CoCoA » CoCoA-5

TO DO JAA can try the same computation but from CoCoALib; perhaps some time is spent converting to CoCoA-5 data structures?

Here is body of the CoCoALib code I used to speed testing in CoCoALib:

void program()
{
  GlobalManager CoCoAFoundations;

#ifndef CoCoA_WITH_NORMALIZ
  cout << "Normaliz library is not available to CoCoALib." << endl;
#else // NORMALIZ is available
  cout << boolalpha; // so that bools print out as true/false

  int nrows, ncols;
  cin >> nrows;
  cin >> ncols;

  vector<vector<BigInt> > M(nrows, vector<BigInt>(ncols));
  for (int i=0; i < nrows; ++i)
    for (int j=0; j < ncols; ++j)
    {
      cin >> M[i][j];
    }

  cin >> nrows;
  cin >> ncols;

  vector<vector<BigInt> > G(nrows, vector<BigInt>(ncols));
  for (int i=0; i < nrows; ++i)
    for (int j=0; j < ncols; ++j)
    {
      cin >> G[i][j];
    }

  libnormaliz::Type::InputType InputType = libnormaliz::Type::equations;

  std::map< libnormaliz::InputType, std::vector<std::vector<BigInt> > > CtorArgs;
  CtorArgs[libnormaliz::Type::equations] = M;
  CtorArgs[libnormaliz::Type::grading] = G;

  Normaliz::cone C3(CtorArgs);
  cout << "Cone created: " << endl << C3 << endl << endl;
  vector<vector<BigInt> > res;
  double t0;
  t0 = CpuTime();
  C3.myComputation(); // compute everything
  cout << "time everything  -> " << CpuTime()-t0 << endl;

#endif // CoCoA_WITH_NORMALIZ
}

Here is the original Normaliz input file (called 5x5.in in their source tree):

11
25
1 1 1 1 1 -1 -1 -1 -1 -1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
1 1 1 1 1  0  0  0  0  0 -1 -1 -1 -1 -1  0  0  0  0  0  0  0  0  0  0
1 1 1 1 1  0  0  0  0  0  0  0  0  0  0 -1 -1 -1 -1 -1  0  0  0  0  0
1 1 1 1 1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1 -1 -1 -1 -1
0 1 1 1 1 -1  0  0  0  0 -1  0  0  0  0 -1  0  0  0  0 -1  0  0  0  0
1 0 1 1 1  0 -1  0  0  0  0 -1  0  0  0  0 -1  0  0  0  0 -1  0  0  0
1 1 0 1 1  0  0 -1  0  0  0  0 -1  0  0  0  0 -1  0  0  0  0 -1  0  0
1 1 1 0 1  0  0  0 -1  0  0  0  0 -1  0  0  0  0 -1  0  0  0  0 -1  0
1 1 1 1 0  0  0  0  0 -1  0  0  0  0 -1  0  0  0  0 -1  0  0  0  0 -1
0 1 1 1 1  0 -1  0  0  0  0  0 -1  0  0  0  0  0 -1  0  0  0  0  0 -1
1 1 1 1 0  0  0  0 -1  0  0  0 -1  0  0  0 -1  0  0  0 -1  0  0  0  0
equations
1
25
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
grading

IMPORTANT NOTE to use this as input for the C++ program above, delete the word equations

On my machine (MacBook Pro with OSX 10.5.8, compiler version 4.2.1)

Normaliz 2.12 took 9mins (about 550s)
CoCoA-5 took 14mins (about 840s)
CoCoALib took 13mins (about 790s)

With Christof we ran a side-by-side comparison (on my machine) with "verbose" activated.
The run under CoCoA-5 was apparently uniformly slower than the run directly in Normaliz. In particular we excluded the possibility that the extra time was copying the answer from Normaliz data structures to CoCoA ones.

NOTE: Christof also noted curious behaviour running Normaliz inside GAP; the process seemed to go into swap for no good reason. He is investigating. we have no idea whether this may be related to the strange behaviour seen with CoCoA/CoCoALib.

Attempts to profile the running program on my computer failed :-(
gprof does not work properly in MacOSX, and there were problems in the Linux VM too.

Currently stumped.

For the problem I discovered in the NormalizInterface for GAP we found the problem meanwhile. GAP used to set its own (really stupid) memory manager for the gmpxx classes which lead to a significant slowdown if they were used. See https://github.com/gap-packages/NormalizInterface/issues/17

You could check if it also happens if you call Normaliz::HilbertBasis(C3); instead of C3.myComputation();, there should be almost no use of gmp. (And it should be considerably faster).

I have reconfirmed that there is strange behaviour on the Linux machine here in Kassel. Compiler is g++ version 5.3.1.

If I perform the computation in CoCoA-5, the time taken is about 120s (whether or not I specify UseGMPAllocator).

If I do the computation using the C++ code above, the time taken is about 225s (with UseGMPAllocator being marginally slower).

Why should CoCoALib be so much slower? Maybe I'd better check the inputs!

I was unable to compile Normaliz (version 2.99.4) because linking failed: it did not find

/usr/bin/ld: cannot find -lstdc++
/usr/bin/ld: cannot find -lm
/usr/bin/ld: cannot find -lc

(2021-10-12) Last time this was checked was 4 years ago! We must check to see if it still a problem!