#ifndef DUNE_GFE_LINEARALGEBRA_HH #define DUNE_GFE_LINEARALGEBRA_HH #include <dune/common/fmatrix.hh> #include <dune/common/version.hh> /////////////////////////////////////////////////////////////////////////////////////////// // Various matrix methods /////////////////////////////////////////////////////////////////////////////////////////// namespace Dune { namespace GFE { /** \brief Return the trace of a matrix */ template <class T, int n> static T trace(const FieldMatrix<T,n,n>& A) { T trace = 0; for (int i=0; i<n; i++) trace += A[i][i]; return trace; } /** \brief Return the square of the trace of a matrix */ template <class T, int n> static T traceSquared(const FieldMatrix<T,n,n>& A) { T trace = 0; for (int i=0; i<n; i++) trace += A[i][i]; return trace*trace; } /** \brief Compute the symmetric part of a matrix A, i.e. \f$ \frac 12 (A + A^T) \f$ */ template <class T, int n> static FieldMatrix<T,n,n> sym(const FieldMatrix<T,n,n>& A) { FieldMatrix<T,n,n> result; for (int i=0; i<n; i++) for (int j=0; j<n; j++) result[i][j] = 0.5 * (A[i][j] + A[j][i]); return result; } /** \brief Compute the antisymmetric part of a matrix A, i.e. \f$ \frac 12 (A - A^T) \f$ */ template <class T, int n> static FieldMatrix<T,n,n> skew(const FieldMatrix<T,n,n>& A) { FieldMatrix<T,n,n> result; for (int i=0; i<n; i++) for (int j=0; j<n; j++) result[i][j] = 0.5 * (A[i][j] - A[j][i]); return result; } /** \brief Compute the deviator of a matrix A */ template <class T, int n> static FieldMatrix<T,n,n> dev(const FieldMatrix<T,n,n>& A) { FieldMatrix<T,n,n> result = A; auto t = trace(A); for (int i=0; i<n; i++) result[i][i] -= t / n; return result; } /** \brief Return the transposed matrix */ template <class T, int n> static FieldMatrix<T,n,n> transpose(const FieldMatrix<T,n,n>& A) { FieldMatrix<T,n,n> result; for (int i=0; i<n; i++) for (int j=0; j<n; j++) result[i][j] = A[j][i]; return result; } /** \brief The Frobenius (i.e., componentwise) product of two matrices */ template <class T, int n> static T frobeniusProduct(const FieldMatrix<T,n,n>& A, const FieldMatrix<T,n,n>& B) { T result(0.0); for (int i=0; i<n; i++) for (int j=0; j<n; j++) result += A[i][j] * B[i][j]; return result; } template <class T, int n> static auto dyadicProduct(const FieldVector<T,n>& A, const FieldVector<T,n>& B) { FieldMatrix<T,n,n> result; for (int i=0; i<n; i++) for (int j=0; j<n; j++) result[i][j] = A[i]*B[j]; return result; } #if ADOLC_ADOUBLE_H template <int n> static auto dyadicProduct(const FieldVector<adouble,n>& A, const FieldVector<double,n>& B) -> FieldMatrix<adouble,n,n> { FieldMatrix<adouble,n,n> result; for (int i=0; i<n; i++) for (int j=0; j<n; j++) result[i][j] = A[i]*B[j]; return result; } #endif } } #endif