On Wed, Apr 23, 2008 at 2:37 PM, <[EMAIL PROTECTED]> wrote: > Author: luc > Date: Wed Apr 23 14:37:08 2008 > New Revision: 651074 > > URL: http://svn.apache.org/viewvc?rev=651074&view=rev > Log: > improved documentation > the developers-oriented documentation has been started
Thanks, Luc! <snip/> > > + <p> > + For singularities not related to domain definition boundaries > (like > + <code>Math.abs</code> and conditional branches), the theoretical > derivative is not > + defined as a single value, but as a pair of left and a right > half-derivatives, one for > + each side of the singularity. Since there is little support in > the IEEE754 standard > + to distinguish the left and right hand side of a single value > (except for zero, since > + -0 and +0 both exist), we have decided to adopt a simplified > approach. These cases are > + implemented by simple conditional branches (we added explicitly > such a conditional in the > + <code>Math.abs</code> case). Nabla then simply computes the value > of the smooth > + derivative on the branch of the computation path that is selected > at run time, depending > + on the values of the input parameters. This choice allows to > preserve the property of > + having a derivative that is always consistent with the associated > value, and it is a simple > + arbitrary choice of one of the two possibilities that correspond > to the mathematical result, > + which by itself does not choose between them. > + </p> The problem here is that it is not an "arbitrary choice" between the two different values - the limit that is the derivative does not exist. It would make more sense to me to return NaN or throw IAE in these cases. Is that tractable? Moreover, is it tractable to consistently define differentiability and throw an appopriate exception or return NaN at points where a java-defined function is not differentiable? We should at least document the behavior in the javadoc in any case. Phil --------------------------------------------------------------------- To unsubscribe, e-mail: [EMAIL PROTECTED] For additional commands, e-mail: [EMAIL PROTECTED]
