spline_evaluator_nd.hpp

// Copyright (C) The DDC development team, see COPYRIGHT.md file
//
// SPDX-License-Identifier: MIT
 
#pragma once
 
#include <array>
#include <cstddef>
#include <tuple>
#include <type_traits>
#include <utility>
 
#include <ddc/ddc.hpp>
 
#include <Kokkos_Core.hpp>
 
#include "deriv.hpp"
#include "integrals.hpp"
#include "periodic_extrapolation_rule.hpp"
 
namespace ddc {
 
/**
 * @brief A class to evaluate, differentiate or integrate a spline function of arbitrary dimension.
 *
 * A class which contains an operator () which can be used to evaluate, differentiate or integrate a spline function of arbitrary dimension.
 *
 * @tparam Args... The template parameters of the evaluator:
 * - ExecSpace The Kokkos execution space on which the spline evaluation is performed.
 * - MemorySpace The Kokkos memory space on which the data (spline coefficients and evaluation) is stored.
 * - BSplines A TypeSeq containing the N discrete dimensions representing the B-splines along the dimensions of interest.
 * - EvaluationDDim A TypeSeq containing the discrete dimensions on which evaluation points are defined.
 * - ExtrapolationRule A TypeSeq containing the lower and upper extrapolation rules along each dimension of interest.
 */
template <
        class ExecSpace,
        class MemorySpace,
        class BSplines,
        class EvaluationDDim,
        class ExtrapolationRule>
class SplineEvaluatorND;
 
template <
        class ExecSpace,
        class MemorySpace,
        class... BSplines,
        class... EvaluationDDim,
        class... ExtrapolationRule>
class SplineEvaluatorND<
        ExecSpace,
        MemorySpace,
        detail::TypeSeq<BSplines...>,
        detail::TypeSeq<EvaluationDDim...>,
        detail::TypeSeq<ExtrapolationRule...>>
{
private:
    static constexpr std::size_t dimension = sizeof...(BSplines);
 
    using bsplines_ts = detail::TypeSeq<BSplines...>;
    // A value that can be used to do a pack expansion over (0, 1, ..., Dimension)
    template <class BSpline>
    static constexpr std::size_t s_idx = ddc::type_seq_rank_v<BSpline, bsplines_ts>;
 
    using evaluation_ddim_ts = detail::TypeSeq<EvaluationDDim...>;
    using lower_extrap_rule_ts = detail::TypeSeq<
            ddc::type_seq_element_t<2 * s_idx<BSplines>, detail::TypeSeq<ExtrapolationRule...>>...>;
    using upper_extrap_rule_ts = detail::TypeSeq<ddc::type_seq_element_t<
            2 * s_idx<BSplines> + 1,
            detail::TypeSeq<ExtrapolationRule...>>...>;
 
public:
    /// @brief The type of the Ith evaluation continuous dimension used by this class.
    /// @tparam I the requested dimension
    template <std::size_t I>
    using continuous_dimension_type
            = ddc::type_seq_element_t<I, bsplines_ts>::continuous_dimension_type;
 
    /// @brief The type of the Kokkos execution space used by this class.
    using exec_space = ExecSpace;
 
    /// @brief The type of the Kokkos memory space used by this class.
    using memory_space = MemorySpace;
 
    /// @brief The type of the Ith discrete dimension of interest used by this class.
    template <std::size_t I>
    using evaluation_discrete_dimension_type = ddc::type_seq_element_t<I, evaluation_ddim_ts>;
 
    /// @brief The discrete dimension representing the B-splines along Ith dimension.
    template <std::size_t I>
    using bsplines_type = ddc::type_seq_element_t<I, bsplines_ts>;
 
    /**
     * @brief The type of the domain for the 1D, 2D, ... or ND evaluation mesh along specified dimensions used by this class.
     *
     * @tparam Dims the required dimensions, 0 indexed
     */
    template <std::size_t... Dims>
    using evaluation_domain_type = ddc::DiscreteDomain<evaluation_discrete_dimension_type<Dims>...>;
 
    /**
     * @brief The type of the whole domain representing evaluation points.
     *
     * @tparam The batched discrete domain on which the interpolation points are defined.
     */
    template <concepts::discrete_domain BatchedInterpolationDDom>
    using batched_evaluation_domain_type = BatchedInterpolationDDom;
 
    /**
     * @brief The type of the 1D, 2D, ... or ND spline domain corresponding to the specified dimensions of interest.
     *
     * @tparam Dims the required dimensions, 0 indexed
     */
    template <std::size_t... Dims>
    using spline_domain_type = ddc::DiscreteDomain<bsplines_type<Dims>...>;
 
    /**
     * @brief The type of the batch domain (obtained by removing the dimensions of interest
     * from the whole domain).
     *
     * @tparam The batched discrete domain on which the interpolation points are defined.
     */
    template <concepts::discrete_domain BatchedInterpolationDDom>
    using batch_domain_type
            = ddc::detail::convert_type_seq_to_discrete_domain_t<ddc::type_seq_remove_t<
                    ddc::to_type_seq_t<BatchedInterpolationDDom>,
                    evaluation_ddim_ts>>;
 
    /**
     * @brief The type of the whole spline domain (cartesian product of ND spline domain
     * and batch domain) preserving the underlying memory layout (order of dimensions).
     *
     * @tparam The batched discrete domain on which the interpolation points are defined.
     */
    template <concepts::discrete_domain BatchedInterpolationDDom>
    using batched_spline_domain_type
            = ddc::detail::convert_type_seq_to_discrete_domain_t<ddc::type_seq_replace_t<
                    ddc::to_type_seq_t<BatchedInterpolationDDom>,
                    evaluation_ddim_ts,
                    bsplines_ts>>;
 
    /// @brief The type of the extrapolation rule at the lower boundary along the Ith dimension.
    template <std::size_t I>
    using lower_extrapolation_rule_type = ddc::type_seq_element_t<I, lower_extrap_rule_ts>;
 
    /// @brief The type of the extrapolation rule at the upper boundary along the Ith dimension.
    template <std::size_t I>
    using upper_extrapolation_rule_type = ddc::type_seq_element_t<I, upper_extrap_rule_ts>;
 
private:
    cexa::tuple<ddc::type_seq_element_t<s_idx<BSplines>, lower_extrap_rule_ts>...>
            m_lower_extrap_rules;
    cexa::tuple<ddc::type_seq_element_t<s_idx<BSplines>, upper_extrap_rule_ts>...>
            m_upper_extrap_rules;
 
    /**
     * @brief Build a SplineEvaluatorND acting on batched_spline_domain.
     *
     * @param extrap_rules The extrapolation rules at the lower then upper boundary, for each dimension.
     */
    explicit SplineEvaluatorND(cexa::tuple<ExtrapolationRule...> const& extrap_rules)
        : m_lower_extrap_rules(cexa::get<2 * s_idx<BSplines>>(extrap_rules)...)
        , m_upper_extrap_rules(cexa::get<2 * s_idx<BSplines> + 1>(extrap_rules)...)
    {
    }
 
public:
    static_assert(
            sizeof...(BSplines) == dimension,
            "Number of BSpline dims should be equal to the dimension");
    static_assert(
            sizeof...(EvaluationDDim) == dimension,
            "Number of evaluation dims should be equal to the dimensions");
    static_assert(
            ddc::type_seq_size_v<lower_extrap_rule_ts> == dimension,
            "Number of lower extrapolation rules should be equal to the dimension");
    static_assert(
            ddc::type_seq_size_v<upper_extrap_rule_ts> == dimension,
            "Number of upper extrapolation rules should be equal to the dimension");
 
    static_assert(
            ((std::is_same_v<
                      ddc::type_seq_element_t<s_idx<BSplines>, lower_extrap_rule_ts>,
                      ddc::PeriodicExtrapolationRule<typename BSplines::continuous_dimension_type>>
                      == BSplines::is_periodic()
              && std::is_same_v<
                         ddc::type_seq_element_t<s_idx<BSplines>, upper_extrap_rule_ts>,
                         ddc::PeriodicExtrapolationRule<
                                 typename BSplines::continuous_dimension_type>>
                         == BSplines::is_periodic())
             && ...),
            "PeriodicExtrapolationRule has to be used if and only if dimension is periodic");
    static_assert(
            (std::is_invocable_r_v<
                     double,
                     ddc::type_seq_element_t<s_idx<BSplines>, lower_extrap_rule_ts>,
                     ddc::Coordinate<typename BSplines::continuous_dimension_type...>,
                     ddc::ChunkSpan<
                             double const,
                             ddc::DiscreteDomain<BSplines...>,
                             Kokkos::layout_right,
                             memory_space>>
             && ...),
            "LowerExtrapolationRule::operator() has to be callable "
            "with usual arguments.");
    static_assert(
            (std::is_invocable_r_v<
                     double,
                     ddc::type_seq_element_t<s_idx<BSplines>, upper_extrap_rule_ts>,
                     ddc::Coordinate<typename BSplines::continuous_dimension_type...>,
                     ddc::ChunkSpan<
                             double const,
                             ddc::DiscreteDomain<BSplines...>,
                             Kokkos::layout_right,
                             memory_space>>
             && ...),
            "UpperExtrapolationRule::operator() has to be callable "
            "with usual arguments.");
 
    /**
     * @brief Build a SplineEvaluatorND acting on batched_spline_domain.
     *
     * @param extrap_rules The extrapolation rules at the lower then upper boundary, for each dimension.
     *
     * @see NullExtrapolationRule ConstantExtrapolationRule PeriodicExtrapolationRule
     */
    explicit SplineEvaluatorND(ExtrapolationRule const&... extrap_rules)
        : SplineEvaluatorND(cexa::make_tuple(extrap_rules...))
    {
    }
 
    /**
     * @brief Copy-constructs.
     *
     * @param x A reference to another SplineEvaluator.
     */
    SplineEvaluatorND(SplineEvaluatorND const& x) = default;
 
    /**
     * @brief Move-constructs.
     *
     * @param x An rvalue to another SplineEvaluator.
     */
    SplineEvaluatorND(SplineEvaluatorND&& x) = default;
 
    /// @brief Destructs.
    ~SplineEvaluatorND() = default;
 
    /**
     * @brief Copy-assigns.
     *
     * @param x A reference to another SplineEvaluator.
     * @return A reference to this object.
     */
    SplineEvaluatorND& operator=(SplineEvaluatorND const& x) = default;
 
    /**
     * @brief Move-assigns.
     *
     * @param x An rvalue to another SplineEvaluator.
     * @return A reference to this object.
     */
    SplineEvaluatorND& operator=(SplineEvaluatorND&& x) = default;
 
    /**
     * @brief Get the lower extrapolation rule along the Ith dimension.
     *
     * Extrapolation rules are functors used to define the behavior of the SplineEvaluator out of the domain where the break points of the B-splines are defined.
     *
     * @return The lower extrapolation rule along the Ith dimension.
     *
     * @see NullExtrapolationRule ConstantExtrapolationRule PeriodicExtrapolationRule
     */
    template <std::size_t I>
    auto lower_extrapolation_rule() const
    {
        return cexa::get<I>(m_lower_extrap_rules);
    }
 
    /**
     * @brief Get the upper extrapolation rule along the Ith dimension.
     *
     * Extrapolation rules are functors used to define the behavior of the SplineEvaluator out of the domain where the break points of the B-splines are defined.
     *
     * @return The upper extrapolation rule along the Ith dimension.
     *
     * @see NullExtrapolationRule ConstantExtrapolationRule PeriodicExtrapolationRule
     */
    template <std::size_t I>
    auto upper_extrapolation_rule() const
    {
        return cexa::get<I>(m_upper_extrap_rules);
    }
 
    /**
     * @brief Evaluate ND spline function (described by its spline coefficients) at a given coordinate.
     *
     * The spline coefficients represent a ND spline function defined on a B-splines (basis splines). They can be obtained via various methods, such as using a SplineBuilderND.
     *
     * Remark: calling SplineBuilderND then SplineEvaluatorND corresponds to a ND spline interpolation.
     *
     * @param coord_eval The coordinate where the spline is evaluated. Note that only the components along the dimensions of interest are used.
     * @param spline_coef A ChunkSpan storing the ND spline coefficients.
     *
     * @return The value of the spline function at the desired coordinate.
     */
    template <class Layout, class... CoordsDims>
    KOKKOS_FUNCTION double operator()(
            ddc::Coordinate<CoordsDims...> const& coord_eval,
            ddc::ChunkSpan<
                    double const,
                    ddc::DiscreteDomain<BSplines...>,
                    Layout,
                    memory_space> const spline_coef) const
    {
        return eval(coord_eval, spline_coef);
    }
 
    /**
     * @brief Evaluate ND spline function (described by its spline coefficients) on a mesh.
     *
     * The spline coefficients represent a ND spline function defined on a cartesian product of batch_domain and B-splines
     * (basis splines). They can be obtained via various methods, such as using a SplineBuilderND.
     *
     * This is not a nD evaluation. This is a batched ND evaluation. This means that for each slice of coordinates
     * identified by a batch_domain_type::discrete_element_type, the evaluation is performed with the ND set of
     * spline coefficients identified by the same batch_domain_type::discrete_element_type.
     *
     * Remark: calling SplineBuilderND then SplineEvaluatorND corresponds to a ND spline interpolation.
     *
     * @param[out] spline_eval The values of the ND spline function at the desired coordinates. For practical reasons those are
     * stored in a ChunkSpan defined on a batched_evaluation_domain_type.
     * @param[in] coords_eval The coordinates where the spline is evaluated. Those are
     * stored in a ChunkSpan defined on a batched_evaluation_domain_type. Note that the coordinates of the
     * points represented by this domain are unused and irrelevant (but the points themselves (DiscreteElement) are used to select
     * the set of ND spline coefficients retained to perform the evaluation).
     * @param[in] spline_coef A ChunkSpan storing the ND spline coefficients.
     */
    template <
            class Layout1,
            class Layout2,
            class Layout3,
            class BatchedInterpolationDDom,
            class... CoordsDims>
    void operator()(
            ddc::ChunkSpan<double, BatchedInterpolationDDom, Layout1, memory_space> const
                    spline_eval,
            ddc::ChunkSpan<
                    ddc::Coordinate<CoordsDims...> const,
                    BatchedInterpolationDDom,
                    Layout2,
                    memory_space> const coords_eval,
            ddc::ChunkSpan<
                    double const,
                    batched_spline_domain_type<BatchedInterpolationDDom>,
                    Layout3,
                    memory_space> const spline_coef) const
    {
        using evaluation_domain_type = ddc::DiscreteDomain<EvaluationDDim...>;
        evaluation_domain_type const evaluation_domain(spline_eval.domain());
 
        batch_domain_type<BatchedInterpolationDDom> const batch_domain(coords_eval.domain());
 
        ddc::parallel_for_each(
                "ddc_splines_evaluate_Nd",
                exec_space(),
                batch_domain,
                KOKKOS_CLASS_LAMBDA(
                        batch_domain_type<BatchedInterpolationDDom>::discrete_element_type const
                                j) {
                    auto const spline_eval_ND = spline_eval[j];
                    auto const coords_eval_ND = coords_eval[j];
                    auto const spline_coef_ND = spline_coef[j];
                    ddc::device_for_each(
                            evaluation_domain,
                            [&](evaluation_domain_type::discrete_element_type const i) {
                                spline_eval_ND(i) = eval(coords_eval_ND(i), spline_coef_ND);
                            });
                });
    }
 
    /**
     * @brief Evaluate ND spline function (described by its spline coefficients) on a mesh.
     *
     * The spline coefficients represent a ND spline function defined on a cartesian product of batch_domain and B-splines
     * (basis splines). They can be obtained via various methods, such as using a SplineBuilderND.
     *
     * This is not a multidimensional evaluation. This is a batched ND evaluation.
     * This means that for each slice of spline_eval the evaluation is performed with
     * the ND set of spline coefficients identified by the same batch_domain_type::discrete_element_type.
     *
     * Remark: calling SplineBuilderND then SplineEvaluatorND corresponds to a ND spline interpolation.
     *
     * @param[out] spline_eval The values of the ND spline function at their coordinates.
     * @param[in] spline_coef A ChunkSpan storing the ND spline coefficients.
     */
    template <class Layout1, class Layout2, class BatchedInterpolationDDom>
    void operator()(
            ddc::ChunkSpan<double, BatchedInterpolationDDom, Layout1, memory_space> const
                    spline_eval,
            ddc::ChunkSpan<
                    double const,
                    batched_spline_domain_type<BatchedInterpolationDDom>,
                    Layout2,
                    memory_space> const spline_coef) const
    {
        using evaluation_domain_type = ddc::DiscreteDomain<EvaluationDDim...>;
        evaluation_domain_type evaluation_domain(spline_eval.domain());
 
        batch_domain_type<BatchedInterpolationDDom> const batch_domain(spline_eval.domain());
 
        ddc::parallel_for_each(
                "ddc_splines_evaluate_Nd",
                exec_space(),
                batch_domain,
                KOKKOS_CLASS_LAMBDA(
                        batch_domain_type<BatchedInterpolationDDom>::discrete_element_type const
                                j) {
                    auto const spline_eval_ND = spline_eval[j];
                    auto const spline_coef_ND = spline_coef[j];
 
                    ddc::device_for_each(
                            evaluation_domain,
                            [&](evaluation_domain_type::discrete_element_type const i) {
                                ddc::Coordinate<typename BSplines::continuous_dimension_type...>
                                        coord_eval_ND(ddc::coordinate(i));
                                spline_eval_ND(i) = eval(coord_eval_ND, spline_coef_ND);
                            });
                });
    }
 
    /**
     * @brief Differentiate ND spline function (described by its spline coefficients) at a given coordinate along specified dimensions of interest.
     *
     * The spline coefficients represent a ND spline function defined on a B-splines (basis splines). They can be
     * obtained via various methods, such as using a SplineBuilderND.
     *
     * @param deriv_order A DiscreteElement containing the orders of derivation for each of the dimensions of interest.
     * If one of the dimensions is not present, its corresponding order of derivation is considered to be 0.
     * @param coord_eval The coordinate where the spline is differentiated. Note that only the components along the dimensions of interest are used.
     * @param spline_coef A ChunkSpan storing the ND spline coefficients.
     *
     * @return The derivative of the spline function at the desired coordinate.
     */
    template <class DElem, class Layout, class... CoordsDims>
    KOKKOS_FUNCTION double deriv(
            DElem const& deriv_order,
            ddc::Coordinate<CoordsDims...> const& coord_eval,
            ddc::ChunkSpan<
                    double const,
                    ddc::DiscreteDomain<BSplines...>,
                    Layout,
                    memory_space> const spline_coef) const
    {
        static_assert(ddc::is_discrete_element_v<DElem>);
 
        return eval_no_bc(deriv_order, coord_eval, spline_coef);
    }
 
 
    /**
     * @brief Differentiate spline function (described by its spline coefficients) on a mesh along specified dimensions of interest.
     *
     * The spline coefficients represent a ND spline function defined on a cartesian product of batch_domain and B-splines
     * (basis splines). They can be obtained via various methods, such as using a SplineBuilderND.
     *
     * This is not a nD evaluation. This is a batched ND differentiation.
     * This means that for each slice of coordinates identified by a batch_domain_type::discrete_element_type,
     * the differentiation is performed with the ND set of spline coefficients identified by the same batch_domain_type::discrete_element_type.
     *
     * @param[in] deriv_order A DiscreteElement containing the orders of derivation for each of the dimensions of interest.
     * If one of the dimensions is not present, its corresponding order of derivation is considered to be 0.
     * @param[out] spline_eval The derivatives of the ND spline function at the desired coordinates. For practical reasons those are
     * stored in a ChunkSpan defined on a batched_evaluation_domain_type.
     * @param[in] coords_eval The coordinates where the spline is differentiated. Those are
     * stored in a ChunkSpan defined on a batched_evaluation_domain_type. Note that the coordinates of the
     * points represented by this domain are unused and irrelevant (but the points themselves (DiscreteElement) are used to select
     * the set of ND spline coefficients retained to perform the evaluation).
     * @param[in] spline_coef A ChunkSpan storing the ND spline coefficients.
     */
    template <
            class DElem,
            class Layout1,
            class Layout2,
            class Layout3,
            class BatchedInterpolationDDom,
            class... CoordsDims>
    void deriv(
            DElem const& deriv_order,
            ddc::ChunkSpan<double, BatchedInterpolationDDom, Layout1, memory_space> const
                    spline_eval,
            ddc::ChunkSpan<
                    ddc::Coordinate<CoordsDims...> const,
                    BatchedInterpolationDDom,
                    Layout2,
                    memory_space> const coords_eval,
            ddc::ChunkSpan<
                    double const,
                    batched_spline_domain_type<BatchedInterpolationDDom>,
                    Layout3,
                    memory_space> const spline_coef) const
    {
        static_assert(ddc::is_discrete_element_v<DElem>);
 
        using evaluation_domain_type = ddc::DiscreteDomain<EvaluationDDim...>;
        evaluation_domain_type const evaluation_domain(spline_eval.domain());
 
        batch_domain_type<BatchedInterpolationDDom> const batch_domain(spline_eval.domain());
 
        ddc::parallel_for_each(
                "ddc_splines_cross_differentiate_Nd",
                exec_space(),
                batch_domain,
                KOKKOS_CLASS_LAMBDA(
                        batch_domain_type<BatchedInterpolationDDom>::discrete_element_type const
                                j) {
                    auto const spline_eval_ND = spline_eval[j];
                    auto const coords_eval_ND = coords_eval[j];
                    auto const spline_coef_ND = spline_coef[j];
                    ddc::device_for_each(
                            evaluation_domain,
                            [&](evaluation_domain_type::discrete_element_type const i) {
                                spline_eval_ND(i) = eval_no_bc(
                                        deriv_order,
                                        coords_eval_ND(i),
                                        spline_coef_ND);
                            });
                });
    }
 
    /**
     * @brief Differentiate spline function (described by its spline coefficients) on a mesh along specified dimensions of interest.
     *
     * The spline coefficients represent a ND spline function defined on a cartesian product of batch_domain and B-splines
     * (basis splines). They can be obtained via various methods, such as using a SplineBuilderND.
     *
     * This is not a multidimensional evaluation. This is a batched ND evaluation.
     * This means that for each slice of spline_eval the evaluation is performed with
     * the ND set of spline coefficients identified by the same batch_domain_type::discrete_element_type.
     *
     * @param[in] deriv_order A DiscreteElement containing the orders of derivation for each of the dimensions of interest.
     * If one of the dimensions is not present, its corresponding order of derivation is considered to be 0.
     * @param[out] spline_eval The derivatives of the ND spline function at the desired coordinates.
     * @param[in] spline_coef A ChunkSpan storing the ND spline coefficients.
     */
    template <class DElem, class Layout1, class Layout2, class BatchedInterpolationDDom>
    void deriv(
            DElem const& deriv_order,
            ddc::ChunkSpan<double, BatchedInterpolationDDom, Layout1, memory_space> const
                    spline_eval,
            ddc::ChunkSpan<
                    double const,
                    batched_spline_domain_type<BatchedInterpolationDDom>,
                    Layout2,
                    memory_space> const spline_coef) const
    {
        static_assert(is_discrete_element_v<DElem>);
 
        using evaluation_domain_type = ddc::DiscreteDomain<EvaluationDDim...>;
        evaluation_domain_type evaluation_domain(spline_eval.domain());
 
        batch_domain_type<BatchedInterpolationDDom> const batch_domain(spline_eval.domain());
 
        ddc::parallel_for_each(
                "ddc_splines_cross_differentiate_Nd",
                exec_space(),
                batch_domain,
                KOKKOS_CLASS_LAMBDA(
                        batch_domain_type<BatchedInterpolationDDom>::discrete_element_type const
                                j) {
                    auto const spline_eval_ND = spline_eval[j];
                    auto const spline_coef_ND = spline_coef[j];
                    ddc::device_for_each(
                            evaluation_domain,
                            [&](evaluation_domain_type::discrete_element_type const i) {
                                ddc::Coordinate<typename BSplines::continuous_dimension_type...>
                                        coord_eval_ND(ddc::coordinate(i));
                                spline_eval_ND(i)
                                        = eval_no_bc(deriv_order, coord_eval_ND, spline_coef_ND);
                            });
                });
    }
 
    /** @brief Perform batched ND integrations of a spline function (described by its spline coefficients) along the dimensions of interest and store results on a subdomain of batch_domain.
     *
     * The spline coefficients represent a ND spline function defined on a B-splines (basis splines). They can be obtained via various methods, such as using a SplineBuilderND.
     *
     * This is not a nD integration. This is a batched ND integration.
     * This means that for each element of integrals, the integration is performed with the ND set of
     * spline coefficients identified by the same DiscreteElement.
     *
     * @param[out] integrals The integrals of the ND spline function on the subdomain of batch_domain. For practical reasons those are
     * stored in a ChunkSpan defined on a batch_domain_type. Note that the coordinates of the
     * points represented by this domain are unused and irrelevant.
     * @param[in] spline_coef A ChunkSpan storing the ND spline coefficients.
     */
    template <class Layout1, class Layout2, class BatchedDDom, class BatchedSplineDDom>
    void integrate(
            ddc::ChunkSpan<double, BatchedDDom, Layout1, memory_space> const integrals,
            ddc::ChunkSpan<double const, BatchedSplineDDom, Layout2, memory_space> const
                    spline_coef) const
    {
        static_assert(
                ddc::type_seq_contains_v<bsplines_ts, to_type_seq_t<BatchedSplineDDom>>,
                "The spline coefficients domain must contain the bsplines dimensions");
        static_assert(
                std::is_same_v<batch_domain_type<BatchedDDom>, BatchedDDom>,
                "The integrals domain must only contain the batch dimensions");
 
        using bsplines_domain_type = ddc::DiscreteDomain<BSplines...>;
        bsplines_domain_type const bsplines_domain(spline_coef.domain());
 
        batch_domain_type<BatchedDDom> const batch_domain(integrals.domain());
        auto values_alloc = cexa::make_tuple(
                ddc::
                        Chunk(ddc::DiscreteDomain<BSplines>(spline_coef.domain()),
                              ddc::KokkosAllocator<double, memory_space>())...);
        auto values = cexa::make_tuple(cexa::get<s_idx<BSplines>>(values_alloc).span_view()...);
        (ddc::integrals(exec_space(), cexa::get<s_idx<BSplines>>(values)), ...);
 
        ddc::parallel_for_each(
                "ddc_splines_integrate_bsplines",
                exec_space(),
                batch_domain,
                KOKKOS_LAMBDA(batch_domain_type<BatchedDDom>::discrete_element_type const j) {
                    integrals(j) = 0;
                    ddc::device_for_each(
                            bsplines_domain,
                            [&](bsplines_domain_type::discrete_element_type const i) {
                                integrals(j) += spline_coef(i, j)
                                                * (cexa::get<s_idx<BSplines>>(values)(
                                                           ddc::DiscreteElement<BSplines>(i))
                                                   * ...);
                            });
                });
    }
 
private:
    template <std::size_t I, class... CoordsDims>
    KOKKOS_INLINE_FUNCTION static void update_coord_eval(ddc::Coordinate<CoordsDims...>& coord_eval)
    {
        using Dim = continuous_dimension_type<I>;
        using bsplines_t = bsplines_type<I>;
 
        if constexpr (bsplines_t::is_periodic()) {
            if (ddc::get<Dim>(coord_eval) < ddc::discrete_space<bsplines_t>().rmin()
                || ddc::get<Dim>(coord_eval) > ddc::discrete_space<bsplines_t>().rmax()) {
                ddc::get<Dim>(coord_eval) -= Kokkos::floor(
                                                     (ddc::get<Dim>(coord_eval)
                                                      - ddc::discrete_space<bsplines_t>().rmin())
                                                     / ddc::discrete_space<bsplines_t>().length())
                                             * ddc::discrete_space<bsplines_t>().length();
            }
        }
    }
 
    template <std::size_t I, class Layout, class... CoordsDims>
    KOKKOS_INLINE_FUNCTION bool check_needs_extrapolation(
            ddc::Coordinate<CoordsDims...> coord_eval,
            ddc::ChunkSpan<
                    double const,
                    ddc::DiscreteDomain<BSplines...>,
                    Layout,
                    memory_space> const spline_coef,
            double& res) const
    {
        if constexpr (!bsplines_type<I>::is_periodic()) {
            if (ddc::get<continuous_dimension_type<I>>(coord_eval)
                < ddc::discrete_space<bsplines_type<I>>().rmin()) {
                res = cexa::get<I>(m_lower_extrap_rules)(coord_eval, spline_coef);
                return true;
            }
            if (ddc::get<continuous_dimension_type<I>>(coord_eval)
                > ddc::discrete_space<bsplines_type<I>>().rmax()) {
                res = cexa::get<I>(m_upper_extrap_rules)(coord_eval, spline_coef);
                return true;
            }
        }
        return false;
    }
 
    /**
     * @brief Evaluate the function on B-splines at the coordinate given.
     *
     * This function firstly deals with the boundary conditions and calls the SplineEvaluatorND::eval_no_bc function
     * to evaluate.
     *
     * @param[in] coord_eval The ND coordinate where we want to evaluate.
     * @param[in] spline_coef The B-splines coefficients of the function we want to evaluate.
     * @param[out] vals1 A ChunkSpan with the not-null values of each function of the spline in the first dimension.
     * @param[out] vals2 A ChunkSpan with the not-null values of each function of the spline in the second dimension.
     *
     * @return A double with the value of the function at the coordinate given.
     *
     * @see SplineBoundaryValue
     */
    template <class Layout, class... CoordsDims>
    KOKKOS_INLINE_FUNCTION double eval(
            ddc::Coordinate<CoordsDims...> coord_eval,
            ddc::ChunkSpan<
                    double const,
                    ddc::DiscreteDomain<BSplines...>,
                    Layout,
                    memory_space> const spline_coef) const
    {
        (update_coord_eval<s_idx<BSplines>>(coord_eval), ...);
 
        double res = 0.;
        // We rely on short circuit here. If we need to extrapolate on one of the dims, `res` will be set and `check_needs_extrapolation` will return true.
        bool const needs_extrapolation
                = (... || check_needs_extrapolation<s_idx<BSplines>>(coord_eval, spline_coef, res));
 
        if (needs_extrapolation) {
            return res;
        }
 
        return eval_no_bc(
                ddc::DiscreteElement<>(),
                ddc::Coordinate<typename BSplines::continuous_dimension_type...>(
                        ddc::get<typename BSplines::continuous_dimension_type>(coord_eval)...),
                spline_coef);
    }
 
    template <class BSplinesType, class... DerivDims, class CoordDim>
    KOKKOS_INLINE_FUNCTION static ddc::DiscreteElement<BSplinesType> get_jmin(
            ddc::DiscreteElement<DerivDims...> const& deriv_order,
            Kokkos::mdspan<double, Kokkos::extents<std::size_t, BSplinesType::degree() + 1>> vals,
            ddc::Coordinate<CoordDim> const& coord_eval)
    {
        using deriv_dim = Deriv<typename BSplinesType::continuous_dimension_type>;
        using deriv_dims = detail::TypeSeq<DerivDims...>;
        if constexpr (!in_tags_v<deriv_dim, deriv_dims>) {
            return ddc::discrete_space<BSplinesType>().eval_basis(vals, coord_eval);
        } else {
            auto const order = deriv_order.template uid<deriv_dim>();
            KOKKOS_ASSERT(order > 0 && order <= BSplinesType::degree())
 
            std::array<double, (BSplinesType::degree() + 1) * (BSplinesType::degree() + 1)>
                    derivs_ptr;
            Kokkos::mdspan<
                    double,
                    Kokkos::extents<
                            std::size_t,
                            BSplinesType::degree() + 1,
                            Kokkos::dynamic_extent>> const derivs(derivs_ptr.data(), order + 1);
 
            auto jmin = ddc::discrete_space<BSplinesType>()
                                .eval_basis_and_n_derivs(derivs, coord_eval, order);
 
            for (std::size_t i = 0; i < BSplinesType::degree() + 1; ++i) {
                vals[i] = DDC_MDSPAN_ACCESS_OP(derivs, i, order);
            }
 
            return jmin;
        }
    }
 
    template <std::size_t N, class Functor, class... Is>
    KOKKOS_INLINE_FUNCTION static void for_each(
            std::array<std::size_t, N> const& bounds,
            Functor const& f,
            Is... is)
    {
        static constexpr std::size_t I = sizeof...(Is);
        if constexpr (I == N) {
            f(std::array<std::size_t, N> {is...});
        } else {
            for (std::size_t i = 0; i < bounds[I]; ++i) {
                for_each(bounds, f, is..., i);
            }
        }
    }
 
    /**
     * @brief Evaluate the function or its derivative at the coordinate given.
     *
     * @param[in] deriv_order A DiscreteElement containing the orders of derivation for each of the dimensions of interest.
     * If one of the dimensions is not present, its corresponding order of derivation is considered to be 0.
     * @param[in] coord_eval The coordinate where we want to evaluate.
     * @param[in] splne_coef The B-splines coefficients of the function we want to evaluate.
     */
    template <class... DerivDims, class Layout, class... CoordsDims>
    KOKKOS_INLINE_FUNCTION double eval_no_bc(
            ddc::DiscreteElement<DerivDims...> const& deriv_order,
            ddc::Coordinate<CoordsDims...> const& coord_eval,
            ddc::ChunkSpan<
                    double const,
                    ddc::DiscreteDomain<BSplines...>,
                    Layout,
                    memory_space> const spline_coef) const
    {
        // Check that the tags are valid
        static_assert(
                (in_tags_v<
                         DerivDims,
                         ddc::detail::TypeSeq<Deriv<continuous_dimension_type<s_idx<BSplines>>>...>>
                 && ...),
                "The only valid dimensions for deriv_order are Deriv<Dim1>, Deriv<Dim2>, ..., "
                "Deriv<DimN>");
 
        auto vals_ptr = cexa::make_tuple(std::array<double, BSplines::degree() + 1> {}...);
        auto const vals = cexa::make_tuple(
                Kokkos::mdspan<double, Kokkos::extents<std::size_t, BSplines::degree() + 1>>(
                        cexa::get<s_idx<BSplines>>(vals_ptr).data())...);
 
        auto const jmin = cexa::make_tuple(
                get_jmin<BSplines>(
                        deriv_order,
                        cexa::get<s_idx<BSplines>>(vals),
                        ddc::Coordinate<typename BSplines::continuous_dimension_type>(
                                coord_eval))...);
 
        double y = 0.0;
        for_each(
                std::array<std::size_t, dimension> {(BSplines::degree() + 1)...},
                [&](std::array<std::size_t, dimension> idx) {
                    y += spline_coef(
                                 ddc::DiscreteElement<BSplines...>(
                                         (cexa::get<s_idx<BSplines>>(jmin)
                                          + idx[s_idx<BSplines>])...))
                         * (cexa::get<s_idx<BSplines>>(vals)[idx[s_idx<BSplines>]] * ...);
                });
 
        return y;
    }
};
 
} // namespace ddc