Namespaces
namespace	Interpolation

namespace	Mpi

namespace	Statistics

Classes
class	Accumulator

struct	AccumulatorData

struct	Array

class	Bag
	Bag of elements. More...

class	Cache

class	compact_vector
	Custom vector container optimized for size. More...

struct	conjunction

struct	conjunction< B1 >

struct	conjunction< B1, Bn... >

class	Counter

class	CylindricalHistogram
	Histogram in cylindrical coordinates. More...

class	CylindricalTransformationParameters
	A class to hold and validate parameters for a cylindrical coordinate transformations. More...

struct	decay_to_scalar
	Meta function to turns a Vector<1, T> into T. More...

struct	decay_to_scalar< Vector< T, 1 > >

struct	decay_to_scalar< Vector< T, N > >

class	Factory
	Factory template. More...

struct	function_remove_const
	Remove const from a function signature. More...

struct	function_remove_const< R(Args...) const >

struct	function_remove_const< R(Args...)>

class	Histogram
	Histogram in Cartesian coordinates. More...

struct	is_statically_serializable
	Type trait to indicate that a type is serializable with a static size, e.g. More...

struct	Matrix
	Matrix representation with static size. More...

class	MemcpyIArchive
	Archive that deserializes from a buffer via memcpy. More...

class	MemcpyOArchive
	Archive that serializes to a buffer via memcpy. More...

class	NumeratedContainer
	Container for objects that are identified by a numeric id. More...

struct	Quaternion
	Quaternion representation. More...

struct	size_in_bits
	Size of a type in bits. More...

class	Span
	A stripped-down version of std::span from C++17. More...

struct	tuple_element

struct	tuple_element< I, Array< T, N > >

struct	tuple_element< I, Vector< T, N > >

struct	tuple_size

struct	tuple_size< Array< T, N > >

struct	tuple_size< Vector< T, N > >

class	Vector

Typedefs
using	Vector3b = Utils::Vector< bool, 3 >

template<std::size_t I, class Tuple >
using	tuple_element_t = typename tuple_element< I, Tuple >::type

template<class T >
using	Vector3 = Vector< T, 3 >

template<std::size_t N>
using	VectorXd = Vector< double, N >

using	Vector2d = VectorXd< 2 >

using	Vector3d = VectorXd< 3 >

using	Vector4d = VectorXd< 4 >

using	Vector6d = VectorXd< 6 >

using	Vector9d = VectorXd< 9 >

template<std::size_t N>
using	VectorXf = Vector< float, N >

using	Vector3f = VectorXf< 3 >

template<std::size_t N>
using	VectorXi = Vector< int, N >

using	Vector3i = VectorXi< 3 >

Enumerations
enum class	MemoryOrder { COLUMN_MAJOR , ROW_MAJOR }

Functions
template<std::size_t I, class T , std::size_t N>
auto	get (Array< T, N > const &a) -> std::enable_if_t<(I< N), const T & >

template<typename Body , typename... ForwardRange>
void	cartesian_product (const Body &op, const ForwardRange &...rng)
	Call op with each element of the cartesian product set of rng.

template<typename ParticleRange >
bool	check_charge_neutrality (ParticleRange &prange)

template<class InputIt , class T >
bool	contains (InputIt first, InputIt last, T const &value)
	Check whether an iterator range contains a value.

template<class Range , class T >
bool	contains (const Range &rng, T const &value)
	Check whether a range contains a value.

template<class T >
std::string	demangle ()
	Get a human-readable name for a type.

template<class Range , class OutputIterator >
void	flatten (Range const &v, OutputIterator out)
	Flatten a range of ranges.

template<typename ForwardIterator , typename BinaryOp >
void	for_each_pair (ForwardIterator first, ForwardIterator last, BinaryOp op)
	Execute op for each pair of elements in [first, last) once.

template<typename ForwardRange , typename BinaryOp >
void	for_each_pair (ForwardRange &&rng, BinaryOp &&op)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

template<typename ForwardIterator , typename BinaryOp >
void	for_each_cartesian_pair (ForwardIterator first1, ForwardIterator last1, ForwardIterator first2, ForwardIterator last2, BinaryOp op)
	Execute op for each pair of elements between [first1, last1) and [first2, last2).

template<typename ForwardRange , typename BinaryOp >
void	for_each_cartesian_pair (ForwardRange &&rng1, ForwardRange &&rng2, BinaryOp &&op)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

template<typename ForwardIterator , typename BinaryOp , typename BinaryCmp >
void	for_each_cartesian_pair_if (ForwardIterator first1, ForwardIterator last1, ForwardIterator first2, ForwardIterator last2, BinaryOp op, BinaryCmp cmp)
	Execute op for each pair of elements between [first1, last1) and [first2, last2) if a condition is satisfied.

template<typename ForwardRange , typename BinaryOp , typename BinaryCmp >
void	for_each_cartesian_pair_if (ForwardRange &&rng1, ForwardRange &&rng2, BinaryOp &&op, BinaryCmp cmp)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

template<std::size_t I, typename T >
const std::tuple_element_t< I, T > &	get (const T &v)

int	get_linear_index (int a, int b, int c, const Vector3i &adim, MemoryOrder memory_order=MemoryOrder::COLUMN_MAJOR)
	get the linear index from the position (`a`,`b`,`c`) in a 3D grid of dimensions `adim`.

int	get_linear_index (const Vector3i &ind, const Vector3i &adim, MemoryOrder memory_order=MemoryOrder::COLUMN_MAJOR)

template<class T >
T	lower_triangular (T i, T j)
	Linear index into a lower triangular matrix.

template<typename T , template< T > class F, T min, T max, class... Args>
decltype(auto)	integral_parameter (T i, Args &&...args)
	Generate a call table for an integral non-type template parameter.

template<typename Map >
auto	keys (Map const &m) -> std::vector< typename Map::key_type >
	Return the keys of a map type.

template<typename T , typename Container >
T	linear_interpolation (Container const &table, T hi, T offset, T x)
	Linear interpolation between two data points.

template<class T , class Integral >
auto	mask (Integral mask, T t) -> std::enable_if_t< std::is_unsigned_v< Integral > &&(size_in_bits< Integral >::value >=tuple_size< T >::value), T >
	Pick elements of a tuple-like by a bit mask.

DEVICE_QUALIFIER double	abs (double x)
	Return the absolute value of x.

DEVICE_QUALIFIER float	abs (float x)
	Return the absolute value of x.

template<typename T >
constexpr T	AS_erfc_part (T d)
	Approximate \( \exp(d^2) \mathrm{erfc}(d)\) by applying a formula from [1] chapter 7.

template<int order, typename T >
DEVICE_QUALIFIER auto	bspline (int i, T x) -> std::enable_if_t<(order > 0) &&(order<=7), T >
	Formula of the B-spline.

template<class T >
auto	bspline (int i, T x, int k)
	Calculate B-splines.

template<int order, typename T = double>
DEVICE_QUALIFIER auto	bspline_d (int i, T x) -> std::enable_if_t<(order > 0) &&(order<=7), T >
	Derivative of the B-spline.

Vector3d	basis_change (Vector3d const &b1, Vector3d const &b2, Vector3d const &b3, Vector3d const &v, bool reverse=false)
	Basis change.

Vector3d	transform_coordinate_cartesian_to_cylinder (Vector3d const &pos)
	Coordinate transformation from Cartesian to cylindrical coordinates.

Vector3d	transform_coordinate_cartesian_to_cylinder (Vector3d const &pos, Vector3d const &axis, Vector3d const &orientation)
	Coordinate transformation from Cartesian to cylindrical coordinates with change of basis.

Vector3d	transform_coordinate_cylinder_to_cartesian (Vector3d const &pos)
	Coordinate transformation from cylindrical to Cartesian coordinates.

Vector3d	transform_coordinate_cylinder_to_cartesian (Vector3d const &pos, Vector3d const &axis, Vector3d const &orientation)
	Coordinate transformation from cylindrical to Cartesian coordinates with change of basis.

Vector3d	transform_vector_cartesian_to_cylinder (Vector3d const &vec, Vector3d const &axis, Vector3d const &pos)
	Vector transformation from Cartesian to cylindrical coordinates.

double	gaussian (Vector3d x, Vector3d x0, double sigma)

Utils::Vector3d	del_gaussian (Vector3d x, Vector3d x0, double sigma)

template<unsigned n, typename T >
DEVICE_QUALIFIER constexpr T	int_pow (T x)
	Calculate integer powers.

template<class T >
auto	make_lin_space (T start, T stop, std::size_t number, bool endpoint=true)
	Equally spaced values in interval.

template<typename T , std::size_t N, const std::array< std::array< int, N >, N > & matrix, typename Container >
constexpr std::array< T, N >	matrix_vector_product (const Container &vec)
	Calculate the matrix-vector product for a statically given (square) matrix.

template<typename T , std::size_t N>
Vector< T, N >	calc_orthonormal_vector (Vector< T, N > const &vec)
	Return a vector that is orthonormal to vec.

void	permute_ifield (int *field, int size, int permute)
	permute an integer array field of size size about permute positions.

template<class T >
Vector< T, 3 >	convert_quaternion_to_director (Quaternion< T > const &quat)
	Convert quaternion to director.

template<class T >
Quaternion< T >	convert_director_to_quaternion (Vector< T, 3 > const &d)
	Convert director to quaternion.

template<typename T >
constexpr int	sgn (T val)
	Calculate signum of val.

template<typename T >
DEVICE_QUALIFIER T	sinc (T d)
	Calculates the sinc-function as sin(PIx)/(PIx).

template<typename T >
DEVICE_QUALIFIER constexpr T	sqr (T x)
	Calculates the SQuaRe of x.

template<typename T , std::size_t N, std::size_t M>
Matrix< T, N, M >	tensor_product (const Vector< T, N > &x, const Vector< T, M > &y)

template<typename T , std::size_t N>
Vector< T, N >	tensor_product (const T &x, const Vector< T, N > &y)

Vector3d	get_n_triangle (const Vector3d &P1, const Vector3d &P2, const Vector3d &P3)
	Computes the normal vector of a triangle.

double	area_triangle (const Vector3d &P1, const Vector3d &P2, const Vector3d &P3)
	Computes the area of triangle between vectors P1,P2,P3, by computing the cross product P1P2 x P1P3 and taking the half of its norm.

double	angle_btw_triangles (const Vector3d &P1, const Vector3d &P2, const Vector3d &P3, const Vector3d &P4)
	Computes the angle between two triangles in 3D space.

Vector3d	vec_rotate (const Vector3d &axis, double angle, const Vector3d &vector)
	Rotate a vector around an axis.

double	angle_between (Vector3d const &v1, Vector3d const &v2)
	Determine the angle between two vectors.

template<typename T , std::size_t M, std::size_t N>
Utils::Vector< T, M *N >	flatten (Matrix< T, M, N > const &m)

template<typename T , std::size_t Rows, std::size_t Cols>
Matrix< T, Rows, Cols >	diagonal_mat (Utils::Vector< T, Rows > const &v)

template<typename T , std::size_t Rows, std::size_t Cols>
Matrix< T, Rows, Cols >	identity_mat ()

template<typename T , typename U , std::enable_if_t< std::is_arithmetic_v< U >, bool > = true>
Quaternion< T >	operator* (const U &b, const Quaternion< T > &a)
	Product quaternion and arithmetic type.

template<typename T >
Matrix< T, 3, 3 >	rotation_matrix (Quaternion< T > const &q)
	Convert quaternion to rotation matrix.

template<class T , class F >
auto	raster (Vector< T, 3 > const &offset, Vector< T, 3 > const &grid_spacing, Vector3i size, F f)
	Raster a function over a regular 3d grid.

std::vector< Vector3d >	get_cylindrical_sampling_positions (std::pair< double, double > const &r_limits, std::pair< double, double > const &phi_limits, std::pair< double, double > const &z_limits, std::size_t n_r_bins, std::size_t n_phi_bins, std::size_t n_z_bins, double sampling_density)
	Generate sampling positions for a cylindrical histogram.

template<class T >
std::string	pack (T const &v)
	Pack a serialize type into a string.

template<class T >
T	unpack (std::string const &state)
	Unpack a serialize type into a string.

template<typename T >
DEVICE_QUALIFIER constexpr Span< T >	make_span (T *p, std::size_t N)

template<class C >
DEVICE_QUALIFIER constexpr auto	make_span (C &c)

template<typename T >
DEVICE_QUALIFIER constexpr Span< std::add_const_t< T > >	make_const_span (T *p, std::size_t N)

template<class C >
DEVICE_QUALIFIER constexpr auto	make_const_span (C &c)

template<class F , class Tuple >
void	for_each (F &&f, Tuple &t)

template<class F , class Tuple >
void	for_each (F &&f, Tuple &&t)

constexpr uint64_t	u32_to_u64 (uint32_t high, uint32_t low)

constexpr std::pair< uint32_t, uint32_t >	u64_to_u32 (uint64_t in)

constexpr double	uniform (uint64_t in)
	Uniformly map unsigned integer to double.

template<std::size_t N, typename T >
constexpr bool	operator< (Vector< T, N > const &a, Vector< T, N > const &b)

template<std::size_t N, typename T >
constexpr bool	operator> (Vector< T, N > const &a, Vector< T, N > const &b)

template<std::size_t N, typename T >
constexpr bool	operator<= (Vector< T, N > const &a, Vector< T, N > const &b)

template<std::size_t N, typename T >
constexpr bool	operator>= (Vector< T, N > const &a, Vector< T, N > const &b)

template<std::size_t N, typename T >
constexpr bool	operator== (Vector< T, N > const &a, Vector< T, N > const &b)

template<std::size_t N, typename T >
constexpr bool	operator!= (Vector< T, N > const &a, Vector< T, N > const &b)

template<std::size_t N, typename T , typename U >
auto	operator+ (Vector< T, N > const &a, Vector< U, N > const &b)

template<std::size_t N, typename T >
Vector< T, N > &	operator+= (Vector< T, N > &a, Vector< T, N > const &b)

template<std::size_t N, typename T , typename U >
auto	operator- (Vector< T, N > const &a, Vector< U, N > const &b)

template<std::size_t N, typename T >
Vector< T, N >	operator- (Vector< T, N > const &a)

template<std::size_t N, typename T >
Vector< T, N > &	operator-= (Vector< T, N > &a, Vector< T, N > const &b)

template<std::size_t N, typename T , class U , std::enable_if_t< std::is_arithmetic_v< U >, bool > = true>
auto	operator* (U const &a, Vector< T, N > const &b)

template<std::size_t N, typename T , class U , std::enable_if_t< std::is_arithmetic_v< U >, bool > = true>
auto	operator* (Vector< T, N > const &b, U const &a)

template<std::size_t N, typename T >
Vector< T, N > &	operator*= (Vector< T, N > &b, T const &a)

template<std::size_t N, typename T >
Vector< T, N >	operator/ (Vector< T, N > const &a, T const &b)

template<std::size_t N, typename T >
Vector< T, N > &	operator/= (Vector< T, N > &a, T const &b)

template<std::size_t N, typename T , class U , class = std::enable_if_t<not(detail::is_vector<T>::value or detail::is_vector<U>::value)>>
auto	operator* (Vector< T, N > const &a, Vector< U, N > const &b)

template<std::size_t N, typename T , class U , class = std::enable_if_t<std::is_integral_v<T> and std::is_integral_v<U>>>
auto	operator% (Vector< T, N > const &a, Vector< U, N > const &b)

template<std::size_t N, typename T >
Vector< T, N >	sqrt (Vector< T, N > const &a)

template<class T >
Vector< T, 3 >	vector_product (Vector< T, 3 > const &a, Vector< T, 3 > const &b)

template<class T , std::size_t N>
T	product (Vector< T, N > const &v)

template<class T , class U , std::size_t N>
auto	hadamard_product (Vector< T, N > const &a, Vector< U, N > const &b)

template<class T , class U , std::size_t N, class = std::enable_if_t<not(detail::is_vector<T>::value)>>
auto	hadamard_product (T const &a, Vector< U, N > const &b)

template<class T , class U , std::size_t N, class = std::enable_if_t<not(detail::is_vector<U>::value)>>
auto	hadamard_product (Vector< T, N > const &a, U const &b)

template<typename T , typename U , class = std::enable_if_t<not(detail::is_vector<T>::value or detail::is_vector<U>::value)>>
auto	hadamard_product (T const &a, U const &b)

template<class T , class U , std::size_t N>
auto	hadamard_division (Vector< T, N > const &a, Vector< U, N > const &b)

template<class T , class U , std::size_t N, class = std::enable_if_t<not(detail::is_vector<U>::value)>>
auto	hadamard_division (Vector< T, N > const &a, U const &b)

template<class T , class U , std::size_t N, class = std::enable_if_t<not(detail::is_vector<T>::value)>>
auto	hadamard_division (T const &a, Vector< U, N > const &b)

template<typename T , typename U , class = std::enable_if_t<not(detail::is_vector<T>::value or detail::is_vector<U>::value)>>
auto	hadamard_division (T const &a, U const &b)

template<typename T >
Vector< T, 3 >	unit_vector (unsigned int i)

template<std::size_t I, class T , std::size_t N>
auto	get (Vector< T, N > const &a) -> std::enable_if_t<(I< N), const T & >

Mathematical, physical and chemical constants. <br>
template<class T = double>
DEVICE_QUALIFIER constexpr T	pi ()
	Ratio of diameter and circumference of a circle.

template<class T = double>
DEVICE_QUALIFIER constexpr T	sqrt_pi_i ()
	One over square root of pi.

template<class T = double>
DEVICE_QUALIFIER constexpr T	gamma ()
	Euler-Mascheroni constant.

template<class T = double>
DEVICE_QUALIFIER constexpr T	ln_2 ()
	Natural logarithm of 2.

template<class T = double>
DEVICE_QUALIFIER constexpr T	sqrt_2 ()
	Square root of 2.

template<class T = double>
DEVICE_QUALIFIER constexpr T	cbrt_2 ()
	Cube root of 2.

Typedef Documentation

◆ tuple_element_t

template<std::size_t I, class Tuple >

using Utils::tuple_element_t = typedef typename tuple_element<I, Tuple>::type

Definition at line 37 of file get.hpp.

◆ Vector2d

using Utils::Vector2d = typedef VectorXd<2>

Definition at line 156 of file Vector.hpp.

◆ Vector3

template<class T >

using Utils::Vector3 = typedef Vector<T, 3>

Definition at line 153 of file Vector.hpp.

◆ Vector3b

using Utils::Vector3b = typedef Utils::Vector<bool, 3>

Definition at line 54 of file Variant.hpp.

◆ Vector3d

using Utils::Vector3d = typedef VectorXd<3>

Definition at line 157 of file Vector.hpp.

◆ Vector3f

using Utils::Vector3f = typedef VectorXf<3>

Definition at line 163 of file Vector.hpp.

◆ Vector3i

using Utils::Vector3i = typedef VectorXi<3>

Definition at line 166 of file Vector.hpp.

◆ Vector4d

using Utils::Vector4d = typedef VectorXd<4>

Definition at line 158 of file Vector.hpp.

◆ Vector6d

using Utils::Vector6d = typedef VectorXd<6>

Definition at line 159 of file Vector.hpp.

◆ Vector9d

using Utils::Vector9d = typedef VectorXd<9>

Definition at line 160 of file Vector.hpp.

◆ VectorXd

template<std::size_t N>

using Utils::VectorXd = typedef Vector<double, N>

Definition at line 155 of file Vector.hpp.

◆ VectorXf

template<std::size_t N>

using Utils::VectorXf = typedef Vector<float, N>

Definition at line 162 of file Vector.hpp.

◆ VectorXi

template<std::size_t N>

using Utils::VectorXi = typedef Vector<int, N>

Definition at line 165 of file Vector.hpp.

Enumeration Type Documentation

◆ MemoryOrder

enum class Utils::MemoryOrder

strong

Enumerator
COLUMN_MAJOR
ROW_MAJOR

Definition at line 32 of file index.hpp.

Function Documentation

◆ abs() [1/2]

DEVICE_QUALIFIER double Utils::abs ( double x )

inline

Return the absolute value of x.

Definition at line 32 of file abs.hpp.

Referenced by Shapes::HollowConicalFrustum::calculate_dist(), and sinc().

◆ abs() [2/2]

DEVICE_QUALIFIER float Utils::abs ( float x )

inline

Return the absolute value of x.

Definition at line 37 of file abs.hpp.

◆ angle_between()

double Utils::angle_between	(	Vector3d const &	v1,
		Vector3d const &	v2
	)

inline

Determine the angle between two vectors.

Definition at line 52 of file vec_rotate.hpp.

References Utils::Vector< T, N >::norm2().

Referenced by Observables::CylindricalLBProfileObservable::calculate_sampling_positions(), and transform_vector_cartesian_to_cylinder().

◆ angle_btw_triangles()

double Utils::angle_btw_triangles	(	const Vector3d &	P1,
		const Vector3d &	P2,
		const Vector3d &	P3,
		const Vector3d &	P4
	)

inline

Computes the angle between two triangles in 3D space.

Returns the angle between two triangles in 3D space given by points P1P2P3 and P2P3P4. Note, that the common edge is given as the second and the third argument. Here, the angle can have values from 0 to 2 * PI, depending on the orientation of the two triangles. So the angle can be convex or concave. For each triangle, an inward direction has been defined as the direction of one of the two normal vectors. Particularly, for triangle P1P2P3 it is the vector N1 = P2P1 x P2P3 and for triangle P2P3P4 it is N2 = P2P3 x P2P4. The method first computes the angle between N1 and N2, which gives always value between 0 and PI and then it checks whether this value must be corrected to a value between PI and 2 * PI.

As an example, consider 4 points A,B,C,D in space given by coordinates A = [1,1,1], B = [2,1,1], C = [1,2,1], D = [1,1,2]. We want to determine the angle between triangles ABC and ACD. In case the orientation of the triangle ABC is [0,0,1] and orientation of ACD is [1,0,0], the resulting angle must be PI/2.0. To get correct results, note that the common edge is AC, and one must call the method as angle_btw_triangles(B,A,C,D). With this call we have ensured that N1 = AB x AC (which coincides with [0,0,1]) and N2 = AC x AD (which coincides with [1,0,0]). Alternatively, if the orientations of the two triangles were the opposite, the correct call would be angle_btw_triangles(B,C,A,D) so that N1 = CB x CA and N2 = CA x CD.

Definition at line 79 of file triangle_functions.hpp.

References get_n_triangle(), and pi().

Referenced by OifLocalForcesBond::calc_forces().

◆ area_triangle()

double Utils::area_triangle	(	const Vector3d &	P1,
		const Vector3d &	P2,
		const Vector3d &	P3
	)

inline

Computes the area of triangle between vectors P1,P2,P3, by computing the cross product P1P2 x P1P3 and taking the half of its norm.

Definition at line 48 of file triangle_functions.hpp.

References get_n_triangle(), and Utils::Vector< T, N >::norm().

Referenced by add_oif_global_forces(), OifLocalForcesBond::calc_forces(), and calc_oif_global().

◆ AS_erfc_part()

template<typename T >

constexpr T Utils::AS_erfc_part ( T d )

constexpr

Approximate \( \exp(d^2) \mathrm{erfc}(d)\) by applying a formula from [1] chapter 7.

Definition at line 29 of file AS_erfc_part.hpp.

Referenced by CoulombP3M::pair_energy(), DipolarP3M::pair_energy(), CoulombP3M::pair_force(), and DipolarP3M::pair_force().

◆ basis_change()

Vector3d Utils::basis_change	(	Vector3d const &	b1,
		Vector3d const &	b2,
		Vector3d const &	b3,
		Vector3d const &	v,
		bool	reverse = `false`
	)

inline

Basis change.

Definition at line 47 of file coordinate_transformation.hpp.

References Utils::Vector< T, N >::normalized(), and Utils::Matrix< T, Rows, Cols >::transposed().

Referenced by Shapes::HollowConicalFrustum::calculate_dist(), transform_coordinate_cartesian_to_cylinder(), and transform_coordinate_cylinder_to_cartesian().

◆ bspline() [1/2]

template<int order, typename T >

DEVICE_QUALIFIER auto Utils::bspline	(	int	i,
		T	x
	)		-> std::enable_if_t<(order > 0) && (order <= 7), T>

Formula of the B-spline.

Definition at line 32 of file bspline.hpp.

References DEVICE_ASSERT, DEVICE_THROW, and sqr().

Referenced by Utils::Interpolation::bspline_3d(), Utils::Interpolation::bspline_3d_gradient(), and p3m_calculate_interpolation_weights().

◆ bspline() [2/2]

template<class T >

auto Utils::bspline	(	int	i,
		T	x,
		int	k
	)

Calculate B-splines.

Parameters

i	knot number, using 0-based indexing
x	position in the range (-0.5, 0.5)
k	order of the B-spline, using 1-based indexing, i.e. a B-spline of order `k` is a polynomial of degree `k-1`

Definition at line 186 of file bspline.hpp.

◆ bspline_d()

template<int order, typename T = double>

DEVICE_QUALIFIER auto Utils::bspline_d	(	int	i,
		T	x
	)		-> std::enable_if_t<(order > 0) && (order <= 7), T>

Derivative of the B-spline.

Definition at line 210 of file bspline.hpp.

References DEVICE_ASSERT, and DEVICE_THROW.

◆ calc_orthonormal_vector()

template<typename T , std::size_t N>

Vector< T, N > Utils::calc_orthonormal_vector ( Vector< T, N > const & vec )

Return a vector that is orthonormal to vec.

Definition at line 32 of file orthonormal_vec.hpp.

References Utils::Vector< T, N >::broadcast(), Utils::Vector< T, N >::norm(), Utils::Vector< T, N >::norm2(), and sqrt_2().

◆ cartesian_product()

template<typename Body , typename... ForwardRange>

void Utils::cartesian_product	(	const Body &	op,
		const ForwardRange &...	rng
	)

Call op with each element of the cartesian product set of rng.

Parameters

op	Operation to call for each element of the product set.
rng	Ranges to form the product over

Definition at line 54 of file cartesian_product.hpp.

Referenced by for_each_image().

◆ cbrt_2()

template<class T = double>

DEVICE_QUALIFIER constexpr T Utils::cbrt_2 ( )

constexpr

Cube root of 2.

Definition at line 71 of file constants.hpp.

Referenced by LJcos_Parameters::LJcos_Parameters().

◆ check_charge_neutrality()

template<typename ParticleRange >

bool Utils::check_charge_neutrality ( ParticleRange & prange )

Definition at line 31 of file charge_neutrality.hpp.

◆ contains() [1/2]

template<class Range , class T >

bool Utils::contains	(	const Range &	rng,
		T const &	value
	)

Check whether a range contains a value.

Parameters

rng	The range to search in.
value	The value to search for.

Returns: True iff range contains the value.

Definition at line 49 of file contains.hpp.

References contains().

◆ contains() [2/2]

template<class InputIt , class T >

bool Utils::contains	(	InputIt	first,
		InputIt	last,
		T const &	value
	)

Check whether an iterator range contains a value.

Parameters

first	Beginning of the range
last	End of the range.
value	The value to search for.

Returns: True iff range contains the value.

Definition at line 36 of file contains.hpp.

Referenced by add_exclusion(), contains(), ReactionMethods::ReactionAlgorithm::displacement_mc_move(), gather_traits_for_types(), mindist(), and CellStructure::remove_particle().

◆ convert_director_to_quaternion()

template<class T >

Quaternion< T > Utils::convert_director_to_quaternion ( Vector< T, 3 > const & d )

Convert director to quaternion.

Parameters

d Director

Returns: A (non-normalized) quaternion from the director, or {1, 0, 0, 0} if the director is the null vector.

Definition at line 54 of file math/quaternion.hpp.

References Utils::Vector< T, N >::norm().

Referenced by calculate_vs_relate_to_params(), convert_dip_to_quat(), and ScriptInterface::Particles::ParticleHandle::ParticleHandle().

◆ convert_quaternion_to_director()

template<class T >

Vector< T, 3 > Utils::convert_quaternion_to_director ( Quaternion< T > const & quat )

Convert quaternion to director.

Returns: A (non-normalized) director.

Definition at line 41 of file math/quaternion.hpp.

Referenced by ParticlePosition::calc_director(), connection_vector(), gb_pair_energy(), gb_pair_force(), and ScriptInterface::Particles::ParticleHandle::ParticleHandle().

◆ del_gaussian()

Utils::Vector3d Utils::del_gaussian	(	Vector3d	x,
		Vector3d	x0,
		double	sigma
	)

inline

Definition at line 31 of file utils/include/utils/math/gaussian.hpp.

References gaussian().

◆ demangle()

template<class T >

std::string Utils::demangle ( )

Get a human-readable name for a type.

Uses boost to demangle the name, for details see documentation for boost::core::demangle.

Template Parameters

T type

Returns: name

Definition at line 36 of file demangle.hpp.

◆ diagonal_mat()

template<typename T , std::size_t Rows, std::size_t Cols>

Matrix< T, Rows, Cols > Utils::diagonal_mat ( Utils::Vector< T, Rows > const & v )

Definition at line 225 of file matrix.hpp.

◆ flatten() [1/2]

template<typename T , std::size_t M, std::size_t N>

Utils::Vector< T, M *N > Utils::flatten ( Matrix< T, M, N > const & m )

Definition at line 220 of file matrix.hpp.

References Utils::Matrix< T, Rows, Cols >::begin(), and Utils::Matrix< T, Rows, Cols >::end().

◆ flatten() [2/2]

template<class Range , class OutputIterator >

void Utils::flatten	(	Range const &	v,
		OutputIterator	out
	)

Flatten a range of ranges.

Copy a range of ranges to an output range by subsequently copying the nested ranges to the output. Arbitrary deep nesting is supported, the elements are copied into the output in a depth-first fashion.

Template Parameters

Range	A Forward Range
OutputIterator	An OutputIterator

Parameters

v	Input Range
out	Output iterator

Definition at line 63 of file flatten.hpp.

Referenced by System::System::calculate_pressure(), dpd_stress(), Observables::ParticleObservable< ObsType >::evaluate(), and Utils::Matrix< T, Rows, Cols >::Matrix().

◆ for_each() [1/2]

template<class F , class Tuple >

void Utils::for_each	(	F &&	f,
		Tuple &&	t
	)

Definition at line 52 of file tuple.hpp.

References f.

◆ for_each() [2/2]

template<class F , class Tuple >

void Utils::for_each	(	F &&	f,
		Tuple &	t
	)

Definition at line 46 of file tuple.hpp.

References f.

◆ for_each_cartesian_pair() [1/2]

template<typename ForwardIterator , typename BinaryOp >

void Utils::for_each_cartesian_pair	(	ForwardIterator	first1,
		ForwardIterator	last1,
		ForwardIterator	first2,
		ForwardIterator	last2,
		BinaryOp	op
	)

Execute op for each pair of elements between [first1, last1) and [first2, last2).

Diagonal elements are not excluded. Pairs are traversed ordered, so that for op(*it, *jt), it holds that distance(it - first) < distance(jt - first), and distance(it_n - first) < distance(it_n+1 - first) for consecutive calls.

Definition at line 62 of file for_each_pair.hpp.

Referenced by for_each_cartesian_pair().

◆ for_each_cartesian_pair() [2/2]

template<typename ForwardRange , typename BinaryOp >

void Utils::for_each_cartesian_pair	(	ForwardRange &&	rng1,
		ForwardRange &&	rng2,
		BinaryOp &&	op
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 76 of file for_each_pair.hpp.

References for_each_cartesian_pair().

◆ for_each_cartesian_pair_if() [1/2]

template<typename ForwardIterator , typename BinaryOp , typename BinaryCmp >

void Utils::for_each_cartesian_pair_if	(	ForwardIterator	first1,
		ForwardIterator	last1,
		ForwardIterator	first2,
		ForwardIterator	last2,
		BinaryOp	op,
		BinaryCmp	cmp
	)

Execute op for each pair of elements between [first1, last1) and [first2, last2) if a condition is satisfied.

Diagonal elements are not excluded. Pairs are traversed ordered, so that for op(*it, *jt), it holds that distance(it - first) < distance(jt - first), and distance(it_n - first) < distance(it_n+1 - first) for consecutive calls.

Definition at line 93 of file for_each_pair.hpp.

Referenced by for_each_cartesian_pair_if().

◆ for_each_cartesian_pair_if() [2/2]

template<typename ForwardRange , typename BinaryOp , typename BinaryCmp >

void Utils::for_each_cartesian_pair_if	(	ForwardRange &&	rng1,
		ForwardRange &&	rng2,
		BinaryOp &&	op,
		BinaryCmp	cmp
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 109 of file for_each_pair.hpp.

References for_each_cartesian_pair_if().

◆ for_each_pair() [1/2]

template<typename ForwardIterator , typename BinaryOp >

void Utils::for_each_pair	(	ForwardIterator	first,
		ForwardIterator	last,
		BinaryOp	op
	)

Execute op for each pair of elements in [first, last) once.

Diagonal elements are excluded. Pairs are traversed ordered, so that for op(*it, *jt), it holds that distance(it - first) < distance(jt - first), and distance(it_n - first) < distance(it_n+1 - first) for consecutive calls.

Definition at line 35 of file for_each_pair.hpp.

Referenced by for_each_pair(), and ClusterAnalysis::ClusterStructure::run_for_all_pairs().

◆ for_each_pair() [2/2]

template<typename ForwardRange , typename BinaryOp >

void Utils::for_each_pair	(	ForwardRange &&	rng,
		BinaryOp &&	op
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 47 of file for_each_pair.hpp.

References for_each_pair().

◆ gamma()

template<class T = double>

DEVICE_QUALIFIER constexpr T Utils::gamma ( )

constexpr

Euler-Mascheroni constant.

Definition at line 50 of file constants.hpp.

Referenced by CoulombMMM1D::pair_energy(), and preparePolygammaEven().

◆ gaussian()

double Utils::gaussian	(	Vector3d	x,
		Vector3d	x0,
		double	sigma
	)

inline

Definition at line 27 of file utils/include/utils/math/gaussian.hpp.

Referenced by del_gaussian().

◆ get() [1/3]

template<std::size_t I, class T , std::size_t N>

auto Utils::get ( Array< T, N > const & a ) -> std::enable_if_t<(I < N), const T &>

Definition at line 214 of file Array.hpp.

◆ get() [2/3]

template<std::size_t I, typename T >

const std::tuple_element_t< I, T > & Utils::get ( const T & v )

Definition at line 27 of file get.hpp.

◆ get() [3/3]

template<std::size_t I, class T , std::size_t N>

auto Utils::get ( Vector< T, N > const & a ) -> std::enable_if_t<(I < N), const T &>

Definition at line 481 of file Vector.hpp.

◆ get_cylindrical_sampling_positions()

std::vector< Vector3d > Utils::get_cylindrical_sampling_positions	(	std::pair< double, double > const &	r_limits,
		std::pair< double, double > const &	phi_limits,
		std::pair< double, double > const &	z_limits,
		std::size_t	n_r_bins,
		std::size_t	n_phi_bins,
		std::size_t	n_z_bins,
		double	sampling_density
	)

Generate sampling positions for a cylindrical histogram.

Parameters

r_limits	Range for radial coordinate as std::pair.
phi_limits	Range for azimuthal angle as std::pair.
z_limits	Range for z coordinate as std::pair.
n_r_bins	Number of bins in radial direction.
n_phi_bins	Number of bins in azimuthal direction.
n_z_bins	Number of bins in z direction.
sampling_density	The number of samples per unit volume.

Return values

Cartesian sampling coordinates.

Definition at line 47 of file sampling.hpp.

References Utils::Array< T, N >::begin(), make_lin_space(), and sqr().

Referenced by Observables::CylindricalLBProfileObservable::calculate_sampling_positions().

◆ get_linear_index() [1/2]

int Utils::get_linear_index	(	const Vector3i &	ind,
		const Vector3i &	adim,
		MemoryOrder	memory_order = `MemoryOrder::COLUMN_MAJOR`
	)

inline

Definition at line 56 of file index.hpp.

References get_linear_index().

◆ get_linear_index() [2/2]

int Utils::get_linear_index	(	int	a,
		int	b,
		int	c,
		const Vector3i &	adim,
		MemoryOrder	memory_order = `MemoryOrder::COLUMN_MAJOR`
	)

inline

get the linear index from the position (a,b,c) in a 3D grid of dimensions adim.

Returns: The linear index

Parameters

a,b,c	Position in 3D space
adim	Dimensions of the underlying grid
memory_order	Row- or column-major

Definition at line 43 of file index.hpp.

References COLUMN_MAJOR, and get_linear_index().

Referenced by get_linear_index(), get_linear_index(), grid_influence_function(), grid_influence_function(), grid_influence_function_self_energy(), and p3m_calculate_interpolation_weights().

◆ get_n_triangle()

Vector3d Utils::get_n_triangle	(	const Vector3d &	P1,
		const Vector3d &	P2,
		const Vector3d &	P3
	)

inline

Computes the normal vector of a triangle.

The sign convention is such that P1P2, P1P3 and the normal form a right-handed system. The normal vector is not normalized, i.e. its length is arbitrary.

Definition at line 37 of file triangle_functions.hpp.

References u, and vector_product().

Referenced by add_oif_global_forces(), angle_btw_triangles(), area_triangle(), OifLocalForcesBond::calc_forces(), and calc_oif_global().

◆ hadamard_division() [1/4]

template<typename T , typename U , class = std::enable_if_t<not(detail::is_vector<T>::value or detail::is_vector::value)>>

auto Utils::hadamard_division	(	T const &	a,
		U const &	b
	)

Definition at line 446 of file Vector.hpp.

◆ hadamard_division() [2/4]

template<class T , class U , std::size_t N, class = std::enable_if_t<not(detail::is_vector<T>::value)>>

auto Utils::hadamard_division	(	T const &	a,
		Vector< U, N > const &	b
	)

Definition at line 433 of file Vector.hpp.

References Utils::Array< T, N >::begin().

◆ hadamard_division() [3/4]

template<class T , class U , std::size_t N, class = std::enable_if_t<not(detail::is_vector::value)>>

auto Utils::hadamard_division	(	Vector< T, N > const &	a,
		U const &	b
	)

Definition at line 422 of file Vector.hpp.

◆ hadamard_division() [4/4]

template<class T , class U , std::size_t N>

auto Utils::hadamard_division	(	Vector< T, N > const &	a,
		Vector< U, N > const &	b
	)

Definition at line 407 of file Vector.hpp.

References Utils::Array< T, N >::begin(), Utils::Array< T, N >::cbegin(), and Utils::Array< T, N >::cend().

Referenced by TuningAlgorithm::get_mc_time(), LatticeWalberla::LatticeWalberla(), LocalBox::make_regular_decomposition(), p3m_k_space_error(), P3MParameters::recalc_a_ai_cao_cut(), and BrownianThermostat::sigma().

◆ hadamard_product() [1/4]

template<typename T , typename U , class = std::enable_if_t<not(detail::is_vector<T>::value or detail::is_vector::value)>>

auto Utils::hadamard_product	(	T const &	a,
		U const &	b
	)

Definition at line 402 of file Vector.hpp.

◆ hadamard_product() [2/4]

template<class T , class U , std::size_t N, class = std::enable_if_t<not(detail::is_vector<T>::value)>>

auto Utils::hadamard_product	(	T const &	a,
		Vector< U, N > const &	b
	)

Definition at line 379 of file Vector.hpp.

◆ hadamard_product() [3/4]

template<class T , class U , std::size_t N, class = std::enable_if_t<not(detail::is_vector::value)>>

auto Utils::hadamard_product	(	Vector< T, N > const &	a,
		U const &	b
	)

Definition at line 390 of file Vector.hpp.

◆ hadamard_product() [4/4]

template<class T , class U , std::size_t N>

auto Utils::hadamard_product	(	Vector< T, N > const &	a,
		Vector< U, N > const &	b
	)

Definition at line 364 of file Vector.hpp.

References Utils::Array< T, N >::begin(), Utils::Array< T, N >::cbegin(), and Utils::Array< T, N >::cend().

Referenced by P3MParameters::calc_grid_pos(), FieldCoupling::Fields::Interpolated< T, codim >::fits_in_box(), LB::ParticleCoupling::get_noise_term(), lb_drag_force(), LocalBox::make_regular_decomposition(), and positions_in_halo_impl().

◆ identity_mat()

template<typename T , std::size_t Rows, std::size_t Cols>

Matrix< T, Rows, Cols > Utils::identity_mat ( )

Definition at line 231 of file matrix.hpp.

◆ int_pow()

template<unsigned n, typename T >

DEVICE_QUALIFIER constexpr T Utils::int_pow ( T x )

constexpr

Calculate integer powers.

This functions calculates x^n, where n is a positive integer that is known at compile time. It uses exponentiation by squaring to construct an efficient function.

Definition at line 61 of file int_pow.hpp.

References int_pow().

Referenced by G_opt(), G_opt_dipolar(), gb_pair_energy(), gb_pair_force(), and int_pow().

◆ integral_parameter()

template<typename T , template< T > class F, T min, T max, class... Args>

decltype(auto) Utils::integral_parameter	(	T	i,
		Args &&...	args
	)

Generate a call table for an integral non-type template parameter.

Can be used to dynamically create a switch statement for contiguous values.

Definition at line 57 of file integral_parameter.hpp.

◆ keys()

template<typename Map >

auto Utils::keys ( Map const & m ) -> std::vector<typename Map::key_type>

Return the keys of a map type.

Returns a vector of copies of the keys of a map, unordered_map, ...

Definition at line 34 of file keys.hpp.

Referenced by ComFixed::get_fixed_types(), get_particle_ids(), and get_particle_ids_parallel().

◆ linear_interpolation()

template<typename T , typename Container >

T Utils::linear_interpolation	(	Container const &	table,
		T	hi,
		T	offset,
		T	x
	)

Linear interpolation between two data points.

Parameters

[in]	table	Tabulated values, equally-spaced along the x-axis
[in]	hi	Distance on the x-axis between tabulated values
[in]	offset	Position on the x-axis of the first tabulated value
[in]	x	Position on the x-axis at which to interpolate the value

Returns: Interpolated value on the y-axis at x.

Definition at line 33 of file linear_interpolation.hpp.

Referenced by TabulatedPotential::energy(), and TabulatedPotential::force().

◆ ln_2()

template<class T = double>

DEVICE_QUALIFIER constexpr T Utils::ln_2 ( )

constexpr

Natural logarithm of 2.

Definition at line 57 of file constants.hpp.

Referenced by K0(), K1(), LPK0(), LPK01(), LPK1(), and CoulombMMM1D::pair_energy().

◆ lower_triangular()

template<class T >

T Utils::lower_triangular	(	T	i,
		T	j
	)

Linear index into a lower triangular matrix.

This is row-major.

Template Parameters

T	Integral type

Parameters

i	row index
j	column index

Returns: linear index

Definition at line 71 of file index.hpp.

Referenced by InteractionsNonBonded::get_ia_param_key(), and Observable_stat::Observable_stat().

◆ make_const_span() [1/2]

template<class C >

DEVICE_QUALIFIER constexpr auto Utils::make_const_span ( C & c )

constexpr

Definition at line 126 of file Span.hpp.

References make_const_span().

◆ make_const_span() [2/2]

template<typename T >

DEVICE_QUALIFIER constexpr Span< std::add_const_t< T > > Utils::make_const_span	(	T *	p,
		std::size_t	N
	)

constexpr

Definition at line 122 of file Span.hpp.

References N.

Referenced by p3m_interpolation_cache::load(), make_const_span(), and AssignForces< cao >::operator()().

◆ make_lin_space()

template<class T >

auto Utils::make_lin_space	(	T	start,
		T	stop,
		std::size_t	number,
		bool	endpoint = `true`
	)

Equally spaced values in interval.

Returns a range of equally spaced values in the range of start and stop, like numpy.linspace.

Template Parameters

T	floating point type

Parameters

start	Start value of the interval
stop	End value of the interval
number	Number of partition points
endpoint	If true, the last point is stop, otherwise one less.

Returns: Range of equally spaced values

Definition at line 45 of file make_lin_space.hpp.

Referenced by Observables::ProfileObservable::edges(), get_cylindrical_sampling_positions(), and raster().

◆ make_span() [1/2]

template<class C >

DEVICE_QUALIFIER constexpr auto Utils::make_span ( C & c )

constexpr

Definition at line 116 of file Span.hpp.

References make_span().

◆ make_span() [2/2]

template<typename T >

DEVICE_QUALIFIER constexpr Span< T > Utils::make_span	(	T *	p,
		std::size_t	N
	)

constexpr

◆ mask()

template<class T , class Integral >

auto Utils::mask	(	Integral	mask,
		T	t
	)		-> std::enable_if_t<std::is_unsigned_v<Integral> && (size_in_bits<Integral>::value >= tuple_size<T>::value), T>

Pick elements of a tuple-like by a bit mask.

E.g. every element of the input for which the corresponding bit is set in the mask is set is copied to the output unmodified, the elements that are not set are set to zero (default constructed instance of the type).

Example: mask(0b1011, {1, 2, 3, 4}) => {1, 0, 3, 4}

Template Parameters

T	implements the tuple interface(get, tuple_size, ...)
Integral	An unsigned integral type

Parameters

mask	bit mask, if the i-th bit is set, the i-th element in `t` is copied to the output, otherwise it is set to zero.
t	input elements

Returns: t partially zeroed out according to mask

Definition at line 57 of file mask.hpp.

References mask().

Referenced by mask(), and propagate_omega_quat_particle().

◆ matrix_vector_product()

template<typename T , std::size_t N, const std::array< std::array< int, N >, N > & matrix, typename Container >

constexpr std::array< T, N > Utils::matrix_vector_product ( const Container & vec )

constexpr

Calculate the matrix-vector product for a statically given (square) matrix.

Template Parameters

T	data type for the vector.
N	size of the vector.
matrix	const reference to a static integer array (size N) of arrays (each of size N).
Container	container type for the vector.

Parameters

vec	Container with data of type T and length N with the vector data.

Return values

An	array with the result of the matrix-vector product.

Definition at line 104 of file matrix_vector_product.hpp.

◆ operator!=()

template<std::size_t N, typename T >

constexpr bool Utils::operator!=	(	Vector< T, N > const &	a,
		Vector< T, N > const &	b
	)

constexpr

Definition at line 227 of file Vector.hpp.

◆ operator%()

template<std::size_t N, typename T , class U , class = std::enable_if_t<std::is_integral_v<T> and std::is_integral_v>>

auto Utils::operator%	(	Vector< T, N > const &	a,
		Vector< U, N > const &	b
	)

Definition at line 330 of file Vector.hpp.

◆ operator*() [1/4]

template<typename T , typename U , std::enable_if_t< std::is_arithmetic_v, bool > = true>

Quaternion< T > Utils::operator*	(	const U &	b,
		const Quaternion< T > &	a
	)

Product quaternion and arithmetic type.

Template Parameters

T	Data type of quaternion `a`.
U	Type of multiplier `b`.

Parameters

b	Quaternion.
a	Multiplier.

Returns: Multiplied quaternion.

Definition at line 141 of file quaternion.hpp.

References operator*().

Referenced by operator*(), operator*(), operator*(), and operator*().

◆ operator*() [2/4]

template<std::size_t N, typename T , class U , std::enable_if_t< std::is_arithmetic_v, bool > = true>

auto Utils::operator*	(	U const &	a,
		Vector< T, N > const &	b
	)

Definition at line 264 of file Vector.hpp.

References operator*().

◆ operator*() [3/4]

template<std::size_t N, typename T , class U , class = std::enable_if_t<not(detail::is_vector<T>::value or detail::is_vector::value)>>

auto Utils::operator*	(	Vector< T, N > const &	a,
		Vector< U, N > const &	b
	)

Definition at line 320 of file Vector.hpp.

References operator*().

◆ operator*() [4/4]

template<std::size_t N, typename T , class U , std::enable_if_t< std::is_arithmetic_v, bool > = true>

auto Utils::operator*	(	Vector< T, N > const &	b,
		U const &	a
	)

Definition at line 276 of file Vector.hpp.

References operator*().

◆ operator*=()

template<std::size_t N, typename T >

Vector< T, N > & Utils::operator*=	(	Vector< T, N > &	b,
		T const &	a
	)

Definition at line 287 of file Vector.hpp.

References operator*=().

Referenced by operator*=().

◆ operator+()

template<std::size_t N, typename T , typename U >

auto Utils::operator+	(	Vector< T, N > const &	a,
		Vector< U, N > const &	b
	)

Definition at line 232 of file Vector.hpp.

References operator+().

Referenced by operator+().

◆ operator+=()

template<std::size_t N, typename T >

Vector< T, N > & Utils::operator+=	(	Vector< T, N > &	a,
		Vector< T, N > const &	b
	)

Definition at line 237 of file Vector.hpp.

References operator+=().

Referenced by operator+=().

◆ operator-() [1/2]

template<std::size_t N, typename T >

Vector< T, N > Utils::operator- ( Vector< T, N > const & a )

Definition at line 247 of file Vector.hpp.

References operator-().

◆ operator-() [2/2]

template<std::size_t N, typename T , typename U >

auto Utils::operator-	(	Vector< T, N > const &	a,
		Vector< U, N > const &	b
	)

Definition at line 242 of file Vector.hpp.

References operator-().

Referenced by operator-(), and operator-().

◆ operator-=()

template<std::size_t N, typename T >

Vector< T, N > & Utils::operator-=	(	Vector< T, N > &	a,
		Vector< T, N > const &	b
	)

Definition at line 257 of file Vector.hpp.

References operator-=().

Referenced by operator-=().

◆ operator/()

template<std::size_t N, typename T >

Vector< T, N > Utils::operator/	(	Vector< T, N > const &	a,
		T const &	b
	)

Definition at line 295 of file Vector.hpp.

References Utils::Array< T, N >::begin(), and operator/().

Referenced by operator/().

◆ operator/=()

template<std::size_t N, typename T >

Vector< T, N > & Utils::operator/=	(	Vector< T, N > &	a,
		T const &	b
	)

Definition at line 304 of file Vector.hpp.

References operator/=().

Referenced by operator/=().

◆ operator<()

template<std::size_t N, typename T >

constexpr bool Utils::operator<	(	Vector< T, N > const &	a,
		Vector< T, N > const &	b
	)

constexpr

Definition at line 202 of file Vector.hpp.

◆ operator<=()

template<std::size_t N, typename T >

constexpr bool Utils::operator<=	(	Vector< T, N > const &	a,
		Vector< T, N > const &	b
	)

constexpr

Definition at line 212 of file Vector.hpp.

◆ operator==()

template<std::size_t N, typename T >

constexpr bool Utils::operator==	(	Vector< T, N > const &	a,
		Vector< T, N > const &	b
	)

constexpr

Definition at line 222 of file Vector.hpp.

References operator==().

Referenced by operator==().

◆ operator>()

template<std::size_t N, typename T >

constexpr bool Utils::operator>	(	Vector< T, N > const &	a,
		Vector< T, N > const &	b
	)

constexpr

Definition at line 207 of file Vector.hpp.

◆ operator>=()

template<std::size_t N, typename T >

constexpr bool Utils::operator>=	(	Vector< T, N > const &	a,
		Vector< T, N > const &	b
	)

constexpr

Definition at line 217 of file Vector.hpp.

◆ pack()

template<class T >

std::string Utils::pack ( T const & v )

Pack a serialize type into a string.

Template Parameters

T	Serializable type

Parameters

v	Value to serialize

Returns: String representation

Definition at line 38 of file pack.hpp.

Referenced by ScriptInterface::Particles::ParticleList::get_internal_state(), and ScriptInterface::ContextManager::serialize().

◆ permute_ifield()

void Utils::permute_ifield	(	int *	field,
		int	size,
		int	permute
	)

inline

permute an integer array field of size size about permute positions.

Definition at line 24 of file permute_ifield.hpp.

References permute_ifield().

Referenced by permute_ifield().

◆ pi()

template<class T = double>

DEVICE_QUALIFIER constexpr T Utils::pi ( )

constexpr

Ratio of diameter and circumference of a circle.

Definition at line 36 of file constants.hpp.

Referenced by DipolarLayerCorrection::add_force_corrections(), add_PQ_force(), angle_btw_triangles(), calc_dihedral_angle(), calc_sc_cache(), coldet_do_three_particle_bond(), dipolar_energy_correction(), dipolar_force_corrections(), ScriptInterface::Observables::CylindricalLBProfileObservable< CoreCylLBObs >::do_construct(), ScriptInterface::Observables::CylindricalPidProfileObservable< CoreObs >::do_construct(), dp3m_k_space_error(), dp3m_tune_aliasing_sums(), DipolarLayerCorrection::energy_correction(), far_error(), walberla::FFT< FloatType >::FFT(), G_opt(), G_opt_dipolar(), ReactionMethods::ReactionAlgorithm::get_random_position_in_box(), grid_influence_function(), IBMTribend::IBMTribend(), ICCStar::iteration(), ljcos2_pair_energy(), ljcos2_pair_force_factor(), LJcos_Parameters::LJcos_Parameters(), CoulombP3M::long_range_kernel(), DipolarP3M::long_range_kernel(), CoulombP3M::long_range_pressure(), Random::noise_gaussian(), p3m_analytic_cotangent_sum(), p3m_analytic_cotangent_sum(), p3m_k_space_error_gpu_kernel_ik(), p3m_tune_aliasing_sums(), CoulombMMM1D::pair_energy(), CoulombMMM1D::pair_force(), random_unit_vector(), setup_PoQ(), setup_PQ(), structure_factor(), TabulatedAngleBond::TabulatedAngleBond(), and TabulatedDihedralBond::TabulatedDihedralBond().

◆ product()

template<class T , std::size_t N>

T Utils::product ( Vector< T, N > const & v )

Definition at line 359 of file Vector.hpp.

References Utils::Array< T, N >::cbegin(), and Utils::Array< T, N >::cend().

Referenced by ScriptInterface::CellSystem::CellSystem::CellSystem(), fft_init(), walberla::fill_3D_scalar_array(), walberla::fill_3D_vector_array(), walberla::LBWalberlaImpl< FloatType, Architecture >::get_pressure_tensor(), p3m_gpu_add_farfield_force(), p3m_real_space_error(), walberla::set_boundary_from_grid(), and BoxGeometry::volume().

◆ raster()

template<class T , class F >

auto Utils::raster	(	Vector< T, 3 > const &	offset,
		Vector< T, 3 > const &	grid_spacing,
		Vector3i	size,
		F	f
	)

Raster a function over a regular 3d grid.

This evaluates a function over a regular grid and returns the function values at the grid points.

Parameters

offset	Position of the lowest grid point
grid_spacing	Grid constant
size	Grid size
f	Function to evaluate

Returns: Function values at the grid points.

Definition at line 42 of file raster.hpp.

References Utils::Array< T, N >::data(), f, make_lin_space(), and res.

◆ rotation_matrix()

template<typename T >

Matrix< T, 3, 3 > Utils::rotation_matrix ( Quaternion< T > const & q )

Convert quaternion to rotation matrix.

Template Parameters

T	Data type of quaternion.

Parameters

q	Quaternion.

Returns: Rotation matrix.

Definition at line 151 of file quaternion.hpp.

References Utils::Quaternion< T >::normalized().

◆ sgn()

template<typename T >

constexpr int Utils::sgn ( T val )

constexpr

Calculate signum of val.

Definition at line 27 of file sgn.hpp.

Referenced by BoxGeometry::velocity_difference().

◆ sinc()

template<typename T >

DEVICE_QUALIFIER T Utils::sinc ( T d )

Calculates the sinc-function as sin(PI*x)/(PI*x).

(same convention as in [23]). In order to avoid divisions by 0, arguments, whose modulus is smaller than epsi, will be evaluated by an 8th order Taylor expansion of the sinc function. Note that the difference between sinc(x) and this expansion is smaller than 0.235e-12, if x is smaller than 0.1. (The next term in the expansion is the 10th order contribution PI^10/39916800 * x^10 = 0.2346...*x^12). This expansion should also save time, since it reduces the number of function calls to sin().

Definition at line 45 of file sinc.hpp.

References abs().

Referenced by Aliasing_sums_ik(), dp3m_tune_aliasing_sums(), G_opt(), G_opt_dipolar(), G_opt_dipolar_self_energy(), p3m_k_space_error_gpu_kernel_ik(), and p3m_tune_aliasing_sums().

◆ sqr()

template<typename T >

DEVICE_QUALIFIER constexpr T Utils::sqr ( T x )

constexpr

Calculates the SQuaRe of x.

Definition at line 26 of file sqr.hpp.

References sqr().

Referenced by bspline(), IBMTriel::calc_forces(), calc_part_distribution(), calc_re(), calc_rg(), calc_rh(), Shapes::Ellipsoid::calculate_dist(), Shapes::Slitpore::calculate_dist(), Shapes::Torus::calculate_dist(), CoulombMMM1D::CoulombMMM1D(), CoulombP3M::count_charged_particles(), elc_data::dielectric_layers_self_energy(), elc_data::dielectric_layers_self_forces(), dp3m_k_space_error(), dp3m_real_space_error(), dp3m_tune_aliasing_sums(), dpd_pair_force(), energiesKernel(), HarmonicBond::energy(), QuarticBond::energy(), AngleCosineBond::energy(), AngleCossquareBond::energy(), AngleHarmonicBond::energy(), DipolarLayerCorrection::energy_correction(), Accumulators::fcs_acf(), FeneBond::FeneBond(), force_capping(), AngleCosineBond::forces(), AngleHarmonicBond::forces(), TabulatedAngleBond::forces(), forcesKernel(), G_opt(), G_opt_dipolar(), gaussian_pair_energy(), gaussian_pair_force_factor(), gb_pair_energy(), gb_pair_force(), get_cylindrical_sampling_positions(), get_interacting_neighbors(), get_pairs_filtered(), get_short_range_neighbors(), grid_influence_function(), hzeta(), Collision_parameters::initialize(), lj_pair_energy(), ljcos2_pair_energy(), ljcos_pair_energy(), ljcos_pair_force_factor(), LJcos_Parameters::LJcos_Parameters(), ljgen_pair_force_factor(), CoulombP3M::long_range_kernel(), DipolarP3M::long_range_kernel(), CoulombP3M::long_range_pressure(), modify_p3m_sums(), morse_pair_energy(), morse_pair_force_factor(), numBlocks(), Observables::LBFluidPressureTensor::operator()(), VerletCriterion< CutoffGetter >::operator()(), p3m_analytic_cotangent_sum(), p3m_k_space_error(), p3m_real_space_error(), p3m_tune_aliasing_sums(), DipolarP3M::pair_energy(), DipolarP3M::pair_force(), LB::ParticleCoupling::ParticleCoupling(), SmSt_pair_force_factor(), sqr(), steepest_descent_step(), structure_factor(), CoulombMMM1D::tune(), vectorReductionKernel(), velocity_verlet_npt_finalize_p_inst(), velocity_verlet_npt_propagate_pos(), velocity_verlet_npt_propagate_vel(), velocity_verlet_npt_propagate_vel_final(), and wca_pair_energy().

◆ sqrt()

template<std::size_t N, typename T >

Vector< T, N > Utils::sqrt ( Vector< T, N > const & a )

Definition at line 342 of file Vector.hpp.

References Utils::Array< T, N >::begin().

Referenced by LB::ParticleCoupling::get_noise_term().

◆ sqrt_2()

template<class T = double>

DEVICE_QUALIFIER constexpr T Utils::sqrt_2 ( )

constexpr

Square root of 2.

Definition at line 64 of file constants.hpp.

Referenced by calc_orthonormal_vector(), CoulombTuningAlgorithm::calculate_accuracy(), DipolarTuningAlgorithm::calculate_accuracy(), and dp3m_rtbisection().

◆ sqrt_pi_i()

template<class T = double>

DEVICE_QUALIFIER constexpr T Utils::sqrt_pi_i ( )

constexpr

One over square root of pi.

Definition at line 43 of file constants.hpp.

Referenced by CoulombP3M::long_range_kernel(), DipolarP3M::long_range_kernel(), DipolarP3M::pair_energy(), CoulombP3M::pair_force(), and DipolarP3M::pair_force().

◆ tensor_product() [1/2]

template<typename T , std::size_t N>

Vector< T, N > Utils::tensor_product	(	const T &	x,
		const Vector< T, N > &	y
	)

Definition at line 38 of file tensor_product.hpp.

◆ tensor_product() [2/2]

template<typename T , std::size_t N, std::size_t M>

Matrix< T, N, M > Utils::tensor_product	(	const Vector< T, N > &	x,
		const Vector< T, M > &	y
	)

Definition at line 30 of file tensor_product.hpp.

Referenced by add_non_bonded_pair_virials(), Utils::Interpolation::bspline_3d_gradient_accumulate(), calc_bonded_three_body_pressure_tensor(), calc_bonded_virial_pressure_tensor(), FieldCoupling::Fields::PlaneWave< T, codim >::jacobian(), and Coulomb::ShortRangePressureKernel::operator()().

◆ transform_coordinate_cartesian_to_cylinder() [1/2]

Vector3d Utils::transform_coordinate_cartesian_to_cylinder ( Vector3d const & pos )

inline

Coordinate transformation from Cartesian to cylindrical coordinates.

The origins and z-axis of the coordinate systems co-incide. The \( \phi = 0 \) direction corresponds to the x-axis in the original coordinate system.

Parameters

pos	Vector to transform

Definition at line 72 of file coordinate_transformation.hpp.

References pos.

Referenced by Shapes::HollowConicalFrustum::calculate_dist(), Observables::CylindricalDensityProfile::evaluate(), Observables::CylindricalFluxDensityProfile::evaluate(), Observables::CylindricalLBFluxDensityProfileAtParticlePositions::evaluate(), Observables::CylindricalVelocityProfile::evaluate(), Observables::CylindricalLBVelocityProfileAtParticlePositions::evaluate(), Observables::CylindricalLBVelocityProfile::operator()(), and transform_coordinate_cartesian_to_cylinder().

◆ transform_coordinate_cartesian_to_cylinder() [2/2]

Vector3d Utils::transform_coordinate_cartesian_to_cylinder	(	Vector3d const &	pos,
		Vector3d const &	axis,
		Vector3d const &	orientation
	)

inline

Coordinate transformation from Cartesian to cylindrical coordinates with change of basis.

The origins of the coordinate systems co-incide.

If the parameter axis is not equal to [0, 0, 1], the value of the angle \( \phi \) in cylindrical coordinates is under-defined. To fully define it, it is necessary to provide an orientation vector in Cartesian coordinates that will be used as the reference point (i.e. such that \( \phi = 0 \)), by default it is the x-axis.

Parameters

pos	Vector to transform
axis	Longitudinal axis of the cylindrical coordinates
orientation	Reference point (in untransformed coordinates) for which \( \phi = 0 \)

Definition at line 93 of file coordinate_transformation.hpp.

References basis_change(), pos, transform_coordinate_cartesian_to_cylinder(), and vector_product().

◆ transform_coordinate_cylinder_to_cartesian() [1/2]

Vector3d Utils::transform_coordinate_cylinder_to_cartesian ( Vector3d const & pos )

inline

Coordinate transformation from cylindrical to Cartesian coordinates.

The origins and z-axis of the coordinate systems co-incide. The \( \phi = 0 \) direction corresponds to the x-axis in the transformed coordinate system.

Parameters

pos	Vector to transform

Definition at line 111 of file coordinate_transformation.hpp.

References pos.

Referenced by Shapes::HollowConicalFrustum::calculate_dist(), Observables::CylindricalLBProfileObservable::calculate_sampling_positions(), and transform_coordinate_cylinder_to_cartesian().

◆ transform_coordinate_cylinder_to_cartesian() [2/2]

Vector3d Utils::transform_coordinate_cylinder_to_cartesian	(	Vector3d const &	pos,
		Vector3d const &	axis,
		Vector3d const &	orientation
	)

inline

Coordinate transformation from cylindrical to Cartesian coordinates with change of basis.

The origins of the coordinate systems co-incide.

If the parameter axis is not equal to [0, 0, 1], the value of the angle \( \phi \) in cylindrical coordinates is under-defined. To fully define it, it is necessary to provide an orientation vector in Cartesian coordinates that will be used as the reference point (i.e. such that \( \phi = 0 \)).

Parameters

pos	Vector to transform
axis	Longitudinal axis of the cylindrical coordinates
orientation	Reference point (in Cartesian coordinates) for which \( \phi = 0 \)

Definition at line 133 of file coordinate_transformation.hpp.

References basis_change(), pos, transform_coordinate_cylinder_to_cartesian(), and vector_product().

◆ transform_vector_cartesian_to_cylinder()

Vector3d Utils::transform_vector_cartesian_to_cylinder	(	Vector3d const &	vec,
		Vector3d const &	axis,
		Vector3d const &	pos
	)

inline

Vector transformation from Cartesian to cylindrical coordinates.

Parameters

vec	Vector to transform
axis	Longitudinal axis of the cylindrical coordinates
pos	Origin of the vector

Definition at line 149 of file coordinate_transformation.hpp.

References angle_between(), pos, vec_rotate(), and vector_product().

Referenced by Observables::CylindricalFluxDensityProfile::evaluate(), Observables::CylindricalLBFluxDensityProfileAtParticlePositions::evaluate(), Observables::CylindricalVelocityProfile::evaluate(), Observables::CylindricalLBVelocityProfileAtParticlePositions::evaluate(), and Observables::CylindricalLBVelocityProfile::operator()().

◆ u32_to_u64()

constexpr uint64_t Utils::u32_to_u64	(	uint32_t	high,
		uint32_t	low
	)

inlineconstexpr

Definition at line 26 of file u32_to_u64.hpp.

Referenced by Random::philox_4_uint64s().

◆ u64_to_u32()

constexpr std::pair< uint32_t, uint32_t > Utils::u64_to_u32 ( uint64_t in )

inlineconstexpr

Definition at line 30 of file u32_to_u64.hpp.

◆ uniform()

constexpr double Utils::uniform ( uint64_t in )

inlineconstexpr

Uniformly map unsigned integer to double.

This maps a unsigned integer to the double interval (0., 1.], where 0 is mapped to the smallest representable value larger than 0., and the maximal integer value is mapped to 1.

Parameters

in	Unsigned integer value

Returns: Mapped floating point value.

Definition at line 36 of file uniform.hpp.

◆ unit_vector()

template<typename T >

Vector< T, 3 > Utils::unit_vector ( unsigned int i )

Definition at line 450 of file Vector.hpp.

◆ unpack()

template<class T >

T Utils::unpack ( std::string const & state )

Unpack a serialize type into a string.

Template Parameters

T	Serializable type

Parameters

state String to construct the value from, as returned by Utils::pack.

Returns: Unpacked value

Definition at line 53 of file pack.hpp.

◆ vec_rotate()

Vector3d Utils::vec_rotate	(	const Vector3d &	axis,
		double	angle,
		const Vector3d &	vector
	)

inline

Rotate a vector around an axis.

Parameters

axis	The axis to rotate about
angle	Angle to rotate
vector	Vector to act on

Returns: Rotated vector

Definition at line 40 of file vec_rotate.hpp.

Referenced by Observables::CylindricalLBProfileObservable::calculate_sampling_positions(), draw_polymer_positions(), ScriptInterface::System::rotate_system(), and transform_vector_cartesian_to_cylinder().

◆ vector_product()

template<class T >

Vector< T, 3 > Utils::vector_product	(	Vector< T, 3 > const &	a,
		Vector< T, 3 > const &	b
	)

Definition at line 353 of file Vector.hpp.

Referenced by IBMTriel::calc_forces(), Shapes::HollowConicalFrustum::calculate_dist(), Observables::CylindricalLBProfileObservable::calculate_sampling_positions(), Observables::BondDihedrals::evaluate(), get_n_triangle(), IBMTriel::IBMTriel(), transform_coordinate_cartesian_to_cylinder(), transform_coordinate_cylinder_to_cartesian(), and transform_vector_cartesian_to_cylinder().

Namespaces

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

◆ tuple_element_t

◆ Vector2d

◆ Vector3

◆ Vector3b

◆ Vector3d

◆ Vector3f

◆ Vector3i

◆ Vector4d

◆ Vector6d

◆ Vector9d

◆ VectorXd

◆ VectorXf

◆ VectorXi

Enumeration Type Documentation

◆ MemoryOrder

Function Documentation

◆ abs() [1/2]

◆ abs() [2/2]

◆ angle_between()

◆ angle_btw_triangles()

◆ area_triangle()

◆ AS_erfc_part()

◆ basis_change()

◆ bspline() [1/2]

◆ bspline() [2/2]

◆ bspline_d()

◆ calc_orthonormal_vector()

◆ cartesian_product()

◆ cbrt_2()

◆ check_charge_neutrality()

◆ contains() [1/2]

◆ contains() [2/2]

◆ convert_director_to_quaternion()

◆ convert_quaternion_to_director()

◆ del_gaussian()

◆ demangle()

◆ diagonal_mat()

◆ flatten() [1/2]

◆ flatten() [2/2]

◆ for_each() [1/2]

◆ for_each() [2/2]

◆ for_each_cartesian_pair() [1/2]

◆ for_each_cartesian_pair() [2/2]

◆ for_each_cartesian_pair_if() [1/2]

◆ for_each_cartesian_pair_if() [2/2]

◆ for_each_pair() [1/2]

◆ for_each_pair() [2/2]

◆ gamma()

◆ gaussian()

◆ get() [1/3]

◆ get() [2/3]

◆ get() [3/3]

◆ get_cylindrical_sampling_positions()

◆ get_linear_index() [1/2]

◆ get_linear_index() [2/2]

◆ get_n_triangle()

◆ hadamard_division() [1/4]

◆ hadamard_division() [2/4]

◆ hadamard_division() [3/4]

◆ hadamard_division() [4/4]

◆ hadamard_product() [1/4]

◆ hadamard_product() [2/4]

◆ hadamard_product() [3/4]

◆ hadamard_product() [4/4]

◆ identity_mat()

◆ int_pow()

◆ integral_parameter()

◆ keys()

◆ linear_interpolation()

◆ ln_2()

◆ lower_triangular()

◆ make_const_span() [1/2]

◆ make_const_span() [2/2]

◆ make_lin_space()