#ifndef STAN_MATH_REV_MAT_FUN_MDIVIDE_LEFT_SPD_HPP
#define STAN_MATH_REV_MAT_FUN_MDIVIDE_LEFT_SPD_HPP

#include <stan/math/rev/core.hpp>
#include <stan/math/prim/mat/fun/Eigen.hpp>
#include <stan/math/prim/mat/fun/typedefs.hpp>
#include <stan/math/prim/mat/err/check_multiplicable.hpp>
#include <stan/math/rev/mat/fun/typedefs.hpp>
#include <stan/math/prim/mat/err/check_square.hpp>
#include <vector>

namespace stan {
  namespace math {

    namespace {
      template <int R1, int C1, int R2, int C2>
      class mdivide_left_spd_alloc : public chainable_alloc {
      public:
        virtual ~mdivide_left_spd_alloc() {}

        Eigen::LLT< Eigen::Matrix<double, R1, C1> > llt_;
        Eigen::Matrix<double, R2, C2> C_;
      };

      template <int R1, int C1, int R2, int C2>
      class mdivide_left_spd_vv_vari : public vari {
      public:
        int M_;  // A.rows() = A.cols() = B.rows()
        int N_;  // B.cols()
        vari** variRefA_;
        vari** variRefB_;
        vari** variRefC_;
        mdivide_left_spd_alloc<R1, C1, R2, C2> *alloc_;

        mdivide_left_spd_vv_vari(const Eigen::Matrix<var, R1, C1> &A,
                                 const Eigen::Matrix<var, R2, C2> &B)
          : vari(0.0),
            M_(A.rows()),
            N_(B.cols()),
            variRefA_(reinterpret_cast<vari**>
                      (ChainableStack::memalloc_
                       .alloc(sizeof(vari*) * A.rows() * A.cols()))),
            variRefB_(reinterpret_cast<vari**>
                      (ChainableStack::memalloc_
                       .alloc(sizeof(vari*) * B.rows() * B.cols()))),
            variRefC_(reinterpret_cast<vari**>
                      (ChainableStack::memalloc_
                       .alloc(sizeof(vari*) * B.rows() * B.cols()))),
            alloc_(new mdivide_left_spd_alloc<R1, C1, R2, C2>()) {
          using Eigen::Matrix;
          using Eigen::Map;

          Matrix<double, R1, C1> Ad(A.rows(), A.cols());

          size_t pos = 0;
          for (size_type j = 0; j < M_; j++) {
            for (size_type i = 0; i < M_; i++) {
              variRefA_[pos] = A(i, j).vi_;
              Ad(i, j) = A(i, j).val();
              pos++;
            }
          }

          pos = 0;
          alloc_->C_.resize(M_, N_);
          for (size_type j = 0; j < N_; j++) {
            for (size_type i = 0; i < M_; i++) {
              variRefB_[pos] = B(i, j).vi_;
              alloc_->C_(i, j) = B(i, j).val();
              pos++;
            }
          }

          alloc_->llt_ = Ad.llt();
          alloc_->llt_.solveInPlace(alloc_->C_);

          pos = 0;
          for (size_type j = 0; j < N_; j++) {
            for (size_type i = 0; i < M_; i++) {
              variRefC_[pos] = new vari(alloc_->C_(i, j), false);
              pos++;
            }
          }
        }

        virtual void chain() {
          using Eigen::Matrix;
          using Eigen::Map;
          Eigen::Matrix<double, R1, C1> adjA(M_, M_);
          Eigen::Matrix<double, R2, C2> adjB(M_, N_);

          size_t pos = 0;
          for (size_type j = 0; j < N_; j++)
            for (size_type i = 0; i < M_; i++)
              adjB(i, j) = variRefC_[pos++]->adj_;

          alloc_->llt_.solveInPlace(adjB);
          adjA.noalias() = -adjB * alloc_->C_.transpose();

          pos = 0;
          for (size_type j = 0; j < M_; j++)
            for (size_type i = 0; i < M_; i++)
              variRefA_[pos++]->adj_ += adjA(i, j);

          pos = 0;
          for (size_type j = 0; j < N_; j++)
            for (size_type i = 0; i < M_; i++)
              variRefB_[pos++]->adj_ += adjB(i, j);
        }
      };

      template <int R1, int C1, int R2, int C2>
      class mdivide_left_spd_dv_vari : public vari {
      public:
        int M_;  // A.rows() = A.cols() = B.rows()
        int N_;  // B.cols()
        vari** variRefB_;
        vari** variRefC_;
        mdivide_left_spd_alloc<R1, C1, R2, C2> *alloc_;

        mdivide_left_spd_dv_vari(const Eigen::Matrix<double, R1, C1> &A,
                                 const Eigen::Matrix<var, R2, C2> &B)
          : vari(0.0),
            M_(A.rows()),
            N_(B.cols()),
            variRefB_(reinterpret_cast<vari**>
                      (ChainableStack::memalloc_
                       .alloc(sizeof(vari*) * B.rows() * B.cols()))),
            variRefC_(reinterpret_cast<vari**>
                      (ChainableStack::memalloc_
                       .alloc(sizeof(vari*) * B.rows() * B.cols()))),
            alloc_(new mdivide_left_spd_alloc<R1, C1, R2, C2>()) {
          using Eigen::Matrix;
          using Eigen::Map;

          size_t pos = 0;
          alloc_->C_.resize(M_, N_);
          for (size_type j = 0; j < N_; j++) {
            for (size_type i = 0; i < M_; i++) {
              variRefB_[pos] = B(i, j).vi_;
              alloc_->C_(i, j) = B(i, j).val();
              pos++;
            }
          }

          alloc_->llt_ = A.llt();
          alloc_->llt_.solveInPlace(alloc_->C_);

          pos = 0;
          for (size_type j = 0; j < N_; j++) {
            for (size_type i = 0; i < M_; i++) {
              variRefC_[pos] = new vari(alloc_->C_(i, j), false);
              pos++;
            }
          }
        }

        virtual void chain() {
          using Eigen::Matrix;
          using Eigen::Map;
          Eigen::Matrix<double, R2, C2> adjB(M_, N_);

          size_t pos = 0;
          for (size_type j = 0; j < adjB.cols(); j++)
            for (size_type i = 0; i < adjB.rows(); i++)
              adjB(i, j) = variRefC_[pos++]->adj_;

          alloc_->llt_.solveInPlace(adjB);

          pos = 0;
          for (size_type j = 0; j < adjB.cols(); j++)
            for (size_type i = 0; i < adjB.rows(); i++)
              variRefB_[pos++]->adj_ += adjB(i, j);
        }
      };

      template <int R1, int C1, int R2, int C2>
      class mdivide_left_spd_vd_vari : public vari {
      public:
        int M_;  // A.rows() = A.cols() = B.rows()
        int N_;  // B.cols()
        vari** variRefA_;
        vari** variRefC_;
        mdivide_left_spd_alloc<R1, C1, R2, C2> *alloc_;

        mdivide_left_spd_vd_vari(const Eigen::Matrix<var, R1, C1> &A,
                                 const Eigen::Matrix<double, R2, C2> &B)
          : vari(0.0),
            M_(A.rows()),
            N_(B.cols()),
            variRefA_(reinterpret_cast<vari**>
                      (ChainableStack::memalloc_
                       .alloc(sizeof(vari*) * A.rows() * A.cols()))),
            variRefC_(reinterpret_cast<vari**>
                      (ChainableStack::memalloc_
                       .alloc(sizeof(vari*) * B.rows() * B.cols()))),
            alloc_(new mdivide_left_spd_alloc<R1, C1, R2, C2>()) {
          using Eigen::Matrix;
          using Eigen::Map;

          Matrix<double, R1, C1> Ad(A.rows(), A.cols());

          size_t pos = 0;
          for (size_type j = 0; j < M_; j++) {
            for (size_type i = 0; i < M_; i++) {
              variRefA_[pos] = A(i, j).vi_;
              Ad(i, j) = A(i, j).val();
              pos++;
            }
          }

          alloc_->llt_ = Ad.llt();
          alloc_->C_ = alloc_->llt_.solve(B);

          pos = 0;
          for (size_type j = 0; j < N_; j++) {
            for (size_type i = 0; i < M_; i++) {
              variRefC_[pos] = new vari(alloc_->C_(i, j), false);
              pos++;
            }
          }
        }

        virtual void chain() {
          using Eigen::Matrix;
          using Eigen::Map;
          Eigen::Matrix<double, R1, C1> adjA(M_, M_);
          Eigen::Matrix<double, R1, C2> adjC(M_, N_);

          size_t pos = 0;
          for (size_type j = 0; j < adjC.cols(); j++)
            for (size_type i = 0; i < adjC.rows(); i++)
              adjC(i, j) = variRefC_[pos++]->adj_;

          adjA = -alloc_->llt_.solve(adjC*alloc_->C_.transpose());

          pos = 0;
          for (size_type j = 0; j < adjA.cols(); j++)
            for (size_type i = 0; i < adjA.rows(); i++)
              variRefA_[pos++]->adj_ += adjA(i, j);
        }
      };
    }

    template <int R1, int C1, int R2, int C2>
    inline
    Eigen::Matrix<var, R1, C2>
    mdivide_left_spd(const Eigen::Matrix<var, R1, C1> &A,
                     const Eigen::Matrix<var, R2, C2> &b) {
      Eigen::Matrix<var, R1, C2> res(b.rows(), b.cols());

      check_square("mdivide_left_spd", "A", A);
      check_multiplicable("mdivide_left_spd",
                          "A", A,
                          "b", b);

      // NOTE: this is not a memory leak, this vari is used in the
      // expression graph to evaluate the adjoint, but is not needed
      // for the returned matrix.  Memory will be cleaned up with the
      // arena allocator.
      mdivide_left_spd_vv_vari<R1, C1, R2, C2> *baseVari
        = new mdivide_left_spd_vv_vari<R1, C1, R2, C2>(A, b);

      size_t pos = 0;
      for (size_type j = 0; j < res.cols(); j++)
        for (size_type i = 0; i < res.rows(); i++)
          res(i, j).vi_ = baseVari->variRefC_[pos++];

      return res;
    }

    template <int R1, int C1, int R2, int C2>
    inline
    Eigen::Matrix<var, R1, C2>
    mdivide_left_spd(const Eigen::Matrix<var, R1, C1> &A,
                     const Eigen::Matrix<double, R2, C2> &b) {
      Eigen::Matrix<var, R1, C2> res(b.rows(), b.cols());

      check_square("mdivide_left_spd", "A", A);
      check_multiplicable("mdivide_left_spd",
                          "A", A,
                          "b", b);

      // NOTE: this is not a memory leak, this vari is used in the
      // expression graph to evaluate the adjoint, but is not needed
      // for the returned matrix.  Memory will be cleaned up with the
      // arena allocator.
      mdivide_left_spd_vd_vari<R1, C1, R2, C2> *baseVari
        = new mdivide_left_spd_vd_vari<R1, C1, R2, C2>(A, b);

      size_t pos = 0;
      for (size_type j = 0; j < res.cols(); j++)
        for (size_type i = 0; i < res.rows(); i++)
          res(i, j).vi_ = baseVari->variRefC_[pos++];

      return res;
    }

    template <int R1, int C1, int R2, int C2>
    inline
    Eigen::Matrix<var, R1, C2>
    mdivide_left_spd(const Eigen::Matrix<double, R1, C1> &A,
                     const Eigen::Matrix<var, R2, C2> &b) {
      Eigen::Matrix<var, R1, C2> res(b.rows(), b.cols());

      check_square("mdivide_left_spd", "A", A);
      check_multiplicable("mdivide_left_spd",
                          "A", A,
                          "b", b);

      // NOTE: this is not a memory leak, this vari is used in the
      // expression graph to evaluate the adjoint, but is not needed
      // for the returned matrix.  Memory will be cleaned up with the
      // arena allocator.
      mdivide_left_spd_dv_vari<R1, C1, R2, C2> *baseVari
        = new mdivide_left_spd_dv_vari<R1, C1, R2, C2>(A, b);

      size_t pos = 0;
      for (size_type j = 0; j < res.cols(); j++)
        for (size_type i = 0; i < res.rows(); i++)
          res(i, j).vi_ = baseVari->variRefC_[pos++];

      return res;
    }

  }
}
#endif
