#include <NeighborList.hh>

Detailed Description

The PrimNeighborList gives the coordinates of UnitCell that are neighbors of the origin UnitCell.

The PrimNeighborList is constructed with a weighting matrix, M, that defines the shape of neighborhood
The canonical order of neighboring UnitCell is obtained by lexicographically sorting [r, i, j, k], where r = (i,j,k).transpose() * W * (i,j,k).
The canonical order of UnitCellCoord is obtained by lexicographically sorting [r, i, j, k, b], where r = (i,j,k).transpose() * W * (i,j,k).
The PrimNeighborList can be expanded as needed to increase the range of the neighborhood without affecting the order of the neighbors.

Definition at line 24 of file NeighborList.hh.

Public Types
typedef Eigen::Matrix3l	Matrix3Type

typedef Eigen::Matrix< long, Eigen::Dynamic, 1 >	VectorXType

typedef std::set< UnitCell, std::function< bool(UnitCell, UnitCell)> >	NeighborSet

typedef NeighborSet::size_type	size_type

typedef NeighborSet::const_iterator	const_iterator

typedef std::set< int >	SublatIndices

Public Member Functions
Matrix3Type	weight_matrix () const
	Return the weighting matrix W used to define the canonical order. More...

void	expand (UnitCellCoord uccoord)
	Expand the neighbor list to include the given UnitCellCoord. More...

size_type	size () const
	size of the neighborhood of unit cells More...

const_iterator	begin () const
	const_iterator over the neighborhood of unit cells More...

const_iterator	end () const
	const_iterator over the neighborhood of unit cells More...

const_iterator	cbegin () const
	const_iterator over the neighborhood of unit cells More...

const_iterator	cend () const
	const_iterator over the neighborhood of unit cells More...

const SublatIndices &	sublat_indices () const
	pair of const_iterators over a range of indices of sublattices to include More...

std::unique_ptr< PrimNeighborList >	clone () const
	Clone. More...


template<typename SublatIterator >
	PrimNeighborList (const Matrix3Type &W, SublatIterator begin, SublatIterator end)
	Constructor, specifying the weighting matrix to use and the indices of sublattices to include. More...

template<typename UnitCellCoordIterator >
void	expand (UnitCellCoordIterator begin, UnitCellCoordIterator end)
	Expand the neighbor list to include the given range of UnitCellCoord. More...

Static Public Member Functions
static Matrix3Type	make_weight_matrix (const Eigen::Matrix3d lat_column_mat, Index max_element_value, double tol)
	Returns a NeighborList weighting matrix appropriate for a particular lattice. More...

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef Index	Scalar

Private Member Functions
void	_expand (Scalar prev_range)
	Ensure that all intermediate UnitCell are included in our neighborhood. More...

Scalar	_dist (const UnitCell &A) const
	Calculate A.transpose()MA. More...

VectorXType	_add_dist (const UnitCell &A) const
	Return [r, i, j, k], where r = _dist(A) More...

bool	_compare_unitcell (const UnitCell &A, const UnitCell &B) const
	Convert [i,j,k] -> [r,i,j,k] and then lexicographically compare. More...

Static Private Member Functions
static bool	_compare_vec (const VectorXType &A, const VectorXType &B)
	Lexicographical comparison. More...

Private Attributes
Matrix3Type	m_W
	Weighting matrix. More...

Eigen::MatrixXd	m_Uinv
	Cholesky decomposition: W = U.transpose()*U, useful for getting bounding box. More...

NeighborSet	m_neighborhood
	the neighborhood of [i, j, k] More...

Scalar	m_range
	the neighborhood, m_neighborhood, contains all UnitCell with r <= m_range More...

SublatIndices	m_sublat_indices
	the indices of sublattices that should be included More...

Member Typedef Documentation

typedef NeighborSet::const_iterator CASM::PrimNeighborList::const_iterator

Definition at line 35 of file NeighborList.hh.

typedef Eigen::Matrix3l CASM::PrimNeighborList::Matrix3Type

Definition at line 31 of file NeighborList.hh.

typedef std::set<UnitCell, std::function<bool (UnitCell, UnitCell)> > CASM::PrimNeighborList::NeighborSet

Definition at line 33 of file NeighborList.hh.

typedef NeighborSet::size_type CASM::PrimNeighborList::size_type

Definition at line 34 of file NeighborList.hh.

typedef std::set<int> CASM::PrimNeighborList::SublatIndices

Definition at line 36 of file NeighborList.hh.

typedef Eigen::Matrix<long, Eigen::Dynamic, 1> CASM::PrimNeighborList::VectorXType

Definition at line 32 of file NeighborList.hh.

Constructor & Destructor Documentation

template<typename SublatIterator >

CASM::PrimNeighborList::PrimNeighborList	(	const Matrix3Type &	W,
		SublatIterator	begin,
		SublatIterator	end
	)

Constructor, specifying the weighting matrix to use and the indices of sublattices to include.

Constructor.

Parameters

W	A positive-definite weighting matrix for calculating the weighted squared L2 norm of the unitcell indices.

The canonical order of UnitCell is obtained by lexicographically sorting [r, i, j, k], where r = (i,j,k).transpose() * W * (i,j,k).
The canonical order of UnitCellCoord is obtained by lexicographically sorting [r, i, j, k, b], where r = (i,j,k).transpose() * W * (i,j,k).

Definition at line 188 of file NeighborList.hh.

Member Function Documentation

PrimNeighborList::VectorXType CASM::PrimNeighborList::_add_dist ( const UnitCell & A ) const

private

Return [r, i, j, k], where r = _dist(A)

Definition at line 112 of file NeighborList.cc.

bool CASM::PrimNeighborList::_compare_unitcell	(	const UnitCell &	A,
		const UnitCell &	B
	)		const

private

Convert [i,j,k] -> [r,i,j,k] and then lexicographically compare.

Definition at line 120 of file NeighborList.cc.

bool CASM::PrimNeighborList::_compare_vec	(	const VectorXType &	A,
		const VectorXType &	B
	)

staticprivate

Lexicographical comparison.

Definition at line 125 of file NeighborList.cc.

PrimNeighborList::Scalar CASM::PrimNeighborList::_dist ( const UnitCell & A ) const

private

Calculate A.transpose()*M*A.

Definition at line 107 of file NeighborList.cc.

void CASM::PrimNeighborList::_expand ( Scalar prev_range )

private

Ensure that all intermediate UnitCell are included in our neighborhood.

Definition at line 29 of file NeighborList.cc.

PrimNeighborList::const_iterator CASM::PrimNeighborList::begin ( ) const

const_iterator over the neighborhood of unit cells

Definition at line 82 of file NeighborList.cc.

PrimNeighborList::const_iterator CASM::PrimNeighborList::cbegin ( ) const

const_iterator over the neighborhood of unit cells

Definition at line 92 of file NeighborList.cc.

PrimNeighborList::const_iterator CASM::PrimNeighborList::cend ( ) const

const_iterator over the neighborhood of unit cells

Definition at line 97 of file NeighborList.cc.

std::unique_ptr< PrimNeighborList > CASM::PrimNeighborList::clone ( ) const

Clone.

Definition at line 171 of file NeighborList.cc.

PrimNeighborList::const_iterator CASM::PrimNeighborList::end ( ) const

const_iterator over the neighborhood of unit cells

Definition at line 87 of file NeighborList.cc.

void CASM::PrimNeighborList::expand ( UnitCellCoord uccoord )

Expand the neighbor list to include the given UnitCellCoord.

Definition at line 14 of file NeighborList.cc.

template<typename UnitCellCoordIterator >

void CASM::PrimNeighborList::expand	(	UnitCellCoordIterator	begin,
		UnitCellCoordIterator	end
	)

Expand the neighbor list to include the given range of UnitCellCoord.

The canonical order of UnitCellCoord is obtained by lexicographically sorting [r, i, j, k, b], where r = (i,j,k).transpose() * W * (i,j,k).
The canonical order of UnitCell is obtained by lexicographically sorting [r, i, j, k]
After determining the sorted order of the requested UnitCell, all intermediate UnitCell will also be added so that indices into the neighbor list are always constant and in canonical order

Definition at line 221 of file NeighborList.hh.

PrimNeighborList::Matrix3Type CASM::PrimNeighborList::make_weight_matrix	(	const Eigen::Matrix3d	lat_column_mat,
		Index	max_element_value,
		double	tol
	)

static

Returns a NeighborList weighting matrix appropriate for a particular lattice.

Returns the integer weight matrix, M, closest to lat.transpose()*lat with all elements less than max_element_value.

C = L*F, where L is the lattice vectors as a column matrix
Want r = F.transpose*M*F such that r = C.transpose*C, where F is fractional coordinates, and C is cartesian coordinates.
Find F.t*M*F = F.t*L.t*L*F -> W ~ L.tranpose*L
Approch, calculate L.tranpose*L, then divide by minimum element -> M'
consider integer n=1,2,...,n_last for all n such that all elements of n*M' are less than 'max_element_value'
return the first n*M' that is integer. If none are integer, return n_last*M'

Definition at line 142 of file NeighborList.cc.

PrimNeighborList::size_type CASM::PrimNeighborList::size ( ) const

size of the neighborhood of unit cells

Definition at line 77 of file NeighborList.cc.

const PrimNeighborList::SublatIndices & CASM::PrimNeighborList::sublat_indices ( ) const

pair of const_iterators over a range of indices of sublattices to include

const_iterator over the neighborhood of unit cells

Definition at line 102 of file NeighborList.cc.

PrimNeighborList::Matrix3Type CASM::PrimNeighborList::weight_matrix ( ) const

Return the weighting matrix W used to define the canonical order.

Return the weighting matrix used to define the canonical order.

Definition at line 9 of file NeighborList.cc.

Member Data Documentation

NeighborSet CASM::PrimNeighborList::m_neighborhood

private

the neighborhood of [i, j, k]

Definition at line 108 of file NeighborList.hh.

Scalar CASM::PrimNeighborList::m_range

private

the neighborhood, m_neighborhood, contains all UnitCell with r <= m_range

Definition at line 111 of file NeighborList.hh.

SublatIndices CASM::PrimNeighborList::m_sublat_indices

private

the indices of sublattices that should be included

Definition at line 114 of file NeighborList.hh.

Eigen::MatrixXd CASM::PrimNeighborList::m_Uinv

private

Cholesky decomposition: W = U.transpose()*U, useful for getting bounding box.

Definition at line 105 of file NeighborList.hh.

Matrix3Type CASM::PrimNeighborList::m_W

private

Weighting matrix.

The canonical order of UnitCellCoord is obtained by lexicographically sorting [r, i, j, k, b], where r = (i,j,k).transpose() * W * (i,j,k).

Definition at line 102 of file NeighborList.hh.

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef Index CASM::PrimNeighborList::Scalar

Definition at line 30 of file NeighborList.hh.

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

/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/include/casm/clex/NeighborList.hh
/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/src/casm/clex/NeighborList.cc

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Private Member Functions

Static Private Member Functions

Private Attributes

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation