#ifndef DUNE_GFE_LINEARALGEBRA_HH #define DUNE_GFE_LINEARALGEBRA_HH #include <random> #include <dune/common/fmatrix.hh> #include <dune/common/version.hh> #include <dune/istl/scaledidmatrix.hh> /////////////////////////////////////////////////////////////////////////////////////////// // Various matrix methods /////////////////////////////////////////////////////////////////////////////////////////// namespace Dune { namespace GFE { /** \brief Multiplication of a ScalecIdentityMatrix with another FieldMatrix */ template <class T, int N, int otherCols> Dune::FieldMatrix<T,N,otherCols> operator* ( const Dune::ScaledIdentityMatrix<T, N>& diagonalMatrix, const Dune::FieldMatrix<T, N, otherCols>& matrix) { Dune::FieldMatrix<T,N,otherCols> result(0); for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < otherCols; ++j) result[i][j] = diagonalMatrix[i][i]*matrix[i][j]; return result; } /** \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 /** \brief Return a segment of a FieldVector from lower up to lower+size-1 */ template< int lower, int size,typename field_type,int n> static FieldVector<field_type,size> segment(const FieldVector<field_type,n>& v) { FieldVector<field_type,size> res; std::copy(v.begin()+lower,v.begin()+lower+size,res.begin()); return res; } /** \brief Return a segment of a FieldVector from lower up to lower+size-1 * lower is unkown at compile time*/ template< int size,typename field_type,int n> static FieldVector<field_type,size> segmentAt(const FieldVector<field_type,n>& v,const size_t lower) { FieldVector<field_type,size> res; std::copy(v.begin()+lower,v.begin()+lower+size,res.begin()); return res; } /** \brief Return a block of a FieldMatrix (lower1...lower1+size1-1,lower2...lower2+size2-1 */ template< int lower1, int size1, int lower2,int size2,typename field_type,int n,int m> static auto block(const FieldMatrix<field_type,n,m>& v) { static_assert(lower1+size1<=n && lower2+size2<=m, "Size mismatch for Block!"); FieldMatrix<field_type,size1,size2> res; for(int i=lower1; i<lower1+size1; ++i) for(int j=lower2; j<lower2+size2; ++j) res[i-lower1][j-lower2] = v[i][j]; return res; } /** \brief Return a block of a FieldMatrix (lower1...lower1+size1-1,lower2...lower2+size2-1 * * lower1 and lower2 is unkown at compile time*/ template< int size1,int size2,typename field_type,int n,int m> static auto blockAt(const FieldMatrix<field_type,n,m>& v, const size_t& lower1, const size_t& lower2) { assert(lower1+size1<=n && lower2+size2<=m); FieldMatrix<field_type,size1,size2> res; for(size_t i=lower1; i<lower1+size1; ++i) for(size_t j=lower2; j<lower2+size2; ++j) res[i-lower1][j-lower2] = v[i][j]; return res; } /** \brief Generates FieldVector with random entries in the range -1..1 */ template<typename field_type,int n> auto randomFieldVector(field_type lower=-1, field_type upper=1) { std::random_device rd; std::mt19937 mt(rd()); std::uniform_real_distribution<field_type> dist(lower, upper); auto rand = [&dist,&mt](){ return dist(mt); }; FieldVector<field_type,n> vec; std::generate(vec.begin(), vec.end(), rand); return vec; } } } #endif