[R] A faster way to calculate Trace?

[Giovanni Petris]

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 <berwin at maths.uwa.edu.au>
> Sender: r-help-bounces at stat.math.ethz.ch
> Cc: r-help at stat.math.ethz.ch
> Precedence: list
> 
> G'day Yongwan,
> 
> >>>>> "YC" == YONGWAN CHUN <chun.49 at osu.edu> 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)      
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> Crawley WA 6009                e-mail: berwin at maths.uwa.edu.au
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> 
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-- 

 __________________________________________________
[                                                  ]
[ Giovanni Petris                 GPetris at uark.edu ]
[ Department of Mathematical Sciences              ]
[ University of Arkansas - Fayetteville, AR 72701  ]
[ Ph: (479) 575-6324, 575-8630 (fax)               ]
[ http://definetti.uark.edu/~gpetris/              ]
[__________________________________________________]