NekLinAlgAlgorithms.hpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: NekLinAlgAlgorithms.hpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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//
// Description: Linear Algebra Algorithms
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef NEKTAR_LIB_UTILITIES_LINEAR_ALGEBRA_NEK_LIN_ALG_ALGORITHMS_HPP
#define NEKTAR_LIB_UTILITIES_LINEAR_ALGEBRA_NEK_LIN_ALG_ALGORITHMS_HPP
 
#include <LibUtilities/LinearAlgebra/NekMatrix.hpp>
#include <LibUtilities/LinearAlgebra/NekVector.hpp>
#include <vector>
 
namespace Nektar
{
/// \brief Calculates the orthogonal, normalized vectors from
/// linearly independent input.
/// \return A list of ortogonalized vectors corresponding to the
///         input vectors.  If the size of the output doesn't
///         match the size of the input then an error occurred.
/// This algorithm is taken from "Parallel Scientific Computing in
/// C++ and MPI", Karniadakis and Kirby, page 55.
template <typename DataType>
std::vector<NekVector<DataType>> GramSchmidtOrthogonalization(
    const std::vector<NekVector<DataType>> &x)
{
    typedef NekVector<DataType> VectorType;
    typedef NekMatrix<DataType> MatrixType;
 
    // typename dim = x[0].GetDimension();
    unsigned int dim = x[0].GetDimension();
    std::vector<VectorType> q(x.size(), VectorType());
 
    // This matrix holds the r_ij values.  Using the matrix object
    // is a convenience since it provides a 2D access to a table
    // of values.
    MatrixType r(dim, dim);
    r(0, 0) = x[0].L2Norm();
 
    if (r(0, 0) == DataType(0))
    {
        return q;
    }
 
    q[0] = x[0] / r(0, 0);
 
    for (unsigned int j = 1; j < x.size(); ++j)
    {
        for (unsigned int i = 0; i <= j - 1; ++i)
        {
            r(i, j) = q[i].Dot(x[j]);
        }
 
        VectorType y = x[j];
        for (unsigned int i = 0; i <= j - 1; ++i)
        {
            y = y - r(i, j) * q[i];
        }
 
        r(j, j) = y.L2Norm();
        if (r(j, j) == DataType(0))
        {
            return q;
        }
 
        q[j] = y / r(j, j);
    }
 
    return q;
}
} // namespace Nektar
 
#endif // NEKTAR_LIB_UTILITIES_LINEAR_ALGEBRA_NEK_LIN_ALG_ALGORITHMS_HPP