Work with 3D vectors and matrices. More...

Classes
class	matrix
	Handling of a 3x3 matrix of numerical data types. More...

class	vector
	Simple implementation of 3d vector. More...

Functions
template<typename T , typename U >
vector< decltype(T{}+U{})>	operator+ (vector< T > const &a, vector< U > const &b)

template<typename T , typename U >
vector< decltype(T{} - U{})>	operator- (vector< T > const &a, vector< U > const &b)

template<typename T , typename U >
std::enable_if_t< std::is_scalar< U >::value, vector< decltype(T{} *U{})> >	operator* (vector< T > const &vec, U p)

template<typename T , typename U >
std::enable_if_t< std::is_scalar< U >::value, vector< decltype(T{} *U{})> >	operator* (U p, vector< T > const &vec)

template<typename T , typename U >
std::enable_if_t< std::is_scalar< U >::value, vector< decltype(T{} *U{})> >	operator/ (vector< T > const &vec, U p)

template<typename T , typename U >
auto	dot (vector< T > const a, vector< U > const b) -> decltype(T{} *U{})

template<typename T >
auto	cross (vector< T > const a, vector< T > const b)

template<typename T >
std::ostream &	operator<< (std::ostream &out, r3::vector< T > const &v)

template<typename T , typename U >
std::enable_if_t< std::is_scalar< U >::value, matrix< decltype(T{} *U{})> >	operator* (matrix< T > const &a__, U p__)
	Multiply matrix by a scalar number. More...

template<typename T , typename U >
std::enable_if_t< std::is_scalar< U >::value, matrix< decltype(T{} *U{})> >	operator* (U p__, matrix< T > const &a__)

bool	operator== (matrix< int > const &a__, matrix< int > const &b__)

template<typename T , typename U >
auto	dot (matrix< T > const &a__, matrix< U > const &b__)
	Multiply two matrices. More...

template<typename T , typename U >
auto	dot (matrix< T > const &m__, vector< U > const &b__)
	Matrix-vector multiplication. More...

template<typename T , typename U >
auto	dot (vector< U > const &b__, matrix< T > const &m__)
	Vector-matrix multiplication. More...

template<typename T >
auto	transpose (matrix< T > src)
	Return transpose of the matrix. More...

template<typename T >
auto	inverse_aux (matrix< T > src)

auto	inverse (matrix< int > src)
	Return inverse of the integer matrix. More...

template<typename T >
auto	inverse (matrix< T > src)
	Return inverse of the matrix. More...

template<typename T >
std::ostream &	operator<< (std::ostream &out, matrix< T > const &v)

auto	reduce_coordinates (vector< double > coord__)
	Reduce the coordinates to the first unit cell. More...

auto	find_translations (double radius__, matrix< double > const &lattice_vectors__)
	Find supercell that circumscribes the sphere with a given radius. More...

auto	spherical_coordinates (vector< double > vc)
	Transform Cartesian coordinates [x,y,z] to spherical coordinates [r,theta,phi]. More...

Detailed Description

Work with 3D vectors and matrices.

Function Documentation

◆ operator+()

template<typename T , typename U >

vector< decltype(T{}+U{})> sirius::r3::operator+	(	vector< T > const &	a,
		vector< U > const &	b
	)

inline

Definition at line 157 of file r3.hpp.

◆ operator-()

template<typename T , typename U >

vector< decltype(T{} - U{})> sirius::r3::operator-	(	vector< T > const &	a,
		vector< U > const &	b
	)

inline

Definition at line 168 of file r3.hpp.

◆ operator*() [1/4]

template<typename T , typename U >

std::enable_if_t< std::is_scalar< U >::value, vector< decltype(T{} U{})> > sirius::r3::operator	(	vector< T > const &	vec,
		U	p
	)

inline

Definition at line 179 of file r3.hpp.

◆ operator*() [2/4]

template<typename T , typename U >

std::enable_if_t< std::is_scalar< U >::value, vector< decltype(T{} U{})> > sirius::r3::operator	(	U	p,
		vector< T > const &	vec
	)

inline

Definition at line 190 of file r3.hpp.

◆ operator/()

template<typename T , typename U >

std::enable_if_t< std::is_scalar< U >::value, vector< decltype(T{} *U{})> > sirius::r3::operator/	(	vector< T > const &	vec,
		U	p
	)

inline

Definition at line 197 of file r3.hpp.

◆ dot() [1/4]

template<typename T , typename U >

auto sirius::r3::dot	(	vector< T > const	a,
		vector< U > const	b
	)		-> decltype(T{} * U{})

inline

Definition at line 207 of file r3.hpp.

◆ cross()

template<typename T >

auto sirius::r3::cross	(	vector< T > const	a,
		vector< T > const	b
	)

inline

Definition at line 213 of file r3.hpp.

◆ operator<<() [1/2]

template<typename T >

std::ostream & sirius::r3::operator<<	(	std::ostream &	out,
		r3::vector< T > const &	v
	)

Definition at line 223 of file r3.hpp.

◆ operator*() [3/4]

template<typename T , typename U >

std::enable_if_t< std::is_scalar< U >::value, matrix< decltype(T{} U{})> > sirius::r3::operator	(	matrix< T > const &	a__,
		U	p__
	)

inline

Multiply matrix by a scalar number.

Definition at line 373 of file r3.hpp.

◆ operator*() [4/4]

template<typename T , typename U >

std::enable_if_t< std::is_scalar< U >::value, matrix< decltype(T{} U{})> > sirius::r3::operator	(	U	p__,
		matrix< T > const &	a__
	)

inline

Definition at line 385 of file r3.hpp.

◆ operator==()

bool sirius::r3::operator==	(	matrix< int > const &	a__,
		matrix< int > const &	b__
	)

inline

Definition at line 390 of file r3.hpp.

◆ dot() [2/4]

template<typename T , typename U >

auto sirius::r3::dot	(	matrix< T > const &	a__,
		matrix< U > const &	b__
	)

inline

Multiply two matrices.

Definition at line 404 of file r3.hpp.

◆ dot() [3/4]

template<typename T , typename U >

auto sirius::r3::dot	(	matrix< T > const &	m__,
		vector< U > const &	b__
	)

inline

Matrix-vector multiplication.

Definition at line 419 of file r3.hpp.

◆ dot() [4/4]

template<typename T , typename U >

auto sirius::r3::dot	(	vector< U > const &	b__,
		matrix< T > const &	m__
	)

inline

Vector-matrix multiplication.

Definition at line 432 of file r3.hpp.

◆ transpose()

template<typename T >

auto sirius::r3::transpose ( matrix< T > src )

inline

Return transpose of the matrix.

Definition at line 445 of file r3.hpp.

◆ inverse_aux()

template<typename T >

auto sirius::r3::inverse_aux ( matrix< T > src )

inline

Definition at line 457 of file r3.hpp.

◆ inverse() [1/2]

auto sirius::r3::inverse ( matrix< int > src )

inline

Return inverse of the integer matrix.

Definition at line 475 of file r3.hpp.

◆ inverse() [2/2]

template<typename T >

auto sirius::r3::inverse ( matrix< T > src )

inline

Return inverse of the matrix.

Definition at line 486 of file r3.hpp.

◆ operator<<() [2/2]

template<typename T >

std::ostream & sirius::r3::operator<<	(	std::ostream &	out,
		matrix< T > const &	v
	)

inline

Definition at line 498 of file r3.hpp.

◆ reduce_coordinates()

auto sirius::r3::reduce_coordinates ( vector< double > coord__ )

inline

Reduce the coordinates to the first unit cell.

Split the input vector in lattice coordinates to the sum r0 + T, where T is the lattice translation vector (three integers) and r0 is the vector within the first unit cell with coordinates in [0, 1) range.

Definition at line 523 of file r3.hpp.

◆ find_translations()

auto sirius::r3::find_translations	(	double	radius__,
		matrix< double > const &	lattice_vectors__
	)

inline

Find supercell that circumscribes the sphere with a given radius.

Search for the translation limits (N1, N2, N3) such that the resulting supercell with the lattice vectors a1 * N1, a2 * N2, a3 * N3 fully contains the sphere with a given radius. This is done by equating the expressions for the volume of the supercell: Volume = |(A1 x A2) * A3| = N1 * N2 * N3 * |(a1 x a2) * a3| Volume = h * S = 2 * R * |a_i x a_j| * N_i * N_j

Definition at line 572 of file r3.hpp.

◆ spherical_coordinates()

auto sirius::r3::spherical_coordinates ( vector< double > vc )

inline

Transform Cartesian coordinates [x,y,z] to spherical coordinates [r,theta,phi].

Definition at line 590 of file r3.hpp.

Classes

Functions

Detailed Description

Function Documentation

◆ operator+()

◆ operator-()

◆ operator*() [1/4]

◆ operator*() [2/4]

◆ operator/()

◆ dot() [1/4]

◆ cross()

◆ operator<<() [1/2]

◆ operator*() [3/4]

◆ operator*() [4/4]

◆ operator==()

◆ dot() [2/4]

◆ dot() [3/4]

◆ dot() [4/4]

◆ transpose()

◆ inverse_aux()

◆ inverse() [1/2]

◆ inverse() [2/2]

◆ operator<<() [2/2]

◆ reduce_coordinates()

◆ find_translations()

◆ spherical_coordinates()