Functions
t_complex	fourier_wproj_kernel (const t_real x, const t_real y, const t_real w, const t_real u, const t_real v, const t_real du, const t_real dv)
	integration kernel for 2d fourier transform of chirp, bounded to a circle of radius x/du < 1 More...

t_complex	hankel_wproj_kernel (const t_real r, const t_real w, const t_real u, const t_real v, const t_real du)
	integration kernel for hankel transform with chirp More...

t_complex	exact_w_projection_integration_1d (const t_real u, const t_real v, const t_real w, const t_real du, const t_real oversample_ratio, const std::function< t_complex(t_real)> &ftkerneluv, const t_uint &max_evaluations, const t_real &absolute_error, const t_real &relative_error, const integration::method method, t_uint &evaluations)

t_complex	exact_w_projection_integration (const t_real u, const t_real v, const t_real w, const t_real du, const t_real dv, const t_real oversample_ratio, const std::function< t_complex(t_real)> &ftkernelu, const std::function< t_complex(t_real)> &ftkernelv, const t_uint &max_evaluations, const t_real &absolute_error, const t_real &relative_error, const integration::method method, t_uint &evaluations)
	numerical integration of chirp and kernel in image domain More...

Function Documentation

◆ exact_w_projection_integration()

t_complex purify::projection_kernels::exact_w_projection_integration	(	const t_real	u,
		const t_real	v,
		const t_real	w,
		const t_real	du,
		const t_real	dv,
		const t_real	oversample_ratio,
		const std::function< t_complex(t_real)> &	ftkernelu,
		const std::function< t_complex(t_real)> &	ftkernelv,
		const t_uint &	max_evaluations,
		const t_real &	absolute_error,
		const t_real &	relative_error,
		const integration::method	method,
		t_uint &	evaluations
	)

numerical integration of chirp and kernel in image domain

Definition at line 46 of file wkernel_integration.cc.

                                                                                               {
   auto const func = [&](const Vector<t_real> &x) -> t_complex {
     evaluations++;
     return ftkernelu(x(0)) * ftkernelv(x(1)) * fourier_wproj_kernel(x(0), x(1), w, u, v, du, dv);
   };
   Vector<t_real> xmax = Vector<t_real>::Zero(2);
   xmax(0) = oversample_ratio / 2.;
   xmax(1) = oversample_ratio / 2.;
   const Vector<t_real> xmin = -xmax;
   return integration::integrate(xmin, xmax, func, integration::norm_type::paired, absolute_error,
                                 relative_error, max_evaluations, method) /
          (xmax(0) - xmin(0)) / (xmax(1) - xmin(1));
 }

References fourier_wproj_kernel(), purify::integration::integrate(), purify::integration::paired, operators_test::u, and operators_test::v.

Referenced by purify::details::init_gridding_matrix_2d(), main(), and TEST_CASE().

◆ exact_w_projection_integration_1d()

t_complex purify::projection_kernels::exact_w_projection_integration_1d	(	const t_real	u,
		const t_real	v,
		const t_real	w,
		const t_real	du,
		const t_real	oversample_ratio,
		const std::function< t_complex(t_real)> &	ftkerneluv,
		const t_uint &	max_evaluations,
		const t_real &	absolute_error,
		const t_real &	relative_error,
		const integration::method	method,
		t_uint &	evaluations
	)

numerical integration of chirp and radial symmetric kernel in the image domain using hankel transform

Definition at line 25 of file wkernel_integration.cc.

                                                                                                  {
   evaluations = 0;
   const auto func = [&](const Vector<t_real> &x) -> t_complex {
     evaluations++;
     assert(std::abs(x(0)) <= 1);
     return ftkerneluv(x(0)) * hankel_wproj_kernel(x(0), w, u, v, du);
   };
   const Vector<t_real> xmin = Vector<t_real>::Zero(1);
   const Vector<t_real> xmax = Vector<t_real>::Constant(1, oversample_ratio / 2.);
   return 2. * constant::pi *
          integration::integrate(xmin, xmax, func, integration::norm_type::paired, absolute_error,
                                 relative_error, max_evaluations, method) /
          std::pow(xmax(0), 2);
 }

References hankel_wproj_kernel(), purify::integration::integrate(), purify::integration::paired, purify::constant::pi, operators_test::u, and operators_test::v.

Referenced by purify::details::init_gridding_matrix_2d(), main(), and TEST_CASE().

◆ fourier_wproj_kernel()

t_complex purify::projection_kernels::fourier_wproj_kernel	(	const t_real	x,
		const t_real	y,
		const t_real	w,
		const t_real	u,
		const t_real	v,
		const t_real	du,
		const t_real	dv
	)

integration kernel for 2d fourier transform of chirp, bounded to a circle of radius x/du < 1

Definition at line 7 of file wkernel_integration.cc.

                                                                                  {
   // checking bounds don't go past the horizon...
   if ((std::pow(x / du, 2) + std::pow(y / dv, 2)) < 1)
     return std::exp(t_complex(
         0.,
         -2 * constant::pi *
             (u * x + v * y + w * (std::sqrt(1 - (x * x) / (du * du) - (y * y) / (dv * dv)) - 1))));
   else
     return 0;
 }

References purify::constant::pi, operators_test::u, and operators_test::v.

Referenced by exact_w_projection_integration(), and TEST_CASE().

◆ hankel_wproj_kernel()

t_complex purify::projection_kernels::hankel_wproj_kernel	(	const t_real	r,
		const t_real	w,
		const t_real	u,
		const t_real	v,
		const t_real	du
	)

integration kernel for hankel transform with chirp

Definition at line 18 of file wkernel_integration.cc.

                                                {
   return ((r / du < 1.) ? std::exp(t_complex(
                               0., -2 * constant::pi * w * (std::sqrt(1 - (r * r) / (du * du)) - 1)))
                         : 1) *
          boost::math::cyl_bessel_j(0, 2 * constant::pi * r * std::sqrt(u * u + v * v)) * r;
 }