Some Useful Tips for Usage

The computation is done by floating point arithmetic by both cdd and cddf+, and by exact rational arithmetic by cddr+. Since cddr+ runs much slower (at least for the moment), use it when you need to make sure that the output is correct.

Clearly, there is no guarantee that the programs cdd and cddf+ outputs the correct result. However they seems to work correctly for many different types of polyhedra if one carefully prepares input data files. The followings are some useful tips for input data preparation to avoid badly behaving computations with cddf+.

• In cddf+, any real value is considered as zero if its absolute value is less than $10^{-6}$. Since the computation is performed with double precision arithmetic, the correctness of zero recognition depends greatly on how accurate the input matrix $(b- A)$ is. For example, you should never use $0.9999$ for the value $1$. Just use the correct value $1$ as it is. Unlike many LP softwares, perturbation of data can cause some serious problems. If you want to perturb your data (e.g. right hand side) for some reason, do it with large enough constants, say of order $10^{-3}$.

• If your matrix contains some irrational number, say $\sqrt{5}$, please use an approximation which is correct in at least ten digits, i.e. $2.236067977$. See the sample input file reg600-5.ine in the ine subdirectory.

• For the same arithmetic reason, please try to scale your input matrix as even as possible by multiplying appropriate constants to some rows and columns . The program cdd does not perform any scaling before computation.