compute_kernel_matrix.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 <cstddef>
#include <type_traits>  // IWYU pragma: keep
#include <vector>
 
#include <Eigen/SparseCore>
 
#include "num_collect/base/concepts/dense_matrix.h"
#include "num_collect/base/concepts/sparse_matrix_of.h"
#include "num_collect/base/index_type.h"
#include "num_collect/constants/zero.h"  // IWYU pragma: keep
#include "num_collect/rbf/concepts/csrbf.h"
#include "num_collect/rbf/concepts/distance_function.h"
#include "num_collect/rbf/concepts/length_parameter_calculator.h"
#include "num_collect/rbf/concepts/rbf.h"
#include "num_collect/util/assert.h"
#include "num_collect/util/safe_cast.h"
 
namespace num_collect::rbf {
 
template <concepts::distance_function DistanceFunction, concepts::rbf RBF,
    concepts::length_parameter_calculator LengthParameterCalculator,
    base::concepts::dense_matrix KernelMatrix>
    requires std::is_same_v<
                 typename LengthParameterCalculator::distance_function_type,
                 DistanceFunction> &&
    std::is_same_v<typename DistanceFunction::value_type,
        typename RBF::scalar_type> &&
    std::is_same_v<typename DistanceFunction::value_type,
        typename KernelMatrix::Scalar> &&
    LengthParameterCalculator::uses_global_length_parameter
inline void compute_kernel_matrix(const DistanceFunction& distance_function,
    const RBF& rbf, LengthParameterCalculator& length_parameter_calculator,
    const std::vector<typename DistanceFunction::variable_type>& variables,
    KernelMatrix& kernel_matrix) {
    using scalar_type = typename KernelMatrix::Scalar;
 
    length_parameter_calculator.compute(variables, distance_function);
 
    const scalar_type length_parameter =
        length_parameter_calculator.length_parameter_at(
            static_cast<index_type>(0));
    NUM_COLLECT_ASSERT(length_parameter > static_cast<scalar_type>(0));
 
    const scalar_type diagonal_coeff = rbf(constants::zero<scalar_type>);
 
    const std::size_t num_variables = variables.size();
    kernel_matrix.resize(static_cast<index_type>(num_variables),
        static_cast<index_type>(num_variables));
 
    for (std::size_t i = 0; i < num_variables; ++i) {
        kernel_matrix(static_cast<index_type>(i), static_cast<index_type>(i)) =
            diagonal_coeff;
        for (std::size_t j = i + 1; j < num_variables; ++j) {
            const scalar_type value =
                rbf(distance_function(variables[i], variables[j]) /
                    length_parameter);
            kernel_matrix(
                static_cast<index_type>(i), static_cast<index_type>(j)) = value;
            kernel_matrix(
                static_cast<index_type>(j), static_cast<index_type>(i)) = value;
        }
    }
}
 
template <concepts::distance_function DistanceFunction, concepts::rbf RBF,
    concepts::length_parameter_calculator LengthParameterCalculator,
    base::concepts::dense_matrix KernelMatrix>
    requires std::is_same_v<
                 typename LengthParameterCalculator::distance_function_type,
                 DistanceFunction> &&
    std::is_same_v<typename DistanceFunction::value_type,
        typename RBF::scalar_type> &&
    std::is_same_v<typename DistanceFunction::value_type,
        typename KernelMatrix::Scalar> &&
    (!LengthParameterCalculator::uses_global_length_parameter)
inline void compute_kernel_matrix(const DistanceFunction& distance_function,
    const RBF& rbf, LengthParameterCalculator& length_parameter_calculator,
    const std::vector<typename DistanceFunction::variable_type>& variables,
    KernelMatrix& kernel_matrix) {
    using scalar_type = typename KernelMatrix::Scalar;
 
    length_parameter_calculator.compute(variables, distance_function);
 
    const std::size_t num_variables = variables.size();
    kernel_matrix.resize(static_cast<index_type>(num_variables),
        static_cast<index_type>(num_variables));
 
    for (std::size_t j = 0; j < num_variables; ++j) {
        const scalar_type length_parameter =
            length_parameter_calculator.length_parameter_at(
                static_cast<index_type>(j));
        NUM_COLLECT_ASSERT(length_parameter > static_cast<scalar_type>(0));
 
        for (std::size_t i = 0; i < num_variables; ++i) {
            const scalar_type value =
                rbf(distance_function(variables[i], variables[j]) /
                    length_parameter);
            kernel_matrix(
                static_cast<index_type>(i), static_cast<index_type>(j)) = value;
        }
    }
}
 
template <concepts::distance_function DistanceFunction, concepts::csrbf RBF,
    concepts::length_parameter_calculator LengthParameterCalculator,
    base::concepts::sparse_matrix_of<typename DistanceFunction::value_type>
        KernelMatrix>
    requires std::is_same_v<
                 typename LengthParameterCalculator::distance_function_type,
                 DistanceFunction> &&
    std::is_same_v<typename DistanceFunction::value_type,
        typename RBF::scalar_type> &&
    std::is_same_v<typename DistanceFunction::value_type,
        typename KernelMatrix::Scalar>
inline void compute_kernel_matrix(const DistanceFunction& distance_function,
    const RBF& rbf, LengthParameterCalculator& length_parameter_calculator,
    const std::vector<typename DistanceFunction::variable_type>& variables,
    KernelMatrix& kernel_matrix) {
    using scalar_type = typename KernelMatrix::Scalar;
 
    length_parameter_calculator.compute(variables, distance_function);
 
    const auto num_variables = util::safe_cast<int>(variables.size());
    kernel_matrix.resize(num_variables, num_variables);
 
    const scalar_type support_boundary = RBF::support_boundary();
 
    std::vector<
        Eigen::Triplet<scalar_type, typename KernelMatrix::StorageIndex>>
        triplets;
    for (int j = 0; j < num_variables; ++j) {
        const scalar_type length_parameter =
            length_parameter_calculator.length_parameter_at(j);
        NUM_COLLECT_ASSERT(length_parameter > static_cast<scalar_type>(0));
 
        for (int i = 0; i < num_variables; ++i) {
            const scalar_type distance_rate =
                distance_function(variables[static_cast<std::size_t>(i)],
                    variables[static_cast<std::size_t>(j)]) /
                length_parameter;
            if (distance_rate >= support_boundary) {
                continue;
            }
            const scalar_type value = rbf(distance_rate);
            triplets.emplace_back(i, j, value);
        }
    }
    kernel_matrix.setFromTriplets(triplets.begin(), triplets.end());
}
 
}  // namespace num_collect::rbf