Re: [R] Matrix mulitplication

[Spencer Graves]

     One can also use "crossprod" AND use "solve" to actually "solve" 
the system of linear equations rather than just get the inverse, which 
is later multiplied by t(BA)%*%D.  However, the difference seems very 
small: 

> set.seed(1)
> n <- 500
> A <- array(rnorm(n^2), dim=c(n,n))
> B <- array(rnorm(n^2), dim=c(n,n))
> C. <- array(rnorm(n^2), dim=c(n,n))
> D <- array(rnorm(n^2), dim=c(n,n))
>
> BA <- B%*%A
>
> start.time <- proc.time()
> A1 <- A%*%solve(t(BA)%*%BA+C.)%*%BA%*%D
> proc.time()-start.time
[1] 4.75 0.03 5.13   NA   NA
>
> start.time <- proc.time()
> A2 <- A%*%solve(crossprod(BA)+C., crossprod(t(BA), D))
> proc.time()-start.time
[1] 4.19 0.01 4.49   NA   NA
> all.equal(A1, A2)
[1] TRUE
     This was in R 1.8.1 under Windows 2000 on an IBM Thinkpad T30 with 
a Mobile Intel Pentium 4-M, 1.8Ghz, 1Gbyte RAM.  The same script under 
S-Plus 6.2 produced the following elapsed times: 

[1] 3.325 0.121 3.815 0.000 0.000

[1] 2.934 0.070 3.355 0.000 0.000

     Thus, roughly, using "crossprod" plus "solving with solve" gave a 
10% speed improvement and S-Plus 6.2 gave a 25% speed improvement in 
this one small benchmark.  Using smaller matrices did not show as big a 
difference just because the time was too short to measure accurately, I 
think. 

     Enough trivia for now. 
     Best Wishes,
     spencer graves

(Ted Harding) wrote:

On 16-Feb-04 Peter Dalgaard wrote:
 

(Ted Harding) <[EMAIL PROTECTED]> writes:

   

Sorry! Missed a trick here:

   At <- t(A)
   Bt <- t(B)
   E  <- B%*%A
   Et <- t(E)
   A%*%solve(Et%*%E + C)%*%Et%*%D
(saves 2 multiplications at the relatively cheap cost of 1 transpose)
     

Well, you might consider getting rid of the first two transposes since
you're not actually using them for anything....
   

Touch� ... !
Ted.
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E-Mail: (Ted Harding) <[EMAIL PROTECTED]>
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Date: 16-Feb-04                                       Time: 23:41:57
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