explicit_regularized_solver_base.h

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/*
 * Copyright 2021 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 <cmath>
 
#include "num_collect/base/concepts/dense_matrix.h"
#include "num_collect/logging/log_tag_view.h"
#include "num_collect/regularization/regularized_solver_base.h"
 
namespace num_collect::regularization {
 
template <typename Derived, base::concepts::dense_matrix Data>
class explicit_regularized_solver_base
    : public regularized_solver_base<Derived, Data> {
public:
    using typename regularized_solver_base<Derived, Data>::data_type;
    using typename regularized_solver_base<Derived, Data>::scalar_type;
    using regularized_solver_base<Derived, Data>::data_size;
 
    void solve(const scalar_type& param, data_type& solution) const {
        return derived().solve(param, solution);
    }
 
    [[nodiscard]] auto residual_norm(const scalar_type& param) const
        -> scalar_type {
        return derived().residual_norm(param);
    }
 
    [[nodiscard]] auto regularization_term(const scalar_type& param) const
        -> scalar_type {
        return derived().regularization_term(param);
    }
 
    [[nodiscard]] auto first_derivative_of_residual_norm(
        const scalar_type& param) const -> scalar_type {
        return derived().first_derivative_of_residual_norm(param);
    }
 
    [[nodiscard]] auto first_derivative_of_regularization_term(
        const scalar_type& param) const -> scalar_type {
        return derived().first_derivative_of_regularization_term(param);
    }
 
    [[nodiscard]] auto second_derivative_of_residual_norm(
        const scalar_type& param) const -> scalar_type {
        return derived().second_derivative_of_residual_norm(param);
    }
 
    [[nodiscard]] auto second_derivative_of_regularization_term(
        const scalar_type& param) const -> scalar_type {
        return derived().second_derivative_of_regularization_term(param);
    }
 
    [[nodiscard]] auto sum_of_filter_factor(const scalar_type& param) const
        -> scalar_type {
        return derived().sum_of_filter_factor(param);
    }
 
    [[nodiscard]] auto l_curve_curvature(const scalar_type& param) const {
        const scalar_type res = residual_norm(param);
        const scalar_type reg = regularization_term(param);
        const scalar_type res1 = first_derivative_of_residual_norm(param);
        const scalar_type res2 = second_derivative_of_residual_norm(param);
        const scalar_type reg1 = first_derivative_of_regularization_term(param);
        const scalar_type reg2 =
            second_derivative_of_regularization_term(param);
 
        const scalar_type log_res1 = res1 / res;
        const scalar_type log_reg1 = reg1 / reg;
        const scalar_type log_res2 = (res2 * res - res1 * res1) / (res * res);
        const scalar_type log_reg2 = (reg2 * reg - reg1 * reg1) / (reg * reg);
 
        using std::pow;
        return (log_res1 * log_reg2 - log_res2 * log_reg1) /
            pow(log_res1 * log_res1 + log_reg1 * log_reg1,
                static_cast<scalar_type>(1.5));  // NOLINT
    }
 
    [[nodiscard]] auto gcv(const scalar_type& param) const -> scalar_type {
        const scalar_type den =
            static_cast<scalar_type>(data_size()) - sum_of_filter_factor(param);
        return residual_norm(param) / (den * den);
    }
 
protected:
    explicit explicit_regularized_solver_base(logging::log_tag_view tag)
        : regularized_solver_base<Derived, Data>(tag) {}
 
    using regularized_solver_base<Derived, Data>::derived;
};
 
}  // namespace num_collect::regularization