You can cut execution time by another 50% by using crossprod.
n - 1000
a - matrix(rnorm(n*n),n,n)
b - matrix(rnorm(n*n),n,n)
system.time(print(sum(diag(a %*% b
[1] -905.0063
[1] 8.120 0.000 8.119 0.000 0.000
system.time(print(sum(a*t(b
[1] -905.0063
[1] 1.510 0.000 1.514 0.000 0.000
system.time(print(crossprod(as.vector(a), as.vector(t(b)
[,1]
[1,] -905.0063
[1] 0.700 0.000 0.705 0.000 0.000
system.time(print(sum(diag(a %*% b %*% a %*% b
[1] 1266733
[1] 24.550 0.000 24.567 0.000 0.000
system.time({
+ cmat - a %*% b
+ print(crossprod(as.vector(cmat), as.vector(t(cmat
+ })
[,1]
[1,] 1266733
[1] 8.930 0.010 8.941 0.000 0.000
Cheers,
Giovanni
Date: Fri, 27 Oct 2006 08:42:11 +0800
From: Berwin A Turlach [EMAIL PROTECTED]
Sender: [EMAIL PROTECTED]
Cc: r-help@stat.math.ethz.ch
Precedence: list
G'day Yongwan,
YC == YONGWAN CHUN [EMAIL PROTECTED] writes:
YC I want to know how to get trace of product of matrices
YC **faster** when the matrices are really big. Unfortunately the
YC matrices are not symmetric. If anybody know how to get the
YC trace of it, please help me. An example is as below.
The first one is quite simple to speed up:
n - 2500
a - matrix(rnorm(n*n),n,n)
b - matrix(rnorm(n*n),n,n)
sum(diag(a %*% b))
[1] 1890.638
tb - t(b)
sum(a*tb)
[1] 1890.638
For the second one, you may try:
sum(diag(a %*% b %*% a %*% b))
[1] 10668786
cmat - a %*% b
sum(cmat*t(cmat))
[1] 10668786
It gives somewhat a speedup, since you only have to multiply two huge
matrices once instead of thrice, but I wonder whether further
improvements are possible.
Hope this helps.
Cheers,
Berwin
== Full address
Berwin A Turlach Tel.: +61 (8) 6488 3338 (secr)
School of Mathematics and Statistics+61 (8) 6488 3383 (self)
The University of Western Australia FAX : +61 (8) 6488 1028
35 Stirling Highway
Crawley WA 6009e-mail: [EMAIL PROTECTED]
Australiahttp://www.maths.uwa.edu.au/~berwin
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
--
__
[ ]
[ Giovanni Petris [EMAIL PROTECTED] ]
[ Department of Mathematical Sciences ]
[ University of Arkansas - Fayetteville, AR 72701 ]
[ Ph: (479) 575-6324, 575-8630 (fax) ]
[ http://definetti.uark.edu/~gpetris/ ]
[__]
__
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
