--- title: "_HDF5Array_ performance" author: - name: Hervé Pagès affiliation: Fred Hutch Cancer Center, Seattle, WA date: "Compiled `r doc_date()`; Modified 18 February 2025" package: HDF5Array vignette: | %\VignetteIndexEntry{HDF5Array performance} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} output: BiocStyle::html_document --- # Introduction 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: 1. data representation (i.e. _sparse_ vs _dense_); 2. size of the blocks used for _block-processed_ operations. 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. # Install and load the required packages Let's install and load `r Biocpkg("HDF5Array")` as well as the other packages used in this vignette: ```{r install, eval=FALSE} if (!require("BiocManager", quietly=TRUE)) install.packages("BiocManager") pkgs <- c("HDF5Array", "ExperimentHub", "DelayedMatrixStats", "RSpectra") BiocManager::install(pkgs) ``` Load the packages: ```{r load, message=FALSE} library(HDF5Array) library(ExperimentHub) library(DelayedMatrixStats) library(RSpectra) ``` ```{r source_make_timings_table_R, echo=FALSE, results='hide'} ## Needed for the make_timings_table() function. path <- system.file(package="HDF5Array", "scripts", "make_timings_table.R", mustWork=TRUE) source(path, verbose=FALSE) ``` # The test datasets ## _Sparse_ vs _dense_ representation 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: 1. 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. 2. 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`: ```{r ExperimentHub} 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: ```{r get_EH1039_and_EH1040, message=FALSE} ## 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. ## TENxMatrix vs HDF5Matrix objects 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. ### Bring the sparse dataset in R ```{r brain_s} ## 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: ```{r brain_s_class_and_dim} class(brain_s) dim(brain_s) is_sparse(brain_s) ``` See `?TENxMatrix` in the `r Biocpkg("HDF5Array")` package for more information about TENxMatrix objects. ### Bring the dense dataset in R ```{r brain_D} ## 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`: ```{r brain_D_class_and_dim} 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`: ```{r brain_Ds} 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: ```{r brain_Ds_class_and_dim} 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`: ```{r set_brain_D_and_brain_Ds_dimnames} dimnames(brain_Ds) <- dimnames(brain_D) <- dimnames(brain_s) ``` ## Create the test datasets 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: ```{r create_test_datasets} 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] ``` # Block-processed normalization and PCA ## Code used for normalization and PCA We'll use the following code for normalization: ```{r simple_normalize_function} ## 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: ```{r simple_PCA_function} 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)) } ``` ## Block processing and block size 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 | ## Monitoring memory usage 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 ; sleep 1; done) >ps.log 2>&1 & where `` 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()`. # Normalization and PCA of the 27,998 x 12,500 test dataset ## Normalization 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. ### TENxMatrix (sparse) ```{r norm_brain1_s} 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) ``` ### HDF5Matrix (dense) ```{r norm_brain1_D} 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) ``` ### HDF5Matrix as sparse ```{r norm_brain1_Ds} 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) ``` ## On-disk realization of the normalized datasets 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`: ```{r show_norm_brain1_s_delayed_ops} 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. ```{r set_realization_block_size} DelayedArray::setAutoBlockSize(1e8) ``` ### TENxMatrix (sparse) ```{r writeTENxMatrix_norm_brain1_s} 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: ```{r show_pristine_norm_brain1_s} class(norm_brain1_s) showtree(norm_brain1_s) # "pristine" object (i.e. no more delayed operations) ``` ### HDF5Matrix (dense) ```{r writeHDF5Array_norm_brain1_D} 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: ```{r show_pristine_norm_brain1_D} class(norm_brain1_D) showtree(norm_brain1_D) # "pristine" object (i.e. no more delayed operations) ``` ### HDF5Matrix as sparse ```{r writeHDF5Array_norm_brain1_Ds} 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: ```{r show_pristine_norm_brain1_Ds} class(norm_brain1_Ds) showtree(norm_brain1_Ds) # "pristine" object (i.e. no more delayed operations) ``` ## PCA 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. ### TENxMatrix (sparse) ```{r PCA_norm_brain1_s} DelayedArray::setAutoBlockSize(40e6) # set block size to 40 Mb dim(norm_brain1_s) system.time(pca1s <- simple_PCA(norm_brain1_s)) ``` ### HDF5Matrix (dense) ```{r PCA_norm_brain1_D} DelayedArray::setAutoBlockSize(1e8) # set block size to 100 Mb dim(norm_brain1_D) system.time(pca1D <- simple_PCA(norm_brain1_D)) ``` Sanity check: ```{r sanity_check1d} stopifnot(all.equal(pca1D, pca1s)) ``` ### HDF5Matrix as sparse ```{r PCA_norm_brain1_Ds} DelayedArray::setAutoBlockSize(40e6) # set block size to 40 Mb dim(norm_brain1_Ds) system.time(pca1Ds <- simple_PCA(norm_brain1_Ds)) ``` Sanity check: ```{r sanity_check1ds} stopifnot(all.equal(pca1Ds, pca1s)) ``` # Comprehensive timings obtained on various machines 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). ## Timings for DELL XPS 15 laptop ```{r xps15_specs, echo=FALSE, results='asis'} hdparm1 <- "Output of sudo hdparm -Tt <device>:" hdparm1 <- sprintf("%s", 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("%s", paste(hdparm2, collapse="
")) disk_perf <- paste0(hdparm1, "
", 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) ``` ```{r xps15_timings, echo=FALSE, results='asis'} caption <- "Table 1: Timings for DELL XPS 15 laptop" make_timings_table("xps15", caption=caption) ``` ## Timings for Supermicro SuperServer 1029GQ-TRT ```{r rex3_specs, echo=FALSE, results='asis'} hdparm1 <- "Output of sudo hdparm -Tt <device>:" hdparm1 <- sprintf("%s", 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("%s", paste(hdparm2, collapse="
")) disk_perf <- paste0(hdparm1, "
", 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) ``` ```{r rex3_timings, echo=FALSE, results='asis'} caption <- "Table 2: Timings for Supermicro SuperServer 1029GQ-TRT" make_timings_table("rex3", caption=caption) ``` ## Timings for Apple Silicon Mac Pro ```{r kjohnson3_specs, echo=FALSE, results='asis'} 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") ``` ```{r kjohnson3_timings, echo=FALSE, results='asis'} caption <- "Table 3: Timings for Apple Silicon Mac Pro" make_timings_table("kjohnson3", caption=caption) ``` ## Timings for Intel Mac Pro ```{r lconway_specs, echo=FALSE, results='asis'} 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") ``` ```{r lconway_timings, echo=FALSE, results='asis'} caption <- "Table 4: Timings for Intel Mac Pro" make_timings_table("lconway", caption=caption) ``` # Discussion 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. ## TENxMatrix (sparse) vs HDF5Matrix (dense) ### Normalization 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.]_ ### PCA 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.]_ ### Hybrid approach 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). ### A note about memory usage 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. ## Main takeaways 1. Using the TENxMatrix representation (sparse format), one can perform **normalization and PCA** of the bigger dataset (200,000 cells) on an average consumer-grade laptop like the DELL XPS 15 laptop (model 9520) **in less than 25 minutes and using less than 4Gb of memory**, as shown in the table below. For comparison, normalization and PCA on an _in-memory_ representation of the same dataset (e.g. on a SparseMatrix object) takes less then 4 minutes. However, that consumes about 18.5Gb of memory! This will be the subject of an upcoming vignette in the `r Biocpkg("SparseArray")` package. ```{r summarize_machine_times, echo=FALSE, results='asis'} 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) ``` 2. 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. 3. 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. 4. 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. # Session information ```{r sessionInfo} sessionInfo() ```