Introduction
This vignette demonstrates a benchmark comparing the
writeMM function from the Matrix package
against the write_fmm function from the
fastMatMR package. Since Matrix does not
support reading or writing dense matrices, we focus on the sparse
case.
Benchmarking with Fixed Sparsity
We first benchmark for varying matrix sizes with fixed sparsity.
# Function to create a sparse matrix of given size
create_sparse_matrix <- function(n, sparsity = 0.7) {
mat <- matrix(0, nrow = n, ncol = n)
for (i in 1:n) {
for (j in 1:n) {
if (runif(1) > sparsity) {
mat[i, j] <- rnorm(1)
}
}
}
return(Matrix(mat, sparse = TRUE))
}
# Define a range of matrix sizes
sizes <- c(10, 100, 500, 1000)
# Prepare data frame to store results
results_fixed_sparsity <- data.frame()
# Benchmarking
for (n in sizes) {
message("Benchmarking for matrix size: ", n, "x", n)
# Generate a sparse matrix of size n x n
testmat <- create_sparse_matrix(n)
# Run the benchmarks
bm <- microbenchmark(
Matrix_writeMM = writeMM(testmat, "mat.mtx"),
fastMatMR_write_fmm = write_fmm(testmat, "fmm.mtx"),
times = 10
)
bm$size <- n
results_fixed_sparsity <- rbind(results_fixed_sparsity, bm)
}
#> Benchmarking for matrix size: 10x10
#> Benchmarking for matrix size: 100x100
#> Benchmarking for matrix size: 500x500
#> Benchmarking for matrix size: 1000x1000
This is shown visually represented below:
# Plotting
suppressWarnings(print(
ggplot(results_fixed_sparsity, aes(x = size, y = time, color = expr)) +
geom_point() +
geom_smooth(method = "loess") +
scale_y_log10() +
ggtitle("Benchmarking writes with fixed sparsity for 70% sparsity") +
xlab("Matrix Size") +
ylab("Time (ns, log10)")
))
#> `geom_smooth()` using formula = 'y ~ x'
Benchmarking with Varying Sparsity
Now, we benchmark for varying sparsity patterns on a large
matrix.
# Sparsity levels to test
sparsity_levels <- seq(0.4, 0.95, by = 0.05)
# Prepare data frame to store results
results_varying_sparsity <- data.frame()
# Benchmarking
for (sparsity in sparsity_levels) {
message("Benchmarking for sparsity level: ", sparsity)
# Generate a sparse matrix of size 500 x 500 with varying sparsity
testmat <- create_sparse_matrix(500, sparsity)
# Run the benchmarks
bm <- microbenchmark(
Matrix_writeMM = writeMM(testmat, "mat.mtx"),
fastMatMR_write_fmm = write_fmm(testmat, "fmm.mtx"),
times = 10
)
bm$sparsity <- sparsity
results_varying_sparsity <- rbind(results_varying_sparsity, bm)
}
#> Benchmarking for sparsity level: 0.4
#> Benchmarking for sparsity level: 0.45
#> Benchmarking for sparsity level: 0.5
#> Benchmarking for sparsity level: 0.55
#> Benchmarking for sparsity level: 0.6
#> Benchmarking for sparsity level: 0.65
#> Benchmarking for sparsity level: 0.7
#> Benchmarking for sparsity level: 0.75
#> Benchmarking for sparsity level: 0.8
#> Benchmarking for sparsity level: 0.85
#> Benchmarking for sparsity level: 0.9
#> Benchmarking for sparsity level: 0.95
Now we can plot this:
ggplot(results_varying_sparsity, aes(x = sparsity, y = time, color = expr)) +
geom_point() +
geom_smooth(method = "loess") +
scale_x_log10() +
scale_y_log10() +
ggtitle("Benchmarking writes with varying sparsity for 500 entries") +
xlab("Sparsity Level (log10)") +
ylab("Time (ns, log10)")
#> `geom_smooth()` using formula = 'y ~ x'
Conclusions
Clearly, for larger matrices, and fastMatMR is
consistently around two orders of magnitude faster than
Matrix. For extremely small matrices (<50) and at high
(~.7) levels of sparsity, the difference is not as pronounced, but for
matrices larger than 50x50 fastMatMR retains an order of
magnitude improvement.
Session Info
This vignette was computed in advance, with the corresponding session
info:
sessionInfo()
#> R version 4.3.1 (2023-06-16)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Arch Linux
#>
#> Matrix products: default
#> BLAS: /usr/lib/libblas.so.3.11.0
#> LAPACK: /usr/lib/liblapack.so.3.11.0
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
#> [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: Iceland
#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] ggplot2_3.4.4 microbenchmark_1.4.10 Matrix_1.5-4.1
#> [4] fastMatMR_1.2.5 testthat_3.1.10
#>
#> loaded via a namespace (and not attached):
#> [1] gtable_0.3.4 xfun_0.40 htmlwidgets_1.6.2 devtools_2.4.5
#> [5] remotes_2.4.2.1 processx_3.8.2 lattice_0.21-8 callr_3.7.3
#> [9] generics_0.1.3 vctrs_0.6.3 tools_4.3.1 ps_1.7.5
#> [13] parallel_4.3.1 tibble_3.2.1 fansi_1.0.4 highr_0.10
#> [17] pkgconfig_2.0.3 desc_1.4.2 lifecycle_1.0.3 farver_2.1.1
#> [21] compiler_4.3.1 stringr_1.5.0 brio_1.1.3 munsell_0.5.0
#> [25] decor_1.0.2 httpuv_1.6.11 htmltools_0.5.6 usethis_2.2.2
#> [29] later_1.3.1 pillar_1.9.0 crayon_1.5.2 urlchecker_1.0.1
#> [33] ellipsis_0.3.2 cachem_1.0.8 sessioninfo_1.2.2 nlme_3.1-162
#> [37] mime_0.12 commonmark_1.9.0 tidyselect_1.2.0 digest_0.6.33
#> [41] stringi_1.7.12 dplyr_1.1.2 purrr_1.0.2 labeling_0.4.3
#> [45] splines_4.3.1 rprojroot_2.0.3 fastmap_1.1.1 grid_4.3.1
#> [49] colorspace_2.1-0 cli_3.6.1 magrittr_2.0.3 pkgbuild_1.4.2
#> [53] utf8_1.2.3 withr_2.5.0 prettyunits_1.1.1 scales_1.2.1
#> [57] promises_1.2.1 cpp11_0.4.6 roxygen2_7.2.3 memoise_2.0.1
#> [61] shiny_1.7.5 evaluate_0.21 knitr_1.43 miniUI_0.1.1.1
#> [65] mgcv_1.8-42 profvis_0.3.8 rlang_1.1.1 Rcpp_1.0.11
#> [69] xtable_1.8-4 glue_1.6.2 xml2_1.3.5 pkgload_1.3.2.1
#> [73] rstudioapi_0.15.0 R6_2.5.1 fs_1.6.3
