#include <LatticeMap.hh>

Detailed Description

Find the parent mapping of Lattice _parent onto Lattice _child Denoting _parent.lat_column_mat() as 'parent' and _child.lat_column_mat() as 'child', we want a mapping child = deformation_gradient*parent*N where deformation_gradient is an arbitrary 3x3 matrix and 'N' is a 3x3 unimodular (i.e., determinant=+/-1) integer matrix such that cost(deformation_gradient) is minimized with respect to the matrix 'N' For the cost function we use: cost(deformation_gradient) = (_child.volume()/num_atoms)^(2/3) * trace(D.transpose()*D) / g where 'D' is the isovolumetric strain D = deformation_gradient/det(deformation_gradient)^(1/3)-Identity and 'g' is a const geometric factor. The cost function corresponds to the mean-square displacement of a point on the surface of a sphere having V=_child.volume()/num_atoms (i.e., the atomic volume of the child crystal) when the sphere is deformed at constant volume by deformation_gradient/det(deformation_gradient)^(1/3)

Definition at line 78 of file LatticeMap.hh.

Public Types
typedef Eigen::Matrix< double, 3, 3, Eigen::DontAlign >	DMatType

typedef Eigen::Matrix< int, 3, 3, Eigen::DontAlign >	IMatType

Public Member Functions
	LatticeMap (Lattice const &_parent, Lattice const &_child, Index _num_atoms, int _range, SymOpVector const &_parent_point_group, SymOpVector const &_child_point_group, Eigen::Ref< const Eigen::MatrixXd > const &strain_gram_mat=Eigen::MatrixXd::Identity(9, 9), double _init_better_than=1e20, bool _symmetrize_strain_cost=false, double _xtal_tol=TOL)

	LatticeMap (Eigen::Ref< const DMatType > const &_parent, Eigen::Ref< const DMatType > const &_child, Index _num_atoms, int _range, SymOpVector const &_parent_point_group, SymOpVector const &_child_point_group, Eigen::Ref< const Eigen::MatrixXd > const &strain_gram_mat=Eigen::MatrixXd::Identity(9, 9), double _init_better_than=1e20, bool _symmetrize_strain_cost=false, double _xtal_tol=TOL)

void	reset (double _better_than=1e20)

LatticeMap const &	best_strain_mapping () const

LatticeMap const &	next_mapping_better_than (double max_cost) const

double	strain_cost () const

double	calc_strain_cost (const Eigen::Matrix3d &deformation_gradient) const

const DMatType &	matrixN () const

const DMatType &	deformation_gradient () const

const DMatType &	parent_matrix () const

const DMatType &	child_matrix () const

double	xtal_tol () const

bool	symmetrize_strain_cost () const

Private Member Functions
Eigen::Matrix3i const &	inv_mat () const
	Returns the inverse of the current transformation matrix under consideration. More...

Index	n_mat () const
	Number of unimodular matrices. More...

bool	_check_canonical () const
	Returns true if current transformation is the canonical equivalent. More...

LatticeMap const &	_next_mapping_better_than (double max_cost) const

double	_calc_strain_cost () const

Private Attributes
DMatType	m_parent

DMatType	m_child

DMatType	m_U

DMatType	m_V_inv

StrainCostCalculator	m_calc

double	m_vol_factor

int	m_range

std::vector< Eigen::Matrix3i > const *	m_mvec_ptr

std::vector< Eigen::Matrix3i >	m_parent_fsym_mats

SymOpVector	m_parent_point_group

std::vector< Eigen::Matrix3i >	m_child_fsym_mats

bool	m_symmetrize_strain_cost

double	m_xtal_tol

double	m_cost

Index	m_currmat

DMatType	m_deformation_gradient

DMatType	m_N

DMatType	m_dcache

IMatType	m_icache

Member Typedef Documentation

◆ DMatType

typedef Eigen::Matrix<double, 3, 3, Eigen::DontAlign> CASM::xtal::LatticeMap::DMatType

Definition at line 80 of file LatticeMap.hh.

◆ IMatType

typedef Eigen::Matrix<int, 3, 3, Eigen::DontAlign> CASM::xtal::LatticeMap::IMatType

Definition at line 81 of file LatticeMap.hh.

Constructor & Destructor Documentation

◆ LatticeMap() [1/2]

CASM::xtal::LatticeMap::LatticeMap	(	Lattice const &	_parent,
		Lattice const &	_child,
		Index	_num_atoms,
		int	_range,
		SymOpVector const &	_parent_point_group,
		SymOpVector const &	_child_point_group,
		Eigen::Ref< const Eigen::MatrixXd > const &	strain_gram_mat = `Eigen::MatrixXd::Identity(9, 9)`,
		double	_init_better_than = `1e20`,
		bool	_symmetrize_strain_cost = `false`,
		double	_xtal_tol = `TOL`
	)

Definition at line 129 of file LatticeMap.cc.

◆ LatticeMap() [2/2]

CASM::xtal::LatticeMap::LatticeMap	(	Eigen::Ref< const DMatType > const &	_parent,
		Eigen::Ref< const DMatType > const &	_child,
		Index	_num_atoms,
		int	_range,
		SymOpVector const &	_parent_point_group,
		SymOpVector const &	_child_point_group,
		Eigen::Ref< const Eigen::MatrixXd > const &	strain_gram_mat = `Eigen::MatrixXd::Identity(9, 9)`,
		double	_init_better_than = `1e20`,
		bool	_symmetrize_strain_cost = `false`,
		double	_xtal_tol = `TOL`
	)

Member Function Documentation

◆ _calc_strain_cost()

double CASM::xtal::LatticeMap::_calc_strain_cost ( ) const

private

◆ _check_canonical()

bool CASM::xtal::LatticeMap::_check_canonical ( ) const

private

Returns true if current transformation is the canonical equivalent.

Definition at line 359 of file LatticeMap.cc.

◆ _next_mapping_better_than()

const LatticeMap & CASM::xtal::LatticeMap::_next_mapping_better_than ( double max_cost ) const

private

Definition at line 315 of file LatticeMap.cc.

◆ best_strain_mapping()

const LatticeMap & CASM::xtal::LatticeMap::best_strain_mapping ( ) const

Definition at line 275 of file LatticeMap.cc.

◆ calc_strain_cost()

double CASM::xtal::LatticeMap::calc_strain_cost ( const Eigen::Matrix3d & deformation_gradient ) const

Definition at line 296 of file LatticeMap.cc.

◆ child_matrix()

const DMatType& CASM::xtal::LatticeMap::child_matrix ( ) const

inline

Definition at line 120 of file LatticeMap.hh.

◆ deformation_gradient()

const DMatType& CASM::xtal::LatticeMap::deformation_gradient ( ) const

inline

Definition at line 114 of file LatticeMap.hh.

◆ inv_mat()

Eigen::Matrix3i const& CASM::xtal::LatticeMap::inv_mat ( ) const

inlineprivate

Returns the inverse of the current transformation matrix under consideration.

Definition at line 165 of file LatticeMap.hh.

◆ matrixN()

const DMatType& CASM::xtal::LatticeMap::matrixN ( ) const

inline

Definition at line 112 of file LatticeMap.hh.

◆ n_mat()

Index CASM::xtal::LatticeMap::n_mat ( ) const

inlineprivate

Number of unimodular matrices.

Definition at line 168 of file LatticeMap.hh.

◆ next_mapping_better_than()

const LatticeMap & CASM::xtal::LatticeMap::next_mapping_better_than ( double max_cost ) const

Definition at line 306 of file LatticeMap.cc.

◆ parent_matrix()

const DMatType& CASM::xtal::LatticeMap::parent_matrix ( ) const

inline

Definition at line 118 of file LatticeMap.hh.

◆ reset()

void CASM::xtal::LatticeMap::reset ( double _better_than = 1e20 )

Definition at line 219 of file LatticeMap.cc.

◆ strain_cost()

double CASM::xtal::LatticeMap::strain_cost ( ) const

inline

Definition at line 108 of file LatticeMap.hh.

◆ symmetrize_strain_cost()

bool CASM::xtal::LatticeMap::symmetrize_strain_cost ( ) const

inline

Definition at line 123 of file LatticeMap.hh.

◆ xtal_tol()

double CASM::xtal::LatticeMap::xtal_tol ( ) const

inline

Definition at line 122 of file LatticeMap.hh.

Member Data Documentation

◆ m_calc

StrainCostCalculator CASM::xtal::LatticeMap::m_calc

private

Definition at line 131 of file LatticeMap.hh.

◆ m_child

DMatType CASM::xtal::LatticeMap::m_child

private

Definition at line 126 of file LatticeMap.hh.

◆ m_child_fsym_mats

std::vector<Eigen::Matrix3i> CASM::xtal::LatticeMap::m_child_fsym_mats

private

Definition at line 149 of file LatticeMap.hh.

◆ m_cost

double CASM::xtal::LatticeMap::m_cost

mutableprivate

Definition at line 156 of file LatticeMap.hh.

◆ m_currmat

Index CASM::xtal::LatticeMap::m_currmat

mutableprivate

Definition at line 157 of file LatticeMap.hh.

◆ m_dcache

DMatType CASM::xtal::LatticeMap::m_dcache

private

Definition at line 158 of file LatticeMap.hh.

◆ m_deformation_gradient

DMatType CASM::xtal::LatticeMap::m_deformation_gradient

mutableprivate

Definition at line 158 of file LatticeMap.hh.

◆ m_icache

IMatType CASM::xtal::LatticeMap::m_icache

mutableprivate

Definition at line 159 of file LatticeMap.hh.

◆ m_mvec_ptr

std::vector<Eigen::Matrix3i> const* CASM::xtal::LatticeMap::m_mvec_ptr

private

Definition at line 140 of file LatticeMap.hh.

◆ m_N

DMatType CASM::xtal::LatticeMap::m_N

private

Definition at line 158 of file LatticeMap.hh.

◆ m_parent

DMatType CASM::xtal::LatticeMap::m_parent

private

Definition at line 126 of file LatticeMap.hh.

◆ m_parent_fsym_mats

std::vector<Eigen::Matrix3i> CASM::xtal::LatticeMap::m_parent_fsym_mats

private

Definition at line 143 of file LatticeMap.hh.

◆ m_parent_point_group

SymOpVector CASM::xtal::LatticeMap::m_parent_point_group

private

Definition at line 146 of file LatticeMap.hh.

◆ m_range

int CASM::xtal::LatticeMap::m_range

private

Definition at line 137 of file LatticeMap.hh.

◆ m_symmetrize_strain_cost

bool CASM::xtal::LatticeMap::m_symmetrize_strain_cost

private

Definition at line 153 of file LatticeMap.hh.

◆ m_U

DMatType CASM::xtal::LatticeMap::m_U

private

Definition at line 129 of file LatticeMap.hh.

◆ m_V_inv

DMatType CASM::xtal::LatticeMap::m_V_inv

private

Definition at line 129 of file LatticeMap.hh.

◆ m_vol_factor

double CASM::xtal::LatticeMap::m_vol_factor

private

Definition at line 135 of file LatticeMap.hh.

◆ m_xtal_tol

double CASM::xtal::LatticeMap::m_xtal_tol

private

Definition at line 154 of file LatticeMap.hh.

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

/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/include/casm/crystallography/LatticeMap.hh
/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/src/casm/crystallography/LatticeMap.cc

Detailed Description

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Member Typedef Documentation

◆ DMatType

◆ IMatType

Constructor & Destructor Documentation

◆ LatticeMap() [1/2]

◆ LatticeMap() [2/2]

Member Function Documentation

◆ _calc_strain_cost()

◆ _check_canonical()

◆ _next_mapping_better_than()

◆ best_strain_mapping()

◆ calc_strain_cost()

◆ child_matrix()

◆ deformation_gradient()

◆ inv_mat()

◆ matrixN()

◆ n_mat()

◆ next_mapping_better_than()

◆ parent_matrix()

◆ reset()

◆ strain_cost()

◆ symmetrize_strain_cost()

◆ xtal_tol()

Member Data Documentation

◆ m_calc

◆ m_child

◆ m_child_fsym_mats

◆ m_cost

◆ m_currmat

◆ m_dcache

◆ m_deformation_gradient

◆ m_icache

◆ m_mvec_ptr

◆ m_N

◆ m_parent

◆ m_parent_fsym_mats

◆ m_parent_point_group

◆ m_range

◆ m_symmetrize_strain_cost

◆ m_U

◆ m_V_inv

◆ m_vol_factor

◆ m_xtal_tol