Spectral::Swsh Namespace Reference

Namespace for spin-weighted spherical harmonic utilities. More...

Classes
class	Collocation
	A wrapper class for the spherical harmonic library collocation data. More...
struct	LibsharpCollocationPoint
	A container for reporting a single collocation point for libsharp compatible data structures. More...

Enumerations
enum	ComplexRepresentation { Interleaved, RealsThenImags }
	A set of labels for the possible representations of complex numbers for the ComplexDataView and the computations performed in the spin-weighted spherical harmonic transform library. More...

Functions
template<ComplexRepresentation Representation>
const Collocation< Representation > &	precomputed_spherical_harmonic_collocation (size_t l_max) noexcept
	precomputation function for those collocation grids that are requested More...

Variables
constexpr size_t	collocation_maximum_l_max = 200

Detailed Description

Namespace for spin-weighted spherical harmonic utilities.

Enumeration Type Documentation

ComplexRepresentation

enum Spectral::Swsh::ComplexRepresentation

strong

A set of labels for the possible representations of complex numbers for the ComplexDataView and the computations performed in the spin-weighted spherical harmonic transform library.

Details

The representation describes one of two behaviors:

• Interleaved: The vectors of complex numbers will be represented by alternating doubles in memory. This causes both the real and imaginary part at a given gridpoint to be near one another, but successive real values farther. This is the native representation of complex data in the C++ standard, and is the representation needed for Blaze math operations. Therefore, using this representation type in libsharp computations will cause operations which access only the real or imaginary parts individually to trace over larger memory regions. However, this representation will give rise to fewer copying operations to perform the libsharp operations.
• RealsThenImags: The vectors of complex numbers will primarily be represented by a pair of vectors of doubles, one for the real values and one for the imaginary values (the full computation cannot be performed exclusively in this representation, as it must return to a vector of std::complex<double> for Blaze math operations). This causes the successive real values for different gridpoints to be closer in memory, but the real and imaginary parts for a given gridpoint to be farther in memory. This is not the native representation for complex data in C++, so the data must be transformed between operations which use Blaze and the transform operations which use RealsThenImags. Therefore, using this representation in libsharp computations will cause operations which act on real or imaginary parts individually to have better memory locality (so likely improved cache performance, but such statements are highly hardware-dependent). However, this representation will give rise to more copying operations to perform the libsharp operations.

Note

The pair of representations is provided as a means to 'turn a dial' in optimizations. It is unclear which of these representations will be preferable, and it may well be the case that different representations are better for different calculation types or different hardware. Therefore, when optimizing code which uses libsharp, it is encouraged to profile the cost of each representation for a computation and choose the one which performs best.

Function Documentation

precomputed_spherical_harmonic_collocation()

template<ComplexRepresentation Representation>

const Collocation< Representation > & Spectral::Swsh::precomputed_spherical_harmonic_collocation ( size_t  l_max )

noexcept

precomputation function for those collocation grids that are requested

Details

keeps a compile-time structure which acts as a thread-safe lookup table for all l_max values that have been requested so far during execution, so that the libsharp generation need not be re-run. If it has been generated, it's returned by reference. Otherwise, the new grid is generated and put in the lookup table before it is returned by reference.