integrator_p2_1ang.hh

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#pragma once
 
// DiFfRG
#include <DiFfRG/common/math.hh>
#include <DiFfRG/physics/integration/quadrature_integrator.hh>
 
// standard libraries
#include <array>
 
namespace DiFfRG
{
  namespace internal
  {
    template <int dim, typename NT, typename KERNEL> class Transform_p2_1ang
    {
    public:
      using ctype = typename get_type::ctype<NT>;
 
      // The polar angle (loop vs. external momentum) of a 2-point loop in d dims carries the zonal
      // measure (1-c^2)^{(d-3)/2} dc, supplied by the Gauss-Jacobi(alpha=beta=(d-3)/2) angular
      // quadrature (see the class below). The remaining (d-2)-sphere gives S_{d-2} = S_d_prec(dim-1).
      static constexpr ctype int_prefactor = S_d_prec<ctype>(dim - 1)     // remaining solid angle after the polar angle
                                             / powr<dim>(2 * (ctype)M_PI); // fourier factor
 
      template <typename... T>
      static KOKKOS_FORCEINLINE_FUNCTION NT kernel(const ctype q, const ctype cos, const T &...t)
        requires provides_kernel<NT, KERNEL, ctype, 2, T...>
      {
        using namespace DiFfRG::compute;
 
        const ctype int_element = powr<dim - 1>(q); // from p integral
        const NT result = KERNEL::kernel(q, cos, t...);
 
        return int_prefactor * int_element * result;
      }
 
      template <typename... T>
      static KOKKOS_FORCEINLINE_FUNCTION NT constant(const T &...t)
        requires provides_constant<NT, KERNEL, T...>
      {
        return KERNEL::constant(t...);
      }
    };
 
  } // namespace internal
 
  template <int dim, typename NT, typename KERNEL, typename ExecutionSpace>
  class Integrator_p2_1ang
      : public QuadratureIntegrator<2, NT, internal::Transform_p2_1ang<dim, NT, KERNEL>, ExecutionSpace>
  {
    using Base = QuadratureIntegrator<2, NT, internal::Transform_p2_1ang<dim, NT, KERNEL>, ExecutionSpace>;
 
    // Gauss-Jacobi quadrature on [-1,1] with weight (1-c^2)^{(d-3)/2} for the polar angle.
    // Dimension-agnostic: reduces to Chebyshev-1 (d=2), Legendre (d=3), Chebyshev-2 (d=4), ...
    static QuadratureType polar_quadrature()
    {
      QuadratureType t(QuadratureType::jacobi);
      t.a = static_cast<double>(-1);
      t.b = static_cast<double>(1);
      t.alpha = (static_cast<double>(dim) - 3.) / 2.;
      t.beta = t.alpha;
      return t;
    }
 
  public:
    using ctype = typename get_type::ctype<NT>;
    using execution_space = ExecutionSpace;
 
    Integrator_p2_1ang(QuadratureProvider &quadrature_provider, const JSONValue &json)
      requires provides_regulator<KERNEL>
        : Integrator_p2_1ang(quadrature_provider, internal::make_int_grid<2, NT>(json, {"x_order", "cos1_order"}),
                             optimize_x_extent<typename KERNEL::Regulator>(json))
    {
    }
 
    Integrator_p2_1ang(QuadratureProvider &quadrature_provider, const std::array<size_t, 2> grid_size,
                       ctype x_extent = 2.)
        : Base(quadrature_provider, grid_size, {0, 0.}, {std::sqrt(x_extent), 1.},
               {QuadratureType(QuadratureType::legendre), polar_quadrature()}),
          x_extent(x_extent), k(1.)
    {
    }
 
    void set_x_extent(ctype x_extent)
    {
      this->x_extent = x_extent;
      Base::set_grid_extents({0, 0.}, {std::sqrt(x_extent) * k, 1.});
    }
 
    void set_k(ctype k)
    {
      this->k = k;
      Base::set_grid_extents({0, 0.}, {std::sqrt(x_extent) * k, 1.});
    }
 
  private:
    ctype x_extent;
    ctype k;
  };
} // namespace DiFfRG