#include <Niggli.hh>

Detailed Description

Returns a values of A, B, C, ksi, eta and zeta. If the initialization cell has vector lenghts a, b and c, with angles alpha, beta, gamma, then the niggli values are

A=a*a B=b*b C=c*c ksi=2bc*cos(alpha) eta=2ac*cos(beta) zeta=2ab*cos(gamma)

Put another way, if the initialization lattice has vectors a, b and c then

A=aa B=bb C=cc ksi=2*bc eta=2*ac zeta=2*ab

See also: I. Krivy and B. Gruber, Acta Cryst. (1976). A32, 297. [doi:10.1107/S0567739476000636] R. W. Grosse-Kunstleve, N. K. Sauter and P. D. Adams, Acta Cryst. (2004). A60, 1. [doi:10.1107/S010876730302186X]

Definition at line 52 of file Niggli.hh.

Public Member Functions
	NiggliRep (const Lattice &init_lat)

	NiggliRep (const Eigen::Matrix3d &init_lat_col_mat)

double	A () const
	Square of lattice length a. More...

double	B () const
	Square of lattice length b. More...

double	C () const
	Square of lattice length c. More...

double	ksi () const
	2bc*cos(alpha) More...

double	eta () const
	2ac*cos(beta) More...

double	zeta () const
	2ab*cos(gamma) More...

const Eigen::Matrix3d &	metrical_matrix () const

bool	meets_criteria_1 (double compare_tol) const
	A<=B OR (A==B, \|ksi\| <= \|eta\|) More...

bool	meets_criteria_2 (double compare_tol) const
	B<=C OR (B==C, \|eta\| <= \|zeta\|) More...

bool	meets_criteria_3 (double compare_tol) const
	For type I: ksi>0 && eta>0 && zeta>0 (all angles < 90) More...

bool	meets_criteria_4 (double compare_tol) const
	For type II: ksi<=0 && eta<=0 && zeta<=0 (all angles >= 90) More...

bool	meets_criteria_5 (double compare_tol) const
	\|ksi\|<=B OR (ksi==B, zeta<=2*eta) OR (ksi==-B, zeta==0) More...

bool	meets_criteria_6 (double compare_tol) const
	\|eta\|<=A OR (eta==A, zeta<=2*ksi) OR (eta==-A, zeta==0) More...

bool	meets_criteria_7 (double compare_tol) const
	\|zeta\|<=A OR (zeta==A, eta<=2*ksi) OR (zeta==-A, eta==0) More...

bool	meets_criteria_8 (double compare_tol) const

bool	is_niggli (double compare_tol) const
	True if all conditions are true, and either 4 OR 3 is false. More...

bool	is_niggli_type1 (double compare_tol) const
	True if all conditions except 4 are true. More...

bool	is_niggli_type2 (double compare_tol) const
	True if all conditions except 3 are true. More...

void	debug_criteria (double compare_tol) const

Index	niggli_index (double compare_tol) const
	Number of criteria met. More...

Static Public Member Functions
static std::vector< Eigen::Matrix3d > const &	cell_invariant_transforms ()

Private Attributes
const Eigen::Matrix3d	m_metrical_matrix
	Transpose of initialization lattice dotted with itself. More...

const double	m_scale_factor
	Scaling factor for niggli comparisons. More...

Constructor & Destructor Documentation

◆ NiggliRep() [1/2]

CASM::xtal::NiggliRep::NiggliRep ( const Lattice & init_lat )

Definition at line 54 of file Niggli.cc.

◆ NiggliRep() [2/2]

CASM::xtal::NiggliRep::NiggliRep ( const Eigen::Matrix3d & init_lat_col_mat )

Definition at line 50 of file Niggli.cc.

Member Function Documentation

◆ A()

double CASM::xtal::NiggliRep::A ( ) const

Square of lattice length a.

Definition at line 57 of file Niggli.cc.

◆ B()

double CASM::xtal::NiggliRep::B ( ) const

Square of lattice length b.

Definition at line 59 of file Niggli.cc.

◆ C()

double CASM::xtal::NiggliRep::C ( ) const

Square of lattice length c.

Definition at line 61 of file Niggli.cc.

◆ cell_invariant_transforms()

std::vector< Eigen::Matrix3d > const & CASM::xtal::NiggliRep::cell_invariant_transforms ( )

static

List of all 24 operations that permute or reflect lattice vectors without changing cell shape or handedness of lattice vectors

Definition at line 45 of file Niggli.cc.

◆ debug_criteria()

void CASM::xtal::NiggliRep::debug_criteria ( double compare_tol ) const

Definition at line 244 of file Niggli.cc.

◆ eta()

double CASM::xtal::NiggliRep::eta ( ) const

2ac*cos(beta)

Definition at line 65 of file Niggli.cc.

◆ is_niggli()

bool CASM::xtal::NiggliRep::is_niggli ( double compare_tol ) const

True if all conditions are true, and either 4 OR 3 is false.

Definition at line 232 of file Niggli.cc.

◆ is_niggli_type1()

bool CASM::xtal::NiggliRep::is_niggli_type1 ( double compare_tol ) const

True if all conditions except 4 are true.

Definition at line 224 of file Niggli.cc.

◆ is_niggli_type2()

bool CASM::xtal::NiggliRep::is_niggli_type2 ( double compare_tol ) const

True if all conditions except 3 are true.

Definition at line 228 of file Niggli.cc.

◆ ksi()

double CASM::xtal::NiggliRep::ksi ( ) const

2bc*cos(alpha)

Definition at line 63 of file Niggli.cc.

◆ meets_criteria_1()

bool CASM::xtal::NiggliRep::meets_criteria_1 ( double compare_tol ) const

A<=B OR (A==B, |ksi| <= |eta|)

Definition at line 73 of file Niggli.cc.

◆ meets_criteria_2()

bool CASM::xtal::NiggliRep::meets_criteria_2 ( double compare_tol ) const

B<=C OR (B==C, |eta| <= |zeta|)

Definition at line 90 of file Niggli.cc.

◆ meets_criteria_3()

bool CASM::xtal::NiggliRep::meets_criteria_3 ( double compare_tol ) const

For type I: ksi>0 && eta>0 && zeta>0 (all angles < 90)

Definition at line 108 of file Niggli.cc.

◆ meets_criteria_4()

bool CASM::xtal::NiggliRep::meets_criteria_4 ( double compare_tol ) const

For type II: ksi<=0 && eta<=0 && zeta<=0 (all angles >= 90)

Definition at line 120 of file Niggli.cc.

◆ meets_criteria_5()

bool CASM::xtal::NiggliRep::meets_criteria_5 ( double compare_tol ) const

|ksi|<=B OR (ksi==B, zeta<=2*eta) OR (ksi==-B, zeta==0)

Definition at line 133 of file Niggli.cc.

◆ meets_criteria_6()

bool CASM::xtal::NiggliRep::meets_criteria_6 ( double compare_tol ) const

|eta|<=A OR (eta==A, zeta<=2*ksi) OR (eta==-A, zeta==0)

Definition at line 156 of file Niggli.cc.

◆ meets_criteria_7()

bool CASM::xtal::NiggliRep::meets_criteria_7 ( double compare_tol ) const

|zeta|<=A OR (zeta==A, eta<=2*ksi) OR (zeta==-A, eta==0)

Definition at line 180 of file Niggli.cc.

◆ meets_criteria_8()

bool CASM::xtal::NiggliRep::meets_criteria_8 ( double compare_tol ) const

ksi+eta+zeta+A+B<0 OR (ksi+eta+zeta+A+B==0, 2*A+2*eta+zeta>0) C<=A+B+C+ksi+eta+zeta OR (C==A+B+C+ksi+eta+zeta, 2*A+2*eta+zeta<=0)

Definition at line 204 of file Niggli.cc.

◆ metrical_matrix()

const Eigen::Matrix3d & CASM::xtal::NiggliRep::metrical_matrix ( ) const

Definition at line 69 of file Niggli.cc.

◆ niggli_index()

Index CASM::xtal::NiggliRep::niggli_index ( double compare_tol ) const

Number of criteria met.

Definition at line 257 of file Niggli.cc.

◆ zeta()

double CASM::xtal::NiggliRep::zeta ( ) const

2ab*cos(gamma)

Definition at line 67 of file Niggli.cc.

Member Data Documentation

◆ m_metrical_matrix

const Eigen::Matrix3d CASM::xtal::NiggliRep::m_metrical_matrix

private

Transpose of initialization lattice dotted with itself.

Definition at line 123 of file Niggli.hh.

◆ m_scale_factor

const double CASM::xtal::NiggliRep::m_scale_factor