//    Copyright 2021 Jij Inc.

//    Licensed under the Apache License, Version 2.0 (the "License");
//    you may not use this file except in compliance with the License.
//    You may obtain a copy of the License at

//        http://www.apache.org/licenses/LICENSE-2.0

//    Unless required by applicable law or agreed to in writing, software
//    distributed under the License is distributed on an "AS IS" BASIS,
//    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
//    See the License for the specific language governing permissions and
//    limitations under the License.

#ifndef OPENJIJ_SYSTEM_CONTINUOUS_TIME_ISING_HPP__
#define OPENJIJ_SYSTEM_CONTINUOUS_TIME_ISING_HPP__

#include <system/system.hpp>
#include <graph/all.hpp>
#include <cassert>
#include <vector>
#include <utility>

#include <utility/eigen.hpp>

namespace openjij {
    namespace system {
        
        /**
         * @brief Continuous Time Quantum Ising system
         *
         * @tparam GraphType
         */

        template<typename GraphType>
        struct ContinuousTimeIsing;


        /**
         * @brief Continuous Time Quantum Ising system (for Sparse graph)
         *
         * @tparam FloatType
         */
        template<typename FloatType>
        struct ContinuousTimeIsing<graph::Sparse<FloatType>> {
            using GraphType = graph::Sparse<FloatType>;
            using system_type = transverse_field_system;
            using TimeType = FloatType;
            using CutPoint = std::pair<TimeType, graph::Spin>;

            /**
             * @brief Interaction type (Eigen sparse matrix)
             */
            using SparseMatrixXx = Eigen::SparseMatrix<FloatType, Eigen::RowMajor>;

            /**
             * @brief spin configuration in real and continuous time space
             * spin_config[i][j] -> at i th site, j th pair of imaginary time point and spin value after the point
             */
            using SpinConfiguration = std::vector<std::vector<CutPoint>>;

            /**
             * @brief ContinuousTimeIsing constructor
             *
             * @param init_spin_config
             * @param init_interaction
             * @param gamma
             */
            ContinuousTimeIsing(const SpinConfiguration& init_spin_config,
                                const GraphType& init_interaction,
                                const double gamma)
                : spin_config(init_spin_config),
                  num_spins(init_spin_config.size()+1),
                  interaction(utility::gen_matrix_from_graph<Eigen::RowMajor>(init_interaction)),
                  gamma(gamma) {

                assert(init_spin_config.size() == init_interaction.get_num_spins());

                // insert numbers to diagnonal elements in the interaction
                SparseMatrixXx diag(init_interaction.get_num_spins()+1, init_interaction.get_num_spins()+1);

                for(typename SparseMatrixXx::InnerIterator it(interaction, init_interaction.get_num_spins()); it; ++it) {
                    std::size_t j = it.index();
                    FloatType v = it.value();
                    if(j != init_interaction.get_num_spins()){
                        diag.insert(j,j) = v;
                    }
                    else{
                        diag.insert(j,j) = -1;
                    }
                }


                interaction += diag;

                spin_config.push_back(std::vector<CutPoint> { CutPoint(0.0, 1) });
                // initialize auxiliary spin with 1 along entire timeline
            }

            /**
             * @brief ContinuousTimeIsing constructor
             *
             * @details create timeline which has only one cut at time zero with given spin state for each site
             *
             * @param init_spins
             * @param init_interaction
             * @param gamma
             */
            ContinuousTimeIsing(const graph::Spins& init_spins,
                                const GraphType& init_interaction,
                                const double gamma) :
                ContinuousTimeIsing(convert_to_spin_config(init_spins),
                                    init_interaction,
                                    gamma) {} // constructor delegation

            /* initialization helper functions */
        private:

            /**
             * @brief convert classical spins to spin configuration; each site has only one cut with given spin state at time zero
             *
             * @param spins
             */
            static SpinConfiguration convert_to_spin_config(const graph::Spins& spins) {
                SpinConfiguration spin_config;
                spin_config.reserve(spins.size());

                /* set spin configuration for each site, which has only one cut at time zero */
                for(auto spin : spins) {
                    spin_config.push_back(std::vector<CutPoint>{ CutPoint(TimeType(), spin) }); // TimeType() is zero value of the type
                }

                return spin_config;
            }

            /* member functions*/
        public:

            /**
             * @brief reset spins with given spin configuration
             *
             * @param init_spin_config spin configuration to be set, which must NOT contain auxiliary one
             */
            void reset_spins(const SpinConfiguration& init_spin_config) {
                assert(init_spin_config.size() == this->num_spins-1);

                this->spin_config = init_spin_config;
                this->spin_config.push_back(std::vector<CutPoint> { CutPoint(TimeType(), 1) });
                // add auxiliary timeline
            }

            /**
             * @brief reset spins with given spin configuration
             *
             * @param classical_spins
             */
            void reset_spins(const graph::Spins& classical_spins) {
                assert(classical_spins.size() == this->num_spins-1);

                for(size_t i = 0;i < this->num_spins - 1;i++) {
                    this->spin_config[i] = std::vector<CutPoint> {
                        CutPoint(TimeType(), classical_spins[i]) // TimeType() is zero value of the type
                    };
                }
                this->spin_config[this->num_spins-1] = std::vector<CutPoint> { CutPoint(TimeType(), 1) };
            }

            /**
             * @brief return time-direction index which exists just before time_point at "site_index"th site.
             * The periodic boundary condition for time direction is taken into account.
             *
             * @param site_index spacial index of site
             * @param time_point time-direction point
             */
            size_t get_temporal_spin_index(graph::Index site_index, TimeType time_point) const {
                static const auto first_lt = [](CutPoint x, CutPoint y) { return x.first < y.first; };
                // function to compare two time points (lt; less than)

                const auto& timeline = this->spin_config[site_index];
                const auto dummy_cut = CutPoint(time_point, 0); // dummy variable for binary search
                auto found_itr = std::upper_bound(timeline.begin(),
                                                  timeline.end(),
                                                  dummy_cut,
                                                  first_lt);

                if(found_itr == timeline.begin()) { // if the time_point lies before any time points
                    found_itr = timeline.end() - 1; // periodic boundary condition
                } else {
                    found_itr--;
                }

                return std::distance(timeline.begin(), found_itr);
            }

            /*
             * @brief return spin configuration at given temporal slice, not containing auxiliary spin
             *
             * @param slice_time
             */
            graph::Spins get_slice_at(TimeType slice_time) const {
                graph::Spins slice;

                for(graph::Index i = 0;i < this->spin_config.size()-1;i++) {
                    auto temporal_index = get_temporal_spin_index(i, slice_time);
                    slice.push_back(this->spin_config[i][temporal_index].second);
                }

                return slice;
            }

            /*
             * @brief return auxiliary spin state at given temporal slice
             *
             * @param slice_time
             */
            graph::Spin get_auxiliary_spin(TimeType slice_time) const {
                auto last_index = this->spin_config.size()-1;
                auto temporal_index = get_temporal_spin_index(last_index, slice_time);
                return this->spin_config[last_index][temporal_index].second;
            }


            /* Member variables */

            /**
             * @brief spin configuration
             */
            SpinConfiguration spin_config;

            /**
             * @brief number of spins, including auxiliary spin for longitudinal magnetic field
             */
            const std::size_t num_spins;

            /**
             * @brief interaction
             */
            SparseMatrixXx interaction;

            /**
             * @brief coefficient of transverse field term, actual field would be gamma * s, where s = [0:1]
             */
            const FloatType gamma;
        };

        /**
         * @brief helper function for ContinuousTimeIsing constructor
         *
         * @tparam GraphType
         * @param init_spins
         * @param interaction
         * @param gamma
         *
         * @return generated object
         */
        template<typename GraphType>
        ContinuousTimeIsing<GraphType> make_continuous_time_ising(const graph::Spins& init_spins,
                                                                  const GraphType& init_interaction,
                                                                  double gamma) {
            return ContinuousTimeIsing<GraphType>(init_spins,
                                                  init_interaction,
                                                  gamma);
        }
    } // namespace system
} // namespace openjij

#endif
