Re: Hypergeometric 1F1 and numerical evaluation

• To: mathgroup at smc.vnet.net
• Subject: [mg18062] Re: Hypergeometric 1F1 and numerical evaluation
• From: Alan Lewis <alanlewis at home.com>
• Date: Tue, 15 Jun 1999 01:43:23 -0400
• Delivery-date: Tue Jun 15 08:40:12 1999
• Organization: @Home Network
• References: <7jubur\$57s@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```I think you need to give more detail as to why the 1F1 functions
evaluations are too slow for your purposes. Perhaps you should list
typical values of the 3 arguments, and then report the timing to
evaluate the function. Perhaps the evaluation is slow because it takes
a long time to evaluate your arguments. Given the arguments, you
may get some suggestions on speeding up the function evaluation, since
its possible you're in an asymptotic regime that Mathematica is
having trouble with.

Atul Sharma wrote:
>
> I  am working with a multicompartmental pharmacokinetic model, which must be
> solved for unknown parameters by comparison with blood compartment
> measurements. My initial approach was to solve the differential equations
> numerically, using NDSolve and FindMinimum to fit the unknown parameters, an
> approach which works well and in a reasonable time frame, since we propose
> to use this model at the 'bedside' as it were, to guide patient management.
> However,  through simplifying assumptions and straightforward variable
> transformations,  I am able to reduce the system of governing differential
> equations to the Kummer equation, soluble in terms of confluent
> hypergeometric functions.
>
> informative thread in the archives dating back to 1994-95 (thanks to Bob
> Hanlon etc etc). I understand now that numerical evaluation of this function
> is quite time consuming. In fact, knowing the 'exact' closed form solution
> doesn't help me, insofar as NDSolve returns a result considerably more
> quickly (even though I have to integrate through an entire week of repeated
> doses and multiple body water compartments). A recent discussion in this
> performs more reliably.
>
> My questions is
>
> Is there a faster way to evaluate the 1F1 function to take advantage of this
> solution? Path integrals don't sound much faster to me, though I was hoping
> that someone with some experience in this area could advise me as to whether
> this merited further consideration. Even an approximate solution might be
> preferable, since the time needed to perform the curve fitting will be, in
> my mind, the major obstacle to using this model for its intended purpose.
>