FourthOrderTensor.hpp

/*

Copyright (C) University of Oxford, 2005-2011

University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.

This file is part of Chaste.

Chaste is free software: you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation, either version 2.1 of the License, or
(at your option) any later version.

Chaste 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 Lesser General Public
License for more details. The offer of Chaste under the terms of the
License is subject to the License being interpreted in accordance with
English Law and subject to any action against the University of Oxford
being under the jurisdiction of the English Courts.

You should have received a copy of the GNU Lesser General Public License
along with Chaste. If not, see <http://www.gnu.org/licenses/>.

*/

#ifndef _FOURTHORDERTENSOR_HPP_
#define _FOURTHORDERTENSOR_HPP_

#include <cassert>
#include <vector>

#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/matrix.hpp>
using namespace boost::numeric::ublas;
#include "Exception.hpp"

template<unsigned DIM1, unsigned DIM2, unsigned DIM3, unsigned DIM4>
class FourthOrderTensor
{
private:

    std::vector<double> mData;  
    unsigned GetVectorIndex(unsigned M, unsigned N, unsigned P, unsigned Q)
    {
        assert(M<DIM1);
        assert(N<DIM2);
        assert(P<DIM3);
        assert(Q<DIM4);
        return M + DIM1*N + DIM1*DIM2*P + DIM1*DIM2*DIM3*Q;
    }

public:

    FourthOrderTensor();

    template<unsigned CONTRACTED_DIM>
    void SetAsContractionOnFirstDimension(const c_matrix<double,DIM1,CONTRACTED_DIM>& rMatrix, FourthOrderTensor<CONTRACTED_DIM,DIM2,DIM3,DIM4>& rTensor);


    template<unsigned CONTRACTED_DIM>
    void SetAsContractionOnSecondDimension(const c_matrix<double,DIM2,CONTRACTED_DIM>& rMatrix, FourthOrderTensor<DIM1,CONTRACTED_DIM,DIM3,DIM4>& rTensor);

    template<unsigned CONTRACTED_DIM>
    void SetAsContractionOnThirdDimension(const c_matrix<double,DIM3,CONTRACTED_DIM>& rMatrix, FourthOrderTensor<DIM1,DIM2,CONTRACTED_DIM,DIM4>& rTensor);

    template<unsigned CONTRACTED_DIM>
    void SetAsContractionOnFourthDimension(const c_matrix<double,DIM4,CONTRACTED_DIM>& rMatrix, FourthOrderTensor<DIM1,DIM2,DIM3,CONTRACTED_DIM>& rTensor);

    double& operator()(unsigned M, unsigned N, unsigned P, unsigned Q);

    void Zero();

    std::vector<double>& rGetData()
    {
        return mData;
    }
};

// Implementation (lots of possibilities for the dimensions so no point with explicit instantiation)

template<unsigned DIM1, unsigned DIM2, unsigned DIM3, unsigned DIM4>
FourthOrderTensor<DIM1,DIM2,DIM3,DIM4>::FourthOrderTensor()
{
    unsigned size = DIM1*DIM2*DIM3*DIM4;
    mData.resize(size, 0.0);
}

template<unsigned DIM1, unsigned DIM2, unsigned DIM3, unsigned DIM4>
template<unsigned CONTRACTED_DIM>
void FourthOrderTensor<DIM1,DIM2,DIM3,DIM4>::SetAsContractionOnFirstDimension(const c_matrix<double,DIM1,CONTRACTED_DIM>& rMatrix, FourthOrderTensor<CONTRACTED_DIM,DIM2,DIM3,DIM4>& rTensor)
{
    Zero();

    std::vector<double>::iterator iter = mData.begin();
    std::vector<double>::iterator other_tensor_iter = rTensor.rGetData().begin();

    for (unsigned d=0; d<DIM4; d++)
    {
        for (unsigned c=0; c<DIM3; c++)
        {
            for (unsigned b=0; b<DIM2; b++)
            {
                for (unsigned a=0; a<DIM1; a++)
                {
                    for (unsigned N=0; N<CONTRACTED_DIM; N++)
                    {
                        /*
                         * The following just does
                         *
                         * mData[GetVectorIndex(a,b,c,d)] += rMatrix(a,N) * rTensor(N,b,c,d);
                         *
                         * but more efficiently using iterators into the data vector, not
                         * using random access.
                         */
                        *iter += rMatrix(a,N) * *other_tensor_iter;
                        other_tensor_iter++;
                    }

                    iter++;

                    if (a != DIM1-1)
                    {
                        other_tensor_iter -= CONTRACTED_DIM;
                    }
                }
            }
        }
    }
}

template<unsigned DIM1, unsigned DIM2, unsigned DIM3, unsigned DIM4>
template<unsigned CONTRACTED_DIM>
void FourthOrderTensor<DIM1,DIM2,DIM3,DIM4>::SetAsContractionOnSecondDimension(const c_matrix<double,DIM2,CONTRACTED_DIM>& rMatrix, FourthOrderTensor<DIM1,CONTRACTED_DIM,DIM3,DIM4>& rTensor)
{
    Zero();

    std::vector<double>::iterator iter = mData.begin();
    std::vector<double>::iterator other_tensor_iter = rTensor.rGetData().begin();

    for (unsigned d=0; d<DIM4; d++)
    {
        for (unsigned c=0; c<DIM3; c++)
        {
            for (unsigned b=0; b<DIM2; b++)
            {
                for (unsigned N=0; N<CONTRACTED_DIM; N++)
                {
                    for (unsigned a=0; a<DIM1; a++)
                    {
                        /*
                         * The following just does
                         *
                         * mData[GetVectorIndex(a,b,c,d)] += rMatrix(b,N) * rTensor(a,N,c,d);
                         *
                         * but more efficiently using iterators into the data vector, not
                         * using random access.
                         */
                        *iter += rMatrix(b,N) * *other_tensor_iter;
                        iter++;
                        other_tensor_iter++;
                    }

                    if (N != CONTRACTED_DIM-1)
                    {
                        iter -= DIM1;
                    }
                }
                if (b != DIM2-1)
                {
                    other_tensor_iter -= CONTRACTED_DIM*DIM1;
                }
            }
        }
    }
}

template<unsigned DIM1, unsigned DIM2, unsigned DIM3, unsigned DIM4>
template<unsigned CONTRACTED_DIM>
void FourthOrderTensor<DIM1,DIM2,DIM3,DIM4>::SetAsContractionOnThirdDimension(const c_matrix<double,DIM3,CONTRACTED_DIM>& rMatrix, FourthOrderTensor<DIM1,DIM2,CONTRACTED_DIM,DIM4>& rTensor)
{
    Zero();

    std::vector<double>::iterator iter = mData.begin();
    std::vector<double>::iterator other_tensor_iter = rTensor.rGetData().begin();

    for (unsigned d=0; d<DIM4; d++)
    {
        for (unsigned c=0; c<DIM3; c++)
        {
            for (unsigned N=0; N<CONTRACTED_DIM; N++)
            {
                for (unsigned b=0; b<DIM2; b++)
                {
                    for (unsigned a=0; a<DIM1; a++)
                    {
                        /*
                         * The following just does
                         *
                         * mData[GetVectorIndex(a,b,c,d)] += rMatrix(c,N) * rTensor(a,b,N,d);
                         *
                         * but more efficiently using iterators into the data vector, not
                         * using random access.
                         */
                        *iter += rMatrix(c,N) * *other_tensor_iter;
                        iter++;
                        other_tensor_iter++;
                    }
                }

                if (N != CONTRACTED_DIM-1)
                {
                    iter -= DIM1*DIM2;
                }
            }

            if (c != DIM3-1)
            {
                other_tensor_iter -= CONTRACTED_DIM*DIM1*DIM2;
            }
        }
    }
}

template<unsigned DIM1, unsigned DIM2, unsigned DIM3, unsigned DIM4>
template<unsigned CONTRACTED_DIM>
void FourthOrderTensor<DIM1,DIM2,DIM3,DIM4>::SetAsContractionOnFourthDimension(const c_matrix<double,DIM4,CONTRACTED_DIM>& rMatrix, FourthOrderTensor<DIM1,DIM2,DIM3,CONTRACTED_DIM>& rTensor)
{
    Zero();

    std::vector<double>::iterator iter = mData.begin();
    std::vector<double>::iterator other_tensor_iter = rTensor.rGetData().begin();

    for (unsigned d=0; d<DIM4; d++)
    {
        for (unsigned N=0; N<CONTRACTED_DIM; N++)
        {
            for (unsigned c=0; c<DIM3; c++)
            {
                for (unsigned b=0; b<DIM2; b++)
                {
                    for (unsigned a=0; a<DIM1; a++)
                    {
                        /*
                         * The following just does
                         *
                         * mData[GetVectorIndex(a,b,c,d)] += rMatrix(d,N) * rTensor(a,b,c,N);
                         *
                         * but more efficiently using iterators into the data vector, not
                         * using random access.
                         */
                        *iter += rMatrix(d,N) * *other_tensor_iter;

                        iter++;
                        other_tensor_iter++;
                    }
                }
            }

            if (N != CONTRACTED_DIM-1)
            {
                iter-= DIM1*DIM2*DIM3;
            }
        }

        other_tensor_iter -= CONTRACTED_DIM*DIM1*DIM2*DIM3;
    }
}

template<unsigned DIM1, unsigned DIM2, unsigned DIM3, unsigned DIM4>
double& FourthOrderTensor<DIM1,DIM2,DIM3,DIM4>::operator()(unsigned M, unsigned N, unsigned P, unsigned Q)
{
    assert(M<DIM1);
    assert(N<DIM2);
    assert(P<DIM3);
    assert(Q<DIM4);

    return mData[GetVectorIndex(M,N,P,Q)];
}

template<unsigned DIM1, unsigned DIM2, unsigned DIM3, unsigned DIM4>
void FourthOrderTensor<DIM1,DIM2,DIM3,DIM4>::Zero()
{
    for (unsigned i=0; i<mData.size(); i++)
    {
        mData[i] = 0.0;
    }
}

#endif //_FOURTHORDERTENSOR_HPP_