Detailed Description

Enumerates Lattice.

Namespaces
	CASM::HermiteCounter_impl

Classes
class	CASM::LatticeEnumEquivalents
	Enumerate equivalent Lattics, given a SymGroup. More...

class	CASM::ScelEnumProps
	Data structure for holding supercell enumeration properties. More...

class	CASM::HermiteCounter

class	CASM::SupercellEnumerator< UnitType >
	A fake container of supercell matrices. More...

class	CASM::SupercellIterator< UnitType >
	Iterators used with SupercellEnumerator. More...

Functions
Eigen::Matrix3i	CASM::make_unit_cell (PrimClex &primclex, const jsonParser &json)
	Read unit cell transformation matrix from JSON input. More...

ScelEnumProps	CASM::make_scel_enum_props (PrimClex &primclex, const jsonParser &input)
	Make a ScelEnumProps object from JSON input. More...

template<typename UnitType >
Eigen::Matrix3i	CASM::enforce_min_volume (const UnitType &unit, const Eigen::Matrix3i &T, const SymGroup &point_grp, Index volume, bool fix_shape=false)
	Return a transformation matrix that ensures a supercell of at least some volume. More...

template<>
Eigen::Matrix3i	CASM::enforce_min_volume< Lattice > (const Lattice &unit, const Eigen::Matrix3i &T, const SymGroup &point_grp, Index volume, bool fix_shape)

Eigen::Matrix3i	CASM::canonical_hnf (const Eigen::Matrix3i &T, const SymGroup &effective_pg, const Lattice &ref_lattice)
	Return canonical hermite normal form of the supercell matrix, and op used to find it. More...

	CASM::SupercellIterator< UnitType >::SupercellIterator (const SupercellEnumerator< UnitType > &enumerator, int volume, int dims)

SupercellIterator< UnitType > &	CASM::SupercellIterator< UnitType >::operator= (const SupercellIterator< UnitType > &B)

bool	CASM::SupercellIterator< UnitType >::operator== (const SupercellIterator< UnitType > &B) const
	Iterator comparison. More...

bool	CASM::SupercellIterator< UnitType >::operator!= (const SupercellIterator< UnitType > &B) const
	Iterator comparison. More...

reference	CASM::SupercellIterator< UnitType >::operator* () const
	Access the supercell. More...

pointer	CASM::SupercellIterator< UnitType >::operator-> () const
	Access the supercell. More...

HermiteCounter::value_type	CASM::SupercellIterator< UnitType >::volume () const
	current volume More...

Eigen::Matrix3i	CASM::SupercellIterator< UnitType >::matrix () const
	constructed supercell matrix More...

const SupercellEnumerator < UnitType > &	CASM::SupercellIterator< UnitType >::enumerator () const
	const reference to the SupercellEnumerator this is iterating with More...

SupercellIterator< UnitType > &	CASM::SupercellIterator< UnitType >::operator++ ()
	Prefix increment operator. Increment to next unique supercell. More...

void	CASM::SupercellIterator< UnitType >::_increment ()
	Postfix increment operator. Increment to next unique supercell. More...

const UnitType &	CASM::SupercellEnumerator< UnitType >::unit () const
	Access the unit the is being made into supercells. More...

const Lattice &	CASM::SupercellEnumerator< UnitType >::lattice () const
	Access the unit lattice. More...

const SymGroup &	CASM::SupercellEnumerator< UnitType >::point_group () const
	Access the unit point group. More...

const Eigen::Matrix3i &	CASM::SupercellEnumerator< UnitType >::gen_mat () const
	Get the transformation matrix that's being applied to the unit vectors. More...

int	CASM::SupercellEnumerator< UnitType >::dimension () const
	Get the dimensions of the enumerator (1D, 2D or 3D) More...

size_type	CASM::SupercellEnumerator< UnitType >::begin_volume () const
	Get the beginning volume. More...

size_type	CASM::SupercellEnumerator< UnitType >::end_volume () const
	Get the end volume. More...

const_iterator	CASM::SupercellEnumerator< UnitType >::begin () const
	A const iterator to the beginning volume, specify here how the iterator should jump through the enumeration. More...

const_iterator	CASM::SupercellEnumerator< UnitType >::end () const
	A const iterator to the past-the-last volume. More...

const_iterator	CASM::SupercellEnumerator< UnitType >::cbegin () const
	A const iterator to the beginning volume. More...

const_iterator	CASM::SupercellEnumerator< UnitType >::cend () const
	A const iterator to the past-the-last volume. More...

const_iterator	CASM::SupercellEnumerator< UnitType >::citerator (size_type volume) const
	A const iterator to a specified volume. More...

Function Documentation

template<typename UnitType >

void CASM::SupercellIterator< UnitType >::_increment ( )

private

Postfix increment operator. Increment to next unique supercell.

Uses _try_increment until the next unique supercell is found.

Definition at line 571 of file SupercellEnumerator.hh.

template<typename UnitType >

SupercellEnumerator< UnitType >::const_iterator CASM::SupercellEnumerator< UnitType >::begin ( ) const

A const iterator to the beginning volume, specify here how the iterator should jump through the enumeration.

Definition at line 641 of file SupercellEnumerator.hh.

template<typename UnitType >

SupercellEnumerator< UnitType >::size_type CASM::SupercellEnumerator< UnitType >::begin_volume ( ) const

Get the beginning volume.

Definition at line 623 of file SupercellEnumerator.hh.

Eigen::Matrix3i canonical_hnf	(	const Eigen::Matrix3i &	T,
		const SymGroup &	effective_pg,
		const Lattice &	ref_lattice
	)

Return canonical hermite normal form of the supercell matrix, and op used to find it.

Return canonical hermite normal form of the supercell matrix.

Returns: Eigen::Matrix3i of H in canonical form

Parameters

T	A supercell matrix (Eigen::Matrix3i), such that S = U*T, where S is the superlattice and U the unit lattice, as column vector matrices
ref_lattice	The lattice the transformation matrix T is meant to be acting on
effective_pg	Group of symmetry operations to use for determining whether a canonical HNF matrix has been found. This is probably the point group of a structure or configuration Canonical form is such that T is in Hermite normal form (as from CASM::hermite_normal_form), and the unrolled coefficients [a f e] [0 b d] -> abcdef [0 0 c] form the highest lexicographic order when considering equivalent superlattices by point group operations.

Equivalent superlattices can be obtained using point group operations: S' = op*S = U*H*V, where V is integer and has determinant +/- 1
Substituting S = U*T, we have op*U*T = U*H*V.
Or H*V = U.inverse*op*U*T, which is the hermite normal form of U.inverse*op*U*T
So T is canonical if it is in hermite normal form and for all point group operations it has a higher lexicographic order than the resulting H

Definition at line 653 of file SupercellEnumerator.cc.

template<typename UnitType >

SupercellEnumerator< UnitType >::const_iterator CASM::SupercellEnumerator< UnitType >::cbegin ( ) const

A const iterator to the beginning volume.

Definition at line 651 of file SupercellEnumerator.hh.

template<typename UnitType >

SupercellEnumerator< UnitType >::const_iterator CASM::SupercellEnumerator< UnitType >::cend ( ) const

A const iterator to the past-the-last volume.

Definition at line 656 of file SupercellEnumerator.hh.

template<typename UnitType >

SupercellEnumerator< UnitType >::const_iterator CASM::SupercellEnumerator< UnitType >::citerator ( size_type volume ) const

A const iterator to a specified volume.

Definition at line 661 of file SupercellEnumerator.hh.

template<typename UnitType >

int CASM::SupercellEnumerator< UnitType >::dimension ( ) const

Get the dimensions of the enumerator (1D, 2D or 3D)

Definition at line 610 of file SupercellEnumerator.hh.

template<typename UnitType >

SupercellEnumerator< UnitType >::const_iterator CASM::SupercellEnumerator< UnitType >::end ( ) const

A const iterator to the past-the-last volume.

Definition at line 646 of file SupercellEnumerator.hh.

template<typename UnitType >

SupercellEnumerator< UnitType >::size_type CASM::SupercellEnumerator< UnitType >::end_volume ( ) const

Get the end volume.

Definition at line 636 of file SupercellEnumerator.hh.

template<typename UnitType >

Eigen::Matrix3i CASM::enforce_min_volume	(	const UnitType &	unit,
		const Eigen::Matrix3i &	T,
		const SymGroup &	point_grp,
		Index	volume,
		bool	fix_shape = `false`
	)

Return a transformation matrix that ensures a supercell of at least some volume.

Parameters

unit	The thing that is tiled to form supercells. May not be the primitive cell.
T	The transformation matrix of the unit, relative the prim. The volume of the unit is determined from T.determinant().
point_grp	Point group operations to use for checking supercell uniqueness.
volume	The beginning volume to enumerate
end_volume	The past-the-last volume to enumerate
fix_shape	If true, enforce that S = TmI, where m is a scalar and I is the identity matrix.

Returns: M, a transformation matrix, S = T*M, where M is an integer matrix and S.determinant() >= volume

template<>

Eigen::Matrix3i CASM::enforce_min_volume< Lattice >	(	const Lattice &	unit,
		const Eigen::Matrix3i &	T,
		const SymGroup &	point_grp,
		Index	volume,
		bool	fix_shape
	)

Definition at line 582 of file SupercellEnumerator.cc.

template<typename UnitType >

const SupercellEnumerator< UnitType > & CASM::SupercellIterator< UnitType >::enumerator ( ) const

const reference to the SupercellEnumerator this is iterating with

Definition at line 547 of file SupercellEnumerator.hh.

template<typename UnitType >

const Eigen::Matrix3i & CASM::SupercellEnumerator< UnitType >::gen_mat ( ) const

Get the transformation matrix that's being applied to the unit vectors.

Definition at line 605 of file SupercellEnumerator.hh.

template<typename UnitType >

const Lattice & CASM::SupercellEnumerator< UnitType >::lattice ( ) const

Access the unit lattice.

Definition at line 595 of file SupercellEnumerator.hh.

ScelEnumProps CASM::make_scel_enum_props	(	PrimClex &	primclex,
		const jsonParser &	input
	)

Make a ScelEnumProps object from JSON input.

min: int (default=1)
max: int (default=max existing supercell size)
dirs: string, (default="abc")
unit_cell: 3x3 matrix of int, or string (default=identity matrix)
{

"min" : 1,

"max" : 5,

"dirs" : "abc",

"unit_cell" : [

[0, 0, 0],

[0, 0, 0],

[0, 0, 0]

],

"unit_cell" : "SCEL...",

}

Definition at line 68 of file SupercellEnumerator.cc.

Eigen::Matrix3i CASM::make_unit_cell	(	PrimClex &	primclex,
		const jsonParser &	input
	)

Read unit cell transformation matrix from JSON input.

Input json with one of the following forms:

{

"unit_cell" : [

[X, X, X],

[X, X, X],

[X, X, X]

]

}
{ "unit_cell" : "SCEL..."}
If input is null or does not contain "unit_cell", returns identity matrix.

Definition at line 28 of file SupercellEnumerator.cc.

template<typename UnitType >

Eigen::Matrix3i CASM::SupercellIterator< UnitType >::matrix ( ) const

constructed supercell matrix

Definition at line 541 of file SupercellEnumerator.hh.

template<typename UnitType>

bool CASM::SupercellIterator< UnitType >::operator!= ( const SupercellIterator< UnitType > & B ) const

Iterator comparison.

Definition at line 513 of file SupercellEnumerator.hh.

template<typename UnitType >

SupercellIterator< UnitType >::reference CASM::SupercellIterator< UnitType >::operator* ( ) const

Access the supercell.

Definition at line 518 of file SupercellEnumerator.hh.

template<typename UnitType >

SupercellIterator< UnitType > & CASM::SupercellIterator< UnitType >::operator++ ( )

Prefix increment operator. Increment to next unique supercell.

Definition at line 553 of file SupercellEnumerator.hh.

template<typename UnitType >

SupercellIterator< UnitType >::pointer CASM::SupercellIterator< UnitType >::operator-> ( ) const

Access the supercell.

Definition at line 527 of file SupercellEnumerator.hh.

template<typename UnitType>

SupercellIterator< UnitType > & CASM::SupercellIterator< UnitType >::operator= ( const SupercellIterator< UnitType > & B )

Definition at line 498 of file SupercellEnumerator.hh.

template<typename UnitType>

bool CASM::SupercellIterator< UnitType >::operator== ( const SupercellIterator< UnitType > & B ) const

Iterator comparison.

Definition at line 508 of file SupercellEnumerator.hh.

template<typename UnitType >

const SymGroup & CASM::SupercellEnumerator< UnitType >::point_group ( ) const

Access the unit point group.

Definition at line 600 of file SupercellEnumerator.hh.

template<typename UnitType>

CASM::SupercellIterator< UnitType >::SupercellIterator	(	const SupercellEnumerator< UnitType > &	enumerator,
		int	volume,
		int	dims
	)

Definition at line 474 of file SupercellEnumerator.hh.

template<typename UnitType >

const UnitType & CASM::SupercellEnumerator< UnitType >::unit ( ) const

Access the unit the is being made into supercells.

Definition at line 590 of file SupercellEnumerator.hh.

template<typename UnitType >

HermiteCounter::value_type CASM::SupercellIterator< UnitType >::volume ( ) const

current volume

Definition at line 536 of file SupercellEnumerator.hh.

Detailed Description

Namespaces

Classes

Functions

Function Documentation