lagrange1d.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__LAGRANGE1D__
#define __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__COMMON__LAGRANGE1D__
 
#include "./polynomial1d.h"
#include "common/math/ugmath.h"
#include <vector>
 
namespace ug{
 
class Lagrange1D
  : public Polynomial1D
{
  public:
    Lagrange1D(const size_t i, const std::vector<number>& vPos)
    {
    //  compute coefficients
      compute_coeffs(i, vPos);
 
    //  remember positions
      m_vPos = vPos;
    }
 
    number position(const size_t i) const
    {
      UG_ASSERT(i < m_vPos.size(), "Invalid index");
      return m_vPos[i];
    }
 
  protected:
    void compute_coeffs(const size_t i, const std::vector<number>& vPos)
    {
    //  start coefficients
      std::vector<number> vStart(1, 1.0);
 
    //  start polynomial
      this->set_coefficients(vStart);
 
    //  help polynomial used for each factor
      std::vector<number> vFactor(2,1.0);
 
    //  scaling of polynom
      number scale = 1.0;
 
    //  fill coefficients
      for(size_t j = 0; j < vPos.size(); ++j)
      {
        if(j == i) continue;
 
      //  set first coefficent to minus position
        vFactor[0] = -vPos[j];
      //  create polynom for (-vPos, 1)
        Polynomial1D tmpPol(vFactor);
      //  multiply
        (*this) *= tmpPol;
      //  multiply scale
        scale *= 1./(vPos[i]-vPos[j]);
      }
 
    //  multiply by scale
      (*this) *= scale;
    }
 
  private:
    std::vector<number> m_vPos;
};
 
class EquidistantLagrange1D
  : public Polynomial1D
{
  public:
    EquidistantLagrange1D(const size_t i, const size_t degree)
    {
      UG_ASSERT(i <= degree, "Only #degree shape functions.");
      compute_coeffs(i, degree);
    }
 
    static number position(const size_t i, const size_t degree)
    {
      UG_ASSERT(i <= degree, "Invalid index");
      return (number)i/(number)degree;
    }
 
  protected:
    void compute_coeffs(const int i, const int p)
    {
    //  start coefficients
      std::vector<number> vStart(1, 1.0);
 
    //  start polynomial
      this->set_coefficients(vStart);
 
    //  help polynomial used for each factor
      std::vector<number> vFactor(2, p);
 
    //  scaling of polynom
      number scale = 1.0;
 
    //  fill coefficients
      for(int j = 0; j <= p; ++j)
      {
        if(j == i) continue;
 
      //  set first coefficent to minus position
        vFactor[0] = -j;
      //  create polynom for (-j, p)
        Polynomial1D tmpPol(vFactor);
      //  multiply
        (*this) *= tmpPol;
      //  multiply scale
        scale *= 1./(i-j);
      }
 
    //  multiply by scale
      (*this) *= scale;
    }
};
 
class TruncatedEquidistantLagrange1D
  : public Polynomial1D
{
  public:
    TruncatedEquidistantLagrange1D(const size_t i, const size_t degree)
    {
      UG_ASSERT(i <= degree, "Only #degree shape functions.");
 
      compute_coeffs(i, degree);
    }
 
    static number position(const size_t i, const size_t degree)
    {
      UG_ASSERT(i <= degree, "Invalid index");
      return (number)i/(number)degree;
    }
 
  protected:
    void compute_coeffs(const int i, const int p)
    {
    //  start coefficients
      std::vector<number> vStart(1, 1.0);
 
    //  start polynomial
      this->set_coefficients(vStart);
 
    //  help polynomial used for each factor
      std::vector<number> vFactor(2, p);
 
    //  scaling of polynom
      number scale = 1.0;
 
    //  fill coefficients
      for(int j = 0; j < i; ++j)
      {
      //  set first coefficent to minus position
        vFactor[0] = -j;
      //  create polynom for (-j, p)
        Polynomial1D tmpPol(vFactor);
      //  multiply
        (*this) *= tmpPol;
      //  multiply scale
        scale *= 1./(i-j);
      }
 
    //  multiply by scale
      (*this) *= scale;
    }
};
 
class BoundedEquidistantLagrange1D
  : public Polynomial1D
{
  public:
    BoundedEquidistantLagrange1D(const size_t i, const size_t degree,
                                 const size_t bound)
    {
      UG_ASSERT(i <= bound, "Only #bound shape functions.");
      UG_ASSERT(bound <= degree, "Only #bound shape functions.");
 
    //  init coefficients
      compute_coeffs(i, degree, bound);
    }
 
    static number position(const size_t i, const size_t degree)
    {
      UG_ASSERT(i <= degree, "Invalid index");
      return (number)i/(number)degree;
    }
 
  protected:
    void compute_coeffs(const int i, const int p, const int b)
    {
    //  start coefficients
      std::vector<number> vStart(1, 1.0);
 
    //  start polynomial
      this->set_coefficients(vStart);
 
    //  help polynomial used for each factor
      std::vector<number> vFactor(2, p);
 
    //  scaling of polynom
      number scale = 1.0;
 
    //  fill coefficients
      for(int j = 0; j <= b; ++j)
      {
        if(j == i) continue;
 
      //  set first coefficent to minus position
        vFactor[0] = -j;
      //  create polynom for (-j, p)
        Polynomial1D tmpPol(vFactor);
      //  multiply
        (*this) *= tmpPol;
      //  multiply scale
        scale *= 1./(i-j);
      }
 
    //  multiply by scale
      (*this) *= scale;
    }
};
 
 
} // end namespace ug
 
#endif /* __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__COMMON__LAGRANGE1D__ */