include/openjij/system/k_local_polynomial.hpp
// Copyright 2023 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.
#pragma once
#include <sstream>
#include <nlohmann/json.hpp>
#include "openjij/graph/all.hpp"
#include "openjij/graph/json/parse.hpp"
#include "openjij/utility/thres_hold.hpp"
namespace openjij {
namespace system {
//! @brief KLocalPolynomial class, which is a system to solve higher order
//! unconstrained binary optimization (HUBO) problems with vartype being
//! "BINARY"
//! @tparam GraphType type of graph
template <class GraphType> class KLocalPolynomial;
//! @brief KLocalPolynomial class
template <typename FloatType>
class KLocalPolynomial<graph::Polynomial<FloatType>> {
public:
//! @brief system type
using system_type = classical_system;
//! @brief The number of binaries
const int64_t num_binaries;
//! @brief k-local update is activated per rate_call_k_local times
int rate_call_k_local = 10;
//! @brief Counter of calling updater
int64_t count_call_updater = 0;
//! @brief Binary configurations
graph::Binaries binaries;
//! @brief The model's type. SPIN or BINARY
const cimod::Vartype vartype = cimod::Vartype::BINARY;
//! @brief Constructor of KLocalPolynomial system class
//! @param init_binaries const graph::Binaries&. The initial binary
//! configurations.
//! @param poly_graph const graph::Polynomial<FloatType>& (Polynomial graph
//! class). The initial interacrtions.
KLocalPolynomial(const graph::Binaries &init_binaries,
const graph::Polynomial<FloatType> &poly_graph)
: num_binaries(init_binaries.size()), binaries(init_binaries),
binaries_v_(init_binaries) {
cimod::CheckVariables(binaries, vartype);
const auto &poly_key_list = poly_graph.get_keys();
const auto &poly_value_list = poly_graph.get_values();
if (poly_key_list.size() != poly_value_list.size()) {
throw std::runtime_error(
"The sizes of key_list and value_list must match each other");
}
if (poly_key_list.size() == 0) {
throw std::runtime_error("The interaction is empty.");
}
std::unordered_set<graph::Index> active_binary_set;
poly_key_list_.clear();
poly_value_list_.clear();
for (std::size_t i = 0; i < poly_key_list.size(); ++i) {
if (poly_value_list[i] != 0.0) {
poly_key_list_.push_back(poly_key_list[i]);
poly_value_list_.push_back(poly_value_list[i]);
for (const auto &it : poly_key_list[i]) {
active_binary_set.emplace(it);
}
}
}
num_interactions_ = static_cast<int64_t>(poly_key_list_.size());
SortInteractions();
active_binaries_ = std::vector<graph::Index>(active_binary_set.begin(),
active_binary_set.end());
std::sort(active_binaries_.begin(), active_binaries_.end());
SetAdj();
ResetZeroCount();
reset_dE();
const FloatType thres_hold =
std::abs(FindMaxInteraction().second * utility::THRESHOLD<FloatType>);
min_effective_dE_ = std::abs(FindMinInteraction(thres_hold).second);
}
//! @brief Constructor of KLocalPolynomial system class.
//! @param init_binaries const graph::Binaries&. The initial binary
//! configurations.
//! @param j const nlohmann::json&
KLocalPolynomial(const graph::Binaries &init_binaries,
const nlohmann::json &j)
: num_binaries(init_binaries.size()), binaries(init_binaries),
binaries_v_(init_binaries) {
cimod::CheckVariables(binaries, vartype);
if (j.at("vartype") != "BINARY") {
throw std::runtime_error("Only binary variables are supported");
}
const auto &v_k_v = graph::json_parse_polynomial<FloatType>(j);
const auto &poly_key_list = std::get<0>(v_k_v);
const auto &poly_value_list = std::get<1>(v_k_v);
if (poly_key_list.size() != poly_value_list.size()) {
throw std::runtime_error(
"The sizes of key_list and value_list must match each other");
}
if (poly_key_list.size() == 0) {
throw std::runtime_error("The interaction is empty.");
}
num_interactions_ = static_cast<int64_t>(poly_key_list.size());
poly_key_list_.resize(num_interactions_);
poly_value_list_.resize(num_interactions_);
#pragma omp parallel for
for (int64_t i = 0; i < num_interactions_; ++i) {
poly_key_list_[i] = poly_key_list[i];
poly_value_list_[i] = poly_value_list[i];
}
SortInteractions();
active_binaries_.resize(num_binaries);
std::iota(active_binaries_.begin(), active_binaries_.end(), 0);
SetAdj();
ResetZeroCount();
reset_dE();
const FloatType thres_hold =
std::abs(FindMaxInteraction().second * utility::THRESHOLD<FloatType>);
min_effective_dE_ = std::abs(FindMinInteraction(thres_hold).second);
}
//! @brief Reset KLocalPolynomial system with new binary configurations.
//! @param init_binaries const graph::Binaries&
void reset_binaries(const graph::Binaries &init_binaries) {
cimod::CheckVariables(init_binaries, vartype);
if (init_binaries.size() != binaries.size()) {
throw std::runtime_error(
"The size of initial binaries does not equal to system size");
}
for (const auto &index_binary : active_binaries_) {
if (binaries[index_binary] != init_binaries[index_binary]) {
update_system_single(index_binary);
}
if (binaries[index_binary] != init_binaries[index_binary]) {
std::stringstream ss;
ss << "Unknown error detected in " << __func__;
throw std::runtime_error(ss.str());
}
}
}
//! @brief Reset energy differences (dE), which is used to determine whether
//! to flip the binary or not.
void reset_dE() {
dE_.clear();
dE_v_.clear();
dE_.resize(num_binaries);
dE_v_.resize(num_binaries);
// Initialize
max_effective_dE_ = std::abs(poly_value_list_.front());
for (const auto &index_binary : active_binaries_) {
FloatType val = 0.0;
FloatType abs_val = 0.0;
bool flag = false;
const graph::Binary binary = binaries[index_binary];
for (const auto &index_key : adj_[index_binary]) {
if (zero_count_[index_key] + binary == 1) {
val += poly_value_list_[index_key];
}
flag = true;
abs_val += std::abs(poly_value_list_[index_key]);
}
dE_[index_binary] = (-2 * binary + 1) * val;
dE_v_[index_binary] = dE_[index_binary];
if (flag && max_effective_dE_ < abs_val) {
max_effective_dE_ = abs_val;
}
}
}
//! @brief Return the energy difference of single spin flip update
//! @param index_binary const graph::Index
//! @return the energy difference corresponding to "index_binary"
inline FloatType dE_single(const graph::Index index_binary) const {
return dE_[index_binary];
}
//! @brief Return the energy difference of k-local update
//! @details Note that this function changes the internal state of
//! KLocalPolynomial system. This function virtually update the system by
//! k-local update.
//! @param index_key const graph::Index
//! @return the energy difference corresponding to "index_key"
FloatType dE_k_local(const std::size_t index_key) {
FloatType dE = 0.0;
for (const auto &index_binary : poly_key_list_[index_key]) {
if (binaries_v_[index_binary] == 0) {
dE += dE_v_[index_binary];
virtual_update_system_single(index_binary);
}
if (dE < 0.0) {
break;
}
}
return dE;
}
//! @brief Update binary configurations by k-local update
void update_system_k_local() {
for (const auto &index_binary : update_index_binaries_v_) {
binaries[index_binary] = binaries_v_[index_binary];
}
for (const auto &index_zero_count : update_index_zero_count_v_) {
zero_count_[index_zero_count] = zero_count_v_[index_zero_count];
}
for (const auto &index_dE : update_index_dE_v_) {
dE_[index_dE] = dE_v_[index_dE];
}
update_index_binaries_v_.clear();
update_index_zero_count_v_.clear();
update_index_dE_v_.clear();
}
//! @brief Flip specified binary by single spin flip.
//! @param index_update_binary const graph::Index
void update_system_single(const graph::Index index_update_binary) {
const graph::Binary update_binary = binaries[index_update_binary];
const int coeef = -2 * update_binary + 1;
const int count = +2 * update_binary - 1;
for (const auto &index_key : adj_[index_update_binary]) {
const FloatType val = poly_value_list_[index_key];
for (const auto &index_binary : poly_key_list_[index_key]) {
const graph::Binary binary = binaries[index_binary];
if (zero_count_[index_key] + update_binary + binary == 2 &&
index_binary != index_update_binary) {
dE_[index_binary] += coeef * (-2 * binary + 1) * val;
dE_v_[index_binary] = dE_[index_binary];
}
}
zero_count_[index_key] += count;
zero_count_v_[index_key] = zero_count_[index_key];
}
dE_[index_update_binary] *= -1;
dE_v_[index_update_binary] = dE_[index_update_binary];
binaries[index_update_binary] = 1 - binaries[index_update_binary];
binaries_v_[index_update_binary] = binaries[index_update_binary];
}
//! @brief Virtually flip specified binary by single spin flip.
//! @param index_update_binary const graph::Index.
void virtual_update_system_single(const graph::Index index_update_binary) {
const graph::Binary update_binary = binaries_v_[index_update_binary];
const int coeef = -2 * update_binary + 1;
const int count = +2 * update_binary - 1;
for (const auto &index_key : adj_[index_update_binary]) {
const FloatType val = poly_value_list_[index_key];
for (const auto &index_binary : poly_key_list_[index_key]) {
const graph::Binary binary = binaries_v_[index_binary];
if (zero_count_v_[index_key] + update_binary + binary == 2 &&
index_binary != index_update_binary) {
dE_v_[index_binary] += coeef * (-2 * binary + 1) * val;
update_index_dE_v_.emplace(index_binary);
}
}
zero_count_v_[index_key] += count;
update_index_zero_count_v_.push_back(index_key);
}
dE_v_[index_update_binary] *= -1;
update_index_dE_v_.emplace(index_update_binary);
binaries_v_[index_update_binary] = 1 - binaries_v_[index_update_binary];
update_index_binaries_v_.push_back(index_update_binary);
}
//! @brief Reset binary configurations virtually updated by k-local update.
void reset_virtual_system() {
for (const auto &index_binary : update_index_binaries_v_) {
binaries_v_[index_binary] = binaries[index_binary];
}
for (const auto &index_zero_count : update_index_zero_count_v_) {
zero_count_v_[index_zero_count] = zero_count_[index_zero_count];
}
for (const auto &index_dE : update_index_dE_v_) {
dE_v_[index_dE] = dE_[index_dE];
}
update_index_binaries_v_.clear();
update_index_zero_count_v_.clear();
update_index_dE_v_.clear();
}
//! @brief Set "rate_call_k_local". k-local update is activated per
//! rate_call_k_local times.
//! @param rate_k_local int.
void set_rate_call_k_local(int rate_k_local) {
if (rate_k_local <= 0) {
throw std::runtime_error("rate_k_local must be larger than zero");
}
rate_call_k_local = rate_k_local;
}
//! @brief Get the number of interactions.
inline int64_t GetNumInteractions() const { return num_interactions_; }
//! @brief Return the number of variables taking the zero in the interaction
//! specified by "index_key".
//! @param index_key const std::size_t
//! @return Corresponding number of variables taking the zero.
inline int64_t GetZeroCount(const std::size_t index_key) const {
return zero_count_[index_key];
}
//! @brief Get the value of the interaction specified by "index_key".
//! @param index_key const std::size_t
//! @return Corresponding value.
inline FloatType GetPolyValue(const std::size_t index_key) const {
return poly_value_list_[index_key];
}
//! @brief Get the adjacency list (the index of interactions) of the binary
//! specified by "index_binary".
//! @param index_binary const std::size_t
//! @return Corresponding adjacency list.
inline const std::vector<graph::Index> &
get_adj(const std::size_t index_binary) const {
return adj_[index_binary];
}
//! @brief Get "active_binaries_", which is the list of the binaries connected
//! by at least one interaction.
//! @return active_binaries_
inline const std::vector<graph::Index> &get_active_binaries() const {
return active_binaries_;
}
//! @brief Get "max_effective_dE_", which is a upper bound of energy gap.
//! @return max_effective_dE_
FloatType get_max_effective_dE() const { return max_effective_dE_; }
//! @brief Get "min_effective_dE_", which is a rough lower bound of energy
//! gap.
//! @return min_effective_dE_
FloatType get_min_effective_dE() const { return min_effective_dE_; }
//! @brief Get the PolynomialValueList object, which is the list of the values
//! of the polynomial interactions as std::vector<FloatType>.
//! @return "poly_value_list_"
const cimod::PolynomialValueList<FloatType> &get_values() const {
return poly_value_list_;
}
//! @brief Get the PolynomialKeyList object, which is the list of the indices
//! of the polynomial interactions as std::vector<std::vector<graph::Index>>.
//! @return "poly_key_list_"
const cimod::PolynomialKeyList<graph::Index> &get_keys() const {
return poly_key_list_;
}
//! @brief Get the adjacency list, which is the list of the indices of
//! polynomial interactions including specific binary.
//! @return adjacency list
const std::vector<std::vector<graph::Index>> &get_adj() const { return adj_; }
//! @brief Get the vartype as std::string, which must be "BINARY".
//! @return "BINARY" as std::string
std::string get_vartype_string() const { return "BINARY"; }
///----------------------------------------------------------------------------------------
///----------------The following functions are for debugging. Disable when
///release.----------------
///----------------------------------------------------------------------------------------
/*
void print_dE() const {
for (std::size_t i = 0; i < dE_.size(); ++i) {
printf("dE[%2ld]=%+.15lf\n", i, dE_[i]);
}
}
void print_zero_count() const {
for (int64_t i = 0; i < num_interactions_; ++i) {
printf("zero_count[");
for (const auto &index_binary: poly_key_list_[i]) {
printf("%ld, ", index_binary);
}
printf("]=%lld\n", zero_count_[i]);
}
}
void print_adj() const {
for (int64_t i = 0; i < num_binaries; ++i) {
printf("adj[%lld]=", i);
for (const auto &index_key: adj_[i]) {
printf("%ld(%+lf), ", index_key, poly_value_list_[index_key]);
}
printf("\n");
}
}
void print_active_binaries() const {
for (std::size_t i = 0; i < active_binaries_.size(); ++i) {
printf("%d, ", binaries[active_binaries_[i]]);
}
printf("\n");
}
void print_interactions() const {
for (int64_t i = 0; i < num_interactions_; ++i) {
printf("%lld: size:%ld val: %lf\n", i, poly_key_list_[i].size(),
poly_value_list_[i]);
}
}
*/
///----------------------------------------------------------------------------------------
private:
//! @brief The number of the interactions.
int64_t num_interactions_;
//! @brief The energy differences when flipping a binary.
std::vector<FloatType> dE_;
//! @brief The number of variables taking the zero in each interaction.
std::vector<int64_t> zero_count_;
//! @brief Adjacency list, which is the list of the indices of polynomial
//! interactions including specific binary.
std::vector<std::vector<graph::Index>> adj_;
//! @brief The list of the indices of the polynomial interactions as
//! std::vector<std::vector<graph::Index>>.
cimod::PolynomialKeyList<graph::Index> poly_key_list_;
//! @brief The list of the values of the polynomial interactions as
//! std::vector<FloatType>.
cimod::PolynomialValueList<FloatType> poly_value_list_;
//! @brief The list of the binaries connected by at least one interaction.
std::vector<graph::Index> active_binaries_;
//! @brief Upper bound of energy gap.
FloatType max_effective_dE_;
//! @brief Rough lower bound of energy gap.
FloatType min_effective_dE_;
///------------------------------------------------------------------------------------------------------------------------------------------------------
///----------------The following member variables are used to virtually update
///the system for k-local update----------------
///------------------------------------------------------------------------------------------------------------------------------------------------------
//! @brief The energy differences when flipping a binary, which is used to
//! implement k-local update.
std::vector<FloatType> dE_v_;
//! @brief Virtually updated binary configulations, which is used to implement
//! k-local update.
graph::Binaries binaries_v_;
//! @brief The list of virtually updated delta E's, which is used to implement
//! k-local update.
std::unordered_set<std::size_t> update_index_dE_v_;
//! @brief The list of virtually updated index of zero_count_v_, which is used
//! to implement k-local update.
std::vector<std::size_t> update_index_zero_count_v_;
//! @brief The list of virtually updated index of binaries_v_, which is used
//! to implement k-local update.
std::vector<std::size_t> update_index_binaries_v_;
//! @brief The list of virtually updated the number of variables taking the
//! zero in each interaction, which is used to implement k-local update.
std::vector<int64_t> zero_count_v_;
///------------------------------------------------------------------------------------------------------------------------------------------------------
//! @brief Sort interactions in accordance with its value and the degree of
//! interactions (ascending order).
void SortInteractions() {
std::vector<graph::Index> index(num_interactions_);
#pragma omp parallel for
for (int64_t i = 0; i < num_interactions_; ++i) {
index[i] = i;
}
auto compare_value = [this](const std::size_t i1, const std::size_t i2) {
return poly_value_list_[i1] < poly_value_list_[i2];
};
auto compare_size = [this](const std::size_t i1, const std::size_t i2) {
return poly_key_list_[i1].size() < poly_key_list_[i2].size();
};
std::stable_sort(index.begin(), index.end(), compare_size);
std::stable_sort(index.begin(), index.end(), compare_value);
cimod::PolynomialValueList<FloatType> vv = poly_value_list_;
#pragma omp parallel for
for (int64_t i = 0; i < num_interactions_; ++i) {
poly_value_list_[i] = vv[index[i]];
}
cimod::PolynomialValueList<FloatType>().swap(vv);
cimod::PolynomialKeyList<graph::Index> ii = poly_key_list_;
#pragma omp parallel for
for (int64_t i = 0; i < num_interactions_; ++i) {
poly_key_list_[i] = ii[index[i]];
}
}
//! @brief Set adjacency list. Note that the list is sorted in accordance with
//! the value of the interactions.
void SetAdj() {
adj_.clear();
adj_.resize(num_binaries);
for (int64_t i = 0; i < num_interactions_; ++i) {
for (const auto &index : poly_key_list_[i]) {
adj_[index].push_back(i);
}
}
// sort by value and key size
auto compare_size = [this](const int64_t i1, const int64_t i2) {
return poly_key_list_[i1].size() < poly_key_list_[i2].size();
};
auto compare_value = [this](const int64_t i1, const int64_t i2) {
return poly_value_list_[i1] < poly_value_list_[i2];
};
int64_t adj_size = static_cast<int64_t>(adj_.size());
#pragma omp parallel for
for (int64_t i = 0; i < adj_size; ++i) {
std::stable_sort(adj_[i].begin(), adj_[i].end(), compare_size);
std::stable_sort(adj_[i].begin(), adj_[i].end(), compare_value);
}
}
//! @brief Set zero_count_ and zero_count_v_
void ResetZeroCount() {
zero_count_.resize(num_interactions_);
zero_count_v_.resize(num_interactions_);
#pragma omp parallel for
for (int64_t i = 0; i < num_interactions_; ++i) {
int64_t zero_count = 0;
for (const auto &index : poly_key_list_[i]) {
if (binaries[index] == 0) {
zero_count++;
}
}
zero_count_[i] = zero_count;
zero_count_v_[i] = zero_count;
}
}
//! @brief Return the key and value of the absolute maximum interaction.
//! @return The key and value of the absolute maximum interaction as
//! std::pair.
std::pair<std::vector<graph::Index>, FloatType> FindMaxInteraction() const {
if (poly_key_list_.size() == 0) {
throw std::runtime_error("Interactions are empty.");
}
FloatType max_val = 0.0;
std::vector<graph::Index> max_key = {};
for (std::size_t i = 0; i < poly_key_list_.size(); ++i) {
if (std::abs(max_val) < std::abs(poly_value_list_[i])) {
max_val = poly_value_list_[i];
max_key = poly_key_list_[i];
}
}
return std::pair<std::vector<graph::Index>, FloatType>(max_key, max_val);
}
//! @brief Return the key and value of the absolute minimum interaction.
//! @return The key and value of the absolute minimum interaction as
//! std::pair.
std::pair<std::vector<graph::Index>, FloatType>
FindMinInteraction(const FloatType threshold = 0.0) const {
if (poly_key_list_.size() == 0) {
throw std::runtime_error("Interactions are empty.");
}
FloatType min_val = poly_value_list_[0];
std::vector<graph::Index> min_key = poly_key_list_[0];
for (std::size_t i = 0; i < poly_key_list_.size(); ++i) {
if (poly_value_list_[i] != 0.0 &&
std::abs(poly_value_list_[i]) < std::abs(min_val) &&
threshold < std::abs(poly_value_list_[i])) {
min_val = poly_value_list_[i];
min_key = poly_key_list_[i];
}
}
if (std::abs(min_val) <= threshold) {
throw std::runtime_error("No minimum value in interactions");
}
return std::pair<std::vector<graph::Index>, FloatType>(min_key, min_val);
}
};
//! @brief Helper function for ClassicalIsingPolynomial constructor
//! @tparam GraphType
//! @param init_binaries const graph::Binaries&. The initial binaries.
//! @param init_interaction GraphType&. The initial interactions.
template <typename GraphType>
auto make_k_local_polynomial(const graph::Binaries &init_binaries,
const GraphType &init_interaction) {
return KLocalPolynomial<GraphType>(init_binaries, init_interaction);
}
//! @brief Helper function for ClassicalIsingPolynomial constructor by using
//! nlohmann::json object
//! @tparam FloatType
//! @param init_binaries const graph::Binaries&. The initial binaries.
//! @param init_obj nlohmann::json&
auto make_k_local_polynomial(const graph::Binaries &init_binaries,
const nlohmann::json &init_obj) {
return KLocalPolynomial<graph::Polynomial<double>>(init_binaries, init_obj);
}
} // namespace system
} // namespace openjij