Lexicographic enumeration of the k-dimensional faces in a tensor product chain complex of dimension n. More...

#include <lexicographic.h>

Public Types
typedef Bint	global_index_t
	Index type for addressing in the tensor product. More...

typedef Sint	fiber_index_t
	Index type for addressing in the fibers. More...

typedef Tint	dimension_index_t
	Index type for addressing dimensions and elements of the chain complex. More...

typedef Element< n, k, Sint, Tint >	value_type
	The type of elements of this set in the complex. More...

Public Member Functions
constexpr	Lexicographic (const std::array< Sint, n > &d)
	Constructor setting the dimensions of the complex. More...

constexpr Bint	size () const
	The number of elements in this set. More...

constexpr Bint	block_size (Tint block) const
	The number of elements in one direction. More...

constexpr Sint	fiber_dimension (Tint i) const
	Dimension of the fiber with given index in the tensor product. More...

value_type	operator[] (Bint index) const
	Descriptor for the element at given `index`. More...

Bint	index_in_slice (const value_type &e) const

Bint	index (const value_type &e) const
	Find index of a given element. More...

template<boundaries bndT = bnd>
constexpr Lexicographic< n, k - 1, bndT, Bint, Sint, Tint >	boundary () const

Static Public Member Functions
static constexpr Tint	order ()
	The tensor order of the chain complex. More...

static constexpr Tint	cell_dimension ()
	The dimension of the elements, index in the chain complex. More...

Private Attributes
std::array< Sint, n >	dimensions
	The dimension of the fibers in each direction. More...

std::array< Bint, binomial(n, k)>	block_sizes
	The number of objects facing the same directions. More...

std::array< Bint, binomial(n, k)>	block_sizes_bnd

Detailed Description

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>
class TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >

Lexicographic enumeration of the k-dimensional faces in a tensor product chain complex of dimension n.

Template Parameters

n	The dimension of the tensor product (the order of the tensor)
k	The dimensions of the object considered
Bint	The big integer used for addressing in the whole tensor product
Sint	The small integer used for addressing in each fiber
Tint	The tiny integer with values addressing the fibers

The numbering for k==0 and k==n is lexicographic with the first coordinate changing fastest and the last one slowest. For k between those values, the set of elements consists of n over k separate sets, one for each combination of k different coordinates.

These sets form the slowest moving part of the enumeration, and they are enumerated based such that the elements orthogonal to the first n-k coordinates are first, those orthogonal to the last coordinates last.

The next level in the enumaration is formed by the fact that these sets can be split into 'sheets', connected sets which are not connected to each other. They are characterized by their coordinates orthogonal to the chosen k. Thus, their enumeration follows a lexicographic scheme with first fastest for these coordinates.

The fastes level of enumeration is inside each sheet, where again the first coordinates run fastest.

Member Typedef Documentation

◆ dimension_index_t

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

typedef Tint TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::dimension_index_t

Index type for addressing dimensions and elements of the chain complex.

◆ fiber_index_t

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

typedef Sint TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::fiber_index_t

Index type for addressing in the fibers.

◆ global_index_t

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

typedef Bint TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::global_index_t

Index type for addressing in the tensor product.

◆ value_type

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

typedef Element<n, k, Sint, Tint> TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::value_type

The type of elements of this set in the complex.

Constructor & Destructor Documentation

◆ Lexicographic()

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

constexpr TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::Lexicographic ( const std::array< Sint, n > & d )

inlineconstexpr

Constructor setting the dimensions of the complex.

Member Function Documentation

◆ block_size()

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

constexpr Bint TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::block_size ( Tint block ) const

inlineconstexpr

The number of elements in one direction.

◆ boundary()

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

template<boundaries bndT = bnd>

constexpr Lexicographic<n, k - 1, bndT, Bint, Sint, Tint> TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::boundary ( ) const

inlineconstexpr

◆ cell_dimension()

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

static constexpr Tint TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::cell_dimension ( )

inlinestaticconstexpr

The dimension of the elements, index in the chain complex.

◆ fiber_dimension()

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

constexpr Sint TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::fiber_dimension ( Tint i ) const

inlineconstexpr

Dimension of the fiber with given index in the tensor product.

◆ index()

template<int n, int k, boundaries bnd, typename Bint , typename Sint , typename Tint >

Bint TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::index ( const value_type & e ) const

Find index of a given element.

◆ index_in_slice()

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

Bint TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::index_in_slice ( const value_type & e ) const

inline

◆ operator[]()

template<int n, int k, boundaries bnd, typename Bint , typename Sint , typename Tint >

Element< n, k, Sint, Tint > TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::operator[] ( Bint index ) const

Descriptor for the element at given index.

◆ order()

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

static constexpr Tint TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::order ( )

inlinestaticconstexpr

The tensor order of the chain complex.

◆ size()

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

constexpr Bint TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::size ( ) const

inlineconstexpr

The number of elements in this set.

Member Data Documentation

◆ block_sizes

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

std::array<Bint, binomial(n, k)> TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::block_sizes

private

The number of objects facing the same directions.

◆ block_sizes_bnd

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

std::array<Bint, binomial(n, k)> TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::block_sizes_bnd

private

◆ dimensions

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>

std::array<Sint, n> TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >::dimensions

private

The dimension of the fibers in each direction.

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

/home/runner/work/HyperHDG/HyperHDG/submodules/tensor_product_chain_complex.git/include/tpcc/lexicographic.h

Public Types

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char> class TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >

Member Typedef Documentation

◆ dimension_index_t

◆ fiber_index_t

◆ global_index_t

◆ value_type

Constructor & Destructor Documentation

◆ Lexicographic()

Member Function Documentation

◆ block_size()

◆ boundary()

◆ cell_dimension()

◆ fiber_dimension()

◆ index()

◆ index_in_slice()

◆ operator[]()

◆ order()

◆ size()

Member Data Documentation

◆ block_sizes

◆ block_sizes_bnd

◆ dimensions

template<int n, int k, boundaries bnd = both, typename Bint = unsigned int, typename Sint = unsigned short, typename Tint = unsigned char>
class TPCC::Lexicographic< n, k, bnd, Bint, Sint, Tint >