From owner-help-octave at bevo dot che dot wisc dot edu  Thu Nov 30 14:47:09 1995
Subject: More Neural Network musings..
From: John Utz <spaz at u dot washington dot edu>
To: Octave Help List <help-octave at bevo dot che dot wisc dot edu>
Date: Thu, 30 Nov 1995 12:47:02 -0800 (PST)

Hi gang;

	As i mentioned in my previous letter, i am trying to use octave 
to solve dynamical systems and neural network problems.

	Both of these items are variations on systems of differential 
equations. 

	One of the key techniques in looking at simple dymanical systems 
is the use of the phase plane. The phase plane display of a dynamical 
system will include locations called singularities. Singularities seem to 
present a problem for a numerical solver such as lsode and dassl.

	The problem with singularities is that they are the points in 
which a function under analysis will equal zero in the numerator ( not 
unusual in any way ) and 0 in the *denominator* ( this is usually 
construed as a Bad Thing (tm) ).

the following is exerted from octave's online manual:  

 {

 The function `dassl' can be used Solve DAEs of the form

     0 = f (x-dot, x, t),    x(t=0) = x_0, x-dot(t=0) = x-dot_0

     dassl (FCN, X_0, XDOT_0, T_OUT, T_CRIT)
 ...

   The fifth argument is optional, and may be used to specify a set of
times that the DAE solver should not integrate past.  It is useful for
avoiding difficulties with singularities and points where there is a
discontinuity in the derivative.

  }

	Well, heck. In my case, i wish to eagerly seek out 
discontinuities and singularities! Worse yet. I want to plot them!

	Has anybody had any experience with this that they would like to 
share with me?

*******************************************************************************
 John Utz	spaz at u dot washington dot edu
	idiocy is the impulse function in the convolution of life