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Re: calculating euler products [newbie]
Posted:
Jan 5, 2012 3:21 PM
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On 5 jan, 19:32, "John D'Errico" <woodch...@rochester.rr.com> wrote:
> Jean Dupont <jeandupont...@gmail.com> wrote in message <9e730b1e-4327-4e8d-82b7-5201e21a2...@z17g2000vbe.googlegroups.com>...
> > I've written the function below to calculate euler-products, I was
> > wondering how it can be improved i.e. written more in "matlab-style"
> > perhaps reducing execution time for large numbers
>
> > regards,
> > Jean
>
> > function eulerprod(n)
> > %calculate PI(1/(1-p^-1)) for all primes smaller than n
> > prime=primes(n);
> > nop=length(prime)
> > factor=1
> > for i=1:nop
> > factor=factor/(1-prime(i)^(-1));
> > y(i)=factor;
> > end
> > plot([1:nop],y)
>
> You need to start thinking in terms of vectors. Skip
> the loops.
>
> First of all, this first is fine. Always use existing tools (like
> primes) when you can.
>
> p = primes(n);
>
> But then why not process them all at once? Can you invert
> every element of a vector, all at once? What does this do?
>
> 1./p
>
> Or this?
>
> 1 - 1./p
>
> Or this?
>
> 1./(1 - 1./p)
>
> Now, is there any function that can take the product of an
> entire vector? Look for it. Of course, you actually want what
> might be called the cumulative product. Is there such a thing
> already defined in matlab as a function?
>
> Learn to use the lookfor function when you are not sure what
> the name of a function might be. In this case I'll bet that
>
> lookfor product
>
> might yield something very useful.
>
> John
I think this is what you had in mind?
function cumeulerprod(n)
%calculate PI(1/(1-p^-1)) for all primes smaller than n
p=primes(n);
y=cumprod(1./(1-1./p));
plot(y)
regards,
Jean
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