R help - Oct 2006 - A faster way to calculate Trace?

I want to know how to get trace of product of matrices **faster** when the
matrices are really big. Unfortunately the matrices are not symmetric. If
anybody know how to get the trace of it, please help me. An example is as below.

n <- 2500
a <- matrix(rnorm(n*n),n,n)
b <- matrix(rnorm(n*n),n,n)
tr1 <- sum(diag(a %*% b))
tr2 <- sum(diag(a %*% b %*% a %*% b))

Thanks,

Yongwan Chun

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
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