatever block-processed operations will come next.
We will use blocks of 100 Mb for all the writing operations.
DelayedArray::setAutoBlockSize(1e8)
dim(norm_brain1_s) system.time(norm_brain1_s <- writeTENxMatrix(norm_brain1_s, level=0))
The new norm_brain1_s
object is a pristine TENxMatrix object:
class(norm_brain1_s) showtree(norm_brain1_s) # "pristine" object (i.e. no more delayed operations)
dim(norm_brain1_D) system.time(norm_brain1_D <- writeHDF5Array(norm_brain1_D, level=0))
The new norm_brain1_D
object is a pristine HDF5Matrix object:
class(norm_brain1_D) showtree(norm_brain1_D) # "pristine" object (i.e. no more delayed operations)
dim(norm_brain1_Ds) system.time(norm_brain1_Ds <- writeHDF5Array(norm_brain1_Ds, level=0))
The new norm_brain1_Ds
object is a pristine sparse HDF5Matrix object:
class(norm_brain1_Ds) showtree(norm_brain1_Ds) # "pristine" object (i.e. no more delayed operations)
In this section we run simple_pca()
on the normalized datasets obtained
in the previous section and report the time of each run.
See the Comprehensive timings obtained on various machines section
below in this document for simple_normalize()
and simple_pca()
timings
obtained on various machines on all our test datasets and using four different
block sizes: 16 Mb, 40 Mb, 100 Mb, and 250 Mb.
DelayedArray::setAutoBlockSize(40e6) # set block size to 40 Mb dim(norm_brain1_s) system.time(pca1s <- simple_PCA(norm_brain1_s))
DelayedArray::setAutoBlockSize(1e8) # set block size to 100 Mb dim(norm_brain1_D) system.time(pca1D <- simple_PCA(norm_brain1_D))
Sanity check:
stopifnot(all.equal(pca1D, pca1s))
DelayedArray::setAutoBlockSize(40e6) # set block size to 40 Mb dim(norm_brain1_Ds) system.time(pca1Ds <- simple_PCA(norm_brain1_Ds))
Sanity check:
stopifnot(all.equal(pca1Ds, pca1s))
Here we report timings (and memory usage) observed on various machines. For each machine, the results are presented in a table that shows the normalization & realization & PCA timings obtained for all our test datasets and using four different block sizes: 16 Mb, 40 Mb, 100 Mb, and 250 Mb. For each operation, the best time across the four different block sizes is displayed in bold.
All the timings (and memory usage) were produced by running
the run_benchmarks.sh
script located in the HDF5Array/inst/scripts/
folder of the package, using R 4.5 and r Biocpkg("HDF5Array")
1.35.12
(Bioconductor 3.21).
hdparm1 <- "Output of <code>sudo hdparm -Tt <device></code>:" hdparm1 <- sprintf("<span style=\"font-style: italic\">%s</span>", hdparm1) hdparm2 <- c( "Timing cached reads: 35188 MB in 2.00 seconds = 17620.75 MB/sec", "Timing buffered disk reads: 7842 MB in 3.00 seconds = 2613.57 MB/sec" ) hdparm2 <- sprintf("<code>%s</code>", paste(hdparm2, collapse="<br />")) disk_perf <- paste0(hdparm1, "<br />", hdparm2) make_machine_specs_table("Specs for DELL XPS 15 laptop (model 9520)", specs=c(`OS`="Linux Ubuntu 24.04", `RAM`="32GB", `Disk`="1TB SSD"), disk_perf=disk_perf)
caption <- "Table 1: Timings for DELL XPS 15 laptop" make_timings_table("xps15", caption=caption)
hdparm1 <- "Output of <code>sudo hdparm -Tt <device></code>:" hdparm1 <- sprintf("<span style=\"font-style: italic\">%s</span>", hdparm1) hdparm2 <- c( "Timing cached reads: 20592 MB in 1.99 seconds = 10361.41 MB/sec", "Timing buffered disk reads: 1440 MB in 3.00 seconds = 479.66 MB/sec" ) hdparm2 <- sprintf("<code>%s</code>", paste(hdparm2, collapse="<br />")) disk_perf <- paste0(hdparm1, "<br />", hdparm2) make_machine_specs_table("Specs for Supermicro SuperServer 1029GQ-TRT", specs=c(`OS`="Linux Ubuntu 22.04", `RAM`="384GB", `Disk`="1.3TB ATA Disk"), disk_perf=disk_perf)
caption <- "Table 2: Timings for Supermicro SuperServer 1029GQ-TRT" make_timings_table("rex3", caption=caption)
make_machine_specs_table("Specs for Apple Silicon Mac Pro (Apple M2 Ultra)", specs=c(`OS`="macOS 13.7.1", `RAM`="192GB", `Disk`="2TB SSD"), disk_perf="N/A")
caption <- "Table 3: Timings for Apple Silicon Mac Pro" make_timings_table("kjohnson3", caption=caption)
make_machine_specs_table("Specs for Intel Mac Pro (24-Core Intel Xeon W)", specs=c(`OS`="macOS 12.7.6", `RAM`="96GB", `Disk`="1TB SSD"), disk_perf="N/A")
caption <- "Table 4: Timings for Intel Mac Pro" make_timings_table("lconway", caption=caption)
The "[Ds] HDF5Matrix as sparse" representation didn't live up to
its promise so we leave it alone for now. Note that the code for loading
blocks of data from the dense HDF5 file to memory does not currently
take full advantage of the SVT_SparseArray representation, a new
efficient data structure for multidimensional sparse data implemented
in the r Biocpkg("SparseArray")
package that overcomes some of the
limitations of the dgCMatrix representation from the r CRANpkg("Matrix")
package. This will need to be addressed.
There's no obvious best choice between the "[s] TENxMatrix (sparse)" and "[D] HDF5Matrix (dense)" representations. More precisely, for normalization, the former tends to give the best times when using bigger blocks (e.g. 250 Mb), whereas the latter tends to give the best times when using smaller blocks (e.g. 16 Mb).
Therefore, on a machine with enough memory to support big block sizes, one will get the best results with the [s] representation and blocks of 250 Mb or more. However, on a machine with not enough memory to support such big blocks, one should instead use the [D] representation with blocks of 16 Mb.
[TODO: Add some plots to help vizualize the above observations.]
For PCA, choosing the "[s] TENxMatrix (sparse)" representation and using small block sizes (40 Mb) tends to give the best performance.
[TODO: Add some plots to help vizualize this observation.]
Note that, on a machine where using blocks of 250 Mb or more for normalization is not an option, one should use the following hybrid approach:
Start with the "[D] HDF5Matrix (dense)" representation.
Perform normalization, using very small blocks (16 Mb).
Switch to the "[s] TENxMatrix (sparse)" format when writing
the normalized dataset to disk, that is, use writeTENxMatrix()
instead of writeHDF5Array()
for on-disk realization of the
intermediate dataset.
Perform PCA on the object returned by the on-disk realization step
(writeTENxMatrix()
), using small blocks (40 Mb).
The machines running macOS use between 2x and 3x more memory than the machines running Linux for the same task using the same block size.
Overall, on Linux, and for a given choice of block size, memory usage doesn't seem to be affected too much by the number of cells in the dataset, that is, all operations seem to perform at almost constant memory.
However, the "[D] HDF5Matrix (dense)" representation appears to be better than the "[s] TENxMatrix (sparse)" representation at keeping memory usage (mostly) flat as the number of cells in the dataset increases. This is even more accentuated on macOS where, somehow counter intuitively, using the dense representation manages to keep memory usage at a reasonable level (and more or less capped with respect to the number of cells), while using the sparse representation fails to do that.
r Biocpkg("SparseArray")
package.machine_names <- c( `DELL XPS 15 laptop`="xps15", `Supermicro SuperServer 1029GQ-TRT`="rex3", `Apple Silicon Mac Pro`="kjohnson3", `Intel Mac Pro`="lconway" ) summarize_machine_times(machine_names)
Normalization and PCA are roughly linear in time with respect to the number of cells in the dataset, regardless of representation (sparse or dense) or block size.
Block size matters. When using the TENxMatrix representation (sparse format),
the bigger the blocks the faster normalization will be (at the cost of
increased memory usage). On the other hand, it seems that PCA prefers
small blocks, at least with our naive simple_PCA()
implementation.
Disk performance is important (not surprisingly) as attested by the lower performance of the Supermicro SuperServer 1029GQ-TRT machine, likely due to its slower disk.
sessionInfo()
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