/**
 * \file interac_list.txx
 * \author Dhairya Malhotra, dhairya.malhotra@gmail.com
 * \date 6-11-2012
 * \brief This file contains the implementation of the InteracList class.
 * Handles the logic for different interaction lists, and determines the
 * symmetry class for each interaction.
 */

#include <cmath>
#include <cassert>

#include <parUtils.h>
#include <ompUtils.h>

namespace pvfmm{

/**
 * \brief Initialize.
 */
template <class Node_t>
void InteracList<Node_t>::Initialize(unsigned int dim_, PrecompMat<Real_t>* mat_){
  #ifdef PVFMM_NO_SYMMETRIES
  use_symmetries=false;
  #else
  use_symmetries=true;
  #endif

  dim=dim_;
  assert(dim==3); //Only supporting 3D for now.
  mat=mat_;

  interac_class.resize(Type_Count);
  perm_list.resize(Type_Count);
  rel_coord.resize(Type_Count);
  hash_lut.resize(Type_Count);

  InitList(0,0,1,UC2UE_Type);
  InitList(0,0,1,DC2DE_Type);

  InitList(0,0,1,S2U_Type);
  InitList(1,1,2,U2U_Type);
  InitList(1,1,2,D2D_Type);
  InitList(0,0,1,D2T_Type);

  InitList(3,3,2,U0_Type);
  InitList(1,0,1,U1_Type);
  InitList(3,3,2,U2_Type);

  InitList(3,2,1,V_Type);
  InitList(1,1,1,V1_Type);
  InitList(5,5,2,W_Type);
  InitList(5,5,2,X_Type);
  InitList(0,0,1,BC_Type);
}

/**
 * \brief Number of possible interactions in each list.
 */
template <class Node_t>
size_t InteracList<Node_t>::ListCount(Mat_Type t){
  return rel_coord[t].Dim(0);
}

/**
 * \brief Returns the relative octant coordinates for an interaction i of
 * type t.
 */
template <class Node_t>
int* InteracList<Node_t>::RelativeCoord(Mat_Type t, size_t i){
  return rel_coord[t][i];
}

/**
 * \brief For an interaction of type t and index i, returns the symmetry
 * class for the same.
 */
template <class Node_t>
size_t InteracList<Node_t>::InteracClass(Mat_Type t, size_t i){
  return interac_class[t][i];
}

/**
 * \brief Returns the list of permutations to be applied to the matrix to
 * convert it to its interac_class.
 */
template <class Node_t>
std::vector<Perm_Type>& InteracList<Node_t>::PermutList(Mat_Type t, size_t i){
  return perm_list[t][i];
}

/**
 * \brief Build interaction list for this node.
 */
template <class Node_t>
std::vector<Node_t*> InteracList<Node_t>::BuildList(Node_t* n, Mat_Type t){
  std::vector<Node_t*> interac_list(ListCount(t),NULL);
  static const int n_collg=(int)pow(3.0,(int)dim);
  static const int n_child=(int)pow(2.0,(int)dim);
  int rel_coord[3];

  switch (t){

    case S2U_Type:
    {
      if(!n->IsGhost() && n->IsLeaf()) interac_list[0]=n;
      break;
    }
    case U2U_Type:
    {
      if(n->IsGhost() || n->IsLeaf()) return interac_list;
      for(int j=0;j<n_child;j++){
        rel_coord[0]=-1+(j & 1?2:0);
        rel_coord[1]=-1+(j & 2?2:0);
        rel_coord[2]=-1+(j & 4?2:0);
        int c_hash = coord_hash(rel_coord);
        int idx=hash_lut[t][c_hash];
        Node_t* chld=(Node_t*)n->Child(j);
        if(idx>=0 && !chld->IsGhost()) interac_list[idx]=chld;
      }
      break;
    }
    case D2D_Type:
    {
      if(n->IsGhost() || n->Parent()==NULL) return interac_list;
      Node_t* p=(Node_t*)n->Parent();
      int p2n=n->Path2Node();
      {
        rel_coord[0]=-1+(p2n & 1?2:0);
        rel_coord[1]=-1+(p2n & 2?2:0);
        rel_coord[2]=-1+(p2n & 4?2:0);
        int c_hash = coord_hash(rel_coord);
        int idx=hash_lut[t][c_hash];
        if(idx>=0) interac_list[idx]=p;
      }
      break;
    }
    case D2T_Type:
    {
      if(!n->IsGhost() && n->IsLeaf()) interac_list[0]=n;
      break;
    }
    case U0_Type:
    {
      if(n->IsGhost() || n->Parent()==NULL || !n->IsLeaf()) return interac_list;
      Node_t* p=(Node_t*)n->Parent();
      int p2n=n->Path2Node();
      for(int i=0;i<n_collg;i++){
        Node_t* pc=(Node_t*)p->Colleague(i);
        if(pc!=NULL && pc->IsLeaf()){
          rel_coord[0]=( i %3)*4-4-(p2n & 1?2:0)+1;
          rel_coord[1]=((i/3)%3)*4-4-(p2n & 2?2:0)+1;
          rel_coord[2]=((i/9)%3)*4-4-(p2n & 4?2:0)+1;
          int c_hash = coord_hash(rel_coord);
          int idx=hash_lut[t][c_hash];
          if(idx>=0) interac_list[idx]=pc;
        }
      }
      break;
    }
    case U1_Type:
    {
      if(n->IsGhost() || !n->IsLeaf()) return interac_list;
      for(int i=0;i<n_collg;i++){
        Node_t* col=(Node_t*)n->Colleague(i);
        if(col!=NULL && col->IsLeaf()){
            rel_coord[0]=( i %3)-1;
            rel_coord[1]=((i/3)%3)-1;
            rel_coord[2]=((i/9)%3)-1;
            int c_hash = coord_hash(rel_coord);
            int idx=hash_lut[t][c_hash];
            if(idx>=0) interac_list[idx]=col;
        }
      }
      break;
    }
    case U2_Type:
    {
      if(n->IsGhost() || !n->IsLeaf()) return interac_list;
      for(int i=0;i<n_collg;i++){
        Node_t* col=(Node_t*)n->Colleague(i);
        if(col!=NULL && !col->IsLeaf()){
          for(int j=0;j<n_child;j++){
            rel_coord[0]=( i %3)*4-4+(j & 1?2:0)-1;
            rel_coord[1]=((i/3)%3)*4-4+(j & 2?2:0)-1;
            rel_coord[2]=((i/9)%3)*4-4+(j & 4?2:0)-1;
            int c_hash = coord_hash(rel_coord);
            int idx=hash_lut[t][c_hash];
            if(idx>=0){
              assert(col->Child(j)->IsLeaf()); //2:1 balanced
              interac_list[idx]=(Node_t*)col->Child(j);
            }
          }
        }
      }
      break;
    }
    case V_Type:
    {
      if(n->IsGhost() || n->Parent()==NULL) return interac_list;
      Node_t* p=(Node_t*)n->Parent();
      int p2n=n->Path2Node();
      for(int i=0;i<n_collg;i++){
        Node_t* pc=(Node_t*)p->Colleague(i);
        if(pc!=NULL?!pc->IsLeaf():0){
          for(int j=0;j<n_child;j++){
            rel_coord[0]=( i   %3)*2-2+(j & 1?1:0)-(p2n & 1?1:0);
            rel_coord[1]=((i/3)%3)*2-2+(j & 2?1:0)-(p2n & 2?1:0);
            rel_coord[2]=((i/9)%3)*2-2+(j & 4?1:0)-(p2n & 4?1:0);
            int c_hash = coord_hash(rel_coord);
            int idx=hash_lut[t][c_hash];
            if(idx>=0) interac_list[idx]=(Node_t*)pc->Child(j);
          }
        }
      }
      break;
    }
    case V1_Type:
    {
      if(n->IsGhost() || n->IsLeaf()) return interac_list;
      for(int i=0;i<n_collg;i++){
        Node_t* col=(Node_t*)n->Colleague(i);
        if(col!=NULL && !col->IsLeaf()){
            rel_coord[0]=( i %3)-1;
            rel_coord[1]=((i/3)%3)-1;
            rel_coord[2]=((i/9)%3)-1;
            int c_hash = coord_hash(rel_coord);
            int idx=hash_lut[t][c_hash];
            if(idx>=0) interac_list[idx]=col;
        }
      }
      break;
    }
    case W_Type:
    {
      if(n->IsGhost() || !n->IsLeaf()) return interac_list;
      for(int i=0;i<n_collg;i++){
        Node_t* col=(Node_t*)n->Colleague(i);
        if(col!=NULL && !col->IsLeaf()){
          for(int j=0;j<n_child;j++){
            rel_coord[0]=( i %3)*4-4+(j & 1?2:0)-1;
            rel_coord[1]=((i/3)%3)*4-4+(j & 2?2:0)-1;
            rel_coord[2]=((i/9)%3)*4-4+(j & 4?2:0)-1;
            int c_hash = coord_hash(rel_coord);
            int idx=hash_lut[t][c_hash];
            if(idx>=0) interac_list[idx]=(Node_t*)col->Child(j);
          }
        }
      }
      break;
    }
    case X_Type:
    {
      if(n->IsGhost() || n->Parent()==NULL) return interac_list;
      Node_t* p=(Node_t*)n->Parent();
      int p2n=n->Path2Node();
      for(int i=0;i<n_collg;i++){
        Node_t* pc=(Node_t*)p->Colleague(i);
        if(pc!=NULL && pc->IsLeaf()){
          rel_coord[0]=( i %3)*4-4-(p2n & 1?2:0)+1;
          rel_coord[1]=((i/3)%3)*4-4-(p2n & 2?2:0)+1;
          rel_coord[2]=((i/9)%3)*4-4-(p2n & 4?2:0)+1;
          int c_hash = coord_hash(rel_coord);
          int idx=hash_lut[t][c_hash];
          if(idx>=0) interac_list[idx]=pc;
        }
      }
      break;
    }
    default:
      std::vector<Node_t*> empty_list;
      return empty_list;
      break;
  }
  return interac_list;
}

template <class Node_t>
Matrix<typename Node_t::Real_t>& InteracList<Node_t>::ClassMat(int l, Mat_Type type, size_t indx){
  size_t indx0=InteracClass(type, indx);
  return mat->Mat(l, type, indx0);
}

template <class Node_t>
Permutation<typename Node_t::Real_t>& InteracList<Node_t>::Perm_R(int l, Mat_Type type, size_t indx){
  size_t indx0=InteracClass(type, indx);
  Matrix     <Real_t>& M0      =mat->Mat   (l, type, indx0);
  Permutation<Real_t>& row_perm=mat->Perm_R(l, type, indx );
  if(M0.Dim(0)==0 || M0.Dim(1)==0) return row_perm;

  //Get the necessary permutations.
  if(row_perm.Dim()==0){
    std::vector<Perm_Type> p_list=PermutList(type, indx);
    for(int i=0;i<l;i++) p_list.push_back(Scaling);
    Permutation<Real_t> row_perm_=Permutation<Real_t>(M0.Dim(0));
    for(int i=0;i<C_Perm;i++){
      Permutation<Real_t>& pr=mat->Perm(type, R_Perm + i);
      if(!pr.Dim()) row_perm_=Permutation<Real_t>(0);
    }

    if(row_perm_.Dim()>0)
    for(int i=p_list.size()-1; i>=0; i--){
      assert(type!=V_Type);
      Permutation<Real_t>& pr=mat->Perm(type, R_Perm + p_list[i]);
      row_perm_=pr.Transpose()*row_perm_;
    }
    row_perm=row_perm_;
  }
  return row_perm;
}

template <class Node_t>
Permutation<typename Node_t::Real_t>& InteracList<Node_t>::Perm_C(int l, Mat_Type type, size_t indx){
  size_t indx0=InteracClass(type, indx);
  Matrix     <Real_t>& M0      =mat->Mat   (l, type, indx0);
  Permutation<Real_t>& col_perm=mat->Perm_C(l, type, indx );
  if(M0.Dim(0)==0 || M0.Dim(1)==0) return col_perm;

  //Get the necessary permutations.
  if(col_perm.Dim()==0){
    std::vector<Perm_Type> p_list=PermutList(type, indx);
    for(int i=0;i<l;i++) p_list.push_back(Scaling);
    Permutation<Real_t> col_perm_=Permutation<Real_t>(M0.Dim(1));
    for(int i=0;i<C_Perm;i++){
      Permutation<Real_t>& pc=mat->Perm(type, C_Perm + i);
      if(!pc.Dim()) col_perm_=Permutation<Real_t>(0);
    }

    if(col_perm_.Dim()>0)
    for(int i=p_list.size()-1; i>=0; i--){
      assert(type!=V_Type);
      Permutation<Real_t>& pc=mat->Perm(type, C_Perm + p_list[i]);
      col_perm_=col_perm_*pc;
    }
    col_perm=col_perm_;
  }
  return col_perm;
}

/**
 * \brief A hash function defined on the relative coordinates of octants.
 */
#define PVFMM_MAX_COORD_HASH 2000
template <class Node_t>
int InteracList<Node_t>::coord_hash(int* c){
  const int n=5;
  return ( (c[2]+n) * (2*n) + (c[1]+n) ) *(2*n) + (c[0]+n);
}

template <class Node_t>
int InteracList<Node_t>::class_hash(int* c_){
  if(!use_symmetries) return coord_hash(c_);
  int c[3]={abs(c_[0]), abs(c_[1]), abs(c_[2])};
  if(c[1]>c[0] && c[1]>c[2])
    {int tmp=c[0]; c[0]=c[1]; c[1]=tmp;}
  if(c[0]>c[2])
    {int tmp=c[0]; c[0]=c[2]; c[2]=tmp;}
  if(c[0]>c[1])
    {int tmp=c[0]; c[0]=c[1]; c[1]=tmp;}
  assert(c[0]<=c[1] && c[1]<=c[2]);
  return coord_hash(&c[0]);
}

/**
 * \brief Set relative coordinates of the interacting node in
 * rel_coord[Type][idx][1:3].
 */
template <class Node_t>
void InteracList<Node_t>::InitList(int max_r, int min_r, int step, Mat_Type t){
  size_t count=(size_t)(pow((max_r*2)/step+1.0,(int)dim)-(min_r>0?pow((min_r*2)/step-1.0,(int)dim):0));
  Matrix<int>& M=rel_coord[t];
  M.Resize(count,dim);
  hash_lut[t].assign(PVFMM_MAX_COORD_HASH, -1);

  std::vector<int> class_size_hash(PVFMM_MAX_COORD_HASH, 0);
  std::vector<int> class_disp_hash(PVFMM_MAX_COORD_HASH, 0);
  for(int k=-max_r;k<=max_r;k+=step)
  for(int j=-max_r;j<=max_r;j+=step)
  for(int i=-max_r;i<=max_r;i+=step)
  if(abs(i)>=min_r || abs(j)>=min_r || abs(k) >= min_r){
    int c[3]={i,j,k};
    class_size_hash[class_hash(c)]++;
  }
  omp_par::scan(&class_size_hash[0], &class_disp_hash[0], PVFMM_MAX_COORD_HASH);

  size_t count_=0;
  for(int k=-max_r;k<=max_r;k+=step)
  for(int j=-max_r;j<=max_r;j+=step)
  for(int i=-max_r;i<=max_r;i+=step)
  if(abs(i)>=min_r || abs(j)>=min_r || abs(k) >= min_r){
    int c[3]={i,j,k};
    int& idx=class_disp_hash[class_hash(c)];
    for(size_t l=0;l<dim;l++) M[idx][l]=c[l];
    hash_lut[t][coord_hash(c)]=idx;
    count_++;
    idx++;
  }
  assert(count_==count);

  interac_class[t].resize(count);
  perm_list[t].resize(count);
  if(!use_symmetries){ // Set interac_class=self
    for(size_t j=0;j<count;j++){
      int c_hash = coord_hash(&M[j][0]);
      interac_class[t][j]=hash_lut[t][c_hash];
    }
  }
  else for(size_t j=0;j<count;j++){
    if(M[j][0]<0) perm_list[t][j].push_back(ReflecX);
    if(M[j][1]<0) perm_list[t][j].push_back(ReflecY);
    if(M[j][2]<0) perm_list[t][j].push_back(ReflecZ);
    int coord[3];
    coord[0]=abs(M[j][0]);
    coord[1]=abs(M[j][1]);
    coord[2]=abs(M[j][2]);

    if(coord[1]>coord[0] && coord[1]>coord[2]){
      perm_list[t][j].push_back(SwapXY);
      int tmp=coord[0]; coord[0]=coord[1]; coord[1]=tmp;
    }
    if(coord[0]>coord[2]){
      perm_list[t][j].push_back(SwapXZ);
      int tmp=coord[0]; coord[0]=coord[2]; coord[2]=tmp;
    }
    if(coord[0]>coord[1]){
      perm_list[t][j].push_back(SwapXY);
      int tmp=coord[0]; coord[0]=coord[1]; coord[1]=tmp;
    }
    assert(coord[0]<=coord[1] && coord[1]<=coord[2]);
    int c_hash = coord_hash(&coord[0]);
    interac_class[t][j]=hash_lut[t][c_hash];
  }
}
#undef PVFMM_MAX_COORD_HASH

}//end namespace