leap_frog_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/exception.h"
#include "num_collect/base/index_type.h"
#include "num_collect/base/precondition.h"
#include "num_collect/constants/half.h"  // IWYU pragma: keep
#include "num_collect/logging/log_tag_view.h"
#include "num_collect/logging/logging_macros.h"
#include "num_collect/ode/concepts/multi_variate_problem.h"
#include "num_collect/ode/concepts/problem.h"
#include "num_collect/ode/evaluation_type.h"
#include "num_collect/ode/formula_base.h"
#include "num_collect/ode/simple_solver.h"
 
namespace num_collect::ode::symplectic {
 
template <concepts::multi_variate_problem Problem>
class leap_frog_formula
    : public formula_base<leap_frog_formula<Problem>, Problem> {
public:
    using base_type = formula_base<leap_frog_formula<Problem>, Problem>;
 
    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::problem;
 
    static_assert(!problem_type::allowed_evaluations.mass,
        "Mass matrix is not supported.");
 
protected:
    using base_type::coeff;
 
public:
    static constexpr index_type stages = 3;
 
    static constexpr index_type order = 2;
 
    static constexpr auto log_tag = logging::log_tag_view(
        "num_collect::ode::symplectic::leap_frog_formula");
 
    void step(scalar_type time, scalar_type step_size,
        const variable_type& current, variable_type& estimate) {
        const index_type dim = current.size();
        const index_type half_dim = dim / 2;
        NUM_COLLECT_PRECONDITION(dim % 2 == 0,
            "This formula requires vectors with even dimensions.");
 
        estimate = current;
 
        constexpr auto evaluations = evaluation_type{.diff_coeff = true};
 
        problem().evaluate_on(time, estimate, evaluations);
        estimate.head(half_dim) += step_size * constants::half<scalar_type> *
            problem().diff_coeff().head(half_dim);
 
        problem().evaluate_on(time, estimate, evaluations);
        estimate.tail(half_dim) +=
            step_size * problem().diff_coeff().tail(half_dim);
 
        problem().evaluate_on(time, estimate, evaluations);
        estimate.head(half_dim) += step_size * constants::half<scalar_type> *
            problem().diff_coeff().head(half_dim);
    }
};
 
template <concepts::problem Problem>
using leap_frog_solver = simple_solver<leap_frog_formula<Problem>>;
 
}  // namespace num_collect::ode::symplectic