tensor3.hh

#ifndef DUNE_TENSOR_3_HH
#define DUNE_TENSOR_3_HH

/** \file
    \brief A third-rank tensor
    */

#include <dune/common/array.hh>
#include <dune/common/fmatrix.hh>

/** \brief A third-rank tensor
*/
template <class T, int N1, int N2, int N3>
class Tensor3
    : public Dune::array<Dune::FieldMatrix<T,N2,N3>,N1>
{
    public:

        /** \brief Default constructor */
        Tensor3() {}

        /** \brief Constructor from a scalar */
        Tensor3(const T& c)
        {
            for (int i=0; i<N1; i++)
                (*this)[i] = c;
        }

        T infinity_norm() const
        {
            dune_static_assert(N1>0, "infinity_norm not implemented for empty tensors");
            T norm = (*this)[0].infinity_norm();
            for (int i=1; i<N1; i++)
                norm = std::max(norm, (*this)[i].infinity_norm());
            return norm;
        }

        T frobenius_norm() const
        {
            T norm = 0;
            for (int i=0; i<N1; i++)
                for (int j=0; j<N2; j++)
                    for (int k=0; k<N3; k++)
                        norm += (*this)[i][j][k] * (*this)[i][j][k];

            return std::sqrt(norm);
        }

        Tensor3<T,N1,N2,N3>& axpy(const T& alpha, const Tensor3<T,N1,N2,N3>& other)
        {
            for (int i=0; i<N1; i++)
                (*this)[i].axpy(alpha,other[i]);
            return *this;
        }

        static Tensor3<T,N1,N2,N3> product(const Dune::FieldVector<T,N1>& a, const Dune::FieldVector<T,N2>& b, const Dune::FieldVector<T,N3>& c)
        {
            Tensor3<T,N1,N2,N3> result;

            for (int i=0; i<N1; i++)
                for (int j=0; j<N2; j++)
                    for (int k=0; k<N3; k++)
                        result[i][j][k] = a[i]*b[j]*c[k];

            return result;
        }

        static Tensor3<T,N1,N2,N3> product(const Dune::FieldMatrix<T,N1,N2>& ab, const Dune::FieldVector<T,N3>& c)
        {
            Tensor3<T,N1,N2,N3> result;

            for (int i=0; i<N1; i++)
                for (int j=0; j<N2; j++)
                    for (int k=0; k<N3; k++)
                        result[i][j][k] = ab[i][j]*c[k];

            return result;
        }

        static Tensor3<T,N1,N2,N3> product(const Dune::FieldVector<T,N1>& a, const Dune::FieldMatrix<T,N2,N3>& bc)
        {
            Tensor3<T,N1,N2,N3> result;

            for (int i=0; i<N1; i++)
                for (int j=0; j<N2; j++)
                    for (int k=0; k<N3; k++)
                        result[i][j][k] = a[i]*bc[j][k];

            return result;
        }

        template <int N4>
        friend Tensor3<T,N1,N2,N4> operator*(const Tensor3<T,N1,N2,N3>& a, const Dune::FieldMatrix<T,N3,N4>& b)
        {
            Tensor3<T,N1,N2,N4> result;

            for (int i=0; i<N1; i++)
                for (int j=0; j<N2; j++)
                    for (int k=0; k<N4; k++) {
                        result[i][j][k] = 0;
                        for (int l=0; l<N3; l++)
                            result[i][j][k] += a[i][j][l]*b[l][k];
                    }

            return result;
        }

        template <int N4>
        friend Tensor3<T,N1,N3,N4> operator*(const Dune::FieldMatrix<T,N1,N2>& a, const Tensor3<T,N2,N3,N4>& b)
        {
            Tensor3<T,N1,N3,N4> result;

            for (int i=0; i<N1; i++)
                for (int j=0; j<N3; j++)
                    for (int k=0; k<N4; k++) {
                        result[i][j][k] = 0;
                        for (int l=0; l<N2; l++)
                            result[i][j][k] += a[i][l]*b[l][j][k];
                    }

            return result;
        }

    friend Tensor3<T,N1,N2,N3> operator+(const Tensor3<T,N1,N2,N3>& a, const Tensor3<T,N1,N2,N3>& b)
    {
            Tensor3<T,N1,N2,N3> result;

            for (int i=0; i<N1; i++)
                for (int j=0; j<N2; j++)
                    for (int k=0; k<N3; k++)
                        result[i][j][k] = a[i][j][k] + b[i][j][k];

            return result;
    }

    friend Tensor3<T,N1,N2,N3> operator-(const Tensor3<T,N1,N2,N3>& a, const Tensor3<T,N1,N2,N3>& b)
    {
            Tensor3<T,N1,N2,N3> result;

            for (int i=0; i<N1; i++)
                for (int j=0; j<N2; j++)
                    for (int k=0; k<N3; k++)
                        result[i][j][k] = a[i][j][k] - b[i][j][k];

            return result;
    }

    friend Tensor3<T,N1,N2,N3> operator*(const T& scalar, const Tensor3<T,N1,N2,N3>& tensor)
    {
        Tensor3<T,N1,N2,N3> result;

        for (int i=0; i<N1; i++)
            for (int j=0; j<N2; j++)
                for (int k=0; k<N3; k++)
                    result[i][j][k] = scalar * tensor[i][j][k];

        return result;

    }

    Tensor3<T,N1,N2,N3>& operator*=(const T& scalar)
    {
        for (int i=0; i<N1; i++)
            for (int j=0; j<N2; j++)
                for (int k=0; k<N3; k++)
                    (*this)[i][j][k] *= scalar;

        return *this;
    }

};

//! Output operator for Tensor3
template <class T, int N1, int N2, int N3>
inline std::ostream& operator<< (std::ostream& s, const Tensor3<T,N1,N2,N3>& tensor)
{
    for (int i=0; i<N1; i++)
        s << tensor[i];
    return s;
}



#endif