In various attempts to reduce the computing time of an algorithm I have been coding in the last few days, I wanted to test the effective improvement given by crossprod on the %*%. I surprisingly noticed that using %*%, my algorithm would run faster.
Hence, I decided to compare the two routines using microbenchmark() (as well as system.time()) on general matrices and I got the following results:
M <- 1000
K <- 100
A <- matrix(rnorm(M*K, 10, 1), ncol = M)
b <- rnorm(K, 10, 1)
B <- matrix(rnorm(M*K, 10, 1), ncol = M)
microbenchmark(crossprod(A, A), t(A)%*%A, times = 1000, unit="ms")
Unit: milliseconds
expr min lq mean median uq max neval cld
crossprod(A, A) 112.58885 121.05406 149.8290 129.31873 147.6489 358.3164 1000 b
t(A) %*% A 76.77698 81.68934 108.0526 89.50015 105.9617 304.7395 1000 a
microbenchmark(crossprod(A), t(A)%*%A, times = 1000, unit="ms")
Unit: milliseconds
expr min lq mean median uq max neval cld
crossprod(A) 58.26374 61.56330 69.35781 64.65561 71.42403 314.9268 1000 a
t(A) %*% A 76.97771 81.80069 92.21863 85.75894 93.50332 273.5133 1000 b
microbenchmark(crossprod(A, B), t(A)%*%B, times = 1000, unit="ms")
Unit: milliseconds
expr min lq mean median uq max neval cld
crossprod(A, B) 109.27471 111.6751 118.00118 112.97533 117.55815 284.6910 1000 b
t(A) %*% B 74.36276 77.0441 83.33582 77.89172 82.58609 258.3154 1000 a
microbenchmark(crossprod(A, b), t(A)%*%b, times = 1000, unit="ms")
Unit: milliseconds
expr min lq mean median uq max neval cld
crossprod(A, b) 0.149644 0.1553795 0.1884534 0.1577500 0.167333 6.737466 1000 a
t(A) %*% b 0.338180 0.6239705 0.8052485 0.6423505 0.678017 13.011479 1000 b
microbenchmark(crossprod(b, d), t(b)%*%d, times = 1000, unit="ms")
Unit: milliseconds
expr min lq mean median uq max neval cld
crossprod(b, d) 0.000814 0.0009130 0.001153643 0.000973 0.0010740 0.018912 1000 a
t(b) %*% d 0.002547 0.0029275 0.003554290 0.003087 0.0033005 0.057184 1000 b
microbenchmark(crossprod(b), t(b)%*%b, times = 1000, unit="ms")
Unit: milliseconds
expr min lq mean median uq max neval cld
crossprod(b) 0.000758 0.000801 0.000866091 0.000848 0.000883 0.004277 1000 a
t(b) %*% b 0.002546 0.002686 0.002872259 0.002785 0.002898 0.033779 1000 b
Apparently, at least on my machine, crossprod is faster only when dealing with vectors or when taking the square of a matrix, without specifying y argument.
I know that theoretically, crossprod should be generally faster so, how is this possible?
sessionInfo()
R version 3.6.1 (2019-07-05)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Manjaro Linux
Matrix products: default
BLAS: /usr/lib/libblas.so.3.8.0
LAPACK: /usr/lib/liblapack.so.3.8.0