This is more on post-multiplying a matrix by a diagonal matrix (in six different ways).
The machine-comparison results from this little exercise can be explained by three factors -- CPU speed -- number of threads -- BLAS library Of the six methods, the first two use BLAS, the last four do not. For the last four, times are determined largely by CPU speed. For the first two methods, there are two things going on. First, BLAS in the Windows implementation of R is faster than the vecLib BLAS on OS X. Second, on the Mac Pro with Nehalem, for reasons unknown (bug !!) the OS decides to use a non-parellel single-threaded BLAS. Running the same code, with the same OS and the same R, on a MacBook or an iMac or a MacAir, does use multiple threads. This is all under OS X 10.6.5, by the way, using R-develop from svn. Running the same code in Parallels emulation, using Windows R on the MacPro, uses multiple threads as well. I cannot possibly convey how annoying this is.
matdiag.R
Description: Binary data
========================================================================== 2.66 Ghz dual-core i5 iMac, with 4 GB DDR, R-2.12.0, 64 bit matrix multiplication 34.682 1.474 11.397 tcrossprod 33.461 1.264 9.993 transposition and reuse 20.436 3.654 24.09 elementwise after reshape 8.309 1.932 17.599 columnwise sapply 22.692 18.242 42.006 for loop over columns 29.723 15.832 45.556 ========================================================================== 2 x 2.94 Ghz Quad-core MacPro, 16 GB DDR, R-2.12.0, 64 bit matrix multiplication 31.259 1.814 33.073 tcrossprod 29.693 1.643 31.337 transposition and reuse 24.188 4.931 29.120 elementwise after reshape 9.592 2.464 12.056 columnwise sapply 23.277 22.095 45.373 for loop over columns 29.895 18.662 48.558 ========================================================================== 2 x 2.94 Ghz Quad-core MacPro, 16 GB DDR, R-2.12.0, 64 bit (generic BLAS) matrix multiplication 31.514 1.794 33.838 tcrossprod 29.929 1.614 31.545 transposition and reuse 25.364 4.834 30.206 elementwise after reshape 9.722 2.422 12.144 columnwise sapply 23.516 22.074 45.593 for loop over columns 29.982 18.632 48.617 ========================================================================== 2 x 2.94 Ghz Quad-core MacPro, 16 GB DDR, R-2.11.0, 64 bit, run through R.app matrix multiplication 31.916 3.673 35.384 tcrossprod 30.45 4.379 34.606 transposition and reuse 24.822 7.928 32.476 elementwise after reshape 9.995 3.673 13.559 columnwise sapply 23.708 23.03 46.718 for loop over columns 30.298 19.629 49.745 ========================================================================== 1.8 Ghz dual core MacAir, with 2 GB DDR matrix multiplication 76.154 3.294 49.571 tcrossprod 77.653 3.166 53.702 transposition and reuse 58.258 6.814 65.618 elementwise after reshape 27.091 3.243 30.491 columnwise sapply 48.919 42.725 91.991 for loop over columns 57.727 39.142 97.188 ========================================================================== Windows 7, Parallels emulation, MacPro, R-2.11.0 (64bit) matrix multiplication 8.68 1.86 10.59 tcrossprod 4.0 1.84 5.85 transposition and reuse 39.89 6.92 47.11 elementwise after reshape 10.96 3.24 14.24 columnwise sapply 26.47 10.28 36.9 for loop over columns 34.04 9.75 43.86 ========================================================================== Ubuntu, Parallels emulation, MacPro, R-2.10.1 (64bit) matrix multiplication 25.206 3.072 28.802 tcrossprod 21.209 2.925 24.242 transposition and reuse 32.51 9.564 42.17 elementwise after reshape 10.669 4.368 15.074 columnwise sapply 27.665 10.121 37.869 for loop over columns 35.043 10.193 45.32 ========================================================================== Jeroen on Windows (32 bit): matrix multiplication 9.18 3.09 12.34 tcrossprod 6.27 3.52 9.83 transposition and reuse 41.31 9.96 51.48 elementwise after reshape 18.89 5.06 24.01 columnwise sapply 36.25 15.48 51.9 for loop over columns 41.4 13.7 55.63 ========================================================================== Jeroen on a cheap Ubuntu instance with very limited memory: matrix multiplication 12.86 9.28 22.573 tcrossprod 6.26 9.31 15.668 transposition and reuse 138.39 28.53 169.99 elementwise after reshape 30.22 14.12 44.50 columnwise sapply 36.62 19.17 65.638 for loop over columns 53.72 12.27 66.349 ========================================================================== Masanao on PC matrix multiplication 12.87 3.47 17.11 tcrossprod 10.06 4.38 14.92 transposition and reuse 74.5 13.84 91.42 elementwise after reshape 43.9 7.39 53.36 columnwise sapply 86.5 26.92 124.61 for loop over columns 103.58 25.59 138.88 ========================================================================== Masanao, 2.66 Ghz Dual core i7, 8 GB DDR, MacBook Pro matrix multiplication 58.875 1.801 18.095 tcrossprod 57.423 1.53 16.607 transposition and reuse 31.104 4.181 35.286 elementwise after reshape 9.382 2.052 11.434 columnwise sapply 23.14 20.577 43.718 for loop over columns 29.789 17.516 47.307
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Jan de Leeuw, 11667 Steinhoff Rd, Frazier Park, CA 93225
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I am I because my little dog knows me.
Gertrude Stein
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