FourthOrderTensor.hpp

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#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_