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From: Roland Schwarz (roland.schwarz_at_[hidden])
Date: 2006-03-25 10:46:47

Roland Schwarz wrote:
> Does sinh really belong to the class of c2 functions? sinh has an
> infinite number of derivatives, and AFAIK is not representable within
> this class. It might be approximated however.

I was too fast. Should have had a look at the docs first. Shame on me.

I was exited by the idea of this library however. In the past I needed
to do a lot of calculations with splines (and this triggered me), but at
this time only the (yet unmaintained?) ublas was available. I used this
to handle the splines at this time.

I have seen from the doc's that c2_functions will also deal with root
finding of splines. From my experience with this topic I found that this
is a numerically hard problem when interested in the number of roots, if
the spline is being evaluated at it's splicing points. I.e. the number
of roots might be different depending whether evaluated on the right or
left side. As far as I remember the value of the root(s) could also
differ slightly. I tried to cure this by defining the elementary
functions on half open intervals, but besides forcing the end "interval"
being a single point, I also found the asymmetry somewhat unsatisfying
(which end should be open, based on what rationale?) I would be very
interested if you have some findings in this area.

Al tough it might sound stupid to ask for inversion of a non monotonic
function it might be valuable to get it's main branch, the number of
branches or even an array filled with c2_functions one of each
represents one of the side branches. @Mendenhall: What do you think?

I came across this type of problem when I tried to do "inverse-sampling"
of a spline function. I.e. find the abscissa values that correspond to
equal sized ordinate steps. (Finding the time instances when to apply
impulses to a stepper motor, given the ordinate is the step number, to
control time dependent position of the motor. The spline was the result
of some algorithm where it turned out to be very handy to view it as a
function. )

Do you also intend to build into the library the ability to construct
the splines from the different possible data sets e.g x,y tables and
various boundary conditions?

Did you consider extending the library to multivalued functions too?


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