text: /**
  BSD 3-Clause License
  
  This file is part of the Basalt project.
  https://gitlab.com/VladyslavUsenko/basalt.git
  
  Copyright (c) 2019, Vladyslav Usenko and Nikolaus Demmel.
  All rights reserved.
  
  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are met:
  
  * Redistributions of source code must retain the above copyright notice, this
    list of conditions and the following disclaimer.
  
  * Redistributions in binary form must reproduce the above copyright notice,
    this list of conditions and the following disclaimer in the documentation
    and/or other materials provided with the distribution.
  
  * Neither the name of the copyright holder nor the names of its
    contributors may be used to endorse or promote products derived from
    this software without specific prior written permission.
  
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
  DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
  FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
  SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
  OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  */
  
  #pragma once
  
  #include <Eigen/Dense>
  #include <Eigen/Sparse>
  
  #include <array>
  #include <chrono>
  #include <unordered_map>
  
  #include <basalt/utils/assert.h>
  #include <basalt/utils/hash.h>
  
  #if defined(BASALT_USE_CHOLMOD)
  
  #include <Eigen/CholmodSupport>
  
  template <class T>
  using SparseLLT = Eigen::CholmodSupernodalLLT<T>;
  
  #else
  
  template <class T>
  using SparseLLT = Eigen::SimplicialLDLT<T>;
  
  #endif
  
  namespace basalt {
  
  template <typename Scalar = double>
  class DenseAccumulator {
   public:
    typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> VectorX;
    typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixX;
  
    template <int ROWS, int COLS, typename Derived>
    inline void addH(int i, int j, const Eigen::MatrixBase<Derived>& data) {
      BASALT_ASSERT_STREAM(i >= 0, "i " << i);
      BASALT_ASSERT_STREAM(j >= 0, "j " << j);
  
      BASALT_ASSERT_STREAM(i + ROWS <= H.cols(), "i " << i << " ROWS " << ROWS
                                                      << " H.rows() "
                                                      << H.rows());
      BASALT_ASSERT_STREAM(j + COLS <= H.rows(), "j " << j << " COLS " << COLS
                                                      << " H.cols() "
                                                      << H.cols());
  
      H.template block<ROWS, COLS>(i, j) += data;
    }
  
    template <int ROWS, typename Derived>
    inline void addB(int i, const Eigen::MatrixBase<Derived>& data) {
      BASALT_ASSERT_STREAM(i >= 0, "i " << i);
  
      BASALT_ASSERT_STREAM(i + ROWS <= H.cols(), "i " << i << " ROWS " << ROWS
                                                      << " H.rows() "
                                                      << H.rows());
  
      b.template segment<ROWS>(i) += data;
    }
  
    // inline VectorX solve() const { return H.ldlt().solve(b); }
    inline VectorX solve(const VectorX* diagonal) const {
      if (diagonal == nullptr) {
        return H.ldlt().solve(b);
      } else {
        MatrixX HH = H;
        HH.diagonal() += *diagonal;
        return HH.ldlt().solve(b);
      }
    }
  
    inline void reset(int opt_size) {
      H.setZero(opt_size, opt_size);
      b.setZero(opt_size);
    }
  
    inline void join(const DenseAccumulator<Scalar>& other) {
      H += other.H;
      b += other.b;
    }
  
    inline void print() {
      Eigen::IOFormat CleanFmt(2);
      std::cerr << "H\n" << H.format(CleanFmt) << std::endl;
      std::cerr << "b\n" << b.transpose().format(CleanFmt) << std::endl;
    }
  
    inline void setup_solver(){};
    inline VectorX Hdiagonal() const { return H.diagonal(); }
  
    inline const MatrixX& getH() const { return H; }
    inline const VectorX& getB() const { return b; }
  
    inline MatrixX& getH() { return H; }
    inline VectorX& getB() { return b; }
  
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
   private:
    MatrixX H;
    VectorX b;
  };
  
  template <typename Scalar = double>
  class SparseHashAccumulator {
   public:
    typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> VectorX;
    typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixX;
    typedef Eigen::Triplet<Scalar> T;
    typedef Eigen::SparseMatrix<Scalar> SparseMatrix;
  
    template <int ROWS, int COLS, typename Derived>
    inline void addH(int si, int sj, const Eigen::MatrixBase<Derived>& data) {
      EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, ROWS, COLS);
  
      KeyT id;
      id[0] = si;
      id[1] = sj;
      id[2] = ROWS;
      id[3] = COLS;
  
      auto it = hash_map.find(id);
  
      if (it == hash_map.end()) {
        hash_map.emplace(id, data);
      } else {
        it->second += data;
      }
    }
  
    template <int ROWS, typename Derived>
    inline void addB(int i, const Eigen::MatrixBase<Derived>& data) {
      b.template segment<ROWS>(i) += data;
    }
  
    inline void setup_solver() {
      std::vector<T> triplets;
      triplets.reserve(hash_map.size() * 36 + b.rows());
  
      for (const auto& kv : hash_map) {
        for (int i = 0; i < kv.second.rows(); i++) {
          for (int j = 0; j < kv.second.cols(); j++) {
            triplets.emplace_back(kv.first[0] + i, kv.first[1] + j,
                                  kv.second(i, j));
          }
        }
      }
  
      for (int i = 0; i < b.rows(); i++) {
        triplets.emplace_back(i, i, std::numeric_limits<double>::min());
      }
  
      smm = SparseMatrix(b.rows(), b.rows());
      smm.setFromTriplets(triplets.begin(), triplets.end());
    }
  
    inline VectorX Hdiagonal() const { return smm.diagonal(); }
  
    inline VectorX& getB() { return b; }
  
    inline VectorX solve(const VectorX* diagonal) const {
      auto t2 = std::chrono::high_resolution_clock::now();
  
      SparseMatrix sm = smm;
      if (diagonal) sm.diagonal() += *diagonal;
  
      VectorX res;
  
      if (iterative_solver) {
        // NOTE: since we have to disable Eigen's parallelization with OpenMP
        // (interferes with TBB), the current CG is single-threaded, and we
        // can expect a substantial speedup by switching to a parallel
        // implementation of CG.
        Eigen::ConjugateGradient<Eigen::SparseMatrix<double>,
                                 Eigen::Lower | Eigen::Upper>
            cg;
  
        cg.setTolerance(tolerance);
        cg.compute(sm);
        res = cg.solve(b);
      } else {
        SparseLLT<SparseMatrix> chol(sm);
        res = chol.solve(b);
      }
  
      auto t3 = std::chrono::high_resolution_clock::now();
  
      auto elapsed2 =
          std::chrono::duration_cast<std::chrono::microseconds>(t3 - t2);
  
      if (print_info) {
        std::cout << "Solving linear system: " << elapsed2.count() * 1e-6 << "s."
                  << std::endl;
      }
  
      return res;
    }
  
    inline void reset(int opt_size) {
      hash_map.clear();
      b.setZero(opt_size);
    }
  
    inline void join(const SparseHashAccumulator<Scalar>& other) {
      for (const auto& kv : other.hash_map) {
        auto it = hash_map.find(kv.first);
  
        if (it == hash_map.end()) {
          hash_map.emplace(kv.first, kv.second);
        } else {
          it->second += kv.second;
        }
      }
  
      b += other.b;
    }
  
    double tolerance = 1e-4;
    bool iterative_solver = false;
    bool print_info = false;
  
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
   private:
    using KeyT = std::array<int, 4>;
  
    struct KeyHash {
      inline size_t operator()(const KeyT& c) const {
        size_t seed = 0;
        for (int i = 0; i < 4; i++) {
          hash_combine(seed, c[i]);
        }
        return seed;
      }
    };
  
    std::unordered_map<KeyT, MatrixX, KeyHash> hash_map;
  
    VectorX b;
  
    SparseMatrix smm;
  };
  
  }  // namespace basalt
  