Benchmarking Sparse Matrix Market Read Operations

Introduction

This vignette demonstrates a benchmark comparing the readMM function from the Matrix package against the read_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, 2000, 3000)
 
    # 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)
      write_fmm(testmat, "sparse.mtx")
 
      # Run the benchmarks, we coerce to a sparse matrix for readMM for fairness
      bm <- microbenchmark(
        Matrix_readMM = as(readMM("sparse.mtx"), "CsparseMatrix"),
        fastMatMR_read_fmm = fmm_to_sparse_Matrix("sparse.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
#> Benchmarking for matrix size: 2000x2000
#> Benchmarking for matrix size: 3000x3000

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") +
        ggtitle("Benchmarking reads with fixed sparsity for 70% sparsity") +
        xlab("Matrix Size") +
        ylab("Time (ns)")
))
#> `geom_smooth()` using formula = 'y ~ x'

plot of chunk fixed-sparse-read

Benchmarking with Varying Sparsity

Now, we benchmark for varying sparsity patterns on a large matrix.

# Sparsity levels to test
sparsity_levels <- seq(0.45, 0.95, by = 0.1)

# 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 2000 x 2000 with varying sparsity
  testmat <- create_sparse_matrix(2000, sparsity)
  write_fmm(testmat, "sparse.mtx")

  # Run the benchmarks
  bm <- microbenchmark(
    Matrix_readMM = as(readMM("sparse.mtx"), "CsparseMatrix"),
    fastMatMR_read_fmm = fmm_to_sparse_Matrix("sparse.mtx"),
    times = 10
  )

  bm$sparsity <- sparsity
  results_varying_sparsity <- rbind(results_varying_sparsity, bm)
}
#> Benchmarking for sparsity level: 0.45
#> Benchmarking for sparsity level: 0.55
#> Benchmarking for sparsity level: 0.65
#> Benchmarking for sparsity level: 0.75
#> Benchmarking for sparsity level: 0.85
#> 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 reads with varying sparsity for 2000 entries") +
  xlab("Sparsity Level (log10)") +
  ylab("Time (ns, log10)")
#> `geom_smooth()` using formula = 'y ~ x'

plot of chunk varying-sparse-read

Conclusions

We see that though there are no statistically significant differences in speed for small matrices, the fastMatMR package is significantly faster for large matrices. This is because the readMM function from the Matrix reads data into a triplet form, which gets slower for larger matrices.

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