math_tensor.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__COMMON__MATH_TENSOR__
#define __H__COMMON__MATH_TENSOR__
 
#include <cstddef>
#include <iostream>
#include "../../types.h"
 
namespace ug
{
 
//  MathTensor
 
template <size_t TRank, size_t N, typename T = number> class MathTensor;
 
template <size_t TRank, size_t N, typename T>
class MathTensor
{
  public:
    // type of value
    typedef MathTensor<TRank-1, N, T> value_type;
 
    // size type
    typedef size_t size_type;
 
    // Dimension of tensor
    static const size_t Dimension = N;
 
    // Rank of tensor (i.e. number of indices)
    static const size_t Rank = TRank;
 
  public:
    MathTensor() {}
    MathTensor(const MathTensor& v) {assign(v);}
 
    // operations with other vectors
    MathTensor& operator=  (const MathTensor& v)
    {
      if(this != &v){assign(v);}
      return *this;
    }
    MathTensor& operator=  (const MathTensor& v) {…}
 
    inline size_t size() const {return N;}
    inline size_t rank() const {return TRank;}
 
    MathTensor& operator=(T val) {set(val); return *this;}
    inline void set(T val) {for(size_t i = 0; i < N; ++i) m_data[i].set(val);}
 
    inline value_type& operator[](size_t i)       {UG_ASSERT(i < size(), "Index out of range."); return m_data[i];}
    inline const value_type& operator[](size_t i) const {UG_ASSERT(i < size(), "Index out of range."); return m_data[i];}
 
  protected:
    inline void assign(const MathTensor<TRank, N, T>& v){for(size_t i = 0; i < N; ++i) m_data[i] = v[i];}
 
  protected:
    value_type  m_data[N];
};
class MathTensor {…};
 
 
template <size_t N, typename T>
class MathTensor<1, N, T>
{
  public:
    // type of value
    typedef T value_type;
 
    // size type
    typedef size_t size_type;
 
    // Dimension of tensor
    static const size_t Dimension = N;
 
    // Rank of tensor (i.e. number of indices)
    static const size_t Rank = 1;
 
  public:
    MathTensor(const bool init = true) { if(init) set(0.0);}
    MathTensor(const MathTensor& v) {assign(v);}
 
    // operations with other vectors
    MathTensor& operator=  (const MathTensor& v)
    {
      if(this != &v){assign(v);}
      return *this;
    }
    MathTensor& operator=  (const MathTensor& v) {…}
 
    inline size_t size() const {return N;}
    inline size_t rank() const {return 1;}
 
    MathTensor& operator=(T val) {set(val); return *this;}
    inline void set(T val) {for(size_t i = 0; i < N; ++i) m_data[i] = val;}
 
    inline value_type& operator[](size_t i)       {UG_ASSERT(i < size(), "Index out of range."); return m_data[i];}
    inline const value_type& operator[](size_t i) const {UG_ASSERT(i < size(), "Index out of range."); return m_data[i];}
 
  protected:
    inline void assign(const MathTensor<1, N, T>& v) {for(size_t i = 0; i < N; ++i) m_data[i] = v[i];}
 
  protected:
    value_type  m_data[N];
};
class MathTensor<1, N, T> {…};
 
template <size_t TRank, size_t N, typename T>
std::ostream& operator<< (std::ostream& outStream, const ug::MathTensor<TRank, N, T>& v)
{
  outStream << "[";
  for(size_t i = 0; i < v.size()-1; ++i)
      outStream << v[i] << ", ";
  outStream << v[v.size()-1] << "]";
  return outStream;
}
std::ostream& operator<< (std::ostream& outStream, const ug::MathTensor<TRank, N, T>& v) {…}
 
 
// unfortunately, not all tensor are like 3x3x3x3, but also 3x2x3x2.
// merge this if possible with MathVector<MathVector<2> > ?
 
template <typename TEntry, size_t N>
class MathTensorX
{
public:
  // type of value
  typedef TEntry value_type;
 
  // size type
  typedef size_t size_type;
 
  // Dimension of tensor
  static const size_t Dimension = N;
 
  // Rank of tensor (i.e. number of indices)
  static const size_t Rank = TEntry::Rank+1;
 
public:
  MathTensorX() { }
  MathTensorX(const MathTensorX& v) {assign(v);}
 
  // operations with other vectors
  MathTensorX& operator=  (const MathTensorX& v)
  {
    if(this != &v){assign(v);}
    return *this;
  }
  MathTensorX& operator=  (const MathTensorX& v) {…}
 
  inline size_t size() const {return N;}
  inline size_t rank() const {return Rank;}
 
  inline value_type& operator[](size_t i)       {UG_ASSERT(i < size(), "Index out of range."); return m_data[i];}
  inline const value_type& operator[](size_t i) const {UG_ASSERT(i < size(), "Index out of range."); return m_data[i];}
 
protected:
  inline void assign(const MathTensorX<TEntry, N>& v) {for(size_t i = 0; i < N; ++i) m_data[i] = v[i];}
 
protected:
  TEntry m_data[N];
};
class MathTensorX {…};
 
template <size_t N, typename T = number>
class MathTensor1 : public MathTensor<1, N, T> { };
 
template <size_t N1, size_t N2, typename T = number>
class MathTensor2 : public MathTensorX<MathTensor1<N2, T>, N1> { };
 
template <size_t N1, size_t N2, size_t N3, typename T = number>
class MathTensor3 : public MathTensorX< MathTensorX<MathTensor1<N3, T>, N2>, N1> { };
 
template <size_t N1, size_t N2, size_t N3, size_t N4, typename T = number>
class MathTensor4 : public MathTensorX< MathTensorX< MathTensorX<MathTensor1<N4, T>, N3>, N2>, N1> { };
 
template <typename TEntry>
std::ostream& operator<< (std::ostream& outStream, const ug::MathTensorX<TEntry, 1>& v)
{
  outStream << "[";
  outStream << v[0] << "]";
  return outStream;
}
std::ostream& operator<< (std::ostream& outStream, const ug::MathTensorX<TEntry, 1>& v) {…}
 
template <typename TEntry, size_t N>
std::ostream& operator<< (std::ostream& outStream, const ug::MathTensorX<TEntry, N>& v)
{
  outStream << "[";
  for(size_t i = 0; i < N-1; ++i)
    outStream << v[i] << ", ";
  outStream << v[N-1] << "]";
  return outStream;
}
std::ostream& operator<< (std::ostream& outStream, const ug::MathTensorX<TEntry, N>& v) {…}
 
// end group math_tensor
 
}// end of namespace
 
 
#endif /* __H__COMMON__MATH_MathVector__ */