Base class for storing wavevectors in the Brillouin zone. More...

#include <points.h>

Collaboration diagram for Points:

Public Member Functions
	Points (Crystal &crystalObj_)
	Default constructor.

	Points (Crystal &crystalObj_, const Eigen::Vector3i &mesh_, const Eigen::Vector3d &offset_=Eigen::Vector3d::Zero())
	Constructor for a Monkhorst-Pack grid of wavevectors. More...

	Points (Crystal &crystal_, const Eigen::Tensor< double, 3 > &pathExtrema, const double &delta)
	Constructor for points on a path. More...

void	setActiveLayer (const Eigen::VectorXi &filter_)
	Constructor for Active Points. More...

	Points (const Points &obj)
	Copy constructor.

Points &	operator= (const Points &obj)
	Copy assignment operator.

std::tuple< Eigen::Vector3i, Eigen::Vector3d >	getMesh ()
	Returns the details of the Monkhorst-pack mesh of wavevectors. More...

int	getNumPoints () const
	Returns the number of wavevectors stored in the points class.

Eigen::Vector3d	crystalToCartesian (const Eigen::Vector3d &point)
	Converts a wavevector from crystal to cartesian coordinates. More...

Eigen::Vector3d	cartesianToCrystal (const Eigen::Vector3d &point)
	Converts a wavevector from cartesian to crystal coordinates. More...

Eigen::Vector3d	bzToWs (const Eigen::Vector3d &point, const int &basis)
	Folds a wavevector in crystal coordinates to the Wigner Seitz zone. More...

Eigen::Vector3d	foldToBz (const Eigen::Vector3d &pointCrystal, const int &basis)

Crystal &	getCrystal ()
	Returns a reference to the crystal object on which the Points are defined.

Point	getPoint (const int &index)
	Returns a Point object given its integer index. More...

Eigen::Vector3d	getPointCoordinates (const int &index, const int &basis=crystalCoordinates)
	Get the coordinates of a wavevector from its index. More...

int	getIndex (const Eigen::Vector3d &point)
	Get the wavevector index given the crystal coordinates of a wavevector. More...

int	isPointStored (const Eigen::Vector3d &crystalCoordinates_)
	Like getIndex, get the wavevector index given the crystal coordinates of a wavevector, but returns -1 if point not found. More...

void	setIrreduciblePoints (std::vector< Eigen::MatrixXd > *groupVelocities=nullptr)
	setIrreduciblePoints analyzes a current set of points to find its irreducible set. More...

std::vector< int >	irrPointsIterator ()
	Returns an iterator on the index of irreducible points. More...

std::vector< int >	parallelIrrPointsIterator ()
	Similar to irrPointsIterator, returns an iterator on the index of irreducible points. More...

int	asIrreducibleIndex (const int &ik)
	Given an index of an irreducible point in the set [0,numPoints[, returns its index in the set of [0,numIrredPoints[ irreducible wavevectors. More...

int	asReducibleIndex (const int &ik)
	Given the index of an irreducible point in the set [0,numIrredPoints[, returns its index in the set of [0,numPoints[ reducible wavevectors. More...

std::tuple< int, Eigen::Matrix3d >	getRotationToIrreducible (const Eigen::Vector3d &x, const int &basis=cartesianCoordinates)
	Given the coordinates of a wavevector, getRotationToIrreducible returns the index of the irreducible point, and the rotation R such that k^irr = R k^red. More...

std::vector< Eigen::Matrix3d >	getRotationsStar (const int &ik)
	Given the index of an irreducible point in the reducible list, returns the set of rotations that allow to map k^red = R k^irr. More...

std::vector< int >	getReducibleStarFromIrreducible (const int &ik)
	Given the index of an irreducible point in the reducible list, returns the list of indices of the symmetry equivalent wavevectors. More...

Static Public Member Functions
static std::tuple< Eigen::Vector3i, Eigen::Vector3d >	findMesh (const Eigen::Matrix< double, 3, Eigen::Dynamic > &points)
	Given a list of points, finds the monkhorst-pack mesh. More...

Static Public Attributes
static const int	crystalCoordinates = crystalCoordinates_

static const int	cartesianCoordinates = cartesianCoordinates_

Protected Member Functions
void	setMesh (const Eigen::Vector3i &mesh_, const Eigen::Vector3d &offset_)
	Change the crystal object for a different one. More...

void	setupGVectors ()

Protected Attributes
Crystal &	crystalObj

Eigen::Vector3i	mesh

Eigen::Vector3d	offset

int	numPoints = 0

Eigen::MatrixXd	gVectors

bool	explicitlyStored = false

bool	isPointsListSorted = false

Eigen::MatrixXd	pointsList

Eigen::VectorXi	filteredToFullIndices

std::vector< Eigen::Matrix3d >	rotationMatricesCrystal

std::vector< Eigen::Matrix3d >	rotationMatricesCartesian

Eigen::VectorXi	mapEquivalenceRotationIndex

Eigen::VectorXi	mapIrreducibleToReducibleList

Eigen::VectorXi	mapReducibleToIrreducibleList

int	numIrrPoints = 0

std::vector< std::vector< int > >	irreducibleStars

Eigen::VectorXi	equiv

Detailed Description

The base class mostly refers to a uniform grid sampling the Brillouin zone. Different subclasses will specialize to different kinds of wavevector sets.

Constructor & Destructor Documentation

◆ Points() [1/2]

Points::Points	(	Crystal &	crystalObj_,
		const Eigen::Vector3i &	mesh_,
		const Eigen::Vector3d &	offset_ = `Eigen::Vector3d::Zero()`
	)

Parameters

crystal	the crystal object that defines the Brillouin zone.
mesh	grid size of the Monkhorst-pack.
offset	the offset of the grid w.r.t. the Gamma point. Offset ranges in values from 0 to 1. 0.5 means half displacement of the grid.

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◆ Points() [2/2]

Points::Points	(	Crystal &	crystal_,
		const Eigen::Tensor< double, 3 > &	pathExtrema,
		const double &	delta
	)

Parameters

crystal	the crystal object that defines the Brillouin zone.
pathExtrema	extrema of segments defining a path of points. PathExtrema has size (numSegments, 2, 3), where the first index spans the segments of the path, 2 is the beginning and the last element of the segment, and 3 is the cartesian coordinates of the extrema. Point coordinates must be in crystal coordinates. Example: if we want a path G->X->L, we have: 2 segments: G->X and X->L pathExtrema(0,0,:) = G. coordinates pathExtrema(0,1,:) = X. coordinates pathExtrema(1,0,:) = X. coordinates pathExtrema(1,1,:) = L. coordinates
delta	segments are populated with points, with a distance "delta" between different points in crystal coordinates.

Member Function Documentation

◆ asIrreducibleIndex()

int Points::asIrreducibleIndex ( const int & ik )

Parameters

ik	index of the irreducible point in the reducible list.

Returns: ikIrr: index in the irreducible list.

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◆ asReducibleIndex()

int Points::asReducibleIndex ( const int & ik )

Parameters

ik	index of the irreducible point in the irreducible list.

Returns: ikIrr: index in the reducible list.

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◆ bzToWs()

Eigen::Vector3d Points::bzToWs	(	const Eigen::Vector3d &	point,
		const int &	basis
	)

Parameters

pointCrystal	the coordinates of a wavevector
basis	basis (Points::cartesianCoordinates or Points::crystalCoordinates) of input and output wavevector.

Returns: wavevector: the wavevector coordinates folded in the WS zone.

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◆ cartesianToCrystal()

Eigen::Vector3d Points::cartesianToCrystal ( const Eigen::Vector3d & point )

Parameters

point the input wavevector in cartesian coordinates.

Returns: wavevector: the output wavevector in crystal coordinates.

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◆ crystalToCartesian()

Eigen::Vector3d Points::crystalToCartesian ( const Eigen::Vector3d & point )

Parameters

point the input wavevector in crystal coordinates.

Returns: wavevector: the output wavevector in cartesian coordinates.

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◆ findMesh()

std::tuple< Eigen::Vector3i, Eigen::Vector3d > Points::findMesh ( const Eigen::Matrix< double, 3, Eigen::Dynamic > & points )

static

Parameters

points a matrix (3,numPoints) of wavevectors in crystal coordinates.

Returns: mesh,offset: the monkhorst-pack grid size and the offset w.r.t. the gamma point, that generates the input points list. Calls an error if the mesh doesn't correspond to a complete list.

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◆ getIndex()

int Points::getIndex ( const Eigen::Vector3d & point )

Throws an error if the wavevector is not found in points.

Parameters

point the wavevector in crystal coordinates.

Returns: index: the index of the wavevector in the range [0,numPoints[

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◆ getMesh()

std::tuple< Eigen::Vector3i, Eigen::Vector3d > Points::getMesh ( )

Returns: <grid, offset>: grid is the 3D integration mesh used for the Brillouin zone sampling, and the 3D offset of the grid w.r.t. the Gamma point (values of offset from 0 to 1).

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◆ getPoint()

Point Points::getPoint ( const int & index )

The Point object is used to move around the code the coordinates of the wavevector.

Parameters

index the integer wavevector index ranging in [0,numPoints[

Returns: point: a point object.

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◆ getPointCoordinates()

Eigen::Vector3d Points::getPointCoordinates	(	const int &	index,
		const int &	basis = `crystalCoordinates`
	)

Parameters

index	the index of the desired wavevector.
basis	specify the basis to be used for the output coordinates. Either Points::crystalCoordinates or Points::cartesianCoordinates.

Returns: wavevector: the coordinates of the desired wavevector.

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◆ getReducibleStarFromIrreducible()

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

Parameters

ik	index of irreducible point in the reducible list.

Returns: vector<int>: a vector with the indices of symmetry-equivalent points

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◆ getRotationsStar()

std::vector< Eigen::Matrix3d > Points::getRotationsStar ( const int & ik )

Parameters

ik	index of irreducible point in the reducible list.

Returns: vector<Matrix3d>: a vector with the set of rotation to reconstruct the star.

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◆ getRotationToIrreducible()

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

Parameters

x	a 3d vector with the coordinates of the wavevector. They can be in crystal or cartesian basis, as specified by basis.
basis	either Points::cartesianCoordinates or crystalCoordinates, specifies the basis in which x is specified.

Returns: tuple: the first element of the tuple is the index of the irreducible point, the second is the 3d matrix with the rotation symmetry operation. The rotation is crystal or cartesian, depending on the value of basis.

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◆ irrPointsIterator()

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

If setIrreduciblePoints has not been called, it just loops on all points.

Returns: std::vector<int>: a list of irreducible wavevector indices.

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◆ isPointStored()

int Points::isPointStored ( const Eigen::Vector3d & crystalCoordinates_ )

Parameters

crystalCoordinates_ a 3d Eigen vector with crystal coordinates of a wavevector.

Returns: index: the index of the wavevector in the range [0,numPoints[ if the point is in the set of points, or -1 if not found.

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◆ parallelIrrPointsIterator()

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

If setIrreduciblePoints has not been called, it just loops on all points. However, the returned list has already been scattered across different MPI processes, so each MPI process has only a subset of irreducible points.

Note that symmetries do introduce some load unbalance. In fact, some irreducible points may have more symmetry-equivalent points than others, and thus may perform more work.

Returns: std::vector<int> a MPI-distributed list of irreducible wavevector indices.

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◆ setActiveLayer()

void Points::setActiveLayer ( const Eigen::VectorXi & filter_ )

Parameters

filter a vector of integers of "filtered" points, i.e. the indices of the wavevectors in parentPoints that we want to keep.

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◆ setIrreduciblePoints()

void Points::setIrreduciblePoints ( std::vector< Eigen::MatrixXd > * groupVelocities = nullptr )

It also builds the logic for storing all symmetry operations, such as finding which rotation maps an reducible point to its irreducible point and similar symmetry operations.

Parameters

groupVelocities an optional parameter, one can pass the values of the group velocities at all wavevectors. If passed, setIrreduciblePoints will try to find the best set of symmetries acting on wavevector that also transforms the group velocities (i.e. there may sometimes be more than one symmetry mapping v and k to irreducible values). Useful since we want symmetries in the BTE to be the same as group velocities.

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◆ setMesh()

void Points::setMesh	(	const Eigen::Vector3i &	mesh_,
		const Eigen::Vector3d &	offset_
	)

protected

Used as a helper by the symmetrize function in the bandstructure class.

Parameters

crystal the new crystal to swap in

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Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Points() [1/2]

◆ Points() [2/2]

Member Function Documentation

◆ asIrreducibleIndex()

◆ asReducibleIndex()

◆ bzToWs()

◆ cartesianToCrystal()

◆ crystalToCartesian()

◆ findMesh()

◆ getIndex()

◆ getMesh()

◆ getPoint()

◆ getPointCoordinates()

◆ getReducibleStarFromIrreducible()

◆ getRotationsStar()

◆ getRotationToIrreducible()

◆ irrPointsIterator()

◆ isPointStored()

◆ parallelIrrPointsIterator()

◆ setActiveLayer()

◆ setIrreduciblePoints()

◆ setMesh()