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James Kuyper wrote:
> firstname.lastname@example.org wrote:
> > In article <38E03BDC.868B8396@hotmail.com>, marc <email@example.com> writes:
> > >Is there a function like TOTAL but for multiplication.
> > >Like the big PI symbol in mathematical notation.
> > >Or this really something for the for loop?
> > >
> > >I.E.
> > >
> > >a=[1,2,3,...]
> > >
> > >result=a*a*a...
> > >
> > if all the elements of a are positive then you can simply do
> > result = exp(total(alog(a)))
> > If some of the elements are negative, you can still handle it. do
> > dum = where(a lt 0, ndum)
> > sig = (-1)^ndum
> > result = sig*exp(total(alog(abs(a))))
> You can't honestly be suggesting that this is a good technique? Ignore
> for a momement what happens if any element of 'a' is 0. That code
> performs two transcendental function evaluations per element of 'a'. IDL
> would have to be very badly engineered (which I suppose is possible),
> for a 'for' loop to execute more slowly than your code.
Only one transcendental is computed for each a, alog(). The exp occurs on the
single value after the total. Results for a 10,000 element random floating
array finely tuned to avoid under or overflow:
Average Time: 0.017213961
Average Time: 0.0049092293
4 times as fast. Suppose you'd like to do an array with 100,000 double
elements... you get:
% Loop limit expression too large for loop variable type.
<LONG ( 99999)>.
Average Time: 0.050116260
And if you hack it with two nested loops to avoid the loop limit error:
c=1. & for j=0L,n/100-1 do for k=0L,99L do c=c*a[j*100L+k]
Hacked Loop Method
Average Time: 0.30190306
Average Time: 0.068175601
A full 5 times faster.
And now, just for fun, the same data set, but with multiplication computed in a
heavily optimized C program. The core of the C code is simply the
straightforward: "for(i=0;i<N;i++) res*=a[i]"; The result:
Got 0.97063262 (Average Time: 0.001710 s)
Ouch! Another speedup of by a factor of 40!
Morals: IDL loops are pitifully slow, and you can't loop over very large arrays
without trickery, and for many operations, compiled C is *significantly* faster.
J.D. Smith |*| WORK: (607) 255-5842
Cornell University Dept. of Astronomy |*| (607) 255-6263
304 Space Sciences Bldg. |*| FAX: (607) 255-5875
Ithaca, NY 14853 |*|