Benchmarking Sparse Matrix Market Write Operations
In fastMatMR: High-Performance Matrix Market File Operations

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.

Loading Packages

First, we load the necessary packages:

library(Matrix)
library(fastMatMR)
library(microbenchmark)
library(ggplot2)

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'

plot of chunk fixed-sparse-write

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'

plot of chunk varying-sparse-write

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