math_matrix_vector_functions_common_impl.hpp

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/*
 * Copyright (c) 2009-2015:  G-CSC, Goethe University Frankfurt
 * Author: Andreas Vogel
 * 
 * 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,
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 */
 
#ifndef __H__LGMATH__MATRIX_VECTOR_FUNCTIONS_COMMON_IMPL__
#define __H__LGMATH__MATRIX_VECTOR_FUNCTIONS_COMMON_IMPL__
 
#include <cmath>
#include "common/error.h"
#include "math_matrix.h"
#include "math_vector.h"
 
namespace ug
{
 
// vOut = m * v
template <typename vector_t_out, typename matrix_t, typename vector_t_in>
inline
void
MatVecMult(vector_t_out& vOut, const matrix_t& m, const vector_t_in& v)
{
  assert(vector_t_out::Size == matrix_t::RowSize);
  assert(vector_t_in::Size == matrix_t::ColSize);
 
  typedef typename matrix_t::size_type size_type;
  for(size_type i = 0; i < vOut.size(); ++i)
  {
    vOut[i] = 0.0;
    for(size_type j = 0; j < v.size(); ++j)
    {
      vOut[i] += m(i,j) * v[j];
    }
  }
}
 
// vOut += m * v
template <typename vector_t_out, typename matrix_t, typename vector_t_in>
inline
void
MatVecMultAppend(vector_t_out& vOut, const matrix_t& m, const vector_t_in& v)
{
  assert(vector_t_out::Size == matrix_t::RowSize);
  assert(vector_t_in::Size == matrix_t::ColSize);
 
  typedef typename matrix_t::size_type size_type;
  for(size_type i = 0; i < vOut.size(); ++i)
  {
    for(size_type j = 0; j < v.size(); ++j)
    {
      vOut[i] += m(i,j) * v[j];
    }
  }
}
 
// vOut += s * m * v
template <typename vector_t_out, typename matrix_t, typename vector_t_in>
inline
void
MatVecScaleMultAppend(vector_t_out& vOut, typename vector_t_out::value_type s, const matrix_t& m, const vector_t_in& v)
{
  assert(vector_t_out::Size == matrix_t::RowSize);
  assert(vector_t_in::Size == matrix_t::ColSize);
 
  typedef typename matrix_t::size_type size_type;
  for(size_type i = 0; i < vOut.size(); ++i)
  {
    for(size_type j = 0; j < v.size(); ++j)
    {
      vOut[i] += s * m(i,j) * v[j];
    }
  }
}
 
 
// vOut = Transpose(m) * v
template <typename vector_t_out, typename matrix_t, typename vector_t_in>
inline
void
TransposedMatVecMult(vector_t_out& vOut, const matrix_t& m, const vector_t_in& v)
{
  assert(vector_t_out::Size == matrix_t::ColSize);
  assert(vector_t_in::Size == matrix_t::RowSize);
 
  typedef typename matrix_t::size_type size_type;
  for(size_type i = 0; i < vOut.size(); ++i)
  {
    vOut[i] = 0.0;
    for(size_type j = 0; j < v.size(); ++j)
    {
      vOut[i] += m(j,i) * v[j];
    }
  }
}
 
// vOut += Transpose(m) * v
template <typename vector_t_out, typename matrix_t, typename vector_t_in>
inline
void
TransposedMatVecMultAdd(vector_t_out& vOut, const matrix_t& m, const vector_t_in& v)
{
  assert(vector_t_out::Size == matrix_t::ColSize);
  assert(vector_t_in::Size == matrix_t::RowSize);
 
  typedef typename matrix_t::size_type size_type;
  for(size_type i = 0; i < vOut.size(); ++i)
  {
    for(size_type j = 0; j < v.size(); ++j)
    {
      vOut[i] += m(j,i) * v[j];
    }
  }
}
 
template <typename matrix_t, typename vector_t>
inline
void
GivensMatVecMult (matrix_t& A, vector_t& v)
{
  typedef typename matrix_t::size_type size_type;
  typedef typename matrix_t::value_type value_type;
  
  assert (vector_t::Size == matrix_t::RowSize);
  assert (matrix_t::RowSize >= matrix_t::ColSize);
  
  value_type s, c;
  value_type d, x, y;
 
  for (size_type i = 0; i < matrix_t::RowSize - 1; i++) // the 1st index of the elementar rotation
    for (size_type k = matrix_t::RowSize - 1; k > i; k--) // the 2nd index of this rotation
    {
      d = A (i, i); x = A (k, i);
      
    // Computation of the entries of the elementar transformation:
      if (std::abs (d) > std::abs (x))
      {
        s = x / d;
        c = 1.0 / std::sqrt (1 + s * s);
        s *= c;
      }
      else if (x != 0) // to ensure that A (k, i) != 0; note that abs(x) >= abs(d) here!
      {
        c = d / x;
        s = 1.0 / std::sqrt (1 + c * c);
        c *= s;
      }
      else continue; // nothing to eliminate
 
    // Multiplication of A by the elementar transformation:
      for (size_type j = i; j < matrix_t::ColSize; j++)
      {
        x = A (i, j); y = A (k, j);
        A (i, j) = c * x + s * y;
        A (k, j) = c * y - s * x;
      }
 
    // Multiplication of v by the elementar transformation:
       x = v [i]; y = v [k];
       v [i] = c * x + s * y;
       v [k] = c * y - s * x;
    }
}
 
template <typename matrix_t, typename vector_t>
inline
void
InvMatVecMult_byGivens (matrix_t& A, vector_t& v)
{
  typedef typename matrix_t::size_type size_type;
  
// I. Multiply 'this' by the Givens rotation:
  GivensMatVecMult (A, v);
  
// II. Computation of the result:
  size_type i = matrix_t::ColSize; // <= matrix_t::RowSize, i.e. we invert only the square block
  do
  {
    i--;
    for (size_type j = i + 1; j < matrix_t::ColSize; j++)
      v [i] -= A (i, j) * v [j];
    if (std::abs (A (i, i)) < SMALL * std::abs (v [i]))
      UG_THROW ("InvMatVecMult_byGivens: Inverting singular matrix by the Givens rotations");
    v [i] /= A (i, i);
  }
  while (i != 0);
}
 
template <typename matrix_t, typename vector_t>
inline
void
OrthogProjectVec (vector_t& v, const matrix_t& A)
{
  typedef typename matrix_t::size_type size_type;
  typedef typename matrix_t::value_type value_type;
  
//  I. Solve the least square problem:
  matrix_t M = A; // we do not work with the original matrix; otherwise it would be destroyed
  InvMatVecMult_byGivens (M, v);
  
//  II. Compute the linear combination of the columns:
  MathVector<matrix_t::ColSize, value_type> coeff;
  for (size_type i = 0; i < matrix_t::ColSize; i++) coeff [i] = v [i];
  MatVecMult (v, A, coeff);
}
 
} // end of namespace ug
 
#endif /* __H__LGMATH__LGMATH_MATRIX_VECTOR_FUNCTIONS_COMMON_IMPL__ */