AntiSymTensor.h

Go to the documentation of this file.

//////////////////////////////////////////////////////////////////////////////////////
// This file is distributed under the University of Illinois/NCSA Open Source License.
// See LICENSE file in top directory for details.
//
// Copyright (c) 2016 Jeongnim Kim and QMCPACK developers.
//
// File developed by: Jeremy McMinnis, jmcminis@gmail.com, University of Illinois at Urbana-Champaign
//
// File created by: Jeongnim Kim, jeongnim.kim@gmail.com, University of Illinois at Urbana-Champaign
//////////////////////////////////////////////////////////////////////////////////////


#ifndef ANTI_SYM_TENZOR_H
#define ANTI_SYM_TENZOR_H

/***************************************************************************
 *
 * The POOMA Framework
 *
 * This program was prepared by the Regents of the University of
 * California at Los Alamos National Laboratory (the University) under
 * Contract No.  W-7405-ENG-36 with the U.S. Department of Energy (DOE).
 * The University has certain rights in the program pursuant to the
 * contract and the program should not be copied or distributed outside
 * your organization.  All rights in the program are reserved by the DOE
 * and the University.  Neither the U.S.  Government nor the University
 * makes any warranty, express or implied, or assumes any liability or
 * responsibility for the use of this software
 *
 * Visit http://www.acl.lanl.gov/POOMA for more details
 *
 ***************************************************************************/


// include files
#include "PETE/PETE.h"
#include "OhmmsPETE/OhmmsTinyMeta.h"
#include "OhmmsPETE/Tensor.h"

#include <iostream>

namespace qmcplusplus
{
//////////////////////////////////////////////////////////////////////
//
// Definition of class AntiSymTensor.
//
//////////////////////////////////////////////////////////////////////

//
//    |  O -x10  -x20 |
//    | x10   0  -x21 |
//    | x20  x21   0  |
//

template<class T, unsigned D>
class AntiSymTensor
{
public:
  using Type_t = T;
  enum
  {
    ElemDim = 2
  };
  enum
  {
    Size = D * (D - 1) / 2
  };

  // Default Constructor
  AntiSymTensor() { OTAssign<AntiSymTensor<T, D>, T, OpAssign>::apply(*this, T(0), OpAssign()); }

  // A noninitializing ctor.
  class DontInitialize
  {};
  AntiSymTensor(DontInitialize) {}

  // Construct an AntiSymTensor from a single T.
  // This doubles as the 2D AntiSymTensor initializer.
  AntiSymTensor(const T& x00) { OTAssign<AntiSymTensor<T, D>, T, OpAssign>::apply(*this, x00, OpAssign()); }
  // construct a 3D AntiSymTensor
  AntiSymTensor(const T& x10, const T& x20, const T& x21)
  {
    X[0] = x10;
    X[1] = x20;
    X[2] = x21;
  }

  // Copy Constructor
  AntiSymTensor(const AntiSymTensor<T, D>& rhs)
  {
    OTAssign<AntiSymTensor<T, D>, AntiSymTensor<T, D>, OpAssign>::apply(*this, rhs, OpAssign());
  }

  // Construct from a Tensor.
  // Extract the antisymmetric part.
  AntiSymTensor(const Tensor<T, D>& t)
  {
    for (int i = 1; i < D; ++i)
    {
      for (int j = 0; j < i; ++j)
        (*this)[((i - 1) * i / 2) + j] = (t(i, j) - t(j, i)) * 0.5;
    }
  }

  ~AntiSymTensor(){};

  // assignment operators
  AntiSymTensor<T, D>& operator=(const AntiSymTensor<T, D>& rhs)
  {
    OTAssign<AntiSymTensor<T, D>, AntiSymTensor<T, D>, OpAssign>::apply(*this, rhs, OpAssign());
    return *this;
  }
  template<class T1>
  AntiSymTensor<T, D>& operator=(const AntiSymTensor<T1, D>& rhs)
  {
    OTAssign<AntiSymTensor<T, D>, AntiSymTensor<T1, D>, OpAssign>::apply(*this, rhs, OpAssign());
    return *this;
  }
  AntiSymTensor<T, D>& operator=(const T& rhs)
  {
    OTAssign<AntiSymTensor<T, D>, T, OpAssign>::apply(*this, rhs, OpAssign());
    return *this;
  }

  // accumulation operators
  template<class T1>
  AntiSymTensor<T, D>& operator+=(const AntiSymTensor<T1, D>& rhs)
  {
    OTAssign<AntiSymTensor<T, D>, AntiSymTensor<T1, D>, OpAddAssign>::apply(*this, rhs, OpAddAssign());
    return *this;
  }

  template<class T1>
  AntiSymTensor<T, D>& operator-=(const AntiSymTensor<T1, D>& rhs)
  {
    OTAssign<AntiSymTensor<T, D>, AntiSymTensor<T1, D>, OpSubtractAssign>::apply(*this, rhs, OpSubtractAssign());
    return *this;
  }

  template<class T1>
  AntiSymTensor<T, D>& operator*=(const AntiSymTensor<T1, D>& rhs)
  {
    OTAssign<AntiSymTensor<T, D>, AntiSymTensor<T1, D>, OpMultiplyAssign>::apply(*this, rhs, OpMultiplyAssign());
    return *this;
  }
  AntiSymTensor<T, D>& operator*=(const T& rhs)
  {
    OTAssign<AntiSymTensor<T, D>, T, OpMultiplyAssign>::apply(*this, rhs, OpMultiplyAssign());
    return *this;
  }

  template<class T1>
  AntiSymTensor<T, D>& operator/=(const AntiSymTensor<T1, D>& rhs)
  {
    OTAssign<AntiSymTensor<T, D>, AntiSymTensor<T1, D>, OpDivideAssign>::apply(*this, rhs, OpDivideAssign());
    return *this;
  }
  AntiSymTensor<T, D>& operator/=(const T& rhs)
  {
    OTAssign<AntiSymTensor<T, D>, T, OpDivideAssign>::apply(*this, rhs, OpDivideAssign());
    return *this;
  }

  // Methods

  int len(void) const { return Size; }
  int size(void) const { return sizeof(*this); }
  int get_Size(void) const { return Size; }

  class AssignProxy
  {
  public:
    AssignProxy(Type_t& elem, int where) : elem_m(elem), where_m(where) {}
    AssignProxy(const AssignProxy& model) : elem_m(model.elem_m), where_m(where_m) {}
    AssignProxy& operator=(const AssignProxy& a)
    {
      PAssert(where_m != 0 || a.elem_m == -a.elem_m);
      elem_m = where_m < 0 ? -a.elem_m : a.elem_m;
      return *this;
    }
    AssignProxy& operator=(const Type_t& e)
    {
      PAssert(where_m != 0 || e == -e);
      elem_m = where_m < 0 ? -e : e;
      return *this;
    }

    operator Type_t() const { return (where_m < 0 ? -elem_m : elem_m); }

  private:
    //mutable Type_t &elem_m;
    //mutable int where_m;
    Type_t& elem_m;
    int where_m;
  };

  // Operators

  Type_t operator()(unsigned int i, unsigned int j) const
  {
    if (i == j)
      return T(0.0);
    else if (i < j)
      return -X[((j - 1) * j / 2) + i];
    else
      return X[((i - 1) * i / 2) + j];
  }

  //    Type_t operator()( std::pair<int,int> a) const {
  //      int i = a.first;
  //      int j = a.second;
  //      return (*this)(i, j);
  //    }

  AssignProxy operator()(unsigned int i, unsigned int j)
  {
    if (i == j)
      return AssignProxy(AntiSymTensor<T, D>::Zero, 0);
    else
    {
      int lo = i < j ? i : j;
      int hi = i > j ? i : j;
      return AssignProxy(X[((hi - 1) * hi / 2) + lo], i - j);
    }
  }

  //    AssignProxy operator()(std::pair<int,int> a) {
  //      int i = a.first;
  //      int j = a.second;
  //      return (*this)(i, j);
  //    }

  Type_t& operator[](unsigned int i)
  {
    PAssert(i < Size);
    return X[i];
  }

  Type_t operator[](unsigned int i) const
  {
    PAssert(i < Size);
    return X[i];
  }

  // These are the same as operator[] but with () instead:

  Type_t& operator()(unsigned int i)
  {
    PAssert(i < Size);
    return X[i];
  }

  Type_t operator()(unsigned int i) const
  {
    PAssert(i < Size);
    return X[i];
  }

  //    //----------------------------------------------------------------------
  //    // Comparison operators.
  //    bool operator==(const AntiSymTensor<T,D>& that) const {
  //      return TSV_MetaCompareArrays<T,T,D*(D-1)/2>::apply(X,that.X);
  //    }
  //    bool operator!=(const AntiSymTensor<T,D>& that) const {
  //      return !(*this == that);
  //    }

  //    //----------------------------------------------------------------------
  //    // parallel communication
  //    Message& putMessage(Message& m) const {
  //      m.setCopy(true);
  //      ::putMessage(m, X, X + Size);
  //      return m;
  //    }

  //    Message& getMessage(Message& m) {
  //      ::getMessage(m, X, X + Size);
  //      return m;
  //    }

private:
  friend class AssignProxy;

  // The elements themselves.
  T X[Size];

  // A place to store a zero element.
  // We need to return a reference to this
  // for the diagonal element.
  static T Zero;
};


///////////////////////////////////////////////////////////////////////////
// Specialization for 1D  -- this is basically just the zero tensor
///////////////////////////////////////////////////////////////////////////

template<class T>
class AntiSymTensor<T, 1>
{
public:
  using Type_t = T;
  enum
  {
    ElemDim = 2
  };

  // Default Constructor
  AntiSymTensor() {}

  // Copy Constructor
  AntiSymTensor(const AntiSymTensor<T, 1>&) {}

  ~AntiSymTensor() {}

  // assignment operators
  AntiSymTensor<T, 1>& operator=(const AntiSymTensor<T, 1>&) { return *this; }
  template<class T1>
  AntiSymTensor<T, 1>& operator=(const AntiSymTensor<T1, 1>&)
  {
    return *this;
  }
  AntiSymTensor<T, 1>& operator=(const T& rhs) { return *this; }

  // accumulation operators
  template<class T1>
  AntiSymTensor<T, 1>& operator+=(const AntiSymTensor<T1, 1>&)
  {
    return *this;
  }

  template<class T1>
  AntiSymTensor<T, 1>& operator-=(const AntiSymTensor<T1, 1>&)
  {
    return *this;
  }

  template<class T1>
  AntiSymTensor<T, 1>& operator*=(const AntiSymTensor<T1, 1>&)
  {
    return *this;
  }
  AntiSymTensor<T, 1>& operator*=(const T&) { return *this; }

  template<class T1>
  AntiSymTensor<T, 1>& operator/=(const AntiSymTensor<T1, 1>&)
  {
    return *this;
  }
  AntiSymTensor<T, 1>& operator/=(const T&) { return *this; }

  // Methods

  int len(void) const { return Size; }
  int size(void) const { return sizeof(*this); }
  int get_Size(void) const { return Size; }

  class AssignProxy
  {
  public:
    AssignProxy(Type_t& elem, int where) : elem_m(elem), where_m(where) {}
    AssignProxy(const AssignProxy& model) : elem_m(model.elem_m), where_m(where_m) {}
    AssignProxy& operator=(const AssignProxy& a)
    {
      PAssert(where_m != 0 || a.elem_m == -a.elem_m);
      elem_m = where_m < 0 ? -a.elem_m : a.elem_m;
      return *this;
    }
    AssignProxy& operator=(const Type_t& e)
    {
      PAssert(where_m != 0 || e == -e);
      elem_m = where_m < 0 ? -e : e;
      return *this;
    }

    operator Type_t() const { return (where_m < 0 ? -elem_m : elem_m); }

  private:
    //mutable Type_t &elem_m;
    //mutable int where_m;
    Type_t& elem_m;
    int where_m;
  };

  // Operators

  Type_t operator()(unsigned int i, unsigned int j) const
  {
    PAssert(i == j);
    return T(0.0);
  }

  //    Type_t operator()( std::pair<int,int> a) const {
  //      int i = a.first;
  //      int j = a.second;
  //      return (*this)(i, j);
  //    }

  AssignProxy operator()(unsigned int i, unsigned int j)
  {
    PAssert(i == j);
    return AssignProxy(AntiSymTensor<T, 1>::Zero, 0);
  }

  //    AssignProxy operator()(std::pair<int,int> a) {
  //      int i = a.first;
  //      int j = a.second;
  //      return (*this)(i, j);
  //    }

  Type_t operator[](unsigned int i) const
  {
    PAssert(i == 0);
    return AntiSymTensor<T, 1>::Zero;
  }

  // These are the same as operator[] but with () instead:

  Type_t operator()(unsigned int i) const
  {
    PAssert(i == 0);
    return AntiSymTensor<T, 1>::Zero;
  }

  //----------------------------------------------------------------------
  // Comparison operators.
  bool operator==(const AntiSymTensor<T, 1>& that) const { return true; }
  bool operator!=(const AntiSymTensor<T, 1>& that) const { return !(*this == that); }

  //----------------------------------------------------------------------
  // parallel communication
  //    Message& putMessage(Message& m) const {
  //      m.setCopy(true);
  //      m.put(AntiSymTensor<T,1>::Zero);
  //      return m;
  //    }

  //    Message& getMessage(Message& m) {
  //      T zero;
  //      m.get(zero);
  //      return m;
  //    }

private:
  friend class AssignProxy;

  // The number of elements.
  enum
  {
    Size = 0
  };

  // A place to store a zero element.
  // We need to return a reference to this
  // for the diagonal element.
  static T Zero;
};


//////////////////////////////////////////////////////////////////////
//
// Free functions
//
//////////////////////////////////////////////////////////////////////

template<class T, unsigned D>
T trace(const AntiSymTensor<T, D>&)
{
  return T(0.0);
}

template<class T, unsigned D>
AntiSymTensor<T, D> transpose(const AntiSymTensor<T, D>& rhs)
{
  return -rhs;
}
//////////////////////////////////////////////////////////////////////
//
// Unary Operators
//
//////////////////////////////////////////////////////////////////////

//----------------------------------------------------------------------
// unary operator-
//  template<class T, unsigned D>
//  inline AntiSymTensor<T,D> operator-(const AntiSymTensor<T,D> &op)
//  {
//    return MetaUnary< AntiSymTensor<T,D> , OpUnaryMinus > :: apply(op,OpUnaryMinus());
//  }

//----------------------------------------------------------------------
// unary operator+
template<class T, unsigned D>
inline const AntiSymTensor<T, D>& operator+(const AntiSymTensor<T, D>& op)
{
  return op;
}

//////////////////////////////////////////////////////////////////////
//
// Binary Operators
//
//////////////////////////////////////////////////////////////////////

//
// Elementwise operators.
//

OHMMS_META_BINARY_OPERATORS(AntiSymTensor, operator+, OpAdd)
OHMMS_META_BINARY_OPERATORS(AntiSymTensor, operator-, OpSubtract)
OHMMS_META_BINARY_OPERATORS(AntiSymTensor, operator*, OpMultiply)
OHMMS_META_BINARY_OPERATORS(AntiSymTensor, operator/, OpDivide)

//----------------------------------------------------------------------
// dot products.
//----------------------------------------------------------------------

template<class T1, class T2, unsigned D>
inline Tensor<typename BinaryReturn<T1, T2, OpMultiply>::Type_t, D> dot(const AntiSymTensor<T1, D>& lhs,
                                                                        const AntiSymTensor<T2, D>& rhs)
{
  return OTDot<AntiSymTensor<T1, D>, AntiSymTensor<T2, D>>::apply(lhs, rhs);
}

template<class T1, class T2, unsigned D>
inline Tensor<typename BinaryReturn<T1, T2, OpMultiply>::Type_t, D> dot(const AntiSymTensor<T1, D>& lhs,
                                                                        const Tensor<T2, D>& rhs)
{
  return OTDot<Tensor<T1, D>, Tensor<T2, D>>::apply(Tensor<T1, D>(lhs), rhs);
}

template<class T1, class T2, unsigned D>
inline Tensor<typename BinaryReturn<T1, T2, OpMultiply>::Type_t, D> dot(const Tensor<T1, D>& lhs,
                                                                        const AntiSymTensor<T2, D>& rhs)
{
  return OTDot<Tensor<T1, D>, Tensor<T2, D>>::apply(lhs, Tensor<T2, D>(rhs));
}

template<class T1, class T2, unsigned D>
inline Tensor<typename BinaryReturn<T1, T2, OpMultiply>::Type_t, D> dot(const AntiSymTensor<T1, D>& lhs,
                                                                        const SymTensor<T2, D>& rhs)
{
  return OTDot<Tensor<T1, D>, Tensor<T2, D>>::apply(Tensor<T1, D>(lhs), Tensor<T2, D>(rhs));
}

template<class T1, class T2, unsigned D>
inline Tensor<typename BinaryReturn<T1, T2, OpMultiply>::Type_t, D> dot(const SymTensor<T1, D>& lhs,
                                                                        const AntiSymTensor<T2, D>& rhs)
{
  return OTDot<Tensor<T1, D>, Tensor<T2, D>>::apply(Tensor<T1, D>(lhs), Tensor<T2, D>(rhs));
}

template<class T1, class T2, unsigned D>
inline TinyVector<typename BinaryReturn<T1, T2, OpMultiply>::Type_t, D> dot(const TinyVector<T1, D>& lhs,
                                                                            const AntiSymTensor<T2, D>& rhs)
{
  return OTDot<TinyVector<T1, D>, AntiSymTensor<T2, D>>::apply(lhs, rhs);
}

template<class T1, class T2, unsigned D>
inline TinyVector<typename BinaryReturn<T1, T2, OpMultiply>::Type_t, D> dot(const AntiSymTensor<T1, D>& lhs,
                                                                            const TinyVector<T2, D>& rhs)
{
  return OTDot<AntiSymTensor<T1, D>, TinyVector<T2, D>>::apply(lhs, rhs);
}

//----------------------------------------------------------------------
// double dot products.
//----------------------------------------------------------------------

//template < class T1, class T2, unsigned D >
//inline typename BinaryReturn<T1,T2,OpMultiply>::Type_t
//dotdot(const AntiSymTensor<T1,D> &lhs, const AntiSymTensor<T2,D> &rhs)
//{
//  return MetaDotDot< AntiSymTensor<T1,D> , AntiSymTensor<T2,D> > ::
//    apply(lhs,rhs);
//}

//template < class T1, class T2, unsigned D >
//inline typename BinaryReturn<T1,T2,OpMultiply>::Type_t
//dotdot(const AntiSymTensor<T1,D> &lhs, const Tensor<T2,D> &rhs)
//{
//  return MetaDotDot< Tensor<T1,D> , Tensor<T2,D> > ::
//    apply(Tensor<T1,D>(lhs),rhs);
//}

//template < class T1, class T2, unsigned D >
//inline typename BinaryReturn<T1,T2,OpMultiply>::Type_t
//dotdot(const Tensor<T1,D> &lhs, const AntiSymTensor<T2,D> &rhs)
//{
//  return MetaDotDot< Tensor<T1,D> , Tensor<T2,D> > ::
//    apply(lhs,Tensor<T2,D>(rhs));
//}

//template < class T1, class T2, unsigned D >
//inline typename BinaryReturn<T1,T2,OpMultiply>::Type_t
//dotdot(const AntiSymTensor<T1,D> &lhs, const SymTensor<T2,D> &rhs)
//{
//  return MetaDotDot< Tensor<T1,D> , Tensor<T2,D> > ::
//    apply(Tensor<T1,D>(lhs),Tensor<T2,D>(rhs));
//}

//template < class T1, class T2, unsigned D >
//inline typename BinaryReturn<T1,T2,OpMultiply>::Type_t
//dotdot(const SymTensor<T1,D> &lhs, const AntiSymTensor<T2,D> &rhs)
//{
//  return MetaDotDot< Tensor<T1,D> , Tensor<T2,D> > ::
//    apply(Tensor<T1,D>(lhs),Tensor<T2,D>(rhs));
//}

//----------------------------------------------------------------------
// I/O
template<class T, unsigned D>
std::ostream& operator<<(std::ostream& out, const AntiSymTensor<T, D>& rhs)
{
  if (D >= 1)
  {
    for (int i = 0; i < D; i++)
    {
      for (int j = 0; j < D - 1; j++)
      {
        out << rhs(i, j) << " ";
      }
      out << rhs(i, D - 1) << " ";
      if (i < D - 1)
        out << std::endl;
    }
  }
  else
  {
    out << " " << rhs(0, 0) << " ";
  }
  return out;
}

//////////////////////////////////////////////////////////////////////

template<class T, unsigned int D>
T AntiSymTensor<T, D>::Zero = 0;

} // namespace qmcplusplus
#endif // ANTI_SYM_TENZOR_H