On Mon, 7 Nov 2011, Alet Roux wrote:
Dear Dr. Hill
I am working in Mathematical Finance at the University of York, in the area of asset pricing under proportional transaction costs. As part of our work, we have developed algorithms that perform certain operations on polyhedra, most notably intersection and taking convex hulls. (I also have high hopes that we might one day be able to handle unions in some way...)
Part of my contribution to the project is to implement our algorithms in C/C++. I was very pleased to come across the the well-documented and easy-to-use Parma Polyhedra Library. I note that the library allows integral coefficients only. However, for our needs, we require floating point or (probably more practical from a precision point of view) rational coefficients.
It is good to know you find it well-documented and easy-to-use.
Yes, the coefficients of constraints and generators have to be integers (mpz_class in the default configuration). However, the PPL implements a domain of convex _rational_ polyhedra. The restriction to integer coefficients is just for the representation and input/output. We can do this since any constraint having rational coefficients can be normalized so as to have integer coefficients. For generators, the same is achieved by including an integer divisor, (which by default is 1, but not necessarily so).
I see from your email that you already have written your own algorithms for intersection and convex-hull. These as well as union are operations provided by the PPL. Documentation for these is in the PPL; but if you miss the exact information needed to make full use of the PPL, you should not hesitate to ask.
It appears to me that it may be possible to tweak the Parma Polyhedra Library for our use by simply changing the data type Variable, but I am a bit nervous about this (I am a mathematician, and enthusiastic C++ programmer, but not a computer scientist by any means). My question is, in your view, is this a reasonable thing to try out? Any health warnings? Or will it simply not work?
There is no need (nor would it be advisable) to change the data types.
I would be very grateful for any other advice that you might have on this issue.
Note that I am cc'ing this to the PPL-devel mailing list in case other users/developers may wish to give more advice.
I hope this helps,
Pat
Thank you very much in advance,
Alet Roux