random_multi_quadratic_function.h

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/*
 * Copyright 2023 MusicScience37 (Kenta Kabashima)
 *
 * 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 <random>
 
#include <Eigen/Core>
 
#include "num_collect/base/index_type.h"
 
namespace num_prob_collect::opt {
 
class random_multi_quadratic_function {
public:
    using variable_type = Eigen::VectorXd;
    using value_type = double;
    using hessian_type = Eigen::MatrixXd;
 
    random_multi_quadratic_function(
        Eigen::VectorXd optimal_variable, Eigen::VectorXd coefficients)
        : optimal_variable_(std::move(optimal_variable)),
          coefficients_(std::move(coefficients)) {
        constexpr double two = 2.0;
        hessian_ = two * coefficients_.asDiagonal();
    }
 
    void evaluate_on(const Eigen::VectorXd& variable) noexcept {
        diff_ = variable - optimal_variable_;
        value_ = diff_.array().square().matrix().dot(coefficients_);
        constexpr double two = 2.0;
        grad_ = two * diff_.cwiseProduct(coefficients_);
    }
 
    [[nodiscard]] auto value() const noexcept -> const double& {
        return value_;
    }
 
    [[nodiscard]] auto gradient() const noexcept -> const Eigen::VectorXd& {
        return grad_;
    }
 
    [[nodiscard]] auto hessian() const noexcept -> const Eigen::MatrixXd& {
        return hessian_;
    }
 
    [[nodiscard]] auto optimal_variable() const noexcept
        -> const Eigen::VectorXd& {
        return optimal_variable_;
    }
 
    [[nodiscard]] auto coefficients() const noexcept -> const Eigen::VectorXd& {
        return coefficients_;
    }
 
private:
    Eigen::VectorXd optimal_variable_;
 
    Eigen::VectorXd coefficients_;
 
    Eigen::VectorXd diff_{};
 
    double value_{0.0};
 
    Eigen::VectorXd grad_{};
 
    Eigen::MatrixXd hessian_{};
};
 
class random_multi_quadratic_function_generator {
public:
    static constexpr double min_variable = -10.0;
 
    static constexpr double max_variable = 10.0;
 
    explicit random_multi_quadratic_function_generator(
        num_collect::index_type num_variables)
        : num_variables_(num_variables) {}
 
    [[nodiscard]] auto operator()() noexcept
        -> random_multi_quadratic_function {
        Eigen::VectorXd optimal_variable;
        optimal_variable.resize(num_variables_);
        std::generate(optimal_variable.begin(), optimal_variable.end(),
            [this] { return optimal_variable_dist_(generator_); });
 
        Eigen::VectorXd coefficients;
        coefficients.resize(num_variables_);
        std::generate(coefficients.begin(), coefficients.end(),
            [this] { return coeff_dist_(generator_); });
 
        return random_multi_quadratic_function{
            std::move(optimal_variable), std::move(coefficients)};
    }
 
private:
    std::mt19937
        generator_{};  // NOLINT(cert-msc32-c,cert-msc51-cpp): For reproducibility.
 
    std::uniform_real_distribution<double> coeff_dist_{0.5, 20.0};  // NOLINT
 
    std::uniform_real_distribution<double> optimal_variable_dist_{
        min_variable, max_variable};
 
    num_collect::index_type num_variables_;
};
 
}  // namespace num_prob_collect::opt