ActiveBandStructure Class Reference

Class container of the quasiparticle band structure, i.e. More...

#include <active_bandstructure.h>

Inheritance diagram for ActiveBandStructure:

Collaboration diagram for ActiveBandStructure:

Public Member Functions
	ActiveBandStructure (Particle &particle_, Points &points_)
	Almost empty constructor, to be used internally.
	ActiveBandStructure (const Points &points_, HarmonicHamiltonian *h0, const bool &withEigenvectors, const bool &withVelocities)
	Default constructor. More...
Particle	getParticle () override
	Get the Particle object associated with this class. More...
Points	getPoints () override
	Returns the wavevectors on which the band structure is computed. More...
Point	getPoint (const int &pointIndex) override
	Returns a wavevector, given a wavevector index. More...
int	getNumPoints (const bool &useFullGrid=false) override
	Returns the total number of k/q-points. More...
int	getNumBands () override
	Returns the number of bands. More...
int	getFullNumBands () override
int	getNumBands (WavevectorIndex &ik) override
	Returns the number of bands at a given wavevector. More...
int	hasWindow () override
	Checks whether the bandStructure has been built discarding some Bloch states from those available. More...
bool	getIsDistributed () override
	Returns if this band structure is distributed. More...
size_t	getIndex (const WavevectorIndex &ik, const BandIndex &ib) override
	Builds a Bloch state index, which runs on both wavevector index and band index. More...
std::tuple< WavevectorIndex, BandIndex >	getIndex (const int &is) override
	Given a Bloch state index, finds the corresponding wavevector and band index. More...
std::tuple< WavevectorIndex, BandIndex >	getIndex (StateIndex &is) override
	Given a Bloch state index, finds the corresponding wavevector and band index. More...
int	getNumStates () override
	Returns the total number of Bloch states, equal to numPoints*numBands. More...
const double &	getEnergy (StateIndex &is) override
	Returns the energy of a quasiparticle from its Bloch index. More...
Eigen::VectorXd	getEnergies (WavevectorIndex &ik) override
	Returns the energies of all quasiparticle computed at a specified wavevector. More...
double	getMaxEnergy () override
	Returns the maximum energy value. More...
Eigen::Vector3d	getGroupVelocity (StateIndex &is) override
	Returns the group velocity of a quasiparticle from its Bloch index. More...
Eigen::MatrixXd	getGroupVelocities (WavevectorIndex &ik) override
	Returns the group velocity of a quasiparticle for all bands at a specified wavevector index. More...
Eigen::Tensor< std::complex< double >, 3 >	getVelocities (WavevectorIndex &ik) override
	Returns the velocity operator (including off-diagonal matrix elements) of the quasiparticles at the specified wavevector index. More...
Eigen::MatrixXcd	getEigenvectors (WavevectorIndex &ik) override
	Obtain the eigenvectors of the quasiparticles at a specified wavevector. More...
Eigen::Tensor< std::complex< double >, 3 >	getPhEigenvectors (WavevectorIndex &ik) override
	Obtain the eigenvectors of the quasiparticles at a specified wavevector. More...
Eigen::Vector3d	getWavevector (StateIndex &is) override
	Returns the energy of a quasiparticle from its Bloch index Used for accessing the band structure in the BTE. More...
Eigen::Vector3d	getWavevector (WavevectorIndex &ik) override
	Returns the energy of a quasiparticle from its Bloch index. More...
void	setEnergies (Point &point, Eigen::VectorXd &energies_) override
	Method to save quasiparticle energies inside ActiveBandStructure(). More...
void	setEnergies (Point &point, std::vector< double > &energies_)
	Method to save quasiparticle energies inside ActiveBandStructure(). More...
void	setEigenvectors (Point &point, Eigen::MatrixXcd &eigenvectors_) override
	Method to save quasiparticle eigenvectors inside ActiveBandStructure. More...
void	setVelocities (Point &point, Eigen::Tensor< std::complex< double >, 3 > &velocities_) override
	Method to save quasiparticle velocity operator in ActiveBandStructure. More...
std::vector< Eigen::Matrix3d >	getRotationsStar (WavevectorIndex &ikIndex) override
	Given a irreducible point index, find the list of rotations to reconstruct the equivalent points. More...
std::vector< Eigen::Matrix3d >	getRotationsStar (StateIndex &isIndex) override
	Given an irreducible Bloch state (i.e. More...
std::tuple< int, Eigen::Matrix3d >	getRotationToIrreducible (const Eigen::Vector3d &x, const int &basis=Points::crystalCoordinates) override
	Given a point in crystal or cartesian coordinates, returns the index of the irreducible point and the rotation such that rotation*irrPoint = redPoint. More...
BteIndex	stateToBte (StateIndex &isIndex) override
	Utility method to convert an index over Bloch states in the band structure into a Bloch state index usable by VectorBTE. More...
StateIndex	bteToState (BteIndex &iBteIndex) override
	Utility method to convert an index over Bloch states in a VectorBTE into the Bloch state index in the band structure. More...
std::vector< int >	irrStateIterator () override
	Iterator over the Bloch states in the band structure, over just the irreducible wavevectors, but isn't distributed over MPI processes. More...
std::vector< int >	parallelIrrStateIterator () override
	Iterator over the Bloch states in the band structure, distributed over MPI processes, running only over irreducible wavevectors. More...
std::vector< int >	irrPointsIterator () override
	Iterator over the irreducible points indices. More...
std::vector< int >	parallelIrrPointsIterator () override
	Iterator over the irreducible points indices. More...
int	getNumIrrStates () override
	Returns the number of irr points in this band structure.
int	getPointIndex (const Eigen::Vector3d &crystalCoordinates, const bool &suppressError=false) override
	Find the index of a point in the reducible list of points, given its coordinates in the crystal basis. More...
std::vector< int >	getReducibleStarFromIrreducible (const int &ik) override
	Method to find the points equivalent to an irreducible point. More...
Public Member Functions inherited from BaseBandStructure
virtual	~BaseBandStructure ()=default
	Base destructor for bandstructure class, silences warnings.
virtual std::vector< size_t >	parallelStateIterator ()
	Returns an iterator to be used for loops over the Bloch state index. More...
void	outputComponentsToJSON (const std::string &outFileName="bandstructure.json")
	Outputs the bandstructure information to file, either sym reduced or not. More...
void	printBandStructureStateInfo (const int &fullNumBands)
	A function to print information about how many states are in this bandstructure, and how things were reduced by filtering of states. More...

Static Public Member Functions
static std::tuple< ActiveBandStructure, StatisticsSweep >	builder (Context &context, HarmonicHamiltonian &h0, Points &points, const bool &withEigenvectors=true, const bool &withVelocities=true, const bool &forceBuildAPP=false)
	Preferred method to initialize the ActiveBandStructure class. More...

Protected Member Functions
void	buildIndices ()
void	buildSymmetries ()
size_t	velBloch2Comb (const int &ik, const int &ib1, const int &ib2, const int &i)
size_t	eigBloch2Comb (const int &ik, const int &ibFull, const int &ibRed)
size_t	bloch2Comb (const int &k, const int &b)
std::tuple< int, int >	comb2Bloch (const int &is)
size_t	bteBloch2Comb (const int &k, const int &b)
std::tuple< int, int >	bteComb2Bloch (const int &is)
void	buildOnTheFly (Window &window, Points points_, HarmonicHamiltonian &h0, const bool &withEigenvectors=true, const bool &withVelocities=true)
StatisticsSweep	buildAsPostprocessing (Context &context, Points points_, HarmonicHamiltonian &h0, const bool &withEigenvector=true, const bool &withVelocities=true)
	in this function, useful for electrons, we first compute the band structure on a dense grid of wavevectors, then compute chemical potential/temperatures and then filter it

Protected Attributes
Particle	particle
Points	points
std::vector< double >	energies
std::vector< std::complex< double > >	velocities
std::vector< std::complex< double > >	eigenvectors
bool	hasEigenvectors = false
bool	hasVelocities = false
int	numStates = 0
int	numIrrStates
int	numIrrPoints
int	numPoints
Eigen::VectorXi	numBands
int	numFullBands = 0
int	windowMethod = 0
Eigen::MatrixXi	auxBloch2Comb
Eigen::VectorXi	cumulativeKbOffset
Eigen::MatrixXi	bteAuxBloch2Comb
Eigen::VectorXi	bteCumulativeKbOffset
Eigen::VectorXi	cumulativeKbbOffset

Detailed Description

energies, velocities, eigenvectors and wavevectors. In contrast to FullBandStructure, which stores this information for all wavevectors and bands, ActiveBandStructure stores this data for a specified subset of wavevectors, and a subset of bands which may change from one wavevector to another. Should be initialized through the static method provided below, which makes use of the Window that is selected by user input. The subset of wavevectors is specified using an ActivePoints class.

Constructor & Destructor Documentation

ActiveBandStructure()

ActiveBandStructure::ActiveBandStructure	(	const Points &	points_,
		HarmonicHamiltonian *	h0,
		const bool &	withEigenvectors,
		const bool &	withVelocities
	)

Populate the band structure for the subset of wavevectors specified by points, but saving all bands for such wavevector. Using this constructor, we populate the band structure on the wavevectors specified by points. Currently used for the caching of the 3rd wavevectors info in the 3-phonon scattering matrix.

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Member Function Documentation

bteToState()

StateIndex ActiveBandStructure::bteToState ( BteIndex &  iBteIndex )

overridevirtual

Unlike stateToBte, this should always have a solution.

Parameters

iBteIndex

index of the Bloch state in the BTE

Returns

StateIndex: the index of the Bloch state in the band structure.

Implements BaseBandStructure.

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builder()

std::tuple< ActiveBandStructure, StatisticsSweep > ActiveBandStructure::builder ( Context &  context, HarmonicHamiltonian &  h0, Points &  points, const bool &  withEigenvectors = true, const bool &  withVelocities = true, const bool &  forceBuildAPP = false  )

static

Parameters

context	object with user input variables.
h0	hamiltonian object to be diagonalized.
points	initial unfiltered list of wavevectors, which will be filtered into an ActivePoints object.
withEigenvectors	compute and store the eigenvectors
withVelocities	compute and store the velocity matrix elements
forceBuildAPP	forces activeBandStructure to be built using the internal buildAsPostprocessing method, even if the input H0 is for phonons.

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getEigenvectors()

Eigen::MatrixXcd ActiveBandStructure::getEigenvectors ( WavevectorIndex &  ik )

overridevirtual

Parameters

wavevectorIndex

a WavevectorIndex(ik) object where ik is the integer wavevector index running over [0,numPoints-1].

Returns

eigenvectors: a complex matrix(numBands,numActiveBands) where numBands is the full (before applying the window) number of Bloch states present at the specified wavevector and numActiveBands is the number of filtered bands at the desired wavevector. Eigenvectors are ordered along columns. Note that all band structure interpolations may give eigenvectors.

Implements BaseBandStructure.

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getEnergies()

Eigen::VectorXd ActiveBandStructure::getEnergies ( WavevectorIndex &  ik )

overridevirtual

Parameters

wavevectorIndex

a WavevectorIndex(ik) where ik is an integer index running over the wavevectors [0,numPoints-1]

Returns

energies: an Eigen vector of quasiparticle energies for that given wavevector. Phonon energies are referred to zero, with negative energies being actually complex phonon frequencies. Electronic energies are not saved with any particular reference, and should be used together with the chemical potential computed by StatisticsSweep. In rydberg units.

Implements BaseBandStructure.

getEnergy()

const double & ActiveBandStructure::getEnergy ( StateIndex &  is )

overridevirtual

Same as getEnergy(const int &stateIndex), but using a StateIndex input

Parameters

stateIndex

a StateIndex(is) object where 'is' is an integer running over the number of states [0,numStates-1].

Returns

energy: the value of the QP energy for that given Bloch index. Phonon energies are referred to zero, with negative energies being actually complex phonon frequencies. Electronic energies are not saved with any particular reference, and should be used together with the chemical potential computed by StatisticsSweep. By policy, it's in rydberg units.

Implements BaseBandStructure.

getGroupVelocities()

Eigen::MatrixXd ActiveBandStructure::getGroupVelocities ( WavevectorIndex &  ik )

overridevirtual

Used for accessing the band structure in the BTE.

Parameters

wavevectorIndex

a WavevectorIndex(ik) object where 'ik' is an integer index running over the wavevectors in range [0,numPoints-1]

Returns

velocity: a matrix(numActiveBands,3) with the group velocity, in cartesian basis and in atomic rydberg units, where numActiveBands is the number of active bands present at the specified wavevector.

Implements BaseBandStructure.

getGroupVelocity()

Eigen::Vector3d ActiveBandStructure::getGroupVelocity ( StateIndex &  is )

overridevirtual

Used for accessing the band structure in the BTE.

Parameters

stateIndex

a StateIndex(is) object where 'is' is an integer index in the range [0,numStates[

Returns

velocity: a 3d vector with velocity. By policy, we save it in the cartesian basis and in atomic rydberg units.

Implements BaseBandStructure.

getIndex() [1/3]

std::tuple< WavevectorIndex, BandIndex > ActiveBandStructure::getIndex ( const int &  is )

overridevirtual

Parameters

stateIndex

integer from 0 to numStates-1

Returns

WavevectorIndex: a strong-typed index on wavevector

BandIndex: a strong-typed index on bands

Implements BaseBandStructure.

getIndex() [2/3]

size_t ActiveBandStructure::getIndex ( const WavevectorIndex &  ik, const BandIndex &  ib  )

overridevirtual

Parameters

wavevectorIndex	strong-typed index on wavevector index
bandIndex	strong-typed index on band index. Note that bandIndex has different range for every wavevector

Returns

stateIndex: integer from 0 to numStates-1

Implements BaseBandStructure.

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getIndex() [3/3]

std::tuple< WavevectorIndex, BandIndex > ActiveBandStructure::getIndex ( StateIndex &  is )

overridevirtual

Parameters

stateIndex

a StateIndex(is) object where is is an integer from 0 to numStates-1

Returns

WavevectorIndex: strong-typed index on wavevector

BandIndex: strong-typed index on bands

Implements BaseBandStructure.

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getIsDistributed()

bool ActiveBandStructure::getIsDistributed ( )

overridevirtual

In the case of activeBandStructure, currently always returns false.

Implements BaseBandStructure.

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getMaxEnergy()

double ActiveBandStructure::getMaxEnergy ( )

overridevirtual

This can be useful when setting energy scales based on which phonons are discarded (as in the phel scattering, where the window is set relative to the maximum phonon energies)

Implements BaseBandStructure.

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getNumBands() [1/2]

int ActiveBandStructure::getNumBands ( )

overridevirtual

If the number of bands is not constant, it raises an error. In that case, it's best to check the size of the objects returned by the get*() methods or use getNumBands(ik).

Returns

numBandsFull: the total number of bands of the bandStructure (only returned in the case where the bands have not been filtered.)

Implements BaseBandStructure.

getNumBands() [2/2]

int ActiveBandStructure::getNumBands ( WavevectorIndex &  ik )

overridevirtual

Returns

numBands: the number of bands at the requested ik.

Implements BaseBandStructure.

getNumPoints()

int ActiveBandStructure::getNumPoints ( const bool &  useFullGrid = false )

overridevirtual

Parameters

useFullGrid

default = false. If true, returns the number of points of the full monkhorst-pack grid of wavevectors, otherwise, returns the number of wavevectors stored in the BandStructure. In particular for this class, the number of wavevectors stored in the list is obtained with false, if true, and if activePoints.parentPoints is a FullPoints object, then we will return the number of points in the original full grid of points (useful when normalizing equations).

Returns

numPoints: the total number of wavevectors of the bandStructure.

Implements BaseBandStructure.

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getNumStates()

int ActiveBandStructure::getNumStates ( )

overridevirtual

Returns

numStates: the total number of Bloch states in the class.

Implements BaseBandStructure.

getParticle()

Particle ActiveBandStructure::getParticle ( )

overridevirtual

Returns

particle: a Particle object, describing e.g. whether this is a phonon or electron bandStructure

Implements BaseBandStructure.

getPhEigenvectors()

Eigen::Tensor< std::complex< double >, 3 > ActiveBandStructure::getPhEigenvectors ( WavevectorIndex &  ik )

overridevirtual

It's only meaningful for the phonon band structure, where eigenvectors are more naturally represented in this shape!

Parameters

wavevectorIndex

a WavevectorIndex(ik) object where ik is the integer wavevector index running over [0,numPoints-1].

Returns

eigenvectors: a complex tensor (3,numAtoms,numActiveBands) where numActiveBands is the number of Bloch states present at the specified wavevector, numAtoms is the number of atoms in the crystal unit cell and 3 are the cartesian directions.

Implements BaseBandStructure.

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getPoint()

Point ActiveBandStructure::getPoint ( const int &  pointIndex )

overridevirtual

The wavevector index runs from 0 to numPoints-1, where numPoints is the number of active wavevectors to be used in the calculations.

Implements BaseBandStructure.

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getPointIndex()

int ActiveBandStructure::getPointIndex ( const Eigen::Vector3d &  crystalCoordinates, const bool &  suppressError = false  )

overridevirtual

Parameters

crystalCoordinates	coordinates of the point in crystal basis
suppressError	default false. If false, will throw an error if the point is not found

Returns

ik: the index of the point

Implements BaseBandStructure.

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getPoints()

Points ActiveBandStructure::getPoints ( )

overridevirtual

Returns

Points: the object representing the Brillouin zone wavevectors. Should be an ActivePoints class.

Implements BaseBandStructure.

getReducibleStarFromIrreducible()

std::vector< int > ActiveBandStructure::getReducibleStarFromIrreducible ( const int &  ik )

overridevirtual

Parameters

ik	index of the irreducible point, with ik running on the full list of reducible points.

Returns

vector<int>: the list of indices of the reducible points equivalent to point #ik.

Implements BaseBandStructure.

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getRotationsStar() [1/2]

std::vector< Eigen::Matrix3d > ActiveBandStructure::getRotationsStar ( StateIndex &  isIndex )

overridevirtual

any band at an irreducible point), find the list of rotations to reconstruct the equivalent points.

Parameters

isIndex

Index of the irreducible Bloch State. This index is a number between 0 and numStates.

Returns

rotations: a vector with the rotations used to reconstruct the symmetry-equivalent Bloch states.

Implements BaseBandStructure.

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getRotationsStar() [2/2]

std::vector< Eigen::Matrix3d > ActiveBandStructure::getRotationsStar ( WavevectorIndex &  ikIndex )

overridevirtual

Parameters

ikIndex

Index of the irreducible wavevector. This index is a number between 0 and N_k_reducible.

Returns

rotations: a vector with the rotations used to reconstruct the symmetry-equivalent Bloch states.

Implements BaseBandStructure.

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getRotationToIrreducible()

std::tuple< int, Eigen::Matrix3d > ActiveBandStructure::getRotationToIrreducible ( const Eigen::Vector3d &  x, const int &  basis = Points::crystalCoordinates  )

overridevirtual

Parameters

x	point coordinates
basis	either Points::crystalCoordinates or Points::cartesianCoordinates, this will treat x in the appropriate coordinate. Also the returned rotation will be in the corresponding basis.

Returns

<ik,rot>: a tuple with the index of the irreducible point and the rotation matrix connecting the irreducible and reducible point.

Implements BaseBandStructure.

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getVelocities()

Eigen::Tensor< std::complex< double >, 3 > ActiveBandStructure::getVelocities ( WavevectorIndex &  ik )

overridevirtual

Used for accessing the band structure in the BTE.

Parameters

wavevectorIndex

a WavevectorIndex(ik) object where 'ik' is an integer index running over the wavevectors in range [0,numPoints-1]

Returns

velocity: a tensor (numActiveBands,numActiveBands,3) with the velocity operator matrix elements, in cartesian basis and in atomic rydberg units, where numActiveBands is the number of active bands present at the specified wavevector.

Implements BaseBandStructure.

getWavevector() [1/2]

Eigen::Vector3d ActiveBandStructure::getWavevector ( StateIndex &  is )

overridevirtual

Parameters

stateIndex

an integer index in range [0,numStates[

Returns

wavevector: a 3d vector with the wavevector in cartesian coordinates in units of Bohr^-1.

Implements BaseBandStructure.

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getWavevector() [2/2]

Eigen::Vector3d ActiveBandStructure::getWavevector ( WavevectorIndex &  ik )

overridevirtual

Parameters

wavevectorIndex

a WavevectorIndex(ik) object where 'ik' is an integer index in range [0,numPoints-1].

Returns

wavevector: a 3d vector with the wavevector in cartesian coordinates in units of Bohr^-1.

Implements BaseBandStructure.

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hasWindow()

int ActiveBandStructure::hasWindow ( )

overridevirtual

Returns

windowMethod: one of the values of Window::filterMethod. 0 for no filter.

Implements BaseBandStructure.

irrPointsIterator()

std::vector< int > ActiveBandStructure::irrPointsIterator ( )

overridevirtual

The iterator is serial, not parallelized with MPI.

Returns

k-indices: a std::vector<int> with the indices of the irreducible points.

Implements BaseBandStructure.

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irrStateIterator()

std::vector< int > ActiveBandStructure::irrStateIterator ( )

overridevirtual

Returns

State-indices: a vector<int> with the indices over Bloch states stored in the band structure

Implements BaseBandStructure.

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parallelIrrPointsIterator()

std::vector< int > ActiveBandStructure::parallelIrrPointsIterator ( )

overridevirtual

The iterator is parallelized over MPI processes.

Returns

k-indices: a std::vector<int> with the indices of the irreducible points.

Implements BaseBandStructure.

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parallelIrrStateIterator()

std::vector< int > ActiveBandStructure::parallelIrrStateIterator ( )

overridevirtual

Returns

State-indices: a vector<int> with the indices over Bloch states stored in the band structure

Implements BaseBandStructure.

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setEigenvectors()

void ActiveBandStructure::setEigenvectors ( Point &  point, Eigen::MatrixXcd &  eigenvectors_  )

overridevirtual

Parameters

point	a point object, which will be used to lookup the wavevector index ik.
eigenvectors	a matrix of size (numFullBands, numBands(ik)) with the quasiparticle eigenvectors for this point.

Implements BaseBandStructure.

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setEnergies() [1/2]

void ActiveBandStructure::setEnergies ( Point &  point, Eigen::VectorXd &  energies_  )

overridevirtual

Parameters

point	a point object, which will be used to lookup the wavevector index ik.
energies	a vector of size (numBands(ik)) with the quasiparticle energies for that point.

Implements BaseBandStructure.

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setEnergies() [2/2]

void ActiveBandStructure::setEnergies	(	Point &	point,
		std::vector< double > &	energies_
	)

Parameters

point	a point object, which will be used to lookup the wavevector index ik.
energies	a vector of size (numBands(ik)) with the quasiparticle energies for that point.

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setVelocities()

void ActiveBandStructure::setVelocities ( Point &  point, Eigen::Tensor< std::complex< double >, 3 > &  velocities_  )

overridevirtual

Parameters

point	a point object, which will be used to lookup the wavevector index ik.
velocities	a tensor of size (numBands(ik),numBands(ik),3) with the quasiparticle velocity matrix elements for this wavevector.

Implements BaseBandStructure.

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stateToBte()

BteIndex ActiveBandStructure::stateToBte ( StateIndex &  isIndex )

overridevirtual

If a state is not mapped to the VectorBTE, throws an error.

Parameters

StateIndex

the index of the Bloch state in the band structure.

Returns

BteIndex: index of the Bloch state in the BTE

Implements BaseBandStructure.

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