periodic_sampling.hpp

// Copyright (C) The DDC development team, see COPYRIGHT.md file
//
// SPDX-License-Identifier: MIT
 
#pragma once
 
#include <cassert>
#include <cstddef>
#include <iosfwd>
#include <tuple>
#include <type_traits>
#include <utility>
 
#include <Kokkos_Core.hpp>
 
#include "coordinate.hpp"
#include "discrete_domain.hpp"
#include "discrete_element.hpp"
#include "discrete_space.hpp"
#include "discrete_vector.hpp"
#include "real_type.hpp"
 
namespace ddc {
 
namespace detail {
 
struct PeriodicSamplingBase
{
};
 
void print_periodic_sampling(std::ostream& os, CoordinateElement origin, Real step);
 
} // namespace detail
 
/** PeriodicSampling models a periodic discretization of the provided continuous dimension
 */
template <class CDim>
class PeriodicSampling : detail::PeriodicSamplingBase
{
public:
    using continuous_dimension_type = CDim;
 
    using discrete_dimension_type = PeriodicSampling;
 
public:
    template <class DDim, class MemorySpace>
    class Impl
    {
        template <class ODDim, class OMemorySpace>
        friend class Impl;
 
    private:
        Coordinate<CDim> m_origin;
 
        Real m_step;
 
        std::size_t m_n_period;
 
        DiscreteElement<DDim> m_reference;
 
    public:
        using discrete_dimension_type = PeriodicSampling;
 
        using discrete_domain_type = DiscreteDomain<DDim>;
 
        using discrete_element_type = DiscreteElement<DDim>;
 
        using discrete_vector_type = DiscreteVector<DDim>;
 
        Impl() noexcept
            : m_origin(0)
            , m_step(1)
            , m_n_period(2)
            , m_reference(create_reference_discrete_element<DDim>())
        {
        }
 
        Impl(Impl const&) = delete;
 
        template <class OriginMemorySpace>
        explicit Impl(Impl<DDim, OriginMemorySpace> const& impl)
            : m_origin(impl.m_origin)
            , m_step(impl.m_step)
            , m_n_period(impl.m_n_period)
            , m_reference(impl.m_reference)
        {
        }
 
        Impl(Impl&&) = default;
 
        /** @brief Construct a `Impl` from a point and a spacing step.
         *
         * @param origin the real coordinate of mesh coordinate 0
         * @param step   the real distance between two points of mesh distance 1
         * @param n_period   the number of steps in a period
         */
        Impl(Coordinate<CDim> origin, Real step, std::size_t n_period)
            : m_origin(origin)
            , m_step(step)
            , m_n_period(n_period)
            , m_reference(create_reference_discrete_element<DDim>())
        {
            assert(step > 0);
            assert(n_period > 0);
        }
 
        ~Impl() = default;
 
        Impl& operator=(Impl const& x) = delete;
 
        Impl& operator=(Impl&& x) = default;
 
        /// @brief Lower bound index of the mesh
        KOKKOS_FUNCTION Coordinate<CDim> origin() const noexcept
        {
            return m_origin;
        }
 
        /// @brief Lower bound index of the mesh
        KOKKOS_FUNCTION discrete_element_type front() const noexcept
        {
            return m_reference;
        }
 
        /// @brief Spacing step of the mesh
        KOKKOS_FUNCTION Real step() const
        {
            return m_step;
        }
 
        /// @brief Number of steps in a period
        KOKKOS_FUNCTION std::size_t n_period() const
        {
            return m_n_period;
        }
 
        /// @brief Convert a mesh index into a position in `CDim`
        KOKKOS_FUNCTION Coordinate<CDim> coordinate(
                discrete_element_type const& icoord) const noexcept
        {
            return m_origin
                   + Coordinate<CDim>(
                             static_cast<int>(((icoord - front()) + m_n_period / 2) % m_n_period)
                             - static_cast<int>(m_n_period / 2))
                             * m_step;
        }
    };
 
    /** Construct a Impl<Kokkos::HostSpace> and associated discrete_domain_type from a segment
     *  \f$[a, b] \subset [a, +\infty[\f$ and a number of points `n`.
     *  Note that there is no guarantee that either the boundaries a or b will be exactly represented in the sampling.
     *  One should expect usual floating point rounding errors.
     *
     * @param a coordinate of the first point of the domain
     * @param b coordinate of the last point of the domain
     * @param n number of points to map on the segment \f$[a, b]\f$ including a & b
     * @param n_period   the number of steps in a period
     */
    template <class DDim>
    static std::tuple<typename DDim::template Impl<DDim, Kokkos::HostSpace>, DiscreteDomain<DDim>>
    init(Coordinate<CDim> a,
         Coordinate<CDim> b,
         DiscreteVector<DDim> n,
         DiscreteVector<DDim> n_period)
    {
        assert(a < b);
        assert(n > 1);
        assert(n_period > 1);
        typename DDim::template Impl<DDim, Kokkos::HostSpace>
                disc(a, Coordinate<CDim>((b - a) / (n - 1)), n_period);
        DiscreteDomain<DDim> domain(disc.front(), n);
        return std::make_tuple(std::move(disc), std::move(domain));
    }
 
    /** Construct a periodic `DiscreteDomain` from a segment \f$[a, b] \subset [a, +\infty[\f$ and a
     *  number of points `n`.
     *  Note that there is no guarantee that either the boundaries a or b will be exactly represented in the sampling.
     *  One should expect usual floating point rounding errors.
     *
     * @param a coordinate of the first point of the domain
     * @param b coordinate of the last point of the domain
     * @param n the number of points to map the segment \f$[a, b]\f$ including a & b
     * @param n_period   the number of steps in a period
     * @param n_ghosts_before number of additional "ghost" points before the segment
     * @param n_ghosts_after number of additional "ghost" points after the segment
     */
    template <class DDim>
    std::tuple<
            Impl<DDim, Kokkos::HostSpace>,
            DiscreteDomain<DDim>,
            DiscreteDomain<DDim>,
            DiscreteDomain<DDim>,
            DiscreteDomain<DDim>>
    init_ghosted(
            Coordinate<CDim> a,
            Coordinate<CDim> b,
            DiscreteVector<DDim> n,
            DiscreteVector<DDim> n_period,
            DiscreteVector<DDim> n_ghosts_before,
            DiscreteVector<DDim> n_ghosts_after)
    {
        assert(a < b);
        assert(n > 1);
        assert(n_period > 1);
        Real const discretization_step = (b - a) / (n - 1);
        Impl<DDim, Kokkos::HostSpace>
                disc(a - n_ghosts_before.value() * discretization_step,
                     discretization_step,
                     n_period);
        DiscreteDomain<DDim> ghosted_domain(disc.front(), n + n_ghosts_before + n_ghosts_after);
        DiscreteDomain<DDim> pre_ghost = ghosted_domain.take_first(n_ghosts_before);
        DiscreteDomain<DDim> main_domain = ghosted_domain.remove(n_ghosts_before, n_ghosts_after);
        DiscreteDomain<DDim> post_ghost = ghosted_domain.take_last(n_ghosts_after);
        return std::make_tuple(
                std::move(disc),
                std::move(main_domain),
                std::move(ghosted_domain),
                std::move(pre_ghost),
                std::move(post_ghost));
    }
 
    /** Construct a periodic `DiscreteDomain` from a segment \f$[a, b] \subset [a, +\infty[\f$ and a
     *  number of points `n`.
     *  Note that there is no guarantee that either the boundaries a or b will be exactly represented in the sampling.
     *  One should expect usual floating point rounding errors.
     *
     * @param a coordinate of the first point of the domain
     * @param b coordinate of the last point of the domain
     * @param n the number of points to map the segment \f$[a, b]\f$ including a & b
     * @param n_period   the number of steps in a period
     * @param n_ghosts number of additional "ghost" points before and after the segment
     */
    template <class DDim>
    std::tuple<
            Impl<DDim, Kokkos::HostSpace>,
            DiscreteDomain<DDim>,
            DiscreteDomain<DDim>,
            DiscreteDomain<DDim>,
            DiscreteDomain<DDim>>
    init_ghosted(
            Coordinate<CDim> a,
            Coordinate<CDim> b,
            DiscreteVector<DDim> n,
            DiscreteVector<DDim> n_period,
            DiscreteVector<DDim> n_ghosts)
    {
        return init_ghosted(a, b, n, n_period, n_ghosts, n_ghosts);
    }
};
 
template <class DDim>
struct is_periodic_sampling : public std::is_base_of<detail::PeriodicSamplingBase, DDim>::type
{
};
 
template <class DDim>
constexpr bool is_periodic_sampling_v = is_periodic_sampling<DDim>::value;
 
namespace concepts {
 
template <class DDim>
concept periodic_sampling = is_periodic_sampling_v<DDim>;
 
}
 
template <class DDimImpl>
std::ostream& operator<<(std::ostream& os, DDimImpl const& mesh)
    requires(concepts::periodic_sampling<typename DDimImpl::discrete_dimension_type>)
{
    detail::print_periodic_sampling(os, mesh.origin(), mesh.step());
    return os;
}
 
/// @brief Lower bound index of the mesh
template <concepts::periodic_sampling DDim>
KOKKOS_FUNCTION Coordinate<typename DDim::continuous_dimension_type> origin() noexcept
{
    return discrete_space<DDim>().origin();
}
 
/// @brief Lower bound index of the mesh
template <concepts::periodic_sampling DDim>
KOKKOS_FUNCTION DiscreteElement<DDim> front() noexcept
{
    return discrete_space<DDim>().front();
}
 
/// @brief Spacing step of the mesh
template <concepts::periodic_sampling DDim>
KOKKOS_FUNCTION Real step() noexcept
{
    return discrete_space<DDim>().step();
}
 
template <concepts::periodic_sampling DDim>
KOKKOS_FUNCTION Coordinate<typename DDim::continuous_dimension_type> coordinate(
        DiscreteElement<DDim> const& c)
{
    return discrete_space<DDim>().coordinate(c);
}
 
template <concepts::periodic_sampling DDim>
KOKKOS_FUNCTION Coordinate<typename DDim::continuous_dimension_type> distance_at_left(
        DiscreteElement<DDim>)
{
    return Coordinate<typename DDim::continuous_dimension_type>(step<DDim>());
}
 
template <concepts::periodic_sampling DDim>
KOKKOS_FUNCTION Coordinate<typename DDim::continuous_dimension_type> distance_at_right(
        DiscreteElement<DDim>)
{
    return Coordinate<typename DDim::continuous_dimension_type>(step<DDim>());
}
 
template <concepts::periodic_sampling DDim>
KOKKOS_FUNCTION Coordinate<typename DDim::continuous_dimension_type> rmin(
        DiscreteDomain<DDim> const& d)
{
    return coordinate(d.front());
}
 
template <concepts::periodic_sampling DDim>
KOKKOS_FUNCTION Coordinate<typename DDim::continuous_dimension_type> rmax(
        DiscreteDomain<DDim> const& d)
{
    return coordinate(d.back());
}
 
template <concepts::periodic_sampling DDim>
KOKKOS_FUNCTION Coordinate<typename DDim::continuous_dimension_type> rlength(
        DiscreteDomain<DDim> const& d)
{
    return rmax(d) - rmin(d);
}
 
} // namespace ddc