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MathGroup Archive 2006

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Rapid execution of gaussian integrals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68732] Rapid execution of gaussian integrals
  • From: AES <siegman at stanford.edu>
  • Date: Thu, 17 Aug 2006 04:18:40 -0400 (EDT)
  • Organization: Stanford University
  • Sender: owner-wri-mathgroup at wolfram.com

I recently posted about very slow execution of infinite symbolic 
integrals of the general form

   Integrate[const * Exp[-A x^2 + 2 B x], {x, -Infinity, Infinity},]

when A and B are constant-valued expressions of even modest complexity, 
even when one inserts the necessary Assumptions to make the integral 
convergent.

Daniel Lichtbau replied with some helpful suggestions on how to speed 
things up a bit; but to really speed things up I've since been using the 
brute force approach

   gaussianIntegral[func_, x_] : = Module[ {exp, A, B, C, const},        
         exp = Exponent[func, E];    
         A = Coefficient[-exp ,x, 2];    
         B = Coefficient[ exp, x, 1]/2;    
         C = Coefficient[ exp, x, 0];    
         const=func/Exp[exp];    
         const Sqrt[Pi/A] Exp[ (B^2/A) + C]]

Crude, but seems to work OK for everything I've thrown at it so far.  If 
anyone has any criticism or warnings, I'll be glad to learn from them.


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