ros3w_formula.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 "num_collect/base/index_type.h"
#include "num_collect/logging/log_tag_view.h"
#include "num_collect/ode/concepts/problem.h"
#include "num_collect/ode/concepts/rosenbrock_equation_solver.h"
#include "num_collect/ode/embedded_solver.h"
#include "num_collect/ode/evaluation_type.h"
#include "num_collect/ode/rosenbrock/default_rosenbrock_equation_solver.h"
#include "num_collect/ode/rosenbrock/rosenbrock_formula_base.h"
 
namespace num_collect::ode::rosenbrock {
 
template <concepts::problem Problem,
    concepts::rosenbrock_equation_solver EquationSolver =
        default_rosenbrock_equation_solver_t<Problem>>
class ros3w_formula
    : public rosenbrock_formula_base<ros3w_formula<Problem, EquationSolver>,
          Problem, EquationSolver> {
public:
    using base_type =
        rosenbrock_formula_base<ros3w_formula<Problem, EquationSolver>, Problem,
            EquationSolver>;
 
    using typename base_type::equation_solver_type;
    using typename base_type::problem_type;
    using typename base_type::scalar_type;
    using typename base_type::variable_type;
 
    using base_type::base_type;
    using base_type::equation_solver;
    using base_type::problem;
 
protected:
    using base_type::coeff;
 
public:
    static constexpr index_type stages = 3;
 
    static constexpr index_type order = 3;
 
    static constexpr index_type lesser_order = 2;
 
    static constexpr auto log_tag =
        logging::log_tag_view("num_collect::ode::rosenbrock::ros3w_formula");
 
    static constexpr scalar_type a21 = coeff(6.666666666666666e-01);
    static constexpr scalar_type a31 = coeff(6.666666666666666e-01);
    static constexpr scalar_type a32 = coeff(0);
 
    static constexpr scalar_type b1 = coeff(0);
    static constexpr scalar_type b2 = a21;
    static constexpr scalar_type b3 = a31 + a32;
 
    static constexpr scalar_type g21 = coeff(3.635068368900681e-01);
    static constexpr scalar_type g31 = coeff(-8.996866791992636e-01);
    static constexpr scalar_type g32 = coeff(-1.537997822626885e-01);
    static constexpr scalar_type g = coeff(4.358665215084590e-01);
 
    static constexpr scalar_type g1 = g;
    static constexpr scalar_type g2 = g21 + g;
    static constexpr scalar_type g3 = g31 + g32 + g;
 
    static constexpr scalar_type c1 = coeff(2.500000000000000e-01);
    static constexpr scalar_type c2 = coeff(2.500000000000000e-01);
    static constexpr scalar_type c3 = coeff(5.000000000000000e-01);
 
    static constexpr scalar_type cw1 = coeff(7.467047032740110e-01);
    static constexpr scalar_type cw2 = coeff(1.144064078371002e-01);
    static constexpr scalar_type cw3 = coeff(1.388888888888889e-01);
 
    static constexpr scalar_type ce1 = c1 - cw1;
    static constexpr scalar_type ce2 = c2 - cw2;
    static constexpr scalar_type ce3 = c3 - cw3;
 
    explicit ros3w_formula(const problem_type& problem)
        : base_type(problem, g) {}
 
    void step(scalar_type time, scalar_type step_size,
        const variable_type& current, variable_type& estimate) {
        variable_type unused;
        step_embedded(time, step_size, current, estimate, unused);
    }
 
    void step_embedded(scalar_type time, scalar_type step_size,
        const variable_type& current, variable_type& estimate,
        variable_type& error) {
        equation_solver().evaluate_and_update_jacobian(
            problem(), time, step_size, current);
 
        // 1st stage
        temp_rhs_ = problem().diff_coeff();
        equation_solver().add_time_derivative_term(step_size, g1, temp_rhs_);
        equation_solver().solve(temp_rhs_, k1_);
 
        // 2nd stage
        temp_var_ = g21 * k1_;
        equation_solver().apply_jacobian(temp_var_, temp_rhs_);
        temp_rhs_ *= step_size;
        temp_var_ = current + step_size * (a21 * k1_);
        problem().evaluate_on(time + b2 * step_size, temp_var_,
            evaluation_type{.diff_coeff = true});
        temp_rhs_ += problem().diff_coeff();
        equation_solver().add_time_derivative_term(step_size, g2, temp_rhs_);
        equation_solver().solve(temp_rhs_, k2_);
 
        // 3rd stage
        temp_var_ = g31 * k1_ + g32 * k2_;
        equation_solver().apply_jacobian(temp_var_, temp_rhs_);
        temp_rhs_ *= step_size;
        temp_var_ = current + step_size * (a31 * k1_ + a32 * k2_);
        problem().evaluate_on(time + b3 * step_size, temp_var_,
            evaluation_type{.diff_coeff = true});
        temp_rhs_ += problem().diff_coeff();
        equation_solver().add_time_derivative_term(step_size, g3, temp_rhs_);
        equation_solver().solve(temp_rhs_, k3_);
 
        estimate = current + step_size * (c1 * k1_ + c2 * k2_ + c3 * k3_);
        error = step_size * (ce1 * k1_ + ce2 * k2_ + ce3 * k3_);
    }
 
private:
    variable_type k1_{};
    variable_type k2_{};
    variable_type k3_{};
 
    variable_type temp_var_{};
 
    variable_type temp_rhs_{};
};
 
template <concepts::problem Problem>
using ros3w_solver = embedded_solver<ros3w_formula<Problem>>;
 
}  // namespace num_collect::ode::rosenbrock