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Topic:
MapleV: using evalhf with infinite integral.
Replies:
2
Last Post:
Dec 6, 1996 1:53 AM




Re: MapleV: using evalhf with infinite integral.
Posted:
Dec 6, 1996 1:53 AM


In article <m0viahuy1k.fsf@flash.bfr.co.il>, David Klein <dklein@math.huji.ac.il> wrote: >I would like to integrate a function like
>f:=exp(x^2);
>evalhf(f,x=infinity..infinity));
>but with a more time consuming integrand, f.
>evalf instead of evalhf works, but I am trying to be faster.
>I have tried also sorts of methods such as using "Int" instead of >"int", using g:=unapply(f,x) or g:=unapply(evalhf(f,x)) or >g:=evalhf(unapply(f,x)) or g:=x > evalhf(f). I also tried the above >with combinations of quoting the integrand 'g(x)' or even ''g(x)'' etc...
>Can anyone tell me how to use evalhf as efficiently as possible in >these cases?
As far as I know, this is impossible. In fact, on p. 245 of the Maple V Programming Guide (Release 4) it says "you cannot evaluate an integral using hardware floatingpoint arithmetic". The problem is that "evalhf" is for arithmetic calculations only, without anything symbolic (including intermediate results). And integration, even numerical integration, does a lot of symbolic processing. Especially in a case like yours involving an improper integral, which Maple tries to transform to a proper integral, e.g. by change of variable. For some insight into what it does, try > infolevel[evalf]:= 5; > evalf(Int(...));
In order to use "evalhf", you'll have to come up with a purely numerical procedure for evaluating your integral, one where all intermediate steps evaluate to floats, and there are no symbolic structures except arrays.
Robert Israel israel@math.ubc.ca Department of Mathematics (604) 8223629 University of British Columbia fax 8226074 Vancouver, BC, Canada V6T 1Y4



