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Rapid execution of gaussian integrals

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

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 

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 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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