additional_math.h

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/*
 * Copyright (c) 2013-2015:  G-CSC, Goethe University Frankfurt
 * Author: Martin Rupp
 * 
 * This file is part of UG4.
 * 
 * UG4 is free software: you can redistribute it and/or modify it under the
 * terms of the GNU Lesser General Public License version 3 (as published by the
 * Free Software Foundation) with the following additional attribution
 * requirements (according to LGPL/GPL v3 §7):
 * 
 * (1) The following notice must be displayed in the Appropriate Legal Notices
 * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (2) The following notice must be displayed at a prominent place in the
 * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (3) The following bibliography is recommended for citation and must be
 * preserved in all covered files:
 * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
 *   parallel geometric multigrid solver on hierarchically distributed grids.
 *   Computing and visualization in science 16, 4 (2013), 151-164"
 * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
 *   flexible software system for simulating pde based models on high performance
 *   computers. Computing and visualization in science 16, 4 (2013), 165-179"
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU Lesser General Public License for more details.
 */
 
#ifndef FAMG_ADDITIONAL_MATH_H_
#define FAMG_ADDITIONAL_MATH_H_
#include "lib_algebra/small_algebra/small_matrix/densematrix.h"
namespace ug{
 
inline void vecSum(double &erg, double alpha, double vec)
{
  erg = alpha * vec;
}
 
template<typename T>
inline void vecSum(typename T::value_type &erg, double alpha, const T &vec)
{
  erg = alpha * vec[0];
  for (size_t i = 1; i < vec.size(); i++)
    erg += vec[i];
  erg *= alpha;
}
 
inline double vecSum(double alpha, double vec)
{
  return alpha * vec;
}
template<typename T>
inline typename T::value_type vecSum(double alpha, const T &vec)
{
  typename T::value_type erg;
  vecSum(erg, alpha, vec);
  return erg;
}
 
inline void matSum(double &erg, double alpha, double vec)
{
  erg = alpha * vec;
}
 
template<typename T1, typename T2>
inline void matSum(T1 &erg, double alpha, T2 &mat)
{
  for (size_t r = 0; mat.num_rows(); r++)
  {
    erg[r] = mat(r, 0);
    for (size_t c = 1; c < mat.num_cols(); c++)
      erg[r] += mat(r, c);
    erg[r] *= alpha;
  }
}
 
template<typename T1, typename T2>
inline T1 matSum(double alpha, T2 &mat)
{
  T1 erg;
  matSum(erg, alpha, mat);
  return erg;
}
 
template<typename T1>
inline typename DenseMatrix<T1>::value_type Sum1Mat1(const DenseMatrix<T1> &mat)
{
  typename DenseMatrix<T1>::value_type ret = 0.0;
  for (size_t r = 0; mat.num_rows(); r++)
    for (size_t c = 1; c < mat.num_cols(); c++)
      ret += mat(r, c);
  return ret;
}
 
inline double matTrace(const double d)
{
  return d;
}
 
template<typename T1>
inline double matTrace(const DenseMatrix<T1> &mat)
{
  double tr=0.0;
  const size_t rk = (mat.num_rows() < mat.num_cols()) ? mat.num_rows() : mat.num_cols();
  for (size_t k = 0; k<rk; k++)
  {
    tr += mat(k, k);
  }
  return tr;
}
 
inline double matDiagMax(const double d)
{
  return d;
}
 
template<typename T1>
inline double matDiagMax(const DenseMatrix<T1> &mat)
{
  double val=0.0;
  double max=0.0;
  const size_t rk = (mat.num_rows() < mat.num_cols()) ? mat.num_rows() : mat.num_cols();
  for (size_t k = 0; k<rk; k++)
  {
    double abs=fabs(mat(k, k));
    if (abs>max) {
      val = mat(k, k);
      max = abs;
    }
  }
  return val;
}
 
 
inline double Sum1Mat1(double d)
{
  return d;
}
 
inline void GetDiag(double &a, double b)
{
  a = b;
}
 
template<typename T1, typename T2>
inline void GetDiag(T1 &m1, const T2 &m)
{
  UG_ASSERT(m.num_rows()==m.num_cols(), "");
  m1.resize(m.num_rows(), m.num_rows());
  m1=0.0;
  for (size_t i = 0; i < m.num_rows(); i++)
    m1(i, i) = m(i, i);
}
 
template<typename T1, typename T2>
inline void GetDiagSqrt(T1 &v, const T2 &m)
{
  UG_ASSERT(m.num_rows()==m.num_cols(), "");
  v.resize(m.num_rows());
  for (size_t i = 0; i < m.num_rows(); i++)
    v[i] = sqrt(m(i, i));
}
 
inline void GetDiagSqrt(double &a, double b)
{
  a = sqrt(b);
}
 
inline double EnergyProd(double v1, double M, double v2)
{
  return v1 * M * v2;
}
 
template<typename T1, typename T2>
inline double EnergyProd(const T1 &v1, const DenseMatrix<T2> &M, const T1 &v2)
{
  double sum = 0;
  for (size_t r = 0; r < M.num_rows(); r++)
  {
    double t = 0;
    for (size_t c = 0; c < M.num_cols(); c++)
      t += M(r, c) * v2[c];
    sum += t * v1[r];
  }
  return sum;
}
 
template<typename TMatrix>
void BlockMatrixToDoubleMatrix(DenseMatrix<VariableArray2<double> > &Ad, TMatrix &Ab)
{
  const size_t blockSize = block_traits<typename TMatrix::value_type>::static_num_rows;
  Ad.resize(blockSize*Ab.num_rows(), blockSize*Ab.num_cols());
 
  for(size_t i=0; i<Ab.num_rows(); i++)
  {
    for(size_t j=0; j<Ab.num_cols(); j++)
      for(size_t r=0; r<blockSize; r++)
        for(size_t c=0; c<blockSize; c++)
          Ad(i*blockSize+r, j*blockSize+c) = BlockRef(Ab(i, j), r, c);
  }
}
 
}
#endif /* ADDITIONAL_MATH_H_ */