benchmark

library(microbenchmark)
library(Matrix)
library(data.table)

data Simulation function

nGenes <- 3e4
sim <- function(alpha, beta, nCells){
  m <- matrix(nrow = nGenes, ncol = nCells)
  pi_g <- rbeta(n = nGenes, alpha, beta)
  for(i in seq_len(nGenes))
    m[i, ] <- sample(x = c(0, 10), size = nCells,  prob = c(1-pi_g[i], pi_g[i]),replace = T)
  
  #set 30% rows to all 0s
  m[sample(nGenes, 0.3 * nGenes), ] <- 0
  m
}

benchmark different formats

set.seed(4)
ridx <- sample(nGenes, 1e3)
res <- lapply(c(1e3, 4e3, 6e3,2e4), function(nCells){
  cidx <- sample(nCells, 1e3)
  
  #2d in-memory mat
  mat <- sim(0.5, 0.5, nCells)  
  size <- object.size(mat)/1e9
  timing <- microbenchmark(mat[ridx,], mat[, cidx], mat[ridx, cidx], times = 3, unit = "ms")
  timing <- summary(timing)[["mean"]]
  dt1 <- data.table(nCells = nCells, format = "in-memory 2d mat", size = size, slicing = c("row", "col", "row&col"), time = timing)
  
  #2d in-memory sparse mat
  mat <- Matrix(mat, sparse = T)
  sparsity <- 1- nnzero(mat)/(nCells * nGenes)
  size <- object.size(mat)/1e9
  timing <- microbenchmark(mat[ridx,], mat[, cidx], mat[ridx, cidx], times = 3, unit = "ms")
  timing <- summary(timing)[["mean"]]
  dt2 <- data.table(nCells = nCells, format = "in-memory sparsed 2d mat", size = size, slicing = c("row", "col", "row&col"), time = timing)
  
  thisRes <- rbindlist(list(dt1, dt2))
  thisRes[, sparsity:=sparsity]
  
})
dt <- rbindlist(res)

sparsity (zero-value rate)

dt[, unique(sparsity), by = nCells]

##    nCells        V1
## 1:   1000 0.6495754
## 2:   4000 0.6472751
## 3:   6000 0.6495084
## 4:  20000 0.6530742

plot the result

library(ggplot2)
ggplot(dt, aes(y = time, x = nCells, color = format)) + geom_line() + geom_point() + facet_wrap(~slicing) + ylab("time (ms)")

ggplot(dt, aes(x = nCells, y = size, color = format)) + geom_line() + geom_point() + ylab("size (GB)")