ThirdParty-6/ParaView-5.0.1/ThirdParty/CosmoHaloFinder/SubHaloFinder.cxx

/*=========================================================================

Copyright (c) 2007, Los Alamos National Security, LLC

All rights reserved.

Copyright 2007. Los Alamos National Security, LLC.
This software was produced under U.S. Government contract DE-AC52-06NA25396
for Los Alamos National Laboratory (LANL), which is operated by
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#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <set>
#include <math.h>

#include "Partition.h"
#include "SubHaloFinder.h"
#include "FOFHaloProperties.h"
#include "HaloCenterFinder.h"

#include "Timings.h"

using namespace std;

namespace cosmotk {

/////////////////////////////////////////////////////////////////////////
//
// SubHaloFinder uses the results of the CosmoHaloFinder to locate the
// particles belonging to each FOF halo and then to segment those particles
// into subhalos and fuzz
//
/////////////////////////////////////////////////////////////////////////

SubHaloFinder::SubHaloFinder()
{
  // Get the number of processors and rank of this processor
  this->numProc = Partition::getNumProc();
  this->myProc = Partition::getMyProc();

  this->candidateCount = 0;
  this->bhTree = 0;

  this->particleList = 0;
  this->candidateIndx = 0;
  this->subhaloCount = 0;
  this->subhalos = 0;
}

SubHaloFinder::~SubHaloFinder()
{
  if (this->particleList != 0) delete [] this->particleList;
  if (this->candidateIndx != 0) delete [] this->candidateIndx;
  if (this->bhTree != 0) delete this->bhTree;
  if (this->subhaloCount != 0) delete [] this->subhaloCount;
  if (this->subhalos != 0) delete [] this->subhalos;
}

/////////////////////////////////////////////////////////////////////////
//
// Set the parameters for algorithms
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::setParameters(
                        POSVEL_T avgMass,
                        POSVEL_T G,
                        POSVEL_T alpha,
                        POSVEL_T beta,
                        int minCandSize,
                        int numSPH,
                        int numClose)
{
  this->particleMass = avgMass;
  this->gravityConstant = G;
  this->alphaFactor = 1.0 / alpha;
  this->betaFactor = beta;

  this->minCandidateSize = minCandSize;

  this->numberOfSPHNeighbors = numSPH;
  this->numberOfCloseNeighbors = numClose;
  this->potentialFactor = this->particleMass * this->gravityConstant;
}

/////////////////////////////////////////////////////////////////////////
//
// Set the particle vectors that have already been read and which
// contain only the alive particles for this processor
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::setParticles(
                        ID_T count,
                        POSVEL_T* xLocHalo,
                        POSVEL_T* yLocHalo,
                        POSVEL_T* zLocHalo,
                        POSVEL_T* xVelHalo,
                        POSVEL_T* yVelHalo,
                        POSVEL_T* zVelHalo,
                        POSVEL_T* pmass,
                        ID_T* id)
{
  this->particleCount = count;
  this->xx = xLocHalo;
  this->yy = yLocHalo;
  this->zz = zLocHalo;
  this->vx = xVelHalo;
  this->vy = yVelHalo;
  this->vz = zVelHalo;
  this->mass = pmass;
  this->tag = id;
}

/////////////////////////////////////////////////////////////////////////
//
// Find the subhalos contained in a body of particles
// This is the basic algorithm described in the HSF paper
//
//   i) Calculate local density for each particle
//      This is done by building a BHTree, calculating the smoothing length,
//      and finally calculating a local density using SPH
//
//  ii) Sort by density
//      Iterate over every particle high density to low
//      Find two closest already placed neighbors (higher density neighbors)
//
//      a) 0 neighbors - make a new structure
//
//      b) 1 neighbor  - join to the neighbor structure
//         2 neighbors in same structure - join to that structure
//         2 neighbors in different structures with one being the massive
//           partner of the other, join to massive partner (boundary particle)
//
//      c) 2 neighbors in different structures, neither massive partner of other
//           this is a saddle point (connects 2 branches together in tree)
//           mark one structure as massive compared to other, or mark as same
//         Calculate significance of both structures
//
//         1) If one structure is not significant COMBINE into the other
//            If neither is significant COMBINE smaller into larger
//
//         2) If both are significant
//              If one is alphaFactor times larger than the other
//                 CUT the smaller (meaning keep it but don't add new particles)
//                 All particles below the saddle point which have these
//                 2 structures will be added to the massive partner
//              If not larger consider structures the same size
//                 but still mark the larger as the massive partner and
//                 add the saddle point to the massive partner
//                 but both remain open so both GROW
//
// iii) Iterate over all structures created in reverse order
//         structure with less than N_cut particles is considered insignificant
//         and it is combined with its massive partner.
//         If it does not have a massive partner (never put in tree?)
//         then mark as fuzz
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::findSubHalos()
{
  // Find the range of particles
  POSVEL_T minLoc[DIMENSION];
  POSVEL_T maxLoc[DIMENSION];
  minLoc[0] = maxLoc[0] = this->xx[0];
  minLoc[1] = maxLoc[1] = this->yy[0];
  minLoc[2] = maxLoc[2] = this->zz[0];

  for (int i = 1; i < this->particleCount; i++) {
    if (minLoc[0] > this->xx[i]) minLoc[0] = this->xx[i];
    if (maxLoc[0] < this->xx[i]) maxLoc[0] = this->xx[i];
    if (minLoc[1] > this->yy[i]) minLoc[1] = this->yy[i];
    if (maxLoc[1] < this->yy[i]) maxLoc[1] = this->yy[i];
    if (minLoc[2] > this->zz[i]) minLoc[2] = this->zz[i];
    if (maxLoc[2] < this->zz[i]) maxLoc[2] = this->zz[i];
  }

  // BHTree is constructed from halo particles
  this->bhTree = new BHTree(minLoc, maxLoc,
                            this->particleCount,
                            this->xx, this->yy, this->zz, this->mass,
                            this->particleMass);

  // Calculate smoothing length for density calculation
  this->bhTree->calculateInitialSmoothingLength(this->numberOfSPHNeighbors);

  // Refine smoothing length and calculate local density of particles
  this->bhTree->calculateDensity(this->numberOfSPHNeighbors);

  vector<SPHParticle*>& sphParticle = this->bhTree->getSPHParticle();

  for (int p = 0; p < this->particleCount; p++) {
    ValueInfo info;
    info.value = sphParticle[p]->density;
    info.particleId = p;
    this->data.push_back(info);
  }
  sort(this->data.begin(), this->data.end(), ValueGT());

  calculateSubGroups();

  // Collect the totals across all nodes
  int numberOfCandidates = this->candidates.size();
  int cIndx = numberOfCandidates - 1;
  while (cIndx >= 0 && this->candidates[cIndx]->parent == -1) {
    collectAllTotals(cIndx);
    cIndx--;
  }

#ifdef DEBUG
  // Print the initial candidate tree before unbinding
  cout << "CANDIDATE TREE" << endl;
  cIndx = numberOfCandidates - 1;
  while (cIndx >= 0 && this->candidates[cIndx]->parent == -1) {
    printCandidate(cIndx, 0);
    cIndx--;
  }
#endif

  // Move candidates that are too small to massive partner or to fuzz
  // Move unattached candidates to fuzz if too small
  removeSmallCandidates();

  // Unbind remaining candidates
  unbind();

#ifdef DEBUG
  // Print the candidate tree after unbinding
  cout << "POST UNBIND CANDIDATE TREE" << endl;
  cIndx = numberOfCandidates - 1;
  while (cIndx >= 0 && this->candidates[cIndx]->parent == -1) {
    printCandidate(cIndx, 0);
    cIndx--;
  }
#endif

#ifdef DEBUG
  // Print the candidate tree after unbinding
  cout << "SUBHALO SUMMARY " << endl;
  cIndx = numberOfCandidates - 1;
  while (cIndx >= 0 && this->candidates[cIndx]->parent == -1) {
    printSubHalo(cIndx, 0);
    cIndx--;
  }
#endif

  // Summarize FOF halo's subhalos in the same type of structure
  // suitable for running with FOFHaloProperties.  Particle indices are
  // relative to this FOF halo and will need actualIndx to allow all
  // subhalos to be grouped together
  createSubhaloStructure();
}

/////////////////////////////////////////////////////////////////////////
//
// i) Calculate the subgroups of particles which have been identified as a halo
//    Particles have a local density already calculated through SPH algorithm
//
// ii) Sort all particles in decreasing order of density so that high density
//     particles will be placed in candidates first.
//
// Create the following data structures:
//   "candidateIndx" array which indicates which candidate a particle belongs to
//   "particleList" array which through indirect addressing can locate all
//     particles of a single candidate.  Using this structure combined with
//     the member "first" in a candidate allows quick combining of candidates
//   "candidates" array of standalone candidates created
//     candidates are either leaf which will contain particles or branch
//     which maintain structure of a corresponding tree
//   "candidates" tree will be built bottom up by joining leaf candidates into
//     small branches and then into larger branches until the complete
//     tree is formed.  Some leaves may never be attached to the tree.
//
/////////////////////////////////////////////////////////////////////////
//
// For the first particle:
//   Place it in a new candidate in the candidates list
//
// For each successive particle:
//   Collect the closest "numberOfCloseNeighbors" particles (default 20)
//   Of these particles see if any have a higher density than this particle
//     meaning they have already been placed in candidates.
//   Of these neighbors that have been placed consider the closest two only
//     Record the candidate containing each neighbor
//     Record the topmost branch candidate (parent) containing each neighbor
//   Depending on the location of the neighbors within candidates and tree
//     and if the candidate is cut or growing several actions are possible
//
/////////////////////////////////////////////////////////////////////////
//
//   a) Make a new candidate:
//      If none of the close particles have been placed, make a new candidate
//       and add this particle to that candidate
//       Method: makeNewCandidate()
//
/////////////////////////////////////////////////////////////////////////
//
//   b) Join an existing candidate:
//      If there is only one neighbor, or if there are two neighbors
//        but they are members of the same candidate
//          add this particle to that candidate if it has not been cut
//          otherwise search the massive partners looking for one that
//            is not cut and add the particle there
//          Method: joinCandidate()
//
//      If there are two neighbors in two different candidates which are
//        already placed in the same branch in the tree (top is equal)
//        If neither candidate is cut, but one is much smaller than the other
//          cut the smaller candidate and set massive parter to the larger
//          add this particle to the larger candidate
//        If the larger candidate is not cut
//          add this particle to the larger candidate
//        If the larger candidate is cut and the smaller is not
//          add this particle to the smaller candidate
//        If both candidates are cut search the massive partners to find one
//          that is not cut and add the particle there
//        Method: joinCandidate()
//
/////////////////////////////////////////////////////////////////////////
//
//   c) Merge candidates in tree before joining candidate:
//      If there are two neighbors placed in two candidates which are
//        not yet in the tree (neither has a child or a parent) and
//        If the smaller candidate is not significant (beta factor)
//          or if it is much smaller than the larger (alpha factor)
//            Do not alter the tree (larger remains separate)
//            Combine the smaller candidate into the larger candidate
//            Add saddlepoint particle to the larger
//            Method: combineCandidate()
//
//      Otherwise the two candidates must be merged into the tree
//        with a new branch candidate being created
//        Candidates can be two leaf candidates
//        Candidates can be one leaf candidate and one branch candidate
//        Candidates can be two branch candidates
//
//        Only for leaf candidates set the massive partner
//          of the smaller candidate to the larger candidate
//        If smaller candidate branch is much smaller than the larger
//          cut the smaller candidate and set massive partner to larger
//        If larger candidate branch is much smaller than the smaller
//          cut the larger candidate and set massive partner to smaller
//        Add saddlepoint particle to the uncut candidate
//
/////////////////////////////////////////////////////////////////////////
//
// Make a final candidate which will hold the fuzz which are all particles
//  not bound to any structure
//
/////////////////////////////////////////////////////////////////////////
//
// Note on structures:
//   The "candidates" vector contains all created SubHaloCandidates.
//   An instance of SubHaloCandidate holds the information needed to deduce
//   the tree structure within the "candidates" vector.  It has indices for the
//   parent and each child candidate.  It holds the index of the first
//   particle member of the candidate which can be followed through the
//   "particleList" array to locate all particles in the candidate.
//   It has an index to the top ancestor of the candidate tree which is
//   able to accept new particle members.  This is needed when looking at
//   the two neighbors to see if they are within the same candidate branch.
//   Count of particles in the candidate as well as the count of particles
//   in the entire tree above the candidate are kept.
//
//   The SubHaloCandidate can actually hold particles if it was created by
//   having a new particle placed in it, or it is just a "merge" candidate
//   which holds structure but no actual particles
//
//   The "candidateIndx" array is of particleCount Size.  It indicates which
//   candidate a particle is a member of.  Using this and the "top" variable
//   within the candidate indicates what branch that particle belongs in.
//
//   The "particleList" is of particleCount size.  The SubHaloCandidate points
//   to the index of its first particle member and that position in the
//   particleList points to the next particle in the candidate.  This allows
//   locating all particles in a single candidate.
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::calculateSubGroups()
{
  vector<SPHParticle*>& sphParticle = this->bhTree->getSPHParticle();

  // Create arrays to hold the subhalo candidate particle information
  this->candidateIndx = new int[this->particleCount];
  this->particleList = new int[this->particleCount];
  for (int p = 0; p < this->particleCount; p++) {
    this->particleList[p] = -1;
    this->candidateIndx[p] = -1;
  }

  // Put the most dense particle into the first subhalo candidate
  makeNewCandidate(0);

  // Iterate over the particles by decreasing density
  for (ID_T p = 1; p < this->particleCount; p++) {

    ID_T particleIndx = this->data[p].particleId;

    // Find neighbors of particle within radius of smoothing length h
    POSVEL_T pos[DIMENSION];
    POSVEL_T h, rho;

    pos[0] = this->xx[particleIndx];
    pos[1] = this->yy[particleIndx];
    pos[2] = this->zz[particleIndx];
    h = sphParticle[particleIndx]->smoothingLength;
    rho = sphParticle[particleIndx]->density;

    vector<ValueInfo> neighborList;
    set<int> possibleGroup;
    set<int>::iterator siter;

    this->bhTree->getClosestNeighbors(this->numberOfCloseNeighbors,
                                      particleIndx, pos, h,
                                      this->particleCount, neighborList);

    // Find the neighbors which have already been placed in candidates
    vector<ValueInfo> closeList;
    for (int n = 0; n < this->numberOfCloseNeighbors; n++) {
      int neighbor = neighborList[n].particleId;
      if (rho < sphParticle[neighbor]->density) {
        ValueInfo info;
        info.particleId = neighbor;
        info.value = neighborList[n].value;
        closeList.push_back(info);
      }
    }

    int numNeighbors = closeList.size();
    int cand1 = -1;
    int cand2 = -2;
    int top1 = -1;
    int top2 = -2;

    // If there are two candidates make sure cand1 is the larger
    // Set the candidate index and the top open candidate index
    if (numNeighbors > 0) {
      cand1 = this->candidateIndx[closeList[0].particleId];
      top1 = this->candidates[cand1]->top;
    }
    if (numNeighbors > 1) {
      cand2 = this->candidateIndx[closeList[1].particleId];
      top2 = this->candidates[cand2]->top;

      if (this->candidates[cand1]->count < this->candidates[cand2]->count) {
        int tmp = cand1;
        cand1 = cand2;
        cand2 = tmp;
        tmp = top1;
        top1 = top2;
        top2 = tmp;
      }
    }

    // a) If neither close neighbor is in a candidate make a new candidate
    if (numNeighbors == 0) {
      makeNewCandidate(p);
    }

    // b) Particle has neighbors in one candidate only
    //    Join the particle to that candidate if it is not already cut
    //    Otherwise join to the more massive partner
    else if (numNeighbors == 1 || cand1 == cand2) {

      // Not cut so join directly to the candidate
      if (this->candidates[cand1]->cut == 0) {
        joinCandidate(p, cand1);

      // Candidate is cut so find the massive partner that is still not cut
      } else {
        cand1 = this->candidates[cand1]->partner;
        while (this->candidates[cand1]->cut == 1 && cand1 != -1) {
          cand1 = this->candidates[cand1]->partner;
        }
        joinCandidate(p, cand1);
      }
    }

    // b) Particle has neighbors in two candidates which have been merged
    //    into the same branch of the tree
    //
    //    If neither candidate has been cut, test smaller against the
    //      larger to see if it can be cut, if so cut smaller and set
    //      its massive partner to the larger
    //    Add the particle to the larger candidate
    //    If it has been cut add to the smaller if it was not cut otherwise
    //      search the massive partners
    //
    else if (top1 == top2) {

      // If the smaller candidate is not cut see if it should be cut now
      // and set the massive partner to the larger
      if (this->candidates[cand2]->cut == 0 &&
          this->candidates[cand1]->cut == 0) {
        if (this->candidates[cand1]->count >
            (this->alphaFactor * this->candidates[cand2]->count)) {
          this->candidates[cand2]->cut = 1;
          this->candidates[cand2]->partner = cand1;
        }
      }

      // If the larger is not cut add particle to larger
      if (this->candidates[cand1]->cut == 0) {
        joinCandidate(p, cand1);
      }

      // If larger is cut and smaller is not add particle to smaller
      else if (this->candidates[cand2]->cut == 0) {
        joinCandidate(p, cand2);
      }

      // If both are cut search massive partners of larger
      else {
        cand1 = this->candidates[cand1]->partner;
        while (this->candidates[cand1]->cut == 1 && cand1 != -1) {
          cand1 = this->candidates[cand1]->partner;
        }
        joinCandidate(p, cand1);
      }
    }

    // Particle has neighbors in two candidates
    // Absorb one candidate into the other plus the saddle point
    // or merge the two candidates into a third depending on significance
    else {
      mergeCandidate(p, cand1, cand2, top1, top2);
    }
  }

  // Last candidate holds the fuzz which are unbound particles
  SubHaloCandidate* candidate = new SubHaloCandidate();
  this->fuzz = this->candidateCount;
  candidate->top = -1;
  candidate->first = -1;
  candidate->partner = -1;
  candidate->cut = 0;
  candidate->parent = -1;
  candidate->child1 = -1;
  candidate->child2 = -1;
  candidate->count = 1;
  candidate->totalCount = 0;
  this->candidates.push_back(candidate);
}

/////////////////////////////////////////////////////////////////////////
//
// Create a new candidate with the particle
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::makeNewCandidate(int p)
{
  ID_T particleIndx = this->data[p].particleId;

  SubHaloCandidate* candidate = new SubHaloCandidate();
  candidate->top = this->candidateCount;
  candidate->first = particleIndx;
  candidate->partner = -1;
  candidate->cut = 0;
  candidate->parent = -1;
  candidate->child1 = -1;
  candidate->child2 = -1;
  candidate->count = 1;
  candidate->totalCount = 0;

  this->candidates.push_back(candidate);
  candidateIndx[particleIndx] = this->candidateCount;

  this->candidateCount++;
}

/////////////////////////////////////////////////////////////////////////
//
// Join the particle to an existing candidate.
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::joinCandidate(int p, int cand1)
{
  ID_T particleIndx = this->data[p].particleId;

  // Push particle in front of candidate's particles
  // Increment the candidate and set candidate index for this particle
  this->particleList[particleIndx] = this->candidates[cand1]->first;
  this->candidates[cand1]->first = particleIndx;
  this->candidates[cand1]->count++;
  this->candidateIndx[particleIndx] = cand1;
}

/////////////////////////////////////////////////////////////////////////
//
// Add the particle to an existing candidate
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::addParticleToCandidate(int particleIndx, int cIndx)
{
  // Push particle in front of candidate's particles
  // Increment the candidate and set candidate index for this particle
  this->particleList[particleIndx] = this->candidates[cIndx]->first;
  this->candidates[cIndx]->first = particleIndx;
  this->candidates[cIndx]->count++;
  this->candidateIndx[particleIndx] = cIndx;
}

/////////////////////////////////////////////////////////////////////////
//
// Remove the particle from an existing candidate
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::removeParticleFromCandidate(int particleIndx, int cIndx)
{
  // Is it the first particle that must be removed
  int curPart = this->candidates[cIndx]->first;
  int nextPart;
  int nnextPart;

  if (curPart != -1) {
    if (curPart == particleIndx) {
      nextPart = this->particleList[curPart];
      this->candidates[cIndx]->first = nextPart;
      this->candidates[cIndx]->count--;
    } else while (curPart != -1) {
      nextPart = this->particleList[curPart];
      if (nextPart == particleIndx) {
        nnextPart = this->particleList[nextPart];
        this->particleList[curPart] = nnextPart;
        this->candidates[cIndx]->count--;
        curPart = -1;
      }
      curPart = nextPart;
    }
  }
}

/////////////////////////////////////////////////////////////////////////
//
// Particle is a saddle point between two existing candidates
// The candidates either contain particles or are "merge" candidates
// which contain no particles of their own, but their children do
//
// Check the size and significance of smaller candidate to decide whether
// to COMBINE one candidate into the other or to merge two candidates into third
// If merged the candidates can both be allowed to GROW or one may be CUT
// meaning it takes no additional particles but will continue to exist
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::mergeCandidate(int p,
                                   int cand1, int cand2,
                                   int top1, int top2)
{
  vector<SPHParticle*>& sphParticle = this->bhTree->getSPHParticle();
  ID_T particleIndx = this->data[p].particleId;

  // Is the smaller halo significant, if not absorb its particles into larger
  // Calculate the average density of the small candidate's particles
  int count = candidates[cand2]->count;
  POSVEL_T avgDensity = 0;
  int curPart = this->candidates[cand2]->first;
  while (curPart != -1) {
    avgDensity += sphParticle[curPart]->density;
    curPart = this->particleList[curPart];
  }
  avgDensity /= count;
  POSVEL_T saddleDensity = sphParticle[particleIndx]->density;

  // Use the Poisson Noise beta parameter to decide if smaller is significant
  int significant = 0;
  if (avgDensity > (saddleDensity * (1.0 + betaFactor / sqrt(count))))
    significant = 1;

  // If the smaller candidate has no children or parent it may be absorbed
  int hasChildren2 = 0;
  if (candidates[cand2]->child1 != -1 || candidates[cand2]->parent != -1)
    hasChildren2 = 1;

  // Collect totalCounts of each candidate to decide on CUT or GROW
  int totalCount1 = collectTotal(top1);
  int totalCount2 = collectTotal(top2);
  int cutCandidate1 = 0;
  int cutCandidate2 = 0;

  if (totalCount1 > (this->alphaFactor  * totalCount2))
    cutCandidate2 = 1;
  if (totalCount2 > (this->alphaFactor  * totalCount1))
    cutCandidate1 = 1;

  int removeCandidate2 = 0;
  if (hasChildren2 == 0) {
    if (significant == 0)
      removeCandidate2 = 1;
    else if (cutCandidate2 == 1 &&
             this->candidates[cand2]->count < this->minCandidateSize)
      removeCandidate2 = 1;
  }

  // Small candidate is significant and can't be absorbed
  // c) 2) MERGE two candidates
  //       If one is much smaller than the other CUT it for joins
  //       Any particle to be joined to it should go to the massive partner
  //       If same size, keep both open for GROW
  if (removeCandidate2 == 0) {

    SubHaloCandidate* candidate = new SubHaloCandidate();
    candidate->top = this->candidateCount;
    candidate->first = -1;
    candidate->partner = -1;
    candidate->parent = -1;
    candidate->child1 = top1;
    candidate->child2 = top2;
    candidate->count = 0;
    candidate->totalCount = 0;

    // Set the new candidate as the parent of the children
    this->candidates[top1]->parent = this->candidateCount;
    this->candidates[top2]->parent = this->candidateCount;

    // Recurse through all children of children to set new top open candidate
    setTopCandidate(top1, this->candidateCount);
    setTopCandidate(top2, this->candidateCount);

    // Collect totalCounts of each candidate to decide on CUT or GROW
    this->candidates[top1]->totalCount = totalCount1;
    this->candidates[top2]->totalCount = totalCount2;

    // Set the smaller candidate's massive partner to the larger candidate
    if (this->candidates[cand1]->count >
        this->candidates[cand2]->count) {
      if (this->candidates[cand2]->partner == -1)
        this->candidates[cand2]->partner = cand1;
    } else {
      if (this->candidates[cand1]->partner == -1)
        this->candidates[cand1]->partner = cand2;
    }

    // If one branch is smaller, cut the candidate of the other branch
    int saddlePointCand = cand1;
    if (cutCandidate2 == 1) {
      this->candidates[cand2]->cut = 1;
      this->candidates[cand2]->partner = cand1;
      if (this->candidates[cand1]->cut == 0)
        saddlePointCand = cand1;
      else
        saddlePointCand = cand2;
    }

    // If one branch is smaller, cut the candidate of the other branch
    else if (cutCandidate1 == 1) {
      this->candidates[cand1]->cut = 1;
      this->candidates[cand1]->partner = cand2;
      if (this->candidates[cand2]->cut == 0)
        saddlePointCand = cand2;
      else
        saddlePointCand = cand1;
    }

    // Add in saddle point particle
    this->particleList[particleIndx] = this->candidates[saddlePointCand]->first;
    this->candidates[saddlePointCand]->first = particleIndx;
    this->candidates[saddlePointCand]->count++;
    this->candidateIndx[particleIndx] = saddlePointCand;

    // Add new branch candidate to candidate list
    this->candidates.push_back(candidate);
    this->candidateCount++;
  }

  // c) 1) ABSORB smaller candidate into the larger candidate
  else {
    // If the larger candidate has already been cut join to massive partner
    if (this->candidates[cand1]->cut == 1) {
      cand1 = this->candidates[cand1]->partner;
    }

    // Move all particles in small candidate to the large candidate
    combineCandidate(cand1, cand2);

    // Add saddlepoint to cand1
    this->particleList[particleIndx] = this->candidates[cand1]->first;
    this->candidates[cand1]->first = particleIndx;
    this->candidates[cand1]->count++;
    this->candidateIndx[particleIndx] = cand1;
  }
}

/////////////////////////////////////////////////////////////////////////
//
// Combine one candidate into another candidate
// All particles in second candidate are moved to the first candidate
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::combineCandidate(int cand1, int cand2)
{
  // Have all particles in cand2 change their candidateIndx to cand1
  int curParticle = this->candidates[cand2]->first;
  while (curParticle != -1) {
    this->candidateIndx[curParticle] = cand1;
    curParticle = this->particleList[curParticle];
  }

  // If the cand1 is empty fill with cand2
  if (this->candidates[cand1]->first == -1) {
    this->candidates[cand1]->first = this->candidates[cand2]->first;
    this->candidates[cand1]->count = this->candidates[cand2]->count;
    this->candidates[cand2]->count = 0;
    this->candidates[cand2]->first = -1;
  }

  else {
    // Find last particle in cand2 (points to -1)
    curParticle = this->candidates[cand2]->first;
    int lastParticle = curParticle;
    while (curParticle != -1) {
      lastParticle = curParticle;
      curParticle = this->particleList[curParticle];
    }

    // Add cand1 list to the end of cand2 list, point to start of cand2 list
    if (lastParticle > -1) {
      this->particleList[lastParticle] = this->candidates[cand1]->first;
      this->candidates[cand1]->first = this->candidates[cand2]->first;
      this->candidates[cand1]->count += this->candidates[cand2]->count;
      this->candidates[cand2]->count = 0;
      this->candidates[cand2]->first = -1;
    }
  }
}

/////////////////////////////////////////////////////////////////////////
//
// Recursively set the enclosing candidate that is open to new particles
// This is so that when a neighbor particle is identified, the group containing
// it can be immediately known.  If two neighbors are in two different
// subcandidates which were joined into a single candidate, we want to know
// they are both in the same one.
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::setTopCandidate(int candidate, int top)
{
  this->candidates[candidate]->top = top;
  int child1 = this->candidates[candidate]->child1;
  int child2 = this->candidates[candidate]->child2;
  if (child1 != -1)
    setTopCandidate(child1, top);

  if (child2 != -1)
    setTopCandidate(child2, top);
}

/////////////////////////////////////////////////////////////////////////
//
// Remove candidates that are too small
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::removeSmallCandidates()
{
  int numberOfCandidates = this->candidates.size();
  for (int cIndx = 0; cIndx < (numberOfCandidates-1); cIndx++) {

    int count = this->candidates[cIndx]->count;
    int partner = this->candidates[cIndx]->partner;

    // Only work with candidates with size, not the merge points
    if (count > 0) {

      if (count < this->minCandidateSize) {
        if (partner >= 0)
          combineCandidate(partner, cIndx);
        else
          combineCandidate(fuzz, cIndx);
      }
    }
  }
}

/////////////////////////////////////////////////////////////////////////
//
// Unbind particles with positive total energy
// For now walk the candidate vector in reverse order building the tree
// Possibly more than one root because not all candidates have to join
// in the end.
//
// total_energy = kinetic_energy + potential_energy
//
// kinetic_energy = (mass * velocity * velocity) / 2    always positive
// potential_energy = mass * potential                  always negative
//
// positive total_energy means the particle is able to escape
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::unbind()
{
  int rootIndx = this->candidates.size() - 2;
  int cIndx = rootIndx;
  while (cIndx >= 0 && this->candidates[cIndx]->parent == -1) {
    unbindCandidate(cIndx);
    cIndx--;
  }
}

/////////////////////////////////////////////////////////////////////////
//
// Recursive method to count bound particles on every candidate in tree
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::unbindCandidate(int cIndx)
{
  int child1 = this->candidates[cIndx]->child1;
  int child2 = this->candidates[cIndx]->child2;
  int count = this->candidates[cIndx]->count;

  // Unbind particles in the candidate
  if (count > 0) {
    unbindParticles(cIndx);
  }

  if (child1 != -1 && child2 != -1) {
    if (this->candidates[child1]->totalCount >
        this->candidates[child2]->totalCount) {
      unbindCandidate(child2);
      unbindCandidate(child1);
    } else {
      unbindCandidate(child1);
      unbindCandidate(child2);
    }
  }
}

/////////////////////////////////////////////////////////////////////////
//
// Recursive method to print the subhalo candidate tree with counts
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::printCandidate(int cIndx, int indent)
{
       cout << setw(7) << indent << ": "
       << "Candidate " << setw(7) << cIndx
       << " total " << setw(8) << this->candidates[cIndx]->totalCount
       << " count " << setw(8) << this->candidates[cIndx]->count
       << " parent " << setw(7) << this->candidates[cIndx]->parent
       << " child1 " << setw(7) << this->candidates[cIndx]->child1
       << " child2 " << setw(7) << this->candidates[cIndx]->child2
       << " partner " << setw(7) << this->candidates[cIndx]->partner
       << " cut " << setw(3) << this->candidates[cIndx]->cut
       << " subhalos " << endl;

  if (this->candidates[cIndx]->child1 != -1)
    printCandidate(this->candidates[cIndx]->child1, indent + 1);

  if (this->candidates[cIndx]->child2 != -1)
    printCandidate(this->candidates[cIndx]->child2, indent + 1);
}

/////////////////////////////////////////////////////////////////////////
//
// Recursive method to print the subhalo candidate tree after unbinding
//
/////////////////////////////////////////////////////////////////////////

void SubHaloFinder::printSubHalo(int cIndx, int indent)
{
  if (this->candidates[cIndx]->count > 0) {
         cout << setw(7) << indent << ": "
         << "Subhalo " << setw(7) << cIndx
         << " total " << setw(8) << this->candidates[cIndx]->totalCount
         << " count " << setw(8) << this->candidates[cIndx]->count
         << " parent " << setw(7) << this->candidates[cIndx]->parent
         << " child1 " << setw(7) << this->candidates[cIndx]->child1
         << " child2 " << setw(7) << this->candidates[cIndx]->child2
         << " partner " << setw(7) << this->candidates[cIndx]->partner
         << " cut " << setw(3) << this->candidates[cIndx]->cut << endl;
  }

  if (this->candidates[cIndx]->child1 != -1)
    printSubHalo(this->candidates[cIndx]->child1, indent + 1);

  if (this->candidates[cIndx]->child2 != -1)
    printSubHalo(this->candidates[cIndx]->child2, indent + 1);
}

/////////////////////////////////////////////////////////////////////////
//
// Recursive method to gather the total counts for the subhalo candidates
//
/////////////////////////////////////////////////////////////////////////

int SubHaloFinder::collectTotal(int cIndx)
{
  if (this->candidates[cIndx]->child1 == -1)
    return this->candidates[cIndx]->count;

  int totalChild1 = collectTotal(this->candidates[cIndx]->child1);
  int totalChild2 = collectTotal(this->candidates[cIndx]->child2);

  return (totalChild1 + totalChild2);
}

/////////////////////////////////////////////////////////////////////////
//
// Recursive method to gather the total counts for the subhalo candidates
//
/////////////////////////////////////////////////////////////////////////

int SubHaloFinder::collectAllTotals(int cIndx)
{
  int totalChild1 = 0;
  int totalChild2 = 0;

  if (this->candidates[cIndx]->child1 != -1)
    totalChild1 = collectAllTotals(this->candidates[cIndx]->child1);
  if (this->candidates[cIndx]->child2 != -1)
    totalChild2 = collectAllTotals(this->candidates[cIndx]->child2);

  this->candidates[cIndx]->totalCount = this->candidates[cIndx]->count +
                                        totalChild1 + totalChild2;

  return this->candidates[cIndx]->totalCount;
}

/////////////////////////////////////////////////////////////////////////////
//
// Count the number of bound particles in a candidate with no children
//
/////////////////////////////////////////////////////////////////////////////

void SubHaloFinder::unbindParticles(int cIndx)
{
  int numberOfParticles = this->candidates[cIndx]->count;
  int numberLeft = numberOfParticles;

  int massivePartner = this->candidates[cIndx]->partner;

  POTENTIAL_T* lpot = new POTENTIAL_T[numberOfParticles];
  int* valid = new int[numberOfParticles];
  int* id = new int[numberOfParticles];
  POSVEL_T* xLoc = new POSVEL_T[numberOfParticles];
  POSVEL_T* yLoc = new POSVEL_T[numberOfParticles];
  POSVEL_T* zLoc = new POSVEL_T[numberOfParticles];
  POSVEL_T* xVel = new POSVEL_T[numberOfParticles];
  POSVEL_T* yVel = new POSVEL_T[numberOfParticles];
  POSVEL_T* zVel = new POSVEL_T[numberOfParticles];
  POSVEL_T* MASS = new POSVEL_T[numberOfParticles];

  // Store the location and velocity information in arrays
  int p = this->candidates[cIndx]->first;
  int indx = 0;
  while (p != -1) {
    xLoc[indx] = this->xx[p];
    yLoc[indx] = this->yy[p];
    zLoc[indx] = this->zz[p];
    xVel[indx] = this->vx[p];
    yVel[indx] = this->vy[p];
    zVel[indx] = this->vz[p];
    MASS[indx] = this->mass[p];
    valid[indx] = 1;
    id[indx] = p;
    p = this->particleList[p];
    indx++;
  }

  int bindDone = 0;
  if (numberLeft > MAX_UNBIND_3)
    bindDone = 1;

  while (numberLeft >= this->minCandidateSize && bindDone == 0) {

    vector<ValueInfo>* totalEnergy = new vector<ValueInfo>[numberLeft];

    // Calculate the average velocity of the body of particles
    POSVEL_T xAvg = 0.0;
    POSVEL_T yAvg = 0.0;
    POSVEL_T zAvg = 0.0;
    for (int i = 0; i < numberOfParticles; i++) {
      if (valid[i] == 1) {
        xAvg += xVel[i];
        yAvg += yVel[i];
        zAvg += zVel[i];
      }
    }
    xAvg /= numberLeft;
    yAvg /= numberLeft;
    zAvg /= numberLeft;

    // Calculate the potential of each particle within the body of particles
    for (int i = 0; i < numberOfParticles; i++)
      lpot[i] = 0.0;

    // First particle in halo to calculate minimum potential on
    for (int i = 0; i < numberOfParticles; i++) {

      // Next particle in halo in minimum potential loop
      for (int j = i+1; j < numberOfParticles; j++) {

        if (valid[i] == 1 && valid[j] == 1) {
          POSVEL_T xdist = (POSVEL_T) fabs(xLoc[i] - xLoc[j]);
          POSVEL_T ydist = (POSVEL_T) fabs(yLoc[i] - yLoc[j]);
          POSVEL_T zdist = (POSVEL_T) fabs(zLoc[i] - zLoc[j]);

          POSVEL_T r = sqrt((xdist*xdist) + (ydist*ydist) + (zdist*zdist));

          if (r != 0.0) {
            lpot[i] = (POTENTIAL_T)(lpot[i] - (1.0 / r));
            lpot[j] = (POTENTIAL_T)(lpot[j] - (1.0 / r));
          }
        }
      }
    }

    // Calculate total_energy = kinetic_energy + potential+energy
    int positiveTECount = 0;
    for (int i = 0; i < numberOfParticles; i++) {
      if (valid[i] == 1) {
        POSVEL_T XVel = xVel[i] - xAvg;
        POSVEL_T YVel = yVel[i] - yAvg;
        POSVEL_T ZVel = zVel[i] - zAvg;

        POSVEL_T v = sqrt(XVel * XVel + YVel * YVel + ZVel * ZVel);
        POSVEL_T kineticEnergy = (v * v) / 2.0;
        POSVEL_T potentialEnergy = lpot[i] * this->potentialFactor;
        POSVEL_T totEnergy = kineticEnergy + potentialEnergy;

        if (totEnergy > 0.0) {
          positiveTECount++;
          ValueInfo info;
          info.particleId = i;
          info.value = totEnergy;
          (*totalEnergy).push_back(info);
        }
      }
    }

    // Sort the positive total energy along with particle index if any
    // Mark as invalid the top 10% of positive total energy particles
    if (positiveTECount > 0) {
      sort(totalEnergy->begin(), totalEnergy->end(), ValueGT());

      int maxToDelete = 1;
      if (numberLeft > MAX_UNBIND_1 && numberLeft < MAX_UNBIND_2)
        maxToDelete = (positiveTECount / FACTOR_UNBIND_1) + 1;
      else if (numberLeft >= MAX_UNBIND_2 && numberLeft < MAX_UNBIND_3)
        maxToDelete = (positiveTECount / FACTOR_UNBIND_2) + 1;
#ifdef DEBUG
      cout << "Unbind at most " << maxToDelete
           << " particles numberLeft " << numberLeft
           << " numberOfParticles " << numberOfParticles
           << " total energy " << (*totalEnergy)[maxToDelete - 1].value << endl;
#endif

      for (int i = 0; i < maxToDelete; i++) {
        int pid = (*totalEnergy)[i].particleId;
        valid[pid] = 0;
      }
      numberLeft -= maxToDelete;

      // If we are almost done and the halo is large enough just quit
      if (numberLeft > MAX_UNBIND_2 && maxToDelete <= MAX_UNBIND_DELETE)
        bindDone = 1;

    } else {
      bindDone = 1;
    }

    totalEnergy->clear();
  }

  // Discard any unbound particles
  int numberOfBoundParticles = numberLeft;

  // Not enough bound particles so move all to the massive partner
  if (numberOfBoundParticles < this->minCandidateSize) {
#ifdef DEBUG
    cout << "\tDISCARD move to partner " << massivePartner
         << " number of particles " << numberOfBoundParticles << endl;
#endif
    if (massivePartner >= 0)
      combineCandidate(massivePartner, cIndx);
    else
      combineCandidate(this->fuzz, cIndx);
  }

  // Enough bound particles for subhalo, move only the unbound particles
  else {
#ifdef DEBUG
    cout << "UNBIND " << numberOfBoundParticles
         << " particles to massive partner " << massivePartner << endl;
#endif
    for (int i = 0; i < numberOfParticles; i++) {
      if (valid[i] == 0) {
        removeParticleFromCandidate(id[i], cIndx);

        if (massivePartner != -1) {
          addParticleToCandidate(id[i], massivePartner);
        } else {
          addParticleToCandidate(id[i], this->fuzz);
        }
      }
    }
  }
  delete [] valid;
  delete [] id;
  delete [] xLoc;
  delete [] yLoc;
  delete [] zLoc;
  delete [] xVel;
  delete [] yVel;
  delete [] zVel;
  delete [] MASS;
  delete [] lpot;

#ifdef DEBUG
    cout << "UNBIND CANDIDATE " << setw(7) << cIndx
         << " totalcount " << setw(8) << this->candidates[cIndx]->totalCount
         << " count " << setw(8) << this->candidates[cIndx]->count
         << " partner " << setw(8) << massivePartner
         << " cut " << this->candidates[cIndx]->cut
         << " #bound " << numberLeft << endl;
#endif
}

/////////////////////////////////////////////////////////////////////////////
//
// Write a .cosmo file for ParaView with location, velocity and subhalo
// candidate number in place of the mass variable
//
/////////////////////////////////////////////////////////////////////////////

void SubHaloFinder::writeSubhaloCosmoFile(const string& outFile)
{
  // Collect the candidates with particles for sorting and remapping
  // Fuzz is the last candidate
  int numberOfCandidates = this->candidates.size();
  vector<ValueInfo> groups;

  this->numberOfSubhalos = 0;
  for (int i = 0; i < (numberOfCandidates-1); i++) {
    if (this->candidates[i]->count > 0) {
      this->numberOfSubhalos++;
      ValueInfo info;
      info.particleId = i;
      info.value = (float) this->candidates[i]->count;
      groups.push_back(info);
    }
  }

  // Sort the valid subhalo candidates (not the fuzz candidate) by size
  sort(groups.begin(), groups.end(), ValueGT());

  // Map the actual candidate index into an index based on size
  int* mapCandidate = new int[numberOfCandidates];
  for (int i = 0; i < numberOfCandidates; i++)
    mapCandidate[i] = -1;

  for (int i = 0; i < this->numberOfSubhalos; i++) {
    int oldCandidate = groups[i].particleId;
    mapCandidate[oldCandidate] = i;
#ifdef DEBUG
    cout << "Map candidate " << setw(7) << groups[i].particleId
         << " to subhalo " << setw(7) << i
         << " with count " << setw(10) << groups[i].value << endl;
#endif
  }

  // Set the fuzz candidate to the last subhalo
  mapCandidate[fuzz] = numberOfSubhalos;
#ifdef DEBUG
  cout << "Map fuzz candidate " << fuzz
       << " to candidate " << numberOfSubhalos
       << " with count " << this->candidates[fuzz]->count << endl;
#endif

  // Write the particles with mapped candidate numbers
  ofstream cStream(outFile.c_str(), ios::out|ios::binary);

  float fBlock[COSMO_FLOAT];
  int iBlock[COSMO_INT];

  for (int p = 0; p < this->particleCount; p++) {
    fBlock[0] = this->xx[p];
    fBlock[1] = this->vx[p];
    fBlock[2] = this->yy[p];
    fBlock[3] = this->vy[p];
    fBlock[4] = this->zz[p];
    fBlock[5] = this->vz[p];
    fBlock[6] = (float) mapCandidate[this->candidateIndx[p]];
    cStream.write(reinterpret_cast<char*>(fBlock),
                  COSMO_FLOAT * sizeof(POSVEL_T));
    iBlock[0] = this->tag[p];
    cStream.write(reinterpret_cast<char*>(iBlock),
                  COSMO_INT * sizeof(ID_T));
  }
  cStream.close();
  delete [] mapCandidate;
}

void SubHaloFinder::getSubhaloCosmoData(
    ID_T hid,
    std::vector<POSVEL_T> &shX,
    std::vector<POSVEL_T> &shY,
    std::vector<POSVEL_T> &shZ,
    std::vector<POSVEL_T> &shVX,
    std::vector<POSVEL_T> &shVY,
    std::vector<POSVEL_T> &shVZ,
    std::vector<ID_T> &shTag,
    std::vector<ID_T> &shHID,
    std::vector<ID_T> &shID) {
  // Collect the candidates with particles for sorting and remapping
  // Fuzz is the last candidate
  int numberOfCandidates = this->candidates.size();
  vector<ValueInfo> groups;

  this->numberOfSubhalos = 0;
  for (int i = 0; i < (numberOfCandidates-1); i++) {
    if (this->candidates[i]->count > 0) {
      this->numberOfSubhalos++;
      ValueInfo info;
      info.particleId = i;
      info.value = (float) this->candidates[i]->count;
      groups.push_back(info);
    }
  }

  // Sort the valid subhalo candidates (not the fuzz candidate) by size
  sort(groups.begin(), groups.end(), ValueGT());

  // Map the actual candidate index into an index based on size
  int* mapCandidate = new int[numberOfCandidates];
  for (int i = 0; i < numberOfCandidates; i++)
    mapCandidate[i] = -1;

  for (int i = 0; i < this->numberOfSubhalos; i++) {
    int oldCandidate = groups[i].particleId;
    mapCandidate[oldCandidate] = i;
#ifdef DEBUG
    cout << "Map candidate " << setw(7) << groups[i].particleId
         << " to subhalo " << setw(7) << i
         << " with count " << setw(10) << groups[i].value << endl;
#endif
  }

  // Set the fuzz candidate to the last subhalo
  mapCandidate[fuzz] = numberOfSubhalos;
#ifdef DEBUG
  cout << "Map fuzz candidate " << fuzz
       << " to candidate " << numberOfSubhalos
       << " with count " << this->candidates[fuzz]->count << endl;
#endif

  for (int p = 0; p < this->particleCount; p++) {
    shX.push_back(this->xx[p]);
    shY.push_back(this->yy[p]);
    shZ.push_back(this->zz[p]);
    shVX.push_back(this->vx[p]);
    shVY.push_back(this->vy[p]);
    shVZ.push_back(this->vz[p]);
    shTag.push_back(this->tag[p]);
    shHID.push_back(hid);
    shID.push_back(mapCandidate[this->candidateIndx[p]]);
  }
  delete [] mapCandidate;
}

/////////////////////////////////////////////////////////////////////////////
//
// Gather candidates that were legal subhalos, renumber starting with 0
// for the largest subhalo, update particleIndx to correspond to the
// found subhalos.  This can be returned such that FOFHaloProperties can
// run on each FOF halo's subhalos.  Also we should be able to put the
// original FOF halos that were too small together with the subhalos of
// other FOF halos into a single structure for display or analysis.
//
/////////////////////////////////////////////////////////////////////////////

void SubHaloFinder::createSubhaloStructure()
{
  // Collect the candidates with particles for sorting and remapping
  // Fuzz is the last candidate and is ignored
  int numberOfCandidates = this->candidates.size() - 1;
  vector<ValueInfo> groups;

  this->numberOfSubhalos = 0;
  for (int i = 0; i < numberOfCandidates; i++) {
    if (this->candidates[i]->count > 0) {
      this->numberOfSubhalos++;
      ValueInfo info;
      info.particleId = i;
      info.value = (float) this->candidates[i]->count;
      groups.push_back(info);
    }
  }

  // Sort the valid subhalo candidates (not the fuzz candidate) by size
  sort(groups.begin(), groups.end(), ValueGT());

  // Map the actual candidate index into an index based on size
  int* mapCandidate = new int[numberOfCandidates];
  for (int i = 0; i < numberOfCandidates; i++)
    mapCandidate[i] = -1;

  for (int i = 0; i < this->numberOfSubhalos; i++) {
    int oldCandidate = groups[i].particleId;
    mapCandidate[oldCandidate] = i;
  }

  // Allocate structures similar to FOF structures for returning answer
  this->subhaloCount = new int[this->numberOfSubhalos];
  this->subhalos = new int[this->numberOfSubhalos];

  // Need array of counts of particles within each subhalo
  for (int cindx = 0; cindx < numberOfCandidates; cindx++) {
    int haloIndx = mapCandidate[cindx];
    if (this->candidates[cindx]->count > 0) {
      this->subhaloCount[haloIndx] = this->candidates[cindx]->count;
      this->subhalos[haloIndx] = this->candidates[cindx]->first;
    }
  }

  // Equivalent of haloList from FOF is the particleList which through
  // indirect addressing locates every particle in a subhalo
  delete [] mapCandidate;
}

}