#include <Hull.hh>

Detailed Description

Generate and inspect the convex hull generated from a selection of Configurations.

The underlying Qhull object may not be copy constructed or assigned, so neither can this class. Instead use shared_ptr<Hull>.

Definition at line 17 of file Hull.hh.

Classes
struct	CompareVertex

Public Types
typedef VectorXdAttribute< Configuration >	CompCalculator

typedef ScalarAttribute< Configuration >	EnergyCalculator

typedef std::pair< notstd::cloneable_ptr< CompCalculator >, notstd::cloneable_ptr< EnergyCalculator > >	CalculatorPair

typedef std::map< std::string, CalculatorPair >	CalculatorOptions

Public Member Functions
	Hull (const DB::Selection< Configuration > &_selection, const CompCalculator &_comp_calculator=ConfigIO::SpeciesFrac(), const EnergyCalculator &_energy_calculator=ConfigIO::formation_energy_per_species(), double _singular_value_tol=1e-14, double _bottom_facet_tol=1e-14)
	Constructor for convex hull in composition/energy space. More...

const orgQhull::Qhull &	data () const
	const Access the hull object directly More...

const Eigen::MatrixXd &	reduce () const
	Orthogonal transformation matrix from a point in full comp/energy space to dimension-reduced comp/energy space. More...

const Eigen::Transpose< const Eigen::MatrixXd >	expand () const
	Orthogonal transformation matrix from a point in the dimension-reduced comp/energy space to the full comp/energy space. More...

const Configuration &	configuration (const orgQhull::QhullPoint &point) const
	Return the configuration corresponding to any point. More...

const Configuration &	configuration (const orgQhull::QhullVertex &vertex) const
	Return the configuration corresponding to a hull vertex. More...

Eigen::VectorXd	mu (const orgQhull::QhullFacet facet) const
	Return the chemical potential corresponding to a facet. More...

const Configuration &	groundstate (const Eigen::VectorXd &mu) const
	Return the 0K ground state corresponding to the input chemical potential. More...

double	energy (const Configuration &config) const
	Use the EnergyCalculator to return the energy of a Configuration. More...

Eigen::VectorXd	composition (const Configuration &config) const
	Use the CompCalculator to return the composition of a Configuration. More...

Eigen::VectorXd	point (const Configuration &config) const
	Return a vector corresponding to the coordinate of a given configuration in full composition/energy space. More...

Eigen::VectorXd	reduced_point (const Configuration &config) const
	Return a vector corresponding to the coordinate of a given configuration in the reduced composition/energy space. More...

double	dist_to_hull (const Configuration &config) const
	The distance a Configuration is above the hull along the energy axis. More...

double	dist_to_hull (Eigen::VectorXd _reduced_point) const
	The distance a point in the reduced composition/energy space is above the hull along the energy axis. More...

Private Attributes
orgQhull::Qhull	m_hull

DB::Selection< Configuration >	m_selection

notstd::cloneable_ptr< CompCalculator >	m_comp_calculator

notstd::cloneable_ptr< EnergyCalculator >	m_energy_calculator

Eigen::MatrixXd	m_reduce

std::vector< std::pair< orgQhull::QhullFacet, double > >	m_bottom_facets

std::set< orgQhull::QhullVertex, CompareVertex >	m_bottom_vertices

Member Typedef Documentation

◆ CalculatorOptions

typedef std::map<std::string, CalculatorPair> CASM::Hull::CalculatorOptions

Definition at line 24 of file Hull.hh.

◆ CalculatorPair

typedef std::pair<notstd::cloneable_ptr<CompCalculator>, notstd::cloneable_ptr<EnergyCalculator> > CASM::Hull::CalculatorPair

Definition at line 23 of file Hull.hh.

◆ CompCalculator

typedef VectorXdAttribute<Configuration> CASM::Hull::CompCalculator

Definition at line 19 of file Hull.hh.

◆ EnergyCalculator

typedef ScalarAttribute<Configuration> CASM::Hull::EnergyCalculator

Definition at line 20 of file Hull.hh.

Constructor & Destructor Documentation

◆ Hull()

CASM::Hull::Hull	(	const DB::Selection< Configuration > &	_selection,
		const CompCalculator &	_comp_calculator = `ConfigIO::SpeciesFrac()`,
		const EnergyCalculator &	_energy_calculator = `ConfigIO::formation_energy_per_species()`,
		double	_singular_value_tol = `1e-14`,
		double	_bottom_facet_tol = `1e-14`
	)

Constructor for convex hull in composition/energy space.

Constructor for convex hull in atom_frac & Ef/atom space.

Definition at line 27 of file Hull.cc.

Member Function Documentation

◆ composition()

Eigen::VectorXd CASM::Hull::composition ( const Configuration & config ) const

Use the CompCalculator to return the composition of a Configuration.

Definition at line 211 of file Hull.cc.

◆ configuration() [1/2]

const Configuration & CASM::Hull::configuration ( const orgQhull::QhullPoint & point ) const

Return the configuration corresponding to any point.

Definition at line 137 of file Hull.cc.

◆ configuration() [2/2]

const Configuration & CASM::Hull::configuration ( const orgQhull::QhullVertex & vertex ) const

Return the configuration corresponding to a hull vertex.

Definition at line 145 of file Hull.cc.

◆ data()

const orgQhull::Qhull & CASM::Hull::data ( ) const

const Access the hull object directly

Definition at line 119 of file Hull.cc.

◆ dist_to_hull() [1/2]

double CASM::Hull::dist_to_hull ( const Configuration & config ) const

The distance a Configuration is above the hull along the energy axis.

Definition at line 231 of file Hull.cc.

◆ dist_to_hull() [2/2]

double CASM::Hull::dist_to_hull ( Eigen::VectorXd _reduced_point ) const

The distance a point in the reduced composition/energy space is above the hull along the energy axis.

Definition at line 237 of file Hull.cc.

◆ energy()

double CASM::Hull::energy ( const Configuration & config ) const

Use the EnergyCalculator to return the energy of a Configuration.

Definition at line 206 of file Hull.cc.

◆ expand()

const Eigen::Transpose< const Eigen::MatrixXd > CASM::Hull::expand ( ) const

Orthogonal transformation matrix from a point in the dimension-reduced comp/energy space to the full comp/energy space.

Definition at line 132 of file Hull.cc.

◆ groundstate()

const Configuration & CASM::Hull::groundstate ( const Eigen::VectorXd & mu ) const

Return the 0K ground state corresponding to the input chemical potential.

Units must be appropriate given the composition/energy space

Definition at line 173 of file Hull.cc.

◆ mu()

Eigen::VectorXd CASM::Hull::mu ( const orgQhull::QhullFacet facet ) const

Return the chemical potential corresponding to a facet.

Calculated from the normal of the provided facet, so units depend on composition/energy space

Definition at line 154 of file Hull.cc.

◆ point()

Eigen::VectorXd CASM::Hull::point ( const Configuration & config ) const

Return a vector corresponding to the coordinate of a given configuration in full composition/energy space.

Return a vector corresponding to the coordinate of a given configuration in full comp/energy space.

Definition at line 217 of file Hull.cc.

◆ reduce()

const Eigen::MatrixXd & CASM::Hull::reduce ( ) const

Orthogonal transformation matrix from a point in full comp/energy space to dimension-reduced comp/energy space.

If the points in the provided configuration selection do not span the entire composition space, a principle component analysis identifies the subspace that is spanned and this matrix rotates points into that subspace

Definition at line 128 of file Hull.cc.

◆ reduced_point()

Eigen::VectorXd CASM::Hull::reduced_point ( const Configuration & config ) const

Return a vector corresponding to the coordinate of a given configuration in the reduced composition/energy space.

Definition at line 226 of file Hull.cc.

Member Data Documentation

◆ m_bottom_facets

std::vector<std::pair<orgQhull::QhullFacet, double> > CASM::Hull::m_bottom_facets

private

Definition at line 106 of file Hull.hh.

◆ m_bottom_vertices

std::set<orgQhull::QhullVertex, CompareVertex> CASM::Hull::m_bottom_vertices

private

Definition at line 109 of file Hull.hh.

◆ m_comp_calculator

notstd::cloneable_ptr<CompCalculator> CASM::Hull::m_comp_calculator

private

Definition at line 95 of file Hull.hh.

◆ m_energy_calculator

notstd::cloneable_ptr<EnergyCalculator> CASM::Hull::m_energy_calculator

private

Definition at line 98 of file Hull.hh.

◆ m_hull

orgQhull::Qhull CASM::Hull::m_hull

private

Definition at line 89 of file Hull.hh.

◆ m_reduce

Eigen::MatrixXd CASM::Hull::m_reduce

private

Definition at line 102 of file Hull.hh.

◆ m_selection

DB::Selection<Configuration> CASM::Hull::m_selection

private

Definition at line 92 of file Hull.hh.

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

/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/include/casm/hull/Hull.hh
/Users/bpuchala/Work/codes/CASMcode_v0.2.X_reference/src/casm/hull/Hull.cc

Detailed Description

Classes

Public Types

Public Member Functions

Private Attributes

Member Typedef Documentation

◆ CalculatorOptions

◆ CalculatorPair

◆ CompCalculator

◆ EnergyCalculator

Constructor & Destructor Documentation

◆ Hull()

Member Function Documentation

◆ composition()

◆ configuration() [1/2]

◆ configuration() [2/2]

◆ data()

◆ dist_to_hull() [1/2]

◆ dist_to_hull() [2/2]

◆ energy()

◆ expand()

◆ groundstate()

◆ mu()

◆ point()

◆ reduce()

◆ reduced_point()

Member Data Documentation

◆ m_bottom_facets

◆ m_bottom_vertices

◆ m_comp_calculator

◆ m_energy_calculator

◆ m_hull

◆ m_reduce

◆ m_selection