wendland_csrbf.h

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/*
 * Copyright 2024 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/real_scalar.h"
#include "num_collect/base/index_type.h"
 
namespace num_collect::rbf::rbfs {
 
template <base::concepts::real_scalar Scalar, index_type L, index_type K>
class wendland_csrbf;
 
template <base::concepts::real_scalar Scalar, index_type L>
    requires(L >= 1)
class wendland_csrbf<Scalar, L, 0> {
public:
    using scalar_type = Scalar;
 
    [[nodiscard]] static constexpr auto support_boundary() noexcept
        -> scalar_type {
        return static_cast<scalar_type>(1);
    }
 
    [[nodiscard]] auto operator()(
        const scalar_type& distance_rate) const noexcept -> scalar_type {
        using std::pow;
        if (distance_rate > static_cast<scalar_type>(1)) {
            return static_cast<scalar_type>(0);
        }
        // pow function wrongly returns double even when scalar_type is float.
        return static_cast<scalar_type>(
            pow(static_cast<scalar_type>(1) - distance_rate, L));
    }
};
 
template <base::concepts::real_scalar Scalar, index_type L>
    requires(L >= 1)
class wendland_csrbf<Scalar, L, 1> {
public:
    using scalar_type = Scalar;
 
    [[nodiscard]] static constexpr auto support_boundary() noexcept
        -> scalar_type {
        return static_cast<scalar_type>(1);
    }
 
    [[nodiscard]] auto operator()(
        const scalar_type& distance_rate) const noexcept -> scalar_type {
        using std::pow;
        if (distance_rate > static_cast<scalar_type>(1)) {
            return static_cast<scalar_type>(0);
        }
 
        static constexpr scalar_type scale_coeff = static_cast<scalar_type>(1) /
            (static_cast<scalar_type>(L + 1) * static_cast<scalar_type>(L + 2));
 
        // pow function wrongly returns double even when scalar_type is float.
        const auto pow_value = static_cast<scalar_type>(
            pow(static_cast<scalar_type>(1) - distance_rate, L + 1));
 
        static constexpr auto first_order_term_coeff =
            static_cast<scalar_type>(L + 1);
        static constexpr auto constant_term = static_cast<scalar_type>(1);
        return scale_coeff * pow_value *
            (first_order_term_coeff * distance_rate + constant_term);
    }
};
 
template <base::concepts::real_scalar Scalar, index_type L>
    requires(L >= 1)
class wendland_csrbf<Scalar, L, 2> {
public:
    using scalar_type = Scalar;
 
    [[nodiscard]] static constexpr auto support_boundary() noexcept
        -> scalar_type {
        return static_cast<scalar_type>(1);
    }
 
    [[nodiscard]] auto operator()(
        const scalar_type& distance_rate) const noexcept -> scalar_type {
        using std::pow;
        if (distance_rate > static_cast<scalar_type>(1)) {
            return static_cast<scalar_type>(0);
        }
 
        static constexpr scalar_type scale_coeff = static_cast<scalar_type>(1) /
            (static_cast<scalar_type>(L + 1) * static_cast<scalar_type>(L + 2) *
                static_cast<scalar_type>(L + 3) *
                static_cast<scalar_type>(L + 4));
 
        // pow function wrongly returns double even when scalar_type is float.
        const auto pow_value = static_cast<scalar_type>(
            pow(static_cast<scalar_type>(1) - distance_rate, L + 2));
 
        static constexpr auto second_order_term_coeff =
            static_cast<scalar_type>(L + 1) * static_cast<scalar_type>(L + 3);
        static constexpr auto first_order_term_coeff =
            static_cast<scalar_type>(3) * static_cast<scalar_type>(L + 2);
        static constexpr auto constant_term = static_cast<scalar_type>(3);
        return scale_coeff * pow_value *
            (second_order_term_coeff * distance_rate * distance_rate +
                first_order_term_coeff * distance_rate + constant_term);
    }
};
 
}  // namespace num_collect::rbf::rbfs