[Scilab-users] Struve function, was Re: The 1st order Struve function

[Claus Futtrup]

Hi Christophe

Thanks for the tip on inverting instead of division, I didn't know. 
Interesting.

In my case size(x) = [1 10000] ... (circa) ... but it calculates quickly 
(and only once).

My implementation of the first order Struve function is based on 
approximation.

I was wondering if there's anybody who has made a general 
implementation. (?)

Following http://mathworld.wolfram.com/StruveFunction.html, using the 
gamma function ... maybe this would be better if coded in Fortran?

Best regards,
Claus

On 26-01-2015 11:21, Dang, Christophe wrote:
> Hello,
>
>> De : Claus Futtrup
>> Envoyé : samedi 24 janvier 2015 19:31
>>
>>     z = 2/%pi - besselj(0,x) + (16/%pi - 5) .* (sin(x)./x) ..
>>               + (12 - 36/%pi) * ( (1-cos(x))./(x.^2) );
> A division cost much more than several multiplications (I think something like a 7 factor).
>
> If you have a big amount of data (and thus a long calculation time),
> you can reduce this calculation time,
> but maybe at the expense of the precision if x take very high or very low absolute values
> (overflow or underflow of x^-2),
> with the following trick (not tested):
>
> denominator = x.^(-2);
> pi_inv = 1/%pi;
>
>      z = 2*pi_inv - besselj(0,x) + ((16*pi_inv - 5) .* sin(x).*x ..
>                + (12 - 36*pi_inv) *  (1-cos(x))).*denominator;
>
> It replaces 2*size(x) divisions by 1*size(x) division and 2*size(x) multiplications,
> which is usually less time consuming.
>
> Forget it if size(x) is small or x reach very high or very low absolute values.
>
> HTH
>
> --
> Christophe Dang Ngoc Chan
> Mechanical calculation engineer
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