ScalarFieldCriticalPoints.h

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#pragma once
 
#include <map>
 
// base code includes
#include <ProgressiveTopology.h>
#include <Triangulation.h>
#include <UnionFind.h>
 
namespace ttk {
 
  class ScalarFieldCriticalPoints : public virtual Debug {
 
  public:
    ScalarFieldCriticalPoints();
 
    enum class BACKEND { GENERIC = 0, PROGRESSIVE_TOPOLOGY = 1 };
 
    template <class triangulationType = AbstractTriangulation>
    int execute(const SimplexId *const offsets,
                const triangulationType *triangulation);
 
    template <class triangulationType = AbstractTriangulation>
    int executeLegacy(const SimplexId *const offsets,
                      const triangulationType *triangulation);
 
    template <class triangulationType = AbstractTriangulation>
    int executeProgressive(const SimplexId *const offsets,
                           const triangulationType *triangulation);
 
    template <class triangulationType>
    void checkProgressivityRequirement(const triangulationType *triangulation);
 
    template <class triangulationType = AbstractTriangulation>
    int getLowerUpperComponents(
      const SimplexId vertexId,
      const SimplexId *const offsets,
      const triangulationType *triangulation,
      bool &isLowerOnBoundary,
      bool &isUpperOnBoundary,
      std::vector<std::vector<ttk::SimplexId>> *upperComponents,
      std::vector<std::vector<ttk::SimplexId>> *lowerComponents) const;
 
    template <class triangulationType = AbstractTriangulation>
    char
      getCriticalType(const SimplexId &vertexId,
                      const SimplexId *const offsets,
                      const triangulationType *triangulation,
                      std::vector<std::vector<ttk::SimplexId>> *upperComponents
                      = nullptr,
                      std::vector<std::vector<ttk::SimplexId>> *lowerComponents
                      = nullptr) const;
 
    char getCriticalType(const SimplexId &vertexId,
                         const SimplexId *const offsets,
                         const std::vector<std::pair<SimplexId, SimplexId>>
                           &vertexLinkEdgeList) const;
 
    inline void setDomainDimension(const int &dimension) {
      dimension_ = dimension;
    }
 
    inline void
      setOutput(std::vector<std::pair<SimplexId, char>> *criticalPoints) {
      criticalPoints_ = criticalPoints;
    }
 
    inline void
      preconditionTriangulation(AbstractTriangulation *triangulation) {
      // pre-condition functions
      if(triangulation) {
        triangulation->preconditionVertexNeighbors();
        triangulation->preconditionVertexStars();
        triangulation->preconditionBoundaryVertices();
      }
 
      setDomainDimension(triangulation->getDimensionality());
      setVertexNumber(triangulation->getNumberOfVertices());
    }
 
    inline void setVertexLinkEdgeLists(
      const std::vector<std::vector<std::pair<SimplexId, SimplexId>>>
        *edgeList) {
      vertexLinkEdgeLists_ = edgeList;
    }
 
    int setVertexNumber(const SimplexId &vertexNumber) {
      vertexNumber_ = vertexNumber;
      return 0;
    }
 
    void setNonManifold(const bool b) {
      forceNonManifoldCheck = b;
    }
 
    void displayStats();
 
  protected:
    int dimension_{};
    SimplexId vertexNumber_{};
    const std::vector<std::vector<std::pair<SimplexId, SimplexId>>>
      *vertexLinkEdgeLists_{};
    std::vector<std::pair<SimplexId, char>> *criticalPoints_{};
 
    bool forceNonManifoldCheck{false};
 
    // progressive
    BACKEND BackEnd{BACKEND::PROGRESSIVE_TOPOLOGY};
    ProgressiveTopology progT_{};
    int StartingResolutionLevel{0};
    int StoppingResolutionLevel{-1};
    bool IsResumable{false};
    double TimeLimit{};
  };
} // namespace ttk
 
// template functions
template <class triangulationType>
int ttk::ScalarFieldCriticalPoints::execute(
  const SimplexId *const offsets, const triangulationType *triangulation) {
 
  checkProgressivityRequirement(triangulation);
 
  switch(BackEnd) {
 
    case BACKEND::PROGRESSIVE_TOPOLOGY:
      this->executeProgressive(offsets, triangulation);
      break;
 
    case BACKEND::GENERIC:
      this->executeLegacy(offsets, triangulation);
      break;
 
    default:
      printErr("No method was selected");
  }
 
  printMsg(ttk::debug::Separator::L1);
  return 0;
}
 
template <class triangulationType>
int ttk::ScalarFieldCriticalPoints::executeProgressive(
  const SimplexId *const offsets, const triangulationType *triangulation) {
 
  progT_.setDebugLevel(debugLevel_);
  progT_.setThreadNumber(threadNumber_);
  progT_.setupTriangulation(const_cast<ttk::ImplicitTriangulation *>(
    (const ImplicitTriangulation *)triangulation));
  progT_.setStartingResolutionLevel(StartingResolutionLevel);
  progT_.setStoppingResolutionLevel(StoppingResolutionLevel);
  progT_.setTimeLimit(TimeLimit);
  progT_.setIsResumable(IsResumable);
  progT_.setPreallocateMemory(true);
 
  progT_.computeProgressiveCP(criticalPoints_, offsets);
 
  displayStats();
  return 0;
}
 
template <class triangulationType>
int ttk::ScalarFieldCriticalPoints::executeLegacy(
  const SimplexId *const offsets, const triangulationType *triangulation) {
 
  // check the consistency of the variables -- to adapt
#ifndef TTK_ENABLE_KAMIKAZE
  if((!dimension_) && ((!triangulation) || (triangulation->isEmpty())))
    return -1;
  if((!vertexNumber_) && ((!triangulation) || (triangulation->isEmpty())))
    return -2;
  if((!vertexLinkEdgeLists_) && (!triangulation))
    return -4;
  if(!criticalPoints_)
    return -5;
#endif
 
  if(triangulation) {
    vertexNumber_ = triangulation->getNumberOfVertices();
    dimension_ = triangulation->getCellVertexNumber(0) - 1;
  }
 
  printMsg("Extracting critical points...");
 
  Timer t;
 
  std::vector<char> vertexTypes(vertexNumber_, (char)(CriticalType::Regular));
 
#ifdef TTK_ENABLE_OPENMP
  int chunkSize = std::max(1000, (int)vertexNumber_ / (threadNumber_ * 100));
#endif
 
  if(triangulation) {
 
#ifdef TTK_ENABLE_OPENMP
#pragma omp parallel for schedule(dynamic, chunkSize) num_threads(threadNumber_)
#endif
    for(SimplexId i = 0; i < (SimplexId)vertexNumber_; i++) {
#ifdef TTK_ENABLE_MPI
      if(!isRunningWithMPI()
         || (isRunningWithMPI()
             && (triangulation->getVertexRank(i) == ttk::MPIrank_)))
#endif // TTK_ENABLE_MPI
      {
        vertexTypes[i] = getCriticalType(i, offsets, triangulation);
      }
    }
  } else if(vertexLinkEdgeLists_) {
    // legacy implementation
#ifdef TTK_ENABLE_OPENMP
#pragma omp parallel for schedule(dynamic, chunkSize) num_threads(threadNumber_)
#endif
    for(SimplexId i = 0; i < (SimplexId)vertexNumber_; i++) {
      // can't use MPI there since triangulation (~> rankArray) is nullptr
      vertexTypes[i] = getCriticalType(i, offsets, (*vertexLinkEdgeLists_)[i]);
    }
  }
 
  SimplexId minimumNumber = 0, maximumNumber = 0, saddleNumber = 0,
            oneSaddleNumber = 0, twoSaddleNumber = 0, monkeySaddleNumber = 0;
 
  // debug msg
  if(debugLevel_ >= (int)debug::Priority::INFO) {
    if(dimension_ == 3) {
      for(SimplexId i = 0; i < vertexNumber_; i++) {
        switch(vertexTypes[i]) {
 
          case(char)(CriticalType::Local_minimum):
            minimumNumber++;
            break;
 
          case(char)(CriticalType::Saddle1):
            oneSaddleNumber++;
            break;
 
          case(char)(CriticalType::Saddle2):
            twoSaddleNumber++;
            break;
 
          case(char)(CriticalType::Local_maximum):
            maximumNumber++;
            break;
 
          case(char)(CriticalType::Degenerate):
            monkeySaddleNumber++;
            break;
        }
      }
    } else if(dimension_ == 2) {
      for(SimplexId i = 0; i < vertexNumber_; i++) {
        switch(vertexTypes[i]) {
 
          case(char)(CriticalType::Local_minimum):
            minimumNumber++;
            break;
 
          case(char)(CriticalType::Saddle1):
            saddleNumber++;
            break;
 
          case(char)(CriticalType::Local_maximum):
            maximumNumber++;
            break;
 
          case(char)(CriticalType::Degenerate):
            monkeySaddleNumber++;
            break;
        }
      }
    }
 
    {
      std::vector<std::vector<std::string>> stats;
      stats.push_back({"  #Minima", std::to_string(minimumNumber)});
      if(dimension_ == 3) {
        stats.push_back({"  #1-saddles", std::to_string(oneSaddleNumber)});
        stats.push_back({"  #2-saddles", std::to_string(twoSaddleNumber)});
      }
      if(dimension_ == 2) {
        stats.push_back({"  #Saddles", std::to_string(saddleNumber)});
      }
      stats.push_back({"  #Multi-saddles", std::to_string(monkeySaddleNumber)});
      stats.push_back({"  #Maxima", std::to_string(maximumNumber)});
 
      printMsg(stats);
    }
  }
 
  // prepare the output
  criticalPoints_->clear();
  criticalPoints_->reserve(vertexNumber_);
  for(SimplexId i = 0; i < vertexNumber_; i++) {
    if(vertexTypes[i] != (char)(CriticalType::Regular)) {
      criticalPoints_->emplace_back(i, vertexTypes[i]);
    }
  }
 
  printMsg("Processed " + std::to_string(vertexNumber_) + " vertices", 1,
           t.getElapsedTime(), threadNumber_);
 
  return 0;
}
 
template <class triangulationType>
int ttk::ScalarFieldCriticalPoints::getLowerUpperComponents(
  const SimplexId vertexId,
  const SimplexId *const offsets,
  const triangulationType *triangulation,
  bool &isLowerOnBoundary,
  bool &isUpperOnBoundary,
  std::vector<std::vector<ttk::SimplexId>> *upperComponents,
  std::vector<std::vector<ttk::SimplexId>> *lowerComponents) const {
 
  SimplexId neighborNumber = triangulation->getVertexNeighborNumber(vertexId);
  std::vector<SimplexId> lowerNeighbors, upperNeighbors;
 
  for(SimplexId i = 0; i < neighborNumber; i++) {
    SimplexId neighborId = 0;
    triangulation->getVertexNeighbor(vertexId, i, neighborId);
 
    if(offsets[neighborId] < offsets[vertexId]) {
      lowerNeighbors.push_back(neighborId);
      if(dimension_ == 3) {
        if(triangulation->isVertexOnBoundary(neighborId))
          isLowerOnBoundary = true;
      }
    }
 
    // upper link
    if(offsets[neighborId] > offsets[vertexId]) {
      upperNeighbors.push_back(neighborId);
      if(dimension_ == 3) {
        if(triangulation->isVertexOnBoundary(neighborId))
          isUpperOnBoundary = true;
      }
    }
  }
 
  // now do the actual work
  std::vector<UnionFind> lowerSeeds(lowerNeighbors.size());
  std::vector<UnionFind *> lowerList(lowerNeighbors.size());
  std::vector<UnionFind> upperSeeds(upperNeighbors.size());
  std::vector<UnionFind *> upperList(upperNeighbors.size());
 
  for(SimplexId i = 0; i < (SimplexId)lowerSeeds.size(); i++) {
    lowerList[i] = &(lowerSeeds[i]);
  }
  for(SimplexId i = 0; i < (SimplexId)upperSeeds.size(); i++) {
    upperList[i] = &(upperSeeds[i]);
  }
 
  SimplexId vertexStarSize = triangulation->getVertexStarNumber(vertexId);
 
  for(SimplexId i = 0; i < vertexStarSize; i++) {
    SimplexId cellId = 0;
    triangulation->getVertexStar(vertexId, i, cellId);
 
    SimplexId cellSize = triangulation->getCellVertexNumber(cellId);
    for(SimplexId j = 0; j < cellSize; j++) {
      SimplexId neighborId0 = -1;
      triangulation->getCellVertex(cellId, j, neighborId0);
 
      if(neighborId0 != vertexId) {
        // we are on the link
 
        bool lower0 = offsets[neighborId0] < offsets[vertexId];
 
        // connect it to everybody except himself and vertexId
        for(SimplexId k = j + 1; k < cellSize; k++) {
 
          SimplexId neighborId1 = -1;
          triangulation->getCellVertex(cellId, k, neighborId1);
 
          if((neighborId1 != neighborId0) && (neighborId1 != vertexId)) {
 
            bool lower1 = offsets[neighborId1] < offsets[vertexId];
 
            std::vector<SimplexId> *neighbors = &lowerNeighbors;
            std::vector<UnionFind *> *seeds = &lowerList;
 
            if(!lower0) {
              neighbors = &upperNeighbors;
              seeds = &upperList;
            }
 
            if(lower0 == lower1) {
              // connect their union-find sets!
              SimplexId lowerId0 = -1, lowerId1 = -1;
              for(SimplexId l = 0; l < (SimplexId)neighbors->size(); l++) {
                if((*neighbors)[l] == neighborId0) {
                  lowerId0 = l;
                }
                if((*neighbors)[l] == neighborId1) {
                  lowerId1 = l;
                }
              }
              if((lowerId0 != -1) && (lowerId1 != -1)) {
                (*seeds)[lowerId0] = UnionFind::makeUnion(
                  (*seeds)[lowerId0], (*seeds)[lowerId1]);
                (*seeds)[lowerId1] = (*seeds)[lowerId0];
              }
            }
          }
        }
      }
    }
  }
 
  // let's remove duplicates now
 
  // update the UF if necessary
  for(SimplexId i = 0; i < (SimplexId)lowerList.size(); i++)
    lowerList[i] = lowerList[i]->find();
  for(SimplexId i = 0; i < (SimplexId)upperList.size(); i++)
    upperList[i] = upperList[i]->find();
 
  std::unordered_map<UnionFind *, std::vector<ttk::SimplexId>>::iterator it;
  std::unordered_map<UnionFind *, std::vector<ttk::SimplexId>>
    upperComponentId{};
  std::unordered_map<UnionFind *, std::vector<ttk::SimplexId>>
    lowerComponentId{};
 
  // We retrieve the lower and upper components if we want them
  for(ttk::SimplexId i = 0; i < (SimplexId)upperNeighbors.size(); i++) {
    it = upperComponentId.find(upperList[i]);
    if(it != upperComponentId.end()) {
      upperComponentId[upperList[i]].push_back(upperNeighbors[i]);
    } else {
      upperComponentId[upperList[i]]
        = std::vector<ttk::SimplexId>(1, upperNeighbors[i]);
    }
  }
  for(auto elt : upperComponentId) {
    upperComponents->push_back(std::vector<ttk::SimplexId>());
    for(ttk::SimplexId i = 0; i < (ttk::SimplexId)elt.second.size(); i++) {
      upperComponents->back().push_back(elt.second.at(i));
    }
  }
 
  for(ttk::SimplexId i = 0; i < (SimplexId)lowerNeighbors.size(); i++) {
    it = lowerComponentId.find(lowerList[i]);
    if(it != lowerComponentId.end()) {
      lowerComponentId[lowerList[i]].push_back(lowerNeighbors[i]);
    } else {
      lowerComponentId[lowerList[i]]
        = std::vector<ttk::SimplexId>(1, lowerNeighbors[i]);
    }
  }
  for(auto elt : lowerComponentId) {
    lowerComponents->push_back(std::vector<ttk::SimplexId>());
    for(ttk::SimplexId i = 0; i < (ttk::SimplexId)elt.second.size(); i++) {
      lowerComponents->back().push_back(elt.second.at(i));
    }
  }
 
  if(debugLevel_ >= (int)(debug::Priority::VERBOSE)) {
    printMsg("Vertex #" + std::to_string(vertexId)
               + ": lowerLink-#CC=" + std::to_string(lowerComponentId.size())
               + " upperLink-#CC=" + std::to_string(upperComponentId.size()),
             debug::Priority::VERBOSE);
  }
 
  return 0;
}
 
template <class triangulationType>
char ttk::ScalarFieldCriticalPoints::getCriticalType(
  const SimplexId &vertexId,
  const SimplexId *const offsets,
  const triangulationType *triangulation,
  std::vector<std::vector<ttk::SimplexId>> *upperComponents,
  std::vector<std::vector<ttk::SimplexId>> *lowerComponents) const {
 
  bool isLowerOnBoundary = false, isUpperOnBoundary = false;
  std::vector<std::vector<ttk::SimplexId>> localUpperComponents;
  std::vector<std::vector<ttk::SimplexId>> localLowerComponents;
  if(upperComponents == nullptr) {
    upperComponents = &localUpperComponents;
  }
  if(lowerComponents == nullptr) {
    lowerComponents = &localLowerComponents;
  }
  getLowerUpperComponents(vertexId, offsets, triangulation, isLowerOnBoundary,
                          isUpperOnBoundary, upperComponents, lowerComponents);
  ttk::SimplexId lowerComponentNumber = lowerComponents->size();
  ttk::SimplexId upperComponentNumber = upperComponents->size();
 
  if(dimension_ == 1) {
    if(lowerComponentNumber == 0 && upperComponentNumber != 0) {
      return (char)(CriticalType::Local_minimum);
    } else if(lowerComponentNumber != 0 && upperComponentNumber == 0) {
      return (char)(CriticalType::Local_maximum);
    } else if(lowerComponentNumber == 1 && upperComponentNumber == 1) {
      return (char)(CriticalType::Regular);
    }
    return (char)(CriticalType::Saddle1);
  }
 
  if(lowerComponentNumber == 0 && upperComponentNumber == 1) {
    return (char)(CriticalType::Local_minimum);
  } else if(lowerComponentNumber == 1 && upperComponentNumber == 0) {
    return (char)(CriticalType::Local_maximum);
  } else if(lowerComponentNumber == 1 && upperComponentNumber == 1) {
 
    if((dimension_ == 3) && (triangulation->isVertexOnBoundary(vertexId))) {
      // special case of boundary saddles
      if((isUpperOnBoundary) && (!isLowerOnBoundary))
        return (char)(CriticalType::Saddle1);
      if((!isUpperOnBoundary) && (isLowerOnBoundary))
        return (char)(CriticalType::Saddle2);
    }
 
    // regular point
    return (char)(CriticalType::Regular);
  } else {
    // saddles
    if(dimension_ == 2 || dimension_ == 1) {
      if((lowerComponentNumber == 2 && upperComponentNumber == 1)
         || (lowerComponentNumber == 1 && upperComponentNumber == 2)
         || (lowerComponentNumber == 2 && upperComponentNumber == 2)) {
        // regular saddle
        return (char)(CriticalType::Saddle1);
      } else {
        // monkey saddle, saddle + extremum
        return (char)(CriticalType::Degenerate);
        // NOTE: you may have multi-saddles on the boundary in that
        // configuration
        // to make this computation 100% correct, one would need to
        // disambiguate boundary from interior vertices
      }
    } else if(dimension_ == 3) {
      if(lowerComponentNumber == 2 && upperComponentNumber == 1) {
        return (char)(CriticalType::Saddle1);
      } else if(lowerComponentNumber == 1 && upperComponentNumber == 2) {
        return (char)(CriticalType::Saddle2);
      } else {
        // monkey saddle, saddle + extremum
        return (char)(CriticalType::Degenerate);
        // NOTE: we may have a similar effect in 3D (TODO)
      }
    }
  }
 
  // -2: regular points
  return (char)(CriticalType::Regular);
}
 
template <class triangulationType>
void ttk::ScalarFieldCriticalPoints::checkProgressivityRequirement(
  const triangulationType *ttkNotUsed(triangulation)) {
  if(BackEnd == BACKEND::PROGRESSIVE_TOPOLOGY
     && !std::is_same<ttk::ImplicitWithPreconditions, triangulationType>::value
     && !std::is_same<ttk::ImplicitNoPreconditions, triangulationType>::value) {
 
    printWrn("Explicit, Compact or Periodic triangulation detected.");
    printWrn("Defaulting to the generic backend.");
 
    BackEnd = BACKEND::GENERIC;
  }
}