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#ifndef DUNE_GFE_LINEARALGEBRA_HH
#define DUNE_GFE_LINEARALGEBRA_HH
#include <random>
#include <dune/common/fmatrix.hh>
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#include <dune/istl/scaledidmatrix.hh>
///////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////
namespace Dune {
namespace GFE {
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/** \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;
}
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/** \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
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/** \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;
}
}
}