On Dec 11, 2007 8:34 AM, Rishikesh <[EMAIL PROTECTED]> wrote:
> I have couple of versions of computing the same function below
> f is a polynomial. g is function which returns the same value as f
> for given number. g is 10 times faster. Can it be made closer?
Make your function f be a polynomial ** over the real field ** RR and it
will be significantly faster than even your function g:
{{{id=133|
def g(y):
return y^24+34*y^12+45*y^3+9*y^18 +34*y^10+ 32*y^21
R.<x> = RR[]
f=x^24+34*x^12+45*x^3+9*x^18 +34*x^10+ 32*x^21
}}}
{{{id=134|
%time
for i in range(10000):
a=f(x=RR.random_element())
///
CPU time: 0.35 s, Wall time: 0.35 s
}}}
{{{id=135|
%time
for i in range(10000):
a=g(y=RR.random_element())
///
CPU time: 1.00 s, Wall time: 1.00 s
}}}
NOTE: Don't use RDF for this, evidently, since it seem to be VERY VERY slow,
probably because of something not being rewriting in Cython:
{{{
R.<z> = RDF[]
h = R(f)
}}}
{{{id=137|
%time
for i in range(1000):
a=h(x=RDF.random_element())
///
CPU time: 4.58 s, Wall time: 4.58 s
}}}
> See code below
>
> Rishi
>
> {{{id=133|
> var('x')
>
> f=x^24+34*x^12+45*x^3+9*x^18 +34*x^10+ 32*x^21
>
> def g(y):
> return y^24+34*y^12+45*y^3+9*y^18 +34*y^10+ 32*y^21
> }}}
>
> {{{id=134|
> %time
> for i in range(10000):
> a=f(x=RR.random_element())
> ///
> CPU time: 14.69 s, Wall time: 14.99 s
> }}}
>
> {{{id=135|
> %time
> for i in range(10000):
> a=g(y=RR.random_element())
> ///
> CPU time: 1.66 s, Wall time: 1.68 s
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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