polynomial1d.h

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/*
 * Copyright (c) 2010-2015:  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,
 * 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 __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__COMMON__POLYNOMIAL1D__
#define __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__COMMON__POLYNOMIAL1D__
 
#include "common/math/ugmath.h"
#include <vector>
 
namespace ug{
 
 
class Polynomial1D
{
  public:
    Polynomial1D(size_t degree = 0)
      : m_vCoeff(degree+1, 0.0)
    {}
 
    Polynomial1D(const std::vector<number>& a)
      : m_vCoeff(a)
    {
    //  check that at least constant of polynomial set
      if(m_vCoeff.empty())
        m_vCoeff.resize(1, 0.0);
    };
 
    size_t degree() const {return m_vCoeff.size() - 1;}
 
    number value(const number x) const
    {
    //  get degree of polynomial (is >= 0 by construction)
      const size_t deg = m_vCoeff.size() - 1;
 
    //  loop horner scheme
      number val = m_vCoeff[deg];
      for(size_t i = deg; i > 0; --i)
        val = m_vCoeff[i-1] + val * x;
 
    //  we're done
      return val;
    }
 
    Polynomial1D derivative() const
    {
    //  if only constant present, return empty Polynomial
      if(degree() == 0)
        return Polynomial1D();
 
    //  create empty polynomial of with correct size
      Polynomial1D tmpPol(degree() - 1);
 
    //  differentiate
      for(size_t i = 0; i <= tmpPol.degree(); ++i)
        tmpPol.m_vCoeff[i] = (i+1) * m_vCoeff[i+1];
 
    //  return derivative by copy
      return tmpPol;
    }
 
    Polynomial1D& operator *=(const Polynomial1D& v)
    {
    //  new size of polynomial
      size_t newDeg = degree() + v.degree();
 
    //  create new coefficients
      std::vector<number> vNewCoeff(newDeg+1, 0.0);
 
    //  multiply
      for(size_t i = 0; i <= degree(); ++i)
        for(size_t j = 0; j <= v.degree(); ++j)
          vNewCoeff[i+j] += m_vCoeff[i] * v.m_vCoeff[j];
 
    //  Copy new coeffs
      m_vCoeff = vNewCoeff;
 
    //  we're done
      return *this;
    }
 
    Polynomial1D& operator *=(number scale)
    {
    //  multiply
      for(size_t i = 0; i <= degree(); ++i)
        m_vCoeff[i] *= scale;
 
    //  we're done
      return *this;
    }
 
  //  output
    friend std::ostream& operator<< (std::ostream& outStream, Polynomial1D& v);
 
  protected:
    void set_coefficients(const std::vector<number>& a)
    {
    //  assign coefficients
      m_vCoeff = a;
 
    //  check that at least constant of polynomial set
      if(m_vCoeff.empty())
        m_vCoeff.resize(1, 0.0);
    };
 
  private:
  //  vector holding the coefficients of the polynom
  //  An empty vector is the Polynomial p = 0;
  //  else we have p(x) = sum_i m_vCoeff[i] *x^i
    std::vector<number> m_vCoeff;
};
 
inline std::ostream& operator<< (std::ostream& outStream, Polynomial1D& v)
{
  for(size_t i = 0; i <= v.degree(); ++i)
  {
    outStream << v.m_vCoeff[i] << " *x^" << i;
    if(i != v.degree()) outStream << " + ";
  }
  return outStream;
}
 
} // end namespace ug
 
#endif /* __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__COMMON__POLYNOMIAL1D__ */