/*************************************************************************************

    Grid physics library, www.github.com/paboyle/Grid 

    Source file: ./lib/tensors/Tensor_index.h

    Copyright (C) 2015

Author: Peter Boyle <paboyle@ph.ed.ac.uk>

    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    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 General Public License for more details.

    You should have received a copy of the GNU General Public License along
    with this program; if not, write to the Free Software Foundation, Inc.,
    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

    See the full license in the file "LICENSE" in the top level distribution directory
    *************************************************************************************/
    /*  END LEGAL */
#ifndef GRID_TENSOR_INDEX_H
#define GRID_TENSOR_INDEX_H

////////////////////////////////////////////////////////////////////////////////////////
// Recursion for trace, transpose, peek, poke a specific index
////////////////////////////////////////////////////////////////////////////////////////
// Allow trace to recurse if vector, but never terminate on a vector
// trace of a different index can distribute across the vector index in a replicated way
// but we do not trace a vector index.

namespace Grid {

  /* Needed?
template<int Level> inline ComplexF traceIndex(const ComplexF arg) { return arg;}
template<int Level> inline ComplexD traceIndex(const ComplexD arg) { return arg;}
template<int Level> inline RealF traceIndex(const RealF arg) { return arg;}
template<int Level> inline RealD traceIndex(const RealD arg) { return arg;}
  */
template<int Level> 
class TensorIndexRecursion {

 public:

  ////////////////////////////////////////////////////
  // Type Queries
  ////////////////////////////////////////////////////
  template<class vtype>       static inline int indexRank(const iScalar<vtype> tmp)  { return TensorIndexRecursion<Level-1>::indexRank(tmp._internal);  }
  template<class vtype,int N> static inline int indexRank(const iVector<vtype,N> tmp){ return TensorIndexRecursion<Level-1>::indexRank(tmp._internal[0]);  }
  template<class vtype,int N> static inline int indexRank(const iMatrix<vtype,N> tmp){ return TensorIndexRecursion<Level-1>::indexRank(tmp._internal[0][0]);  }

  template<class vtype>       static inline int isScalar(const iScalar<vtype> tmp)  { return TensorIndexRecursion<Level-1>::isScalar(tmp._internal);  }
  template<class vtype,int N> static inline int isScalar(const iVector<vtype,N> tmp){ return TensorIndexRecursion<Level-1>::isScalar(tmp._internal[0]);  }
  template<class vtype,int N> static inline int isScalar(const iMatrix<vtype,N> tmp){ return TensorIndexRecursion<Level-1>::isScalar(tmp._internal[0][0]);  }

  template<class vtype>       static inline int isVector(const iScalar<vtype> tmp)  { return TensorIndexRecursion<Level-1>::isVector(tmp._internal);  }
  template<class vtype,int N> static inline int isVector(const iVector<vtype,N> tmp){ return TensorIndexRecursion<Level-1>::isVector(tmp._internal[0]);  }
  template<class vtype,int N> static inline int isVector(const iMatrix<vtype,N> tmp){ return TensorIndexRecursion<Level-1>::isVector(tmp._internal[0][0]);  }

  template<class vtype>       static inline int isMatrix(const iScalar<vtype> tmp)  { return TensorIndexRecursion<Level-1>::isMatrix(tmp._internal);  }
  template<class vtype,int N> static inline int isMatrix(const iVector<vtype,N> tmp){ return TensorIndexRecursion<Level-1>::isMatrix(tmp._internal[0]);  }
  template<class vtype,int N> static inline int isMatrix(const iMatrix<vtype,N> tmp){ return TensorIndexRecursion<Level-1>::isMatrix(tmp._internal[0][0]);  }
  ////////////////////////////////////////////////////
  // Trace
  ////////////////////////////////////////////////////
  template<class vtype>
  static auto traceIndex(const iScalar<vtype> arg) ->  iScalar<decltype(TensorIndexRecursion<Level-1>::traceIndex(arg._internal))> 
  {
    iScalar<decltype(TensorIndexRecursion<Level-1>::traceIndex(arg._internal))> ret;
    ret._internal = TensorIndexRecursion<Level-1>::traceIndex(arg._internal);
    return ret;
  }
  template<class vtype,int N>
  static auto traceIndex(const iVector<vtype,N> arg) ->  iVector<decltype(TensorIndexRecursion<Level-1>::traceIndex(arg._internal[0])),N> 
  {
    iVector<decltype(TensorIndexRecursion<Level-1>::traceIndex(arg._internal[0])),N> ret;
    for(int i=0;i<N;i++){
      ret._internal[i] = TensorIndexRecursion<Level-1>::traceIndex(arg._internal[i]);
    }
    return ret;
  }
  template<class vtype,int N>
  static auto traceIndex(const iMatrix<vtype,N> arg) ->  iMatrix<decltype(TensorIndexRecursion<Level-1>::traceIndex(arg._internal[0][0])),N> 
  {
    iMatrix<decltype(TensorIndexRecursion<Level-1>::traceIndex(arg._internal[0][0])),N> ret;
    for(int i=0;i<N;i++){
    for(int j=0;j<N;j++){
      ret._internal[i][j] = TensorIndexRecursion<Level-1>::traceIndex(arg._internal[i][j]);
    }}
    return ret;
  }
  ////////////////////////////////////////////
  // Recursion for peeking a specific index
  ////////////////////////////////////////////
  template<class vtype>
  static auto peekIndex(const iScalar<vtype> arg,int i) ->  iScalar<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal,0))> 
  {
    iScalar<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal,0))> ret;
    ret._internal = TensorIndexRecursion<Level-1>::peekIndex(arg._internal,i);
    return ret;
  }
  template<class vtype>
  static auto peekIndex(const iScalar<vtype> arg,int i,int j) ->  iScalar<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal,0,0))> 
  {
    iScalar<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal,0,0))> ret;
    ret._internal = TensorIndexRecursion<Level-1>::peekIndex(arg._internal,i,j);
    return ret;
  }

  template<class vtype,int N>
  static auto peekIndex(const iVector<vtype,N> arg,int ii) ->  iVector<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal[0],0)),N> 
  {
    iVector<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal[0],0)),N> ret;
    for(int i=0;i<N;i++){
      ret._internal[i] = TensorIndexRecursion<Level-1>::peekIndex(arg._internal[i],ii);
    }
    return ret;
  }
  template<class vtype,int N>
  static auto peekIndex(const iVector<vtype,N> arg,int ii,int jj) ->  iVector<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal[0],0,0)),N> 
  {
    iVector<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal[0],0,0)),N> ret;
    for(int i=0;i<N;i++){
      ret._internal[i] = TensorIndexRecursion<Level-1>::peekIndex(arg._internal[i],ii,jj);
    }
    return ret;
  }

  template<class vtype,int N>
  static auto peekIndex(const iMatrix<vtype,N> arg,int ii) ->  iMatrix<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal[0][0],0)),N> 
  {
    iMatrix<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal[0][0],0)),N> ret;
    for(int i=0;i<N;i++){
    for(int j=0;j<N;j++){
      ret._internal[i][j] = TensorIndexRecursion<Level-1>::peekIndex(arg._internal[i][j],ii);
    }}
    return ret;
  }
  template<class vtype,int N>
  static auto peekIndex(const iMatrix<vtype,N> arg,int ii,int jj) ->  iMatrix<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal[0][0],0,0)),N> 
  {
    iMatrix<decltype(TensorIndexRecursion<Level-1>::peekIndex(arg._internal[0][0],0,0)),N> ret;
    for(int i=0;i<N;i++){
    for(int j=0;j<N;j++){
      ret._internal[i][j] = TensorIndexRecursion<Level-1>::peekIndex(arg._internal[i][j],ii,jj);
    }}
    return ret;
  }
  ////////////////////////////////////////////
  // Recursion for poking a specific index
  ////////////////////////////////////////////

  template<class vtype> inline static 
    void pokeIndex(iScalar<vtype> &ret, const iScalar<decltype(TensorIndexRecursion<Level-1>::peekIndex(ret._internal,0))> &arg, int i)
    {
      TensorIndexRecursion<Level-1>::pokeIndex(ret._internal,arg._internal,i);
    }
  template<class vtype> inline static 
    void pokeIndex(iScalar<vtype> &ret, const iScalar<decltype(TensorIndexRecursion<Level-1>::peekIndex(ret._internal,0,0))> &arg, int i,int j)
    {
      TensorIndexRecursion<Level-1>::pokeIndex(ret._internal,arg._internal,i,j);
    }

  template<class vtype,int N> inline static 
    void pokeIndex(iVector<vtype,N> &ret, const iVector<decltype(TensorIndexRecursion<Level-1>::peekIndex(ret._internal[0],0)),N> &arg, int i)
    {
      for(int ii=0;ii<N;ii++){
	TensorIndexRecursion<Level-1>::pokeIndex(ret._internal[ii],arg._internal[ii],i);
      }
    }
  template<class vtype,int N> inline static 
    void pokeIndex(iVector<vtype,N> &ret, const iVector<decltype(TensorIndexRecursion<Level-1>::peekIndex(ret._internal[0],0,0)),N> &arg, int i,int j)
    {
      for(int ii=0;ii<N;ii++){
	TensorIndexRecursion<Level-1>::pokeIndex(ret._internal[ii],arg._internal[ii],i,j);
      }
    }

  template<class vtype,int N> inline static 
    void pokeIndex(iMatrix<vtype,N> &ret, const iMatrix<decltype(TensorIndexRecursion<Level-1>::peekIndex(ret._internal[0][0],0)),N> &arg, int i)
    {
      for(int ii=0;ii<N;ii++){
      for(int jj=0;jj<N;jj++){
	TensorIndexRecursion<Level-1>::pokeIndex(ret._internal[ii][jj],arg._internal[ii][jj],i);
      }}
    }
  template<class vtype,int N> inline static 
    void pokeIndex(iMatrix<vtype,N> &ret, const iMatrix<decltype(TensorIndexRecursion<Level-1>::peekIndex(ret._internal[0][0],0,0)),N> &arg, int i,int j)
    {
      for(int ii=0;ii<N;ii++){
      for(int jj=0;jj<N;jj++){
	TensorIndexRecursion<Level-1>::pokeIndex(ret._internal[ii][jj],arg._internal[ii][jj],i,j);
      }}
    }

  ////////////////////////////////////////////
  // Recursion for transposing a specific index
  ////////////////////////////////////////////
  template<class vtype>
  static auto transposeIndex(const iScalar<vtype> arg) ->  iScalar<vtype> 
  {
    iScalar<vtype> ret;
    ret._internal = TensorIndexRecursion<Level-1>::transposeIndex(arg._internal);
    return ret;
  }
  template<class vtype,int N>
  static auto transposeIndex(const iVector<vtype,N> arg) ->  iVector<vtype,N> 
  {
    iVector<vtype,N> ret;
    for(int i=0;i<N;i++){
      ret._internal[i] = TensorIndexRecursion<Level-1>::transposeIndex(arg._internal[i]);
    }
    return ret;
  }
  template<class vtype,int N>
  static auto transposeIndex(const iMatrix<vtype,N> arg) ->  iMatrix<vtype,N> 
  {
    iMatrix<vtype,N> ret;
    for(int i=0;i<N;i++){
    for(int j=0;j<N;j++){
      ret._internal[i][j] = TensorIndexRecursion<Level-1>::transposeIndex(arg._internal[i][j]);
    }}
    return ret;
  }
};

////////////////////////////
// strip const & ref quali's
////////////////////////////
#define RemoveCRV(a) typename std::remove_const<typename std::remove_reference<decltype(a)>::type>::type
template<>
class TensorIndexRecursion<0> {
 public:
  ////////////////////////////////////////////////////
  // Type Queries
  ////////////////////////////////////////////////////
  template<class vtype>       static inline int indexRank(const iScalar<vtype> tmp)  { return 1; }
  template<class vtype,int N> static inline int indexRank(const iVector<vtype,N> tmp){ return N; }
  template<class vtype,int N> static inline int indexRank(const iMatrix<vtype,N> tmp){ return N; }

  template<class vtype>       static inline int isScalar(const iScalar<vtype> tmp)  { return true;}
  template<class vtype,int N> static inline int isScalar(const iVector<vtype,N> tmp){ return false;}
  template<class vtype,int N> static inline int isScalar(const iMatrix<vtype,N> tmp){ return false;}

  template<class vtype>       static inline int isVector(const iScalar<vtype> tmp)  { return false;}
  template<class vtype,int N> static inline int isVector(const iVector<vtype,N> tmp){ return true;}
  template<class vtype,int N> static inline int isVector(const iMatrix<vtype,N> tmp){ return false;}

  template<class vtype>       static inline int isMatrix(const iScalar<vtype> tmp)  { return false;}
  template<class vtype,int N> static inline int isMatrix(const iVector<vtype,N> tmp){ return false;}
  template<class vtype,int N> static inline int isMatrix(const iMatrix<vtype,N> tmp){ return true;}

  /////////////////////////////////////////
  // Ends recursion for trace (scalar/vector/matrix)
  /////////////////////////////////////////
  template<class vtype>
  static auto traceIndex(const iScalar<vtype> arg) ->  iScalar<RemoveCRV(arg._internal)>
  {
    iScalar<RemoveCRV(arg._internal)> ret;
    ret._internal = arg._internal;
    return ret;
  }
  template<class vtype,int N>
  static auto traceIndex(const iVector<vtype,N> arg) ->  iScalar<RemoveCRV(arg._internal[0])>
  {
    iScalar<RemoveCRV(arg._internal[0])> ret;
    ret._internal=zero;
    for(int i=0;i<N;i++){
      ret._internal = ret._internal+ arg._internal[i];
    }
    return ret;
  }
  template<class vtype,int N>
  static auto traceIndex(const iMatrix<vtype,N> arg) ->  iScalar<RemoveCRV(arg._internal[0][0])> 
  {
    iScalar<RemoveCRV(arg._internal[0][0])> ret;
    ret=zero;
    for(int i=0;i<N;i++){
      ret._internal = ret._internal+arg._internal[i][i];
    }
    return ret;
  }
  /////////////////////////////////////////
  // Ends recursion for transpose scalar/matrix ; no way to terminate on vector
  /////////////////////////////////////////
  template<class vtype>
  static auto transposeIndex(const iScalar<vtype> arg) ->  iScalar<vtype>
  {
    iScalar<vtype> ret;
    ret._internal = arg._internal;
    return ret;
  }
  template<class vtype,int N>
  static auto transposeIndex(const iMatrix<vtype,N> arg)  ->  iMatrix<vtype,N> 
  {
    iMatrix<vtype,N> ret;
    ret=zero;
    for(int i=0;i<N;i++){
    for(int j=0;j<N;j++){
      ret._internal[i][j] = ret._internal[i][j]+arg._internal[i][j];
    }}
    return ret;
  }
  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////
  // End recursion for peeking a specific index; single index on vector, double index on matrix
  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////
  template<class vtype,int N>
  static auto peekIndex(const iVector<vtype,N> arg,int ii) ->  iScalar<vtype> 
  {
    iScalar<vtype> ret;
    ret._internal = arg._internal[ii];
    return ret;
  }
  template<class vtype,int N>
  static auto peekIndex(const iMatrix<vtype,N> arg,int ii,int jj) ->  iScalar<vtype>
  {
    iScalar<vtype> ret;
    ret._internal = arg._internal[ii][jj];
    return ret;
  }
  // Vector poke, one index
  template<class vtype,int N> inline static 
    void pokeIndex(iVector<vtype,N> &ret, const iScalar<vtype> &arg,int i)
    {
      ret._internal[i] = arg._internal;
    }
  // Matrix poke two indices
  template<class vtype,int N> inline static 
    void pokeIndex(iMatrix<vtype,N> &ret, const iScalar<vtype> &arg,int i,int j)
    {
      ret._internal[i][j] = arg._internal;
    }

};

////////////////////////////////////////////////////////////////////////////////////////////////////////
// External wrappers
////////////////////////////////////////////////////////////////////////////////////////////////////////
template<int Level,class vtype> inline int indexRank(void)
{
  vtype tmp;
  return TensorIndexRecursion<Level>::indexRank(tmp);
}
template<int Level,class vtype> inline int isScalar(void)
{
  vtype tmp;
  return TensorIndexRecursion<Level>::isScalar(tmp);
}
template<int Level,class vtype> inline int isVector(void)
{
  vtype tmp;
  return TensorIndexRecursion<Level>::isVector(tmp);
}
template<int Level,class vtype> inline int isMatrix(void)
{
  vtype tmp;
  return TensorIndexRecursion<Level>::isMatrix(tmp);
}

template<int Level,class vtype> inline auto traceIndex (const vtype &arg) -> RemoveCRV(TensorIndexRecursion<Level>::traceIndex(arg))
{
  RemoveCRV(TensorIndexRecursion<Level>::traceIndex(arg)) ret;
  ret=TensorIndexRecursion<Level>::traceIndex(arg);
  return ret;
}
template<int Level,class vtype> inline auto transposeIndex (const vtype &arg) -> RemoveCRV(TensorIndexRecursion<Level>::transposeIndex(arg))
{
  RemoveCRV(TensorIndexRecursion<Level>::transposeIndex(arg)) ret;
  ret=TensorIndexRecursion<Level>::transposeIndex(arg);
  return ret;
}

template<int Level,class vtype> inline auto peekIndex (const vtype &arg,int i) -> RemoveCRV(TensorIndexRecursion<Level>::peekIndex(arg,0))
{
  RemoveCRV(TensorIndexRecursion<Level>::peekIndex(arg,0)) ret;
  ret=TensorIndexRecursion<Level>::peekIndex(arg,i);
  return ret;
}
template<int Level,class vtype> inline auto peekIndex (const vtype &arg,int i,int j) -> RemoveCRV(TensorIndexRecursion<Level>::peekIndex(arg,0,0))
{
  RemoveCRV(TensorIndexRecursion<Level>::peekIndex(arg,0,0)) ret;
  ret=TensorIndexRecursion<Level>::peekIndex(arg,i,j);
  return ret;
}

template<int Level,class vtype> inline 
void pokeIndex (vtype &ret,const decltype(TensorIndexRecursion<Level>::peekIndex(ret,0)) &arg,int i) 
{
  TensorIndexRecursion<Level>::pokeIndex(ret,arg,i);
}

template<int Level,class vtype> inline 
void pokeIndex (vtype &ret,const decltype(TensorIndexRecursion<Level>::peekIndex(ret,0,0)) &arg,int i,int j) 
{
  TensorIndexRecursion<Level>::pokeIndex(ret,arg,i,j);
}


#undef RemoveCRV

}
#endif