atmodcomp.h

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/////////////////////////////////////////////////////////////////////////////
///
/// \file
///
/// A generic procedure for the computation of chain contraction
/// of a filtered cell complex stored in a file.
/// This is a complete procedure good for simplicial, cubical,
/// or other complexes.
/// It computes an algebraic topological model.
/// This computation fails if homology is not torsion-free.
///
/////////////////////////////////////////////////////////////////////////////

// Copyright (C) 2009-2016 by Pawel Pilarczyk.
//
// This file is part of my research software package. This is free software:
// you can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// This software is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this software; see the file "license.txt". If not,
// please, see <http://www.gnu.org/licenses/>.

// Started on March 24, 2009. Last revision: August 21, 2013.


#ifndef _ATMODCOMP_H_
#define _ATMODCOMP_H_


// include some standard C++ header files
#include <istream>
#include <ostream>

// include selected header files from the CHomP library
#include "chomp/system/config.h"
#include "chomp/system/textfile.h"
#include "chomp/system/timeused.h"
#include "chomp/struct/hashsets.h"

// include relevant local header files
#include "chaincon/cellnames.h"
#include "chaincon/filtcomplex.h"
#include "chaincon/readfcompl.h"
#include "chaincon/boundary.h"
#include "chaincon/atmodel.h"
#include "chaincon/homcohom.h"


// --------------------------------------------------
// ---------------- compute AT model ----------------
// --------------------------------------------------

/// Computes an AT model and the homology of a cellular complex.
/// The cellular complex is read from the given file.
/// Only top-dimensional cells should be listed in the file,
/// or otherwise the filtration may not be generated correctly.
template <class CellT, class LinMap, class CellNames>
inline void computeAlgTopModel (const tFilteredComplex<CellT> &K,
        bool relativeComplex,
        chomp::homology::hashedset<CellT> &H,
        LinMap &pi, LinMap &incl, LinMap &phi,
        CellNames &cellNames,
        bool displayPi, bool displayIncl, bool displayPhi,
        bool displayRepr, bool verify, int algorithmVersion)
{
        using chomp::homology::sout;

        // determine the type of coefficients (for displaying homology only)
        typedef typename LinMap::CoefType CoefT;

        // compute the homology together with the chain contraction
        if (relativeComplex)
        {
                algTopModel (K, H, pi, incl, phi, algorithmVersion, K);
        }
        else
        {
                algTopModel (K, H, pi, incl, phi, algorithmVersion,
                        Unrestricted ());
        }

        // show the computed homology groups
        chomp::homology::hashedset<CellT> emptyCellArray;
        chomp::homology::hashedset<CoefT> emptyCoefArray;
        std::vector<std::vector<CellT> > representants;
        std::vector<int> bettiNumbers;
        std::vector<std::vector<CoefT> > torsion;
        getHomCohom (H, emptyCellArray, emptyCellArray, emptyCoefArray,
                &representants, &bettiNumbers, &torsion, false);
        sout << "Homology groups:\n";
        sout << homcohom2text (bettiNumbers, torsion, "H_", false);

        // prepare correct cell names and show them if requested to
        if (displayRepr)
                sout << "Representants of homology generators:\n";
        int reprSize = representants. size ();
        for (int dim = 0; dim < reprSize; ++ dim)
        {
                int size = representants [dim]. size ();
                for (int i = 0; i < size; ++ i)
                {
                        const CellT &cell (representants [dim] [i]);
                        if (displayRepr)
                        {
                                sout << cellNames (cell) << ": " <<
                                        cell << ".\n";
                        }
                        else
                        {
                                cellNames (cell);
                        }
                }
        }

        // show the computed maps
        tCellOwnNames<CellT> cellOwnNames;
        if (displayPi)
        {
                sout << "The projection map pi:\n" <<
                        cells2names (pi, cellOwnNames, cellNames);
        }
        if (displayIncl)
        {
                sout << "The inclusion map incl:\n" <<
                        cells2names (incl, cellNames, cellOwnNames);
        }
        if (displayPhi)
        {
                sout << "The homology gradient vector field phi:\n" << phi;
        }

        // prepare the boundary map, to be used for verifications
        LinMap boundaryMap;

        // do several verifications to make sure the computed maps are good
        if (verify)
        {
                if (relativeComplex)
                        computeBoundaryMap (K, boundaryMap, K);
                else
                        computeBoundaryMap (K, boundaryMap, Unrestricted ());
                if (phi * boundaryMap * phi == phi)
                        sout << "Verified: 'phi bd phi = phi'.\n";
                else
                        sout << "Failed to verify that "
                                "'phi pd phi = phi'.\n";

                if (boundaryMap * phi * boundaryMap == boundaryMap)
                        sout << "Verified: 'bd phi bd = bd'.\n";
                else
                        sout << "Failed to verify that 'bd phi bd = bd'.\n";

                LinMap zeroMap;
                if (phi * phi == zeroMap)
                        sout << "Verified: 'phi phi = 0'.\n";
                else
                        sout << "Failed to verify that 'phi phi = 0'.\n";

                LinMap composition (boundaryMap * phi);
                composition += phi * boundaryMap;
                composition. negate ();
                addIdentity (K, composition);
                if (incl * pi == composition)
                        sout << "Verified: 'i pi = id - bd phi - phi bd'.\n";
                else
                        sout << "Failed to verify that "
                                "'i pi = id - bd phi - phi bd'.\n";

                LinMap idH;
                addIdentity (H, idH);
                if (pi * incl == idH)
                        sout << "Verified: 'pi i = id_H'.\n";
                else
                        sout << "Failed to verify that 'pi i = id_H'.\n";

                if (pi * phi == zeroMap)
                        sout << "Verified: 'pi phi = 0'.\n";
                else
                        sout << "Failed to verify that 'pi phi = 0'.\n";

                if (phi * incl == zeroMap)
                        sout << "Verified: 'phi i = 0'.\n";
                else
                        sout << "Failed to verify that 'phi i = 0'.\n";
        }

        return;
} /* computeAlgTopModel */


#endif // _ATMODCOMP_H_