[SciPy-user] derivative

Nils Wagner nwagner at mecha.uni-stuttgart.de
Wed Feb 23 12:50:02 CST 2005

On Wed, 23 Feb 2005 09:34:13 -0800
  Stephen Walton <stephen.walton at csun.edu> wrote:
> Numerical derivatives are limited in accuracy by their 
>very nature.  I don't know very much about Pade 
>computations, I'm afraid,  But, if the code you need the 
>derivative of is in C or Fortran, you might try one of 
>the automatic differentation codes out there.  The basic 
>idea is that, since any computation on a real computer is 
>composed of elementary operations with analytic 
>derivatives, repeated automatic application of the chain 
>rule results in a derivative which is accurate to machine 
>precision.  Of course, these codes will only produce a 
>first or second derivative in my experience, not a sixth. 
> Do you need sixth derivatives?

This depends on the order of the Taylor series expansion.
pade(an,8) is quite common in approximating the
matrix exponential.

pade(an, m)
     Given Taylor series coefficients in an, return a Pade 
approximation to
     the function as the ratio of two polynomials p / q 
 where the order of q is m.


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