nda::sym_grp< F, A >

#include <nda/sym_grp.hpp>

Detailed Description

template<typename F, typename A>
requires (Array<A> && NdaSymmetry<F, A>)
class nda::sym_grp< F, A >

Class representing a symmetry group.

A symmetry group detects and stores all different symmetry classes associated with a given nda::Array object.

A symmetry class is simply a set of all the elements of the array that are related to each other by some symmetry. The elements in a symmetry class have all the same values except for a possible sign flip or complex conjugation, i.e. an nda::operation. The symmetry classes form a partition of all the elements of the array.

Template Parameters

F	nda::NdaSymmetry type.
A	nda::Array type.

Definition at line 145 of file sym_grp.hpp.

Public Types
using	arr_idx_t = std::array<long, static_cast<std::size_t>(ndims)>
	Multi-dimensional index type.
using	sym_class_t = std::span<sym_idx_t>
	Symmetry class type.
using	sym_idx_t = std::pair<long, operation>
	Element type of a symmetry class.

Public Member Functions
	sym_grp ()=default
	Default constructor for a symmetry group.
	sym_grp (A const &a, std::vector< F > const &sym_list, long const max_length=0)
	Construct a symmetry group for a given array and a list of its symmetries.
std::vector< get_value_t< A > >	get_representative_data (A const &a) const
	Reduce an nda::Array to its representative data using symmetries.
std::vector< sym_class_t > const &	get_sym_classes () const
	Get the symmetry classes.
template<typename H > requires (NdaInitFunc<H, A>)
void	init (A &a, H const &init_func, bool parallel=false) const
	Initialize an nda::Array using an nda::NdaInitFunc.
template<typename V >
void	init_from_representative_data (A &a, V const &vec) const
	Initialize a multi-dimensional array from its representative data using symmetries.
long	num_classes () const
	Get the number of symmetry classes.
std::pair< double, arr_idx_t >	symmetrize (A &a) const
	Symmetrize an array and return the maximum symmetry violation and its corresponding array index.

Static Public Attributes
static constexpr int	ndims = get_rank<A>
	Rank of the input array.

Constructor & Destructor Documentation

sym_grp()

template<typename F , typename A >

nda::sym_grp< F, A >::sym_grp ( A const & a, std::vector< F > const & sym_list, long const max_length = 0 )

inline

Construct a symmetry group for a given array and a list of its symmetries.

It uses nda::for_each to loop over all possible multi-dimensional indices of the given array and applies the symmetries to each index to generate the different symmetry classes.

Parameters

a	nda::Array object.
sym_list	List of symmetries containing nda::NdaSymmetry objects.
max_length	Maximum recursion depth for out-of-bounds projection. Default is 0.

Definition at line 295 of file sym_grp.hpp.

Member Function Documentation

get_representative_data()

template<typename F , typename A >

std::vector< get_value_t< A > > nda::sym_grp< F, A >::get_representative_data ( A const & a ) const

inlinenodiscard

Reduce an nda::Array to its representative data using symmetries.

Parameters

a	nda::Array object.

Returns

std::vector of data values for the representative elements of each symmetry class.

Definition at line 261 of file sym_grp.hpp.

get_sym_classes()

template<typename F , typename A >

std::vector< sym_class_t > const & nda::sym_grp< F, A >::get_sym_classes ( ) const

inlinenodiscard

Get the symmetry classes.

Returns

std::vector containing the individual classes.

Definition at line 171 of file sym_grp.hpp.

init()

template<typename F , typename A >

template<typename H >
requires (NdaInitFunc<H, A>)

void nda::sym_grp< F, A >::init ( A & a, H const & init_func, bool parallel = false ) const

inline

Initialize an nda::Array using an nda::NdaInitFunc.

The nda::NdaInitFunc object is evaluated only once per symmetry class. The result is then assigned to all elements in the symmetry class after applying the nda::operation.

Template Parameters

H	Callable type of nda::NdaInitFunc.

Parameters

a	nda::Array object to be initialized.
init_func	Callable that is used to initialize the array.
parallel	Parallelize using openmp and mpi.

Definition at line 192 of file sym_grp.hpp.

init_from_representative_data()

template<typename F , typename A >

template<typename V >

void nda::sym_grp< F, A >::init_from_representative_data ( A & a, V const & vec ) const

inline

Initialize a multi-dimensional array from its representative data using symmetries.

Parameters

a	nda::Array object to be initialized.
vec	std::vector of data values for the representative elements of each symmetry class.

Definition at line 275 of file sym_grp.hpp.

num_classes()

template<typename F , typename A >

long nda::sym_grp< F, A >::num_classes ( ) const

inlinenodiscard

Get the number of symmetry classes.

Returns

Number of detected symmetry classes.

Definition at line 177 of file sym_grp.hpp.

symmetrize()

template<typename F , typename A >

std::pair< double, arr_idx_t > nda::sym_grp< F, A >::symmetrize ( A & a ) const

inline

Symmetrize an array and return the maximum symmetry violation and its corresponding array index.

Note

This actually requires the definition of an inverse operation but with the current implementation, all operations are self-inverse (sign flip and complex conjugation).

Parameters

a	nda::Array object to be symmetrized.

Returns

Maximum symmetry violation and corresponding array index.

Definition at line 226 of file sym_grp.hpp.

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The documentation for this class was generated from the following file:

• nda/sym_grp.hpp