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Re: IDL's BESELJ returns NAN for small argument and large order [message #88112 is a reply to message #88072]

Thu, 20 March 2014 17:27

dg86
Messages: 118
Registered: September 2012

Senior Member

On Tuesday, March 18, 2014 7:47:28 PM UTC-4, Phillip Bitzer wrote:
> "That's not a bug, it's a feature" :-)
>
>
>
> The reason you get a NaN can be found in the help:
>
>
>
> ITER
>
> Set this keyword equal to a named variable that will contain the number of iterations performed. If the routine converged, the stored value will be equal to the order N. If X or N are arrays, ITER will contain a scalar representing the maximum number of iterations.
>
> Note: If the routine did not converge for an element of X, the corresponding element of the Result array will be set to the IEEE floating-point value NaN, and ITER will contain the largest order that would have converged for that X value.
>
>
>
> So,
>
> IDL> print,beselj(0.1d,103.d, ITER=n)
>
> IDL> print, n ;get n=102
>
>
>
> So, the algorithm properly converges for order 102, but not 103+. This is why get a number for your second example.

This is a pretty crummy feature, even if it is documented. IDL's implementation of Bessel functions is not nearly so comprehensive as python's (using the mpmath package) or Mathematica's. Even if the bad behavior is documented, it's still bad. These seemingly extreme cases come up regularly in light-scattering calculations, so they're not outlandish.

The developers should update IDL's special functions to bring them up to industry standards. The present Numerical Recipes implementations are not up to that level. The new versions of the Bessel functions might even be spelled correctly, leaving the oddly speled versions for backward compatibility.

Just my 2c,

David

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[Message index]

		IDL's BESELJ returns NAN for small argument and large order By: David Ruffner on Tue, 18 March 2014 07:55
		Re: IDL's BESELJ returns NAN for small argument and large order By: Phillip Bitzer on Tue, 18 March 2014 16:47
		Re: IDL's BESELJ returns NAN for small argument and large order By: David Ruffner on Wed, 19 March 2014 13:48
		Re: IDL's BESELJ returns NAN for small argument and large order By: dg86 on Thu, 20 March 2014 17:27

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