Attempting to fix issues pointed out by Vadim Pisarevsky during the pull
request review. In particular, the following things are done:
*) The mechanism of debug info printing is changed and made more
procedure-style than the previous macro-style
*) z in solveLP() is now returned as a column-vector
*) Func parameter of solveLP() is now allowed to be column-vector, in
which case it is understood to be the transpose of what we need
*) Func and Constr now can contain floats, not only doubles (in the
former case the conversion is done via convertTo())
*)different constructor to allocate space for z in solveLP() is used,
making the size of z more explicit (this is just a notation change, not
functional, both constructors are achieving the same goal)
*) (big) mat.hpp and iostream headers are moved to precomp-headers from
optim.hpp
What we have now corresponds to "formal simplex algorithm", described in
Cormen's "Intro to Algorithms". It will work *only* if the initial
problem has (0,0,0,...,0) as feasible solution (consequently, it will
work unpredictably if problem was unfeasible or did not have zero-vector as
feasible solution). Moreover, it might cycle.
TODO (first priority)
1. Implement initialize_simplex() procedure, that shall check for
feasibility and generate initial feasible solution. (in particular, code
should pass all 4 tests implemented at the moment)
2. Implement Bland's rule to avoid cycling.
3. Make the code more clear.
4. Implement several non-trivial tests (??) and check algorithm against
them. Debug if necessary.
TODO (second priority)
1. Concentrate on stability and speed (make difficult tests)