triqs::lattice::bravais_lattice::point_t

#include <triqs/lattice/bravais_lattice.hpp>

Detailed Description

Lattice point of a Bravais lattice.

A lattice point is defined by an index vector, \( \mathbf{n} = (n_1, \dots, n_d) \), and the Bravais lattice it belongs to.

The corresponding lattice vector, \( \mathbf{R}^{\mathbf{n}} = (R^{\mathbf{n}}_1, \dots, R^{\mathbf{n}}_d) \), can be obtained with

\[ \mathbf{R}^{\mathbf{n}} = \sum_{i=1}^{d} \mathbf{a}_i n_i \; , \]

where \( \{ \mathbf{a}_1, \dots, \mathbf{a}_d \} \) are the basis vectors of the underlying Bravais lattice.

Note

Although the supported dimensions are 1, 2 and 3, the index vectors are always 3-dimensional, i.e. \(\mathbf{n} = (n_1, n_2, n_3) \). Indices \( n_j \) with \( j > d \) are simply ignored when computing the corresponding lattice vector.

Definition at line 97 of file bravais_lattice.hpp.

Inheritance diagram for triqs::lattice::bravais_lattice::point_t:

Public Member Functions
	point_t ()=default
	Default constructor leaves the lattice point uninitialized, i.e. belonging to no Bravais lattice.
	point_t (index_t const &n, bravais_lattice const *bl_ptr)
	Construct a lattice point with a given index vector on the given Bravais lattice.
auto	index () const
	Get the index vector \( \mathbf{n} \) of the lattice point.
auto const &	lattice () const
	Get the underlying Bravais lattice.
	operator r_t () const
	Conversion to the corresponding lattice vector \( \mathbf{R}^{\mathbf{n}} = \sum_{i=1}^{d} \mathbf{a}_i n_i \).
double	operator() (int d) const
	Get the coordinate \( R^{\mathbf{n}}_i \) of the corresponding lattice vector \(\mathbf{R}^{\mathbf{n}} \).
point_t	operator+ (point_t const &pt) const
	Add two lattice points \( \mathbf{R}^{\mathbf{n}} \) and \( \mathbf{R}^{\mathbf{m}} \).
point_t	operator- () const
	Invert the lattice point \( \mathbf{R}^{\mathbf{n}} \).
point_t	operator- (point_t const &pt) const
	Subtract two lattice points \( \mathbf{R}^{\mathbf{n}} \) and \( \mathbf{R}^{\mathbf{m}} \).
double	operator[] (int i) const
	Get the coordinate \( R^{\mathbf{n}}_i \) of the corresponding lattice vector \(\mathbf{R}^{\mathbf{n}} \).

Friends
std::ostream &	operator<< (std::ostream &sout, point_t const &pt)
	Write a lattice point to a std::ostream.

Constructor & Destructor Documentation

point_t()

triqs::lattice::bravais_lattice::point_t::point_t ( index_t const & n, bravais_lattice const * bl_ptr )

inline

Construct a lattice point with a given index vector on the given Bravais lattice.

Parameters

n	Index vector \( \mathbf{n} \).
bl_ptr	Pointer to the Bravais lattice.

Definition at line 108 of file bravais_lattice.hpp.

Member Function Documentation

operator()()

double triqs::lattice::bravais_lattice::point_t::operator() ( int d ) const

inline

Get the coordinate \( R^{\mathbf{n}}_i \) of the corresponding lattice vector \(\mathbf{R}^{\mathbf{n}} \).

Deprecated

Use operator[]() instead.

Definition at line 133 of file bravais_lattice.hpp.

operator+()

point_t triqs::lattice::bravais_lattice::point_t::operator+ ( point_t const & pt ) const

inlinenodiscard

Add two lattice points \( \mathbf{R}^{\mathbf{n}} \) and \( \mathbf{R}^{\mathbf{m}} \).

Parameters

pt	Lattice point \( \mathbf{R}^{\mathbf{m}} \) (has to belong to the same Bravais lattice).

Returns

Lattice point corresponding to the lattice vector \( \mathbf{R}^{\mathbf{n}} + \mathbf{R}^{\mathbf{m}} \).

Definition at line 151 of file bravais_lattice.hpp.

operator-() [1/2]

point_t triqs::lattice::bravais_lattice::point_t::operator- ( ) const

inlinenodiscard

Invert the lattice point \( \mathbf{R}^{\mathbf{n}} \).

Returns

Lattice point corresponding to the lattice vector \( -\mathbf{R}^{\mathbf{n}} \).

Definition at line 172 of file bravais_lattice.hpp.

operator-() [2/2]

point_t triqs::lattice::bravais_lattice::point_t::operator- ( point_t const & pt ) const

inlinenodiscard

Subtract two lattice points \( \mathbf{R}^{\mathbf{n}} \) and \( \mathbf{R}^{\mathbf{m}} \).

Parameters

pt	Lattice point \( \mathbf{R}^{\mathbf{m}} \) (has to belong to the same Bravais lattice).

Returns

Lattice point corresponding to the lattice vector \( \mathbf{R}^{\mathbf{n}} - \mathbf{R}^{\mathbf{m}} \).

Definition at line 163 of file bravais_lattice.hpp.

operator[]()

double triqs::lattice::bravais_lattice::point_t::operator[] ( int i ) const

inline

Get the coordinate \( R^{\mathbf{n}}_i \) of the corresponding lattice vector \(\mathbf{R}^{\mathbf{n}} \).

Parameters

i	Dimension index \( i \).

Returns

Lattice vector coordinate \( R^{\mathbf{n}}_i \).

Definition at line 142 of file bravais_lattice.hpp.

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & sout, point_t const & pt )

friend

Write a lattice point to a std::ostream.

Parameters

sout	std::ostream object.
pt	Lattice point to be written.

Returns

Reference to std::ostream object.

Definition at line 181 of file bravais_lattice.hpp.

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

• triqs/lattice/bravais_lattice.hpp