Class to implement UB matrix. More...

#include <Geometry/Crystal/NiggliCell.h>

Inheritance diagram for Mantid::Geometry::NiggliCell:

Public Member Functions
	NiggliCell (const double _a, const double _b, const double _c, const double _alpha, const double _beta, const double _gamma, const Kernel::DblMatrix &Umatrix=Kernel::DblMatrix(3, 3, true), const int angleunit=angDegrees)
	Constructor. More...

	NiggliCell (const double _a, const double _b, const double _c, const Kernel::DblMatrix &Umatrix=Kernel::DblMatrix(3, 3, true))
	Constructor. More...

	NiggliCell (const Kernel::DblMatrix &Umatrix=Kernel::DblMatrix(3, 3, true))
	Default constructor. More...

	NiggliCell (const UnitCell &uc, const Kernel::DblMatrix &Umatrix=Kernel::DblMatrix(3, 3, true))
	UnitCell constructor. More...

Public Member Functions inherited from Mantid::Geometry::UnitCell
double	a () const
	Get lattice parameter. More...

double	a (int nd) const
	Get lattice parameter a1-a3 as function of index (0-2) More...

double	a1 () const
	Get lattice parameter. More...

double	a2 () const
	Get lattice parameter. More...

double	a3 () const
	Get lattice parameter. More...

double	alpha () const
	Get lattice parameter. More...

double	alpha1 () const
	Get lattice parameter. More...

double	alpha2 () const
	Get lattice parameter. More...

double	alpha3 () const
	Get lattice parameter. More...

double	alphastar () const
	Get reciprocal lattice parameter. More...

double	astar () const
	Get reciprocal lattice parameter. More...

double	b () const
	Get lattice parameter. More...

double	b1 () const
	Get reciprocal lattice parameter. More...

double	b2 () const
	Get reciprocal lattice parameter. More...

double	b3 () const
	Get reciprocal lattice parameter. More...

double	beta () const
	Get lattice parameter. More...

double	beta1 () const
	Get reciprocal lattice parameter. More...

double	beta2 () const
	Get reciprocal lattice parameter. More...

double	beta3 () const
	Get reciprocal lattice parameter. More...

double	betastar () const
	Get reciprocal lattice parameter. More...

double	bstar () const
	Get reciprocal lattice parameter. More...

double	c () const
	Get lattice parameter. More...

double	cstar () const
	Get reciprocal lattice parameter. More...

double	d (const Kernel::V3D &hkl) const
	Return d-spacing ( \( \mbox{ \AA } \)) for a given h,k,l coordinate. More...

double	d (double h, double k, double l) const
	Return d-spacing ( \( \mbox{ \AA } \)) for a given h,k,l coordinate. More...

double	dstar (const Kernel::V3D &hkl) const
	Return d*=1/d ( \( \mbox{ \AA }^{-1} \)) for a given h,k,l coordinate. More...

double	dstar (double h, double k, double l) const
	Return d*=1/d ( \( \mbox{ \AA }^{-1} \)) for a given h,k,l coordinate. More...

double	errora () const
	Get lattice parameter error. More...

double	erroralpha (const int angleunit=angDegrees) const
	Get lattice parameter error. More...

double	errorb () const
	Get lattice parameter error. More...

double	errorbeta (const int angleunit=angDegrees) const
	Get lattice parameter error. More...

double	errorc () const
	Get lattice parameter error. More...

double	errorgamma (const int angleunit=angDegrees) const
	Get lattice parameter error. More...

double	errorvolume () const
	Get lattice parameter error. More...

double	gamma () const
	Get lattice parameter. More...

double	gammastar () const
	Get reciprocal lattice parameter. More...

const Kernel::DblMatrix &	getB () const
	Get the B-matrix. More...

const Kernel::DblMatrix &	getBinv () const
	Get the inverse of the B-matrix. More...

bool	getCrossTerm () const
	Get cross term boolean. More...

double	getdh (int j) const
	Get modulation vectors for satellites. More...

double	getdherr (int j) const
	Get error of modulation vectors for satellites. More...

double	getdk (int j) const
	Get modulation vectors for satellites. More...

double	getdkerr (int j) const
	Get error of modulation vectors for satellites. More...

double	getdl (int j) const
	Get modulation vectors for satellites. More...

double	getdlerr (int j) const
	Get error of modulation vectors for satellites. More...

const Kernel::DblMatrix &	getG () const
	Get the metric tensor. More...

const Kernel::DblMatrix &	getGstar () const
	Get the reciprocal metric tensor. More...

int	getMaxOrder () const
	Get max order. More...

const Kernel::DblMatrix &	getModHKL () const
	Get modulation vectors for satellites. More...

const Kernel::V3D	getModVec (int j) const
	Get modulation vectors for satellites. More...

const Kernel::V3D	getVecErr (int j) const
	Get errors for modulation vectors for satellites. More...

bool	operator!= (const UnitCell &other) const

bool	operator== (const UnitCell &other) const

virtual void	recalculateFromGstar (const Kernel::Matrix< double > &NewGstar)
	Recalculate lattice from reciprocal metric tensor (Gstar=transpose(UB)*UB) More...

double	recAngle (double h1, double k1, double l1, double h2, double k2, double l2, const int angleunit=angDegrees) const
	Calculate the angle in degrees or radians between two reciprocal vectors (h1,k1,l1) and (h2,k2,l2) More...

double	recVolume () const
	Volume of the reciprocal lattice. More...

void	set (double _a, double _b, double _c, double _alpha, double _beta, double _gamma, const int angleunit=angDegrees)
	Set lattice parameters. More...

void	seta (double _a)
	Set lattice parameter. More...

void	setalpha (double _alpha, const int angleunit=angDegrees)
	Set lattice parameter. More...

void	setb (double _b)
	Set lattice parameter. More...

void	setbeta (double _beta, const int angleunit=angDegrees)
	Set lattice parameter. More...

void	setc (double _c)
	Set lattice parameter. More...

void	setCrossTerm (bool CT)
	Set modulation vectors for satellites. More...

void	setError (double _aerr, double _berr, double _cerr, double _alphaerr, double _betaerr, double _gammaerr, const int angleunit=angDegrees)
	Set lattice parameter errors. More...

void	setErrora (double _aerr)
	Set lattice parameter error. More...

void	setErroralpha (double _alphaerr, const int angleunit=angDegrees)
	Set lattice parameter error. More...

void	setErrorb (double _berr)
	Set lattice parameter error. More...

void	setErrorbeta (double _betaerr, const int angleunit=angDegrees)
	Set lattice parameter error. More...

void	setErrorc (double _cerr)
	Set lattice parameter error. More...

void	setErrorgamma (double _gammaerr, const int angleunit=angDegrees)
	Set lattice parameter error. More...

void	setErrorModHKL (const Kernel::DblMatrix &newErrorModHKL)
	Set modulation vectors for satellites. More...

void	setErrorModHKL (double _dh1err, double _dk1err, double _dl1err, double _dh2err, double _dk2err, double _dl2err, double _dh3err, double _dk3err, double _dl3err)
	Set modulation vectors for satellites. More...

void	setgamma (double _gamma, const int angleunit=angDegrees)
	Set lattice parameter. More...

void	setMaxOrder (int MaxO)
	Set modulation vectors for satellites. More...

void	setModerr (int i, double _dherr, double _dkerr, double _dlerr)
	Set modulation vectors for satellites. More...

void	setModerr1 (double _dh1err, double _dk1err, double _dl1err)
	Set modulation vectors for satellites. More...

void	setModerr2 (double _dh2err, double _dk2err, double _dl2err)
	Set modulation vectors for satellites. More...

void	setModerr3 (double _dh3err, double _dk3err, double _dl3err)
	Set modulation vectors for satellites. More...

void	setModHKL (const Kernel::DblMatrix &newModHKL)
	Set modulation vectors for satellites. More...

void	setModHKL (double _dh1, double _dk1, double _dl1, double _dh2, double _dk2, double _dl2, double _dh3, double _dk3, double _dl3)
	Set modulation vectors for satellites. More...

void	setModVec1 (const Kernel::V3D &newModVec)
	Set modulation vectors for satellites. More...

void	setModVec1 (double _dh1, double _dk1, double _dl1)
	Set modulation vectors for satellites. More...

void	setModVec2 (const Kernel::V3D &newModVec)
	Set modulation vectors for satellites. More...

void	setModVec2 (double _dh2, double _dk2, double _dl2)
	Set modulation vectors for satellites. More...

void	setModVec3 (const Kernel::V3D &newModVec)
	Set modulation vectors for satellites. More...

void	setModVec3 (double _dh3, double _dk3, double _dl3)
	Set modulation vectors for satellites. More...

	UnitCell ()
	Default constructor. More...

	UnitCell (const double _a, const double _b, const double _c)
	Constructor. More...

	UnitCell (const double _a, const double _b, const double _c, const double _alpha, const double _beta, const double _gamma, const int angleunit=angDegrees)
	Constructor. More...

double	volume () const
	Volume of the direct unit-cell. More...

virtual	~UnitCell ()=default

Static Public Member Functions
static bool	HasNiggliAngles (const Kernel::V3D &a_dir, const Kernel::V3D &b_dir, const Kernel::V3D &c_dir, double epsilon)
	Check if a,b,c cell has angles satifying Niggli condition within epsilon. More...

static bool	MakeNiggliUB (const Kernel::DblMatrix &UB, Kernel::DblMatrix &newUB)
	Construct a newUB corresponding to a Niggli cell from the given UB. More...

Private Attributes
Kernel::DblMatrix	U

Kernel::DblMatrix	UB

Additional Inherited Members
Protected Member Functions inherited from Mantid::Geometry::UnitCell
void	calculateB ()
	Private function to calculate B matrix. More...

void	calculateG ()

void	calculateGstar ()
	Private function to calculate Gstar matrix. More...

void	calculateReciprocalLattice ()
	Private function to calculate reciprocal lattice parameters. More...

virtual void	recalculate ()
	Private function, called at initialization or whenever lattice parameters are changed. More...

Protected Attributes inherited from Mantid::Geometry::UnitCell
Kernel::DblMatrix	B
	B matrix for a right-handed coordinate system, in Busing-Levy convention. More...

Kernel::DblMatrix	Binv
	Inverse of the B matrix. More...

bool	CrossTerm

std::vector< double >	da
	Lattice parameter a,b,c,alpha,beta,gamma (in \( \mbox{ \AA } \) and radians) More...

std::vector< double >	errorda
	Error in lattice parameters (in \( \mbox{ \AA } \) and radians) More...

Kernel::DblMatrix	errorModHKL

Kernel::DblMatrix	G
	Metric tensor. More...

Kernel::DblMatrix	Gstar
	Reciprocal lattice tensor. More...

int	MaxOrder

Kernel::DblMatrix	ModHKL

std::vector< double >	ra
	Reciprocal lattice parameters (in \( \mbox{ \AA }^{-1} \) and radians) More...

Detailed Description

Class to implement UB matrix.

See documentation about UB matrix in the Mantid repository.

Author: Andrei Savici, SNS, ORNL

Date: 2011-04-15

Definition at line 21 of file NiggliCell.h.

Constructor & Destructor Documentation

◆ NiggliCell() [1/4]

Mantid::Geometry::NiggliCell::NiggliCell ( const Kernel::DblMatrix & Umatrix = Kernel::DblMatrix(3, 3, true) )

Default constructor.

Parameters

Umatrix :: orientation matrix U. By default this will be identity matrix

Definition at line 79 of file NiggliCell.cpp.

References Mantid::Geometry::UnitCell::getB(), Mantid::Kernel::Matrix< T >::isRotation(), U, and UB.

◆ NiggliCell() [2/4]

Mantid::Geometry::NiggliCell::NiggliCell	(	const double	_a,
		const double	_b,
		const double	_c,
		const Kernel::DblMatrix &	Umatrix = `Kernel::DblMatrix(3, 3, true)`
	)

Constructor.

Parameters

_a	:: lattice parameter \( a \) with \(\alpha = \beta = \gamma = 90^\circ \)
_b	:: lattice parameter \( b \) with \(\alpha = \beta = \gamma = 90^\circ \)
_c	:: lattice parameter \( c \) with \(\alpha = \beta = \gamma = 90^\circ \)
Umatrix	:: orientation matrix U

Definition at line 96 of file NiggliCell.cpp.

References Mantid::Geometry::UnitCell::getB(), Mantid::Kernel::Matrix< T >::isRotation(), U, and UB.

◆ NiggliCell() [3/4]

Mantid::Geometry::NiggliCell::NiggliCell	(	const double	_a,
		const double	_b,
		const double	_c,
		const double	_alpha,
		const double	_beta,
		const double	_gamma,
		const Kernel::DblMatrix &	Umatrix = `Kernel::DblMatrix(3, 3, true)`,
		const int	angleunit = `angDegrees`
	)

Constructor.

Parameters

_a	:: lattice parameter \( a \)
_b	:: lattice parameter \( b \)
_c	:: lattice parameter \( c \)
_alpha	:: lattice parameter \( \alpha \)
_beta	:: lattice parameter \( \beta \)
_gamma	:: lattice parameter \( \gamma \)
angleunit	:: units for angle, of type AngleUnits. Default is degrees.
Umatrix	:: orientation matrix U

Definition at line 115 of file NiggliCell.cpp.

References Mantid::Geometry::UnitCell::getB(), Mantid::Kernel::Matrix< T >::isRotation(), U, and UB.

◆ NiggliCell() [4/4]

Mantid::Geometry::NiggliCell::NiggliCell	(	const UnitCell &	uc,
		const Kernel::DblMatrix &	Umatrix = `Kernel::DblMatrix(3, 3, true)`
	)

UnitCell constructor.

Parameters

uc	:: UnitCell
Umatrix	:: orientation matrix U. By default this will be identity matrix

Definition at line 129 of file NiggliCell.cpp.

References Mantid::Geometry::UnitCell::getB(), Mantid::Kernel::Matrix< T >::isRotation(), U, and UB.

Member Function Documentation

◆ HasNiggliAngles()

bool Mantid::Geometry::NiggliCell::HasNiggliAngles	(	const Kernel::V3D &	a_dir,
		const Kernel::V3D &	b_dir,
		const Kernel::V3D &	c_dir,
		double	epsilon
	)

static

Check if a,b,c cell has angles satifying Niggli condition within epsilon.

Specifically, check if all angles are strictly less than 90 degrees, or all angles are greater than or equal to 90 degrees. The inequality requirements are relaxed by an amount specified by the paramter epsilon to accommodate some experimental and/or rounding error in the calculated angles.

Parameters

a_dir	Vector in the direction of the real cell edge vector 'a'
b_dir	Vector in the direction of the real cell edge vector 'b'
c_dir	Vector in the direction of the real cell edge vector 'c'
epsilon	Tolerance (in degrees) around 90 degrees. For example an angle theta will be considered strictly less than 90 degrees, if it is less than 90+epsilon.

Returns: true if all angles are less than 90 degrees, or if all angles are greater than or equal to 90 degrees.

Definition at line 154 of file NiggliCell.cpp.

References Mantid::Geometry::UnitCell::alpha(), Mantid::Kernel::V3D::angle(), Mantid::Geometry::UnitCell::beta(), and Mantid::Geometry::UnitCell::gamma().

Referenced by MakeNiggliUB().

◆ MakeNiggliUB()

bool Mantid::Geometry::NiggliCell::MakeNiggliUB	(	const Kernel::DblMatrix &	UB,
		Kernel::DblMatrix &	newUB
	)

static

Construct a newUB corresponding to a Niggli cell from the given UB.

Try to find a UB that is equivalent to the original UB, but corresponds to a Niggli reduced cell with the smallest sum of edge lengths and with angles that are farthest from 90 degrees.

Parameters

UB	The original UB
newUB	Returns the newUB

Returns: True if a possibly constructive change was made and newUB has been set to a new matrix. It returns false if no constructive change was found and newUB is just set to the original UB.

Definition at line 183 of file NiggliCell.cpp.

References Mantid::Geometry::UnitCell::a(), Mantid::Geometry::UnitCell::b(), Mantid::Geometry::UnitCell::c(), Mantid::Geometry::CompareABCsum(), Mantid::Geometry::CompareDiffFrom90(), Mantid::Kernel::V3D::compareMagnitude(), fabs, Mantid::Geometry::OrientedLattice::GetABC(), Mantid::Geometry::OrientedLattice::GetUB(), HasNiggliAngles(), Mantid::Kernel::V3D::norm(), Mantid::Kernel::V3D::scalar_prod(), and UB.