MatrixOperations.cpph

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template<int Rows, typename Scalar>
tarch::la::Matrix<Rows,Rows,Scalar>  tarch::la::identity() {
  tarch::la::Matrix<Rows,Rows,Scalar> result(0.0);
  
  for (int i=0; i<Rows; i++) {
    result(i,i) = 1.0;
  }
  
  return result;
}
 
 
template<int Rows, int Cols, typename Scalar>
Scalar tarch::la::frobeniusNorm(
  const Matrix<Rows,Cols,Scalar>&  matrix
) {
  Scalar result(0);
 
  for (int row=0; row<Rows; row++)
  for (int col=0; col<Cols; col++) {
    result += matrix(row,col) * matrix(row,col);
  }
 
  return std::sqrt(result);
}
 
 
template<int Rows, int Cols, typename Scalar>
Scalar tarch::la::elementMax(
  const Matrix<Rows,Cols,Scalar>&  matrix
) {
  Scalar result(0);
 
  for (int row=0; row<Rows; row++)
  for (int col=0; col<Cols; col++) {
    result = std::max( result, std::abs( matrix(row,col) ) );
  }
 
  return result;
}
 
 
template<int Rows, int Cols, typename Scalar>
tarch::la::Matrix<Rows,Cols,Scalar> tarch::la::invertEntries (
  const tarch::la::Matrix<Rows,Cols,Scalar>&  matrix
) {
  tarch::la::Matrix<Rows,Cols,Scalar> result(0.0);
  
  for (int i=0; i<Rows; i++) {
    for (int j=0; j<Cols; j++) {
      result(i,j) = 1.0/matrix(i,j);
    }
  }
  
  return result;
}
 
 
 
template<int Rows, int Cols, typename Scalar>
tarch::la::Vector<Cols,Scalar> tarch::la::row(const Matrix<Rows,Cols,Scalar>& matrix, int whichRow) {
  tarch::la::Vector<Cols,Scalar> result;
 
  for (int i=0; i<Cols; i++) {
    result(i) = matrix(whichRow,i);
  }
 
  return result;
}
 
 
template<int Rows, int Cols, typename Scalar>
tarch::la::Vector<Rows,Scalar> tarch::la::col(const Matrix<Rows,Cols,Scalar>& matrix, int whichColumn) {
  tarch::la::Vector<Rows,Scalar> result;
 
  for (int i=0; i<Rows; i++) {
    result(i) = matrix(i,whichColumn);
  }
 
  return result;
}
 
 
template<int Rows, int Cols, typename Scalar>
tarch::la::Matrix<Cols,Rows,Scalar> tarch::la::transpose(const tarch::la::Matrix<Rows,Cols,Scalar>& matrix) {
  tarch::la::Matrix<Cols,Rows,Scalar> result;
  #ifdef CompilerICC
  #pragma ivdep
  #endif
  for (int i=0; i < Rows; i++) {
    for (int j=0; j < Cols; j++) {
      result(j,i) += matrix(i,j);
    }
  }
  return result;
}
 
 
 
template<int Rows, int Cols, typename Scalar>
Scalar tarch::la::sum(const tarch::la::Matrix<Rows,Cols,Scalar>& matrix) {
  Scalar result = 0;
  for (int i=0; i < Rows; i++) {
    for (int j=0; j < Cols; j++) {
      result += matrix(i,j);
    }
  }
  return result;
}
 
 
 
template<int Rows, int Cols, typename Scalar>
std::ostream& operator<< (
  std::ostream& os,
  const tarch::la::Matrix<Rows,Cols,Scalar>& matrix
) {
  os << matrix.toString();
  return os;
}
 
 
template<int Rows, typename Scalar>
tarch::la::Vector<Rows,Scalar> tarch::la::diag(const Matrix<Rows,Rows,Scalar>& matrix) {
  tarch::la::Vector<Rows,Scalar> result;
  for (int i=0; i<Rows; i++) {
      result(i) = matrix(i,i);
  }
  return result;
}