Namespaces
namespace	adjmat

namespace	bias

namespace	blas

namespace	cltools

namespace	clusters

namespace	colvar

namespace	config

namespace	contour

namespace	crystdistrib

namespace	dimred

namespace	drr

namespace	eds

namespace	enum_traits

namespace	envsim

namespace	fisst

namespace	fourier

namespace	function

namespace	funnel

namespace	gch

namespace	generic

namespace	gridtools

namespace	h36
	Tiny namespace for hybrid36 format.

namespace	helpers

namespace	isdb

namespace	landmarks

namespace	lapack

namespace	lepton

namespace	liquid_crystal

namespace	logmfd

namespace	mapping

namespace	matrixtools

namespace	maze

namespace	membranefusion

namespace	mergeVectorTools

namespace	metatomic

namespace	molfile

namespace	multicolvar

namespace	OpenACC

namespace	OpenMP

namespace	opes

namespace	pamm

namespace	piv

namespace	refdist

namespace	s2cm

namespace	sasa

namespace	secondarystructure

namespace	setup

namespace	sizeshape

namespace	sprint

namespace	switchContainers

namespace	symfunc

namespace	valtools

namespace	vatom

namespace	Versors

namespace	ves

namespace	volumes

namespace	wham

namespace	xdrfile

Classes
class	Accelerator

class	Action
	Base class for all the input Actions. More...

class	ActionAnyorder
	Action used to create a PLMD::Action that can go both before and after ActionSetup actions. More...

class	ActionAtomistic
	Action used to create objects that access the positions of the atoms from the MD code. More...

class	ActionForInterface

class	ActionOptions
	This class is used to bring the relevant information to the Action constructor. More...

class	ActionPilot
	This is used to create PLMD::Action objects that are run with some set frequency. More...

class	ActionRegister
	Register holding all the allowed keywords. More...

struct	ActionRegisterPointers

class	ActionRegistration
	Each instance of this specialized class represents an action that can be called with the specified directive. More...

class	ActionSet
	std::vector containing the sequence of Action to be done. More...

class	ActionSetup
	Action used to create a PLMD::Action that do something during setup only e.g. More...

class	ActionShortcut
	Action used to create a command that expands to multiple PLMD::Action commands when read in during input. More...

class	ActionToGetData
	Provides the keyword GET More...

class	ActionToPutData
	Provides the keyword PUT More...

class	ActionWithArguments

class	ActionWithMatrix

class	ActionWithValue
	Used to create a PLMD::Action that has some scalar or vectorial output that may or may not have some derivatives. More...

class	ActionWithVector

class	ActionWithVirtualAtom
	Inherit from here if you are calculating the position of a virtual atom (eg a center of mass) More...

class	Angle
	Class to compute angles. More...

struct	ArgumentBookeepingHolder

struct	ArgumentsBookkeeping

struct	AtomDistribution
	tested in regtest/tools/rt-make-AtomicDistribution Acts as a template for any distribution More...

class	AtomNumber
	Simple class to store the index of an atom. More...

class	BiasRepresentation
	this class implements a general purpose class that aims to provide a Grid/list transparently add gaussians to a bias More...

class	BiasWeight

class	Brent1DRootSearch
	A class for doing parabolic interpolation and minimisation of 1D functions using Brent's method. More...

class	CheckInRange

class	Citations
	Class taking care of bibliography. More...

class	CLTool
	This is the abstract base class to use for implementing new command line tool, within it there is information as to how to go about implemneting a new tool. More...

class	CLToolMain
	Class providing cmd() access to command line tools. More...

class	CLToolOptions

class	CLToolRegister
	Same as ActionRegister, but for CLTools. More...

struct	CLToolRegisterPointers

class	Colvar
	This is the abstract base class to use for implementing new collective variables, within it there is information as to how to go about implementing a new CV. More...

class	ColvarOutput

class	Communicator
	Class containing wrappers to MPI. More...

class	ConjugateGradient

class	DataPassingObject

class	DataPassingObjectTyped

class	DataPassingTools

class	DataPassingToolsTyped

class	DLLoader
	Class taking care of dynamic loading. More...

class	DomainDecomposition

class	ERMSD
	A class that implements ERMSD calculations. More...

class	Exception
	Class to deal with Plumed runtime errors. More...

class	ExceptionDebug
	Class representing a debug error (can only be thrown when using debug options) More...

class	ExceptionError
	Class representing a generic error. More...

class	ExceptionRegisterError
	Class representing an error in a register. More...

class	ExceptionTypeError
	Class representing a type error in the PLMD::Plumed interface. More...

class	ExchangePatterns

class	F1dim

class	FileBase
	Base class for dealing with files. More...

struct	fileDeleter

class	fileParser

class	fileTraj
	atomic distribution from a trajectory file More...

class	FlexibleBin

struct	ForceIndexHolder

class	ForceInput

struct	ForceOutput

class	ForwardDecl
	Utility class for forward declaration of references. More...

class	GenericMolInfo

class	GREX

class	Grid

class	GridBase

class	Group
	Provides the keyword GROUP More...

class	HistogramBead
	A class for calculating whether or not values are within a given range using : \( \sum_i \int_a^b G( s_i, \sigma*(b-a) ) \). More...

class	IFile
	Class for input files. More...

class	KernelFunctions

class	Keywords
	This class holds the keywords and their documentation. More...

class	LatticeReduction
	Class implementing algorithms for lattice reduction. More...

class	LeptonCall

class	LinkCells
	A class for doing link cells. More...

class	Log
	Class containing the log stream. More...

class	LoopUnroller
	Utiliy class for loop unrolling. More...

class	Matrix
	This class stores a full matrix and allows one to do some simple matrix operations. More...

class	MatrixElementOutput

class	MatrixSquareBracketsAccess
	Utility class to add [][] access. More...

class	Minimise1DBrent
	A class for doing parabolic interpolation and minimisation of 1D functions using Brent's method. More...

class	MinimiseBase

class	MolDataClass
	This class provides information on various kinds of molecules for instance the kinds of residues that are in a protein the atoms involved in the backbone of a particular residue etc. More...

class	MPI_Comm
	Surrogate of MPI_Comm when MPI library is not available. More...

class	MPI_Datatype
	Surrogate of MPI_Datatype when MPI library is not available. More...

class	MPI_Request
	Surrogate of MPI_Request when MPI library is not available. More...

class	MPI_Status
	Surrogate of MPI_Status when MPI library is not available. More...

class	NeighborList
	A class that implements neighbor lists from two lists or a single list of atoms. More...

class	OFile
	Class for output files. More...

struct	ParallelActionsInput

struct	ParallelActionsOutput

class	ParallelTaskManager

class	Pbc

class	PbcAction
	Provides the keyword PBC More...

class	PDB
	Minimalistic pdb parser. More...

class	PlumedHandle
	Tiny local class to load a PLUMED kernel. More...

class	PlumedMain
	Main plumed object. More...

class	ProbWeight

class	Random

class	Register
	Base class, with type independent information. More...

class	RegisterBase
	General register. More...

class	repliedTrajectory
	a decorator for replicate the atomic distribution More...

class	RequiredMatrixElements

class	RequiredMatrixElementsUpdater

class	RMSD
	A class that implements RMSD calculations This is a class that implements the various infrastructure to calculate the RMSD or MSD respect a given frame. More...

class	RMSDCoreData
	this is a class which is needed to share information across the various non-threadsafe routines so that the public function of rmsd are threadsafe while the inner core can safely share information More...

class	RootFindingBase

class	SparseGrid

class	Stopwatch

class	Subprocess
	Class managing a subprocess. More...

class	SubprocessPid
	Small utility class, used to avoid inclusion of unistd.h> in a header file. More...

class	SwitchingFunction
	Small class to compute switching functions. More...

class	SwitchingFunctionAccelerable
	Small class to compute switching functions. More...

class	TargetDist

struct	TensorGenericAux
	Small class to contain local utilities. More...

class	TensorTyped
	Class implementing fixed size matrices of doubles. More...

struct	theLine
	A wiggly line of atoms. More...

struct	tiledSimpleCubic

class	TokenizedLine
	This class abstracts the input line in tokens. More...

class	Tools
	Empty class which just contains several (static) tools. More...

class	Torsion
	Class to compute torsional angles. More...

class	TrajectoryParser

class	Tree

struct	twoGlobs
	Atom randomly distribuited between two not overlapping a spheres. More...

class	TypesafePtr
	Class to deal with propoagation of typesafe pointers. More...

struct	uniformCube

struct	uniformSphere
	Atom randomly distribuited in a sphere. More...

class	UniformSphericalVector

class	Units
	Small utility class that contains information about units. More...

class	Value
	A class for holding the value of a function together with its derivatives. More...

class	VectorTyped
	Class implementing fixed size vectors of doubles. More...

class	View
	A not-owning view for generic data. More...

class	View2D
	A not-owning view for accessing array witha 2D interface. More...

class	WeightBase

class	WithCmd
	Base for classes with cmd() method. More...

Typedefs
template<std::size_t N = helpers::dynamic_extent, std::size_t STRIDE = 3>
using	mdMemoryView = View2D<double,N,STRIDE>

template<std::size_t N = 3>
using	MemoryView = View<double,N>

typedef Tensor3d	Tensor

typedef TensorGeneric< 1, 1 >	Tensor1d

typedef TensorTyped< float, 1, 1 >	Tensor1f

typedef TensorGeneric< 2, 2 >	Tensor2d

typedef TensorTyped< float, 2, 2 >	Tensor2f

typedef TensorGeneric< 3, 3 >	Tensor3d

typedef TensorTyped< float, 3, 3 >	Tensor3f

typedef TensorGeneric< 4, 4 >	Tensor4d

typedef TensorTyped< float, 4, 4 >	Tensor4f

typedef TensorGeneric< 5, 5 >	Tensor5d

typedef TensorTyped< float, 5, 5 >	Tensor5f

template<unsigned n, unsigned m>
using	TensorGeneric = TensorTyped<double,n,m>

template<typename T>
using	TensorT = TensorTyped<T,3,3>
	Alias for three by three Tensor of any type:

using	unique_FILE = std::unique_ptr<FILE,fileDeleter>

typedef Vector3d	Vector
	Alias for three dimensional vectors.

typedef VectorGeneric< 1 >	Vector1d
	Alias for one dimensional vectors.

typedef VectorTyped< float, 1 >	Vector1f
	Alias for one dimensional vectors.

typedef VectorGeneric< 2 >	Vector2d
	Alias for two dimensional vectors.

typedef VectorTyped< float, 2 >	Vector2f
	Alias for two dimensional vectors.

typedef VectorGeneric< 3 >	Vector3d
	Alias for three dimensional vectors.

typedef VectorTyped< float, 3 >	Vector3f
	Alias for three dimensional vectors.

typedef VectorGeneric< 4 >	Vector4d
	Alias for four dimensional vectors.

typedef VectorTyped< float, 4 >	Vector4f
	Alias for four dimensional vectors.

typedef VectorGeneric< 5 >	Vector5d
	Alias for five dimensional vectors.

typedef VectorTyped< float, 5 >	Vector5f
	Alias for five dimensional vectors.

template<unsigned n>
using	VectorGeneric = VectorTyped<double, n>

template<typename T>
using	VectorT = VectorTyped<T,3>
	Alias for three dimensional vectors of any type:

using	VectorView = mdMemoryView<helpers::dynamic_extent, 3>

Functions
ActionRegister &	actionRegister ()

ActionRegister &	actionRegister ()
	Function returning a reference to the ActionRegister.

template<typename T>
void	chol_elsolve (const Matrix< T > &M, const std::vector< T > &b, std::vector< T > &y)

template<typename T>
void	cholesky (const Matrix< T > &A, Matrix< T > &B)

CLToolRegister &	cltoolRegister ()

CLToolRegister &	cltoolRegister ()
	Function returning a reference to the CLToolRegister.

template<typename T>
constexpr VectorTyped< T, 3 >	crossProduct (const VectorTyped< T, 3 > &v1, const VectorTyped< T, 3 > &v2)

template<typename T>
constexpr TensorTyped< T, 3, 3 >	dcrossDv1 (const VectorTyped< T, 3 > &v1, const VectorTyped< T, 3 > &v2)

template<typename T>
constexpr TensorTyped< T, 3, 3 >	dcrossDv2 (const VectorTyped< T, 3 > &v1, const VectorTyped< T, 3 > &v2)

template<typename T, unsigned n>
constexpr VectorTyped< T, n >	delta (const VectorTyped< T, n > &v1, const VectorTyped< T, n > &v2)

template<typename T>
VectorTyped< std::remove_const_t< T >, 3 >	delta (const View< T, 3 > v1, const View< T, 3 > v2) noexcept

template<typename T>
TensorTyped< T, 3, 3 >	deriNorm (const VectorTyped< T, 3 > &v1, const TensorTyped< T, 3, 3 > &v2)

template<typename T>
constexpr T	determinant (const TensorTyped< T, 3, 3 > &t)

template<typename T>
int	diagMat (const Matrix< T > &A, std::vector< T > &eigenvals, Matrix< T > &eigenvecs)

template<typename precision, unsigned n, unsigned m>
void	diagMatSym (const TensorTyped< precision, n, n > &mat, VectorTyped< precision, m > &evals, TensorTyped< precision, m, n > &evec)
	Diagonalize tensor.

template<typename T, unsigned n, unsigned m>
void	diagMatSym (const TensorTyped< T, n, n > &, VectorTyped< T, m > &evals, TensorTyped< T, m, n > &evec)
	Diagonalize tensor.

template<typename T>
T	dotProduct (const std::vector< T > &A, const std::vector< T > &B)
	Calculate the dot product between two vectors.

template<typename T, unsigned n>
constexpr T	dotProduct (const VectorTyped< T, n > &v1, const VectorTyped< T, n > &v2)

constexpr double	dp2cutoff (6.25)

static bool	dp2cutoffNoStretch ()

constexpr double	epsilon (std::numeric_limits< double >::epsilon())
	Very small non-zero number.

template<typename T, unsigned n, unsigned m>
constexpr TensorTyped< T, n, m >	extProduct (const VectorTyped< T, n > &v1, const VectorTyped< T, m > &v2)
	returns the transpose of a tensor (same as TensorGeneric(const VectorGeneric&,const VectorGeneric&))

template<typename T, unsigned n, unsigned m>
T	frobeniusNorm (const TensorTyped< T, m, n > &t)
	Compute the Frobenius norm 2.

const std::map< std::string, std::string > &	getModuleMap ()

template<typename T>
static void	getPointer (const TypesafePtr &p, const std::vector< std::size_t > &shape, const unsigned &start, const unsigned &stride, T *&pp)

void	getWords_replicas (gch::small_vector< std::string_view > &words, std::string_view line, const std::string_view separators)

bool	indexed_lt (std::pair< Grid::index_t, double > const &x, std::pair< Grid::index_t, double > const &y)

template<typename T>
constexpr TensorTyped< T, 3, 3 >	inverse (const TensorTyped< T, 3, 3 > &t)

template<typename T>
int	Invert (const Matrix< T > &A, Matrix< T > &inverse)

static bool	isZero (const ExpressionTreeNode &node)

constexpr double	kBoltzmann (0.0083144621)
	Boltzman constant in kj/K.

template<typename T>
int	logdet (const Matrix< T > &M, T &ldet)

template<typename T, unsigned n>
T	lowestEigenpairSym (const TensorTyped< T, n, n > &K, VectorTyped< T, n > &eigenvector, unsigned niter=24)
	Compute lowest eigenvalue and eigenvector, using a branchless iterative implementation.

template<typename CT>
constexpr View< const typename CT::value_type >	make_const_view (const CT &container)
	Returns a complete constant dynamic view of a container.

template<typename T>
View< T >	make_view (const std::vector< T > &d)

template<typename CT>
constexpr View< typename CT::value_type >	make_view (CT &container)
	Returns a complete dynamic view of a container.

template<typename IT>
auto	mapCreator (IT k, IT const end)

template<typename T, unsigned n, unsigned m, unsigned l>
constexpr TensorTyped< T, n, l >	matmul (const TensorTyped< T, n, m > &a, const TensorTyped< T, m, l > &b)
	matrix-matrix multiplication

template<typename T, unsigned n, unsigned m, unsigned l, unsigned i>
constexpr TensorTyped< T, n, i >	matmul (const TensorTyped< T, n, m > &a, const TensorTyped< T, m, l > &b, const TensorTyped< T, l, i > &c)
	matrix-matrix-matrix multiplication

template<typename T, unsigned n, unsigned m, unsigned l>
constexpr VectorTyped< T, n >	matmul (const TensorTyped< T, n, m > &a, const TensorTyped< T, m, l > &b, const VectorTyped< T, l > &c)
	matrix-matrix-vector multiplication

template<typename T, typename TT, unsigned n, unsigned m>
constexpr VectorTyped< T, n >	matmul (const TensorTyped< T, n, m > &a, const VectorTyped< TT, m > &b)
	matrix-vector multiplicationi, the first argument determines the type of the result

template<typename T, typename TT, unsigned n, unsigned m>
constexpr VectorTyped< T, n >	matmul (const VectorTyped< T, m > &a, const TensorTyped< TT, m, n > &b)
	vector-matrix multiplication, the first argument determines the type of the result

template<typename T, unsigned n, unsigned m, unsigned l>
constexpr VectorTyped< T, l >	matmul (const VectorTyped< T, n > &a, const TensorTyped< T, n, m > &b, const TensorTyped< T, m, l > &c)
	vector-matrix-matrix multiplication

template<typename T, unsigned n, unsigned m>
constexpr T	matmul (const VectorTyped< T, n > &a, const TensorTyped< T, n, m > &b, const VectorTyped< T, m > &c)
	vector-matrix-vector multiplication

template<typename T, unsigned n_>
constexpr T	matmul (const VectorTyped< T, n_ > &a, const VectorTyped< T, n_ > &b)
	vector-vector multiplication (maps to dotProduct)

template<typename T>
void	matrixOut (Log &ostr, const Matrix< T > &mat)

constexpr int	max_cell (int celn, const int ncells, const bool usePBC)

constexpr int	min_cell (int celn, const int ncells, const bool usePBC)

template<typename T, unsigned n>
constexpr T	modulo (const VectorTyped< T, n > &v)

template<typename T, unsigned n>
constexpr T	modulo2 (const VectorTyped< T, n > &v)

template<typename T>
void	mult (const Matrix< T > &A, const Matrix< T > &B, Matrix< T > &C)

template<typename T>
void	mult (const Matrix< T > &A, const std::vector< T > &B, std::vector< T > &C)

template<typename T>
void	mult (const std::vector< T > &A, const Matrix< T > &B, std::vector< T > &C)

template<typename T>
T	norm (const std::vector< T > &A)
	Calculate the dot product between a vector and itself.

bool	operator!= (const AtomNumber &a, const AtomNumber &b)

template<typename enumtype>
constexpr std::enable_if_t< enum_traits::BitmaskEnum< enumtype >::has_bit_and, enumtype >	operator& (enumtype a, enumtype b)
	Perform a bitwise AND between two enum values.

template<typename T, typename J, unsigned n, unsigned m>
constexpr TensorTyped< T, n, m >	operator* (const TensorTyped< T, n, m > &t1, J s)

template<typename T, typename J, unsigned n, unsigned m>
constexpr TensorTyped< T, n, m >	operator* (J s, const TensorTyped< T, n, m > &t1)

template<typename T, typename J, unsigned n>
constexpr VectorTyped< T, n >	operator* (J s, VectorTyped< T, n >v)

template<typename T>
Matrix< T >	operator* (T &v, const Matrix< T > &m)
	Multiply matrix by scalar.

template<typename T, typename J, unsigned n>
constexpr VectorTyped< T, n >	operator* (VectorTyped< T, n > v, J s)

template<typename T, unsigned n, unsigned m>
constexpr TensorTyped< T, n, m >	operator+ (const TensorTyped< T, n, m > &t1, const TensorTyped< T, n, m > &t2)

template<typename T, unsigned n>
constexpr VectorTyped< T, n >	operator+ (const VectorTyped< T, n > &v1, const VectorTyped< T, n > &v2)

template<typename T, unsigned n, unsigned m>
constexpr TensorTyped< T, n, m >	operator- (const TensorTyped< T, n, m > &t1, const TensorTyped< T, n, m > &t2)

template<typename T, unsigned n>
constexpr VectorTyped< T, n >	operator- (VectorTyped< T, n >v1, const VectorTyped< T, n > &v2)

template<typename T, typename J, unsigned n, unsigned m>
constexpr TensorTyped< T, n, m >	operator/ (const TensorTyped< T, n, m > &t1, J s)

template<typename T, typename J, unsigned n>
constexpr VectorTyped< T, n >	operator/ (const VectorTyped< T, n > &v, J s)

bool	operator< (const AtomNumber &a, const AtomNumber &b)

template<typename T>
Log &	operator<< (Log &ostr, const Matrix< T > &mat)

Log &	operator<< (Log &ostr, const PDB &pdb)

template<class T>
OFile &	operator<< (OFile &of, const T &t)
	Write using << syntax.

std::ostream &	operator<< (std::ostream &log, const Citations &cit)

std::ostream &	operator<< (std::ostream &log, const Register &reg)

std::ostream &	operator<< (std::ostream &os, const Stopwatch &sw)

template<typename T, unsigned n, unsigned m>
std::ostream &	operator<< (std::ostream &os, const TensorTyped< T, n, m > &t)

template<typename T, unsigned n>
std::ostream &	operator<< (std::ostream &os, const VectorTyped< T, n > &v)

template<class T>
Subprocess &	operator<< (Subprocess &ep, const T &t)

bool	operator<= (const AtomNumber &a, const AtomNumber &b)

bool	operator== (const AtomNumber &a, const AtomNumber &b)

bool	operator> (const AtomNumber &a, const AtomNumber &b)

bool	operator>= (const AtomNumber &a, const AtomNumber &b)

template<typename enumtype>
constexpr std::enable_if_t< enum_traits::BitmaskEnum< enumtype >::has_bit_or, enumtype >	operator\| (enumtype a, enumtype b)
	Perform a bitwise OR between two enum values.

constexpr double	pi (3.141592653589793238462643383279502884197169399375105820974944592307)
	PI.

template<typename T>
int	pseudoInvert (const Matrix< T > &A, Matrix< T > &pseudoinverse)

auto	render (const TokenizedLine::line &l)

Keywords::argType	stoat (std::string_view str)
	Converts a string to the corresponding Keywords::argType.

Keywords::componentType	stoct (std::string_view str)
	Converts a string to the corresponding Keywords::componentType.

static const std::string &	StopwatchEmptyString () noexcept
	Return an empty string.

static bool	SubprocessPidGetenvSignals () noexcept
	Retrieve PLUMED_ENABLE_SIGNALS.

template<typename T, typename TT, unsigned n>
constexpr VectorTyped< T, n >	sumT (const VectorTyped< T, n > &v1, const VectorTyped< TT, n > &v2)

static void	testThrow (const char *what)
	Small utility just used in this file to throw arbitrary exceptions.

std::string	toString (Keywords::argType at)

std::string	toString (Keywords::componentType at)

template<typename T>
void	transpose (const Matrix< T > &A, Matrix< T > &AT)

template<typename T, unsigned n, unsigned m>
constexpr TensorTyped< T, n, m >	transpose (const TensorTyped< T, m, n > &t)
	returns the transpose of a tensor (same as TensorGeneric::transpose())

template<class T>
std::size_t	typesafePtrSizeof ()

template<>
std::size_t	typesafePtrSizeof< const void > ()

template<>
std::size_t	typesafePtrSizeof< void > ()

static bool	typesafePtrSkipCheck ()

template<typename enumtype>
constexpr std::enable_if_t< enum_traits::BitmaskEnum< enumtype >::has_valid, bool >	valid (enumtype a)
	Test if an enum value is valid.

template<typename T>
TensorTyped< T, 3, 3 >	VcrossTensor (const TensorTyped< T, 3, 3 > &v2, const VectorTyped< T, 3 > &v1)

template<typename T>
TensorTyped< T, 3, 3 >	VcrossTensor (const VectorTyped< T, 3 > &v1, const TensorTyped< T, 3, 3 > &v2)

TokenizedLine::line	wholeLineReplicas (const std::string &myLine)

Variables
static const Tools::FastStringUnorderedMap< std::string >	doi_map

constexpr double	DP2CUTOFF =6.25

constexpr double	dp2cutoffA =1.00193418799744762399

constexpr double	dp2cutoffB =-.00193418799744762399

const double	epsilon =1e-14

constexpr double	halfpi =PLMD::pi*0.5
	PI / 2.

template<typename T>
constexpr bool	isActionType = std::is_base_of<Action, T>::value

constexpr double	twopi =PLMD::pi*2.0
	PI * 2.

Typedef Documentation

◆ mdMemoryView

template<std::size_t N = helpers::dynamic_extent, std::size_t STRIDE = 3>

using PLMD::mdMemoryView = View2D<double,N,STRIDE>

◆ MemoryView

template<std::size_t N = 3>

using PLMD::MemoryView = View<double,N>

◆ TensorGeneric

template<unsigned n, unsigned m>

using PLMD::TensorGeneric = TensorTyped<double,n,m>

◆ unique_FILE

using PLMD::unique_FILE = std::unique_ptr<FILE,fileDeleter>

◆ VectorGeneric

template<unsigned n>

using PLMD::VectorGeneric = VectorTyped<double, n>

◆ VectorView

using PLMD::VectorView = mdMemoryView<helpers::dynamic_extent, 3>

Function Documentation

◆ actionRegister() [1/2]

ActionRegister & PLMD::actionRegister ( )

◆ chol_elsolve()

template<typename T>

void PLMD::chol_elsolve	(	const Matrix< T > &	M,
		const std::vector< T > &	b,
		std::vector< T > &	y )

◆ cholesky()

template<typename T>

void PLMD::cholesky	(	const Matrix< T > &	A,
		Matrix< T > &	B )

◆ cltoolRegister() [1/2]

CLToolRegister & PLMD::cltoolRegister ( )

◆ crossProduct()

template<typename T>

VectorTyped< T, 3 > PLMD::crossProduct	(	const VectorTyped< T, 3 > &	v1,
		const VectorTyped< T, 3 > &	v2 )

inlineconstexpr

◆ dcrossDv1()

template<typename T>

TensorTyped< T, 3, 3 > PLMD::dcrossDv1	(	const VectorTyped< T, 3 > &	v1,
		const VectorTyped< T, 3 > &	v2 )

inlineconstexpr

◆ dcrossDv2()

template<typename T>

TensorTyped< T, 3, 3 > PLMD::dcrossDv2	(	const VectorTyped< T, 3 > &	v1,
		const VectorTyped< T, 3 > &	v2 )

inlineconstexpr

◆ delta() [1/2]

template<typename T, unsigned n>

VectorTyped< T, n > PLMD::delta	(	const VectorTyped< T, n > &	v1,
		const VectorTyped< T, n > &	v2 )

constexpr

◆ delta() [2/2]

template<typename T>

VectorTyped< std::remove_const_t< T >, 3 > PLMD::delta	(	const View< T, 3 >	v1,
		const View< T, 3 >	v2 )

noexcept

◆ deriNorm()

template<typename T>

TensorTyped< T, 3, 3 > PLMD::deriNorm	(	const VectorTyped< T, 3 > &	v1,
		const TensorTyped< T, 3, 3 > &	v2 )

inline

◆ determinant()

template<typename T>

T PLMD::determinant ( const TensorTyped< T, 3, 3 > & t )

inlineconstexpr

◆ diagMat()

template<typename T>

int PLMD::diagMat	(	const Matrix< T > &	A,
		std::vector< T > &	eigenvals,
		Matrix< T > &	eigenvecs )

◆ diagMatSym() [1/2]

template<typename precision, unsigned n, unsigned m>

void PLMD::diagMatSym	(	const TensorTyped< precision, n, n > &	mat,
		VectorTyped< precision, m > &	evals,
		TensorTyped< precision, m, n > &	evec )

Diagonalize tensor.

Syntax is the same as Matrix::diagMat. In addition, it is possible to call if with m_ smaller than n_. In this case, only the first (smaller) m_ eigenvalues and eigenvectors are retrieved. If case lapack fails (info!=0) it throws an exception. Notice that tensor is assumed to be symmetric!!!

◆ diagMatSym() [2/2]

template<typename T, unsigned n, unsigned m>

void PLMD::diagMatSym	(	const TensorTyped< T, n, n > &	,
		VectorTyped< T, m > &	evals,
		TensorTyped< T, m, n > &	evec )

Diagonalize tensor.

Syntax is the same as Matrix::diagMat. In addition, it is possible to call if with m smaller than n. In this case, only the first (smaller) m eigenvalues and eigenvectors are retrieved. If case lapack fails (info!=0) it throws an exception. Notice that tensor is assumed to be symmetric!!!

◆ dotProduct() [1/2]

template<typename T>

T PLMD::dotProduct	(	const std::vector< T > &	A,
		const std::vector< T > &	B )

Calculate the dot product between two vectors.

◆ dotProduct() [2/2]

template<typename T, unsigned n>

T PLMD::dotProduct	(	const VectorTyped< T, n > &	v1,
		const VectorTyped< T, n > &	v2 )

constexpr

◆ dp2cutoff()

double PLMD::dp2cutoff ( 6. 25 )

constexpr

◆ dp2cutoffNoStretch()

static bool PLMD::dp2cutoffNoStretch ( )

inlinestatic

◆ extProduct()

template<typename T, unsigned n, unsigned m>

TensorTyped< T, n, m > PLMD::extProduct	(	const VectorTyped< T, n > &	v1,
		const VectorTyped< T, m > &	v2 )

constexpr

returns the transpose of a tensor (same as TensorGeneric(const VectorGeneric&,const VectorGeneric&))

◆ frobeniusNorm()

template<typename T, unsigned n, unsigned m>

T PLMD::frobeniusNorm ( const TensorTyped< T, m, n > & t )

Compute the Frobenius norm 2.

◆ getModuleMap()

const std::map< std::string, std::string > & PLMD::getModuleMap ( )

◆ getPointer()

template<typename T>

static void PLMD::getPointer	(	const TypesafePtr &	p,
		const std::vector< std::size_t > &	shape,
		const unsigned &	start,
		const unsigned &	stride,
		T *&	pp )

static

◆ getWords_replicas()

void PLMD::getWords_replicas	(	gch::small_vector< std::string_view > &	words,
		std::string_view	line,
		const std::string_view	separators )

◆ indexed_lt()

bool PLMD::indexed_lt	(	std::pair< Grid::index_t, double > const &	x,
		std::pair< Grid::index_t, double > const &	y )

◆ inverse()

template<typename T>

TensorTyped< T, 3, 3 > PLMD::inverse ( const TensorTyped< T, 3, 3 > & t )

inlineconstexpr

◆ Invert()

template<typename T>

int PLMD::Invert	(	const Matrix< T > &	A,
		Matrix< T > &	inverse )

◆ isZero()

static bool PLMD::isZero ( const ExpressionTreeNode & node )

static

◆ logdet()

template<typename T>

int PLMD::logdet	(	const Matrix< T > &	M,
		T &	ldet )

◆ lowestEigenpairSym()

template<typename T, unsigned n>

T PLMD::lowestEigenpairSym	(	const TensorTyped< T, n, n > &	K,
		VectorTyped< T, n > &	eigenvector,
		unsigned	niter = 24 )

Compute lowest eigenvalue and eigenvector, using a branchless iterative implementation.

This function is amenable for running on openACC. The accuracy could be controlled increasing the number of iterations. The default value (24) seems sufficient for most applications. In principle, it could be extended to compute m eigenvalues by:

computing the lowest
compute the proper projector and reduce the matrix to <n-1,n-1>
proceed iteratively The interface should then be likely the same as diagMatSym

◆ make_const_view()

template<typename CT>

View< const typename CT::value_type > PLMD::make_const_view ( const CT & container )

constexpr

Returns a complete constant dynamic view of a container.

The container must have defined the methods data() and size() Also the container must have defined a public type value_type For example a std::vector is compatible

◆ make_view() [1/2]

template<typename T>

View< T > PLMD::make_view ( const std::vector< T > & d )

◆ make_view() [2/2]

template<typename CT>

View< typename CT::value_type > PLMD::make_view ( CT & container )

constexpr

Returns a complete dynamic view of a container.

The container must have defined the methods data() and size() Also the container must have defined a public type value_type For example a std::vector is compatible A const std::vector is not compatible with this signature, to avoid confusion

◆ mapCreator()

template<typename IT>

auto PLMD::mapCreator	(	IT	k,
		IT const	end )

◆ matmul() [1/8]

template<typename T, unsigned n, unsigned m, unsigned l>

TensorTyped< T, n, l > PLMD::matmul	(	const TensorTyped< T, n, m > &	a,
		const TensorTyped< T, m, l > &	b )

constexpr

matrix-matrix multiplication

◆ matmul() [2/8]

template<typename T, unsigned n, unsigned m, unsigned l, unsigned i>

TensorTyped< T, n, i > PLMD::matmul	(	const TensorTyped< T, n, m > &	a,
		const TensorTyped< T, m, l > &	b,
		const TensorTyped< T, l, i > &	c )

constexpr

matrix-matrix-matrix multiplication

◆ matmul() [3/8]

template<typename T, unsigned n, unsigned m, unsigned l>

VectorTyped< T, n > PLMD::matmul	(	const TensorTyped< T, n, m > &	a,
		const TensorTyped< T, m, l > &	b,
		const VectorTyped< T, l > &	c )

constexpr

matrix-matrix-vector multiplication

◆ matmul() [4/8]

template<typename T, typename TT, unsigned n, unsigned m>

VectorTyped< T, n > PLMD::matmul	(	const TensorTyped< T, n, m > &	a,
		const VectorTyped< TT, m > &	b )

constexpr

matrix-vector multiplicationi, the first argument determines the type of the result

◆ matmul() [5/8]

template<typename T, typename TT, unsigned n, unsigned m>

VectorTyped< T, n > PLMD::matmul	(	const VectorTyped< T, m > &	a,
		const TensorTyped< TT, m, n > &	b )

constexpr

vector-matrix multiplication, the first argument determines the type of the result

◆ matmul() [6/8]

template<typename T, unsigned n, unsigned m, unsigned l>

VectorTyped< T, l > PLMD::matmul	(	const VectorTyped< T, n > &	a,
		const TensorTyped< T, n, m > &	b,
		const TensorTyped< T, m, l > &	c )

constexpr

vector-matrix-matrix multiplication

◆ matmul() [7/8]

template<typename T, unsigned n, unsigned m>

T PLMD::matmul	(	const VectorTyped< T, n > &	a,
		const TensorTyped< T, n, m > &	b,
		const VectorTyped< T, m > &	c )

constexpr

vector-matrix-vector multiplication

◆ matmul() [8/8]

template<typename T, unsigned n_>

T PLMD::matmul	(	const VectorTyped< T, n_ > &	a,
		const VectorTyped< T, n_ > &	b )

constexpr

vector-vector multiplication (maps to dotProduct)

◆ matrixOut()

template<typename T>

void PLMD::matrixOut	(	Log &	ostr,
		const Matrix< T > &	mat )

◆ max_cell()

int PLMD::max_cell	(	int	celn,
		const int	ncells,
		const bool	usePBC )

inlineconstexpr

◆ min_cell()

int PLMD::min_cell	(	int	celn,
		const int	ncells,
		const bool	usePBC )

inlineconstexpr

◆ modulo()

template<typename T, unsigned n>

T PLMD::modulo ( const VectorTyped< T, n > & v )

constexpr

◆ modulo2()

template<typename T, unsigned n>

T PLMD::modulo2 ( const VectorTyped< T, n > & v )

constexpr

◆ mult() [1/3]

template<typename T>

void PLMD::mult	(	const Matrix< T > &	A,
		const Matrix< T > &	B,
		Matrix< T > &	C )

◆ mult() [2/3]

template<typename T>

void PLMD::mult	(	const Matrix< T > &	A,
		const std::vector< T > &	B,
		std::vector< T > &	C )

◆ mult() [3/3]

template<typename T>

void PLMD::mult	(	const std::vector< T > &	A,
		const Matrix< T > &	B,
		std::vector< T > &	C )

◆ norm()

template<typename T>

T PLMD::norm ( const std::vector< T > & A )

Calculate the dot product between a vector and itself.

◆ operator!=()

bool PLMD::operator!=	(	const AtomNumber &	a,
		const AtomNumber &	b )

inline

◆ operator&()

template<typename enumtype>

std::enable_if_t< enum_traits::BitmaskEnum< enumtype >::has_bit_and, enumtype > PLMD::operator&	(	enumtype	a,
		enumtype	b )

constexpr

Perform a bitwise AND between two enum values.

Parameters

a	The first enum value.
b	The second enum value.

Returns: The result of performing a bitwise AND between the two values.

This operator is only available for enum types that have a specialization of enum_traits::BitmaskEnum with the has_bit_and trait enabled.

Useful for checking composed values agains masks.

Note that the value may be a 0, and if you do not have defined the 0 as a named value you should use valid(enumtype) to check it.

See also: valid(enumtype) for a complete example; operator|(enumtype, enumtype)

◆ operator*() [1/5]

template<typename T, typename J, unsigned n, unsigned m>

TensorTyped< T, n, m > PLMD::operator*	(	const TensorTyped< T, n, m > &	t1,
		J	s )

constexpr

◆ operator*() [2/5]

template<typename T, typename J, unsigned n, unsigned m>

TensorTyped< T, n, m > PLMD::operator*	(	J	s,
		const TensorTyped< T, n, m > &	t1 )

constexpr

◆ operator*() [3/5]

template<typename T, typename J, unsigned n>

VectorTyped< T, n > PLMD::operator*	(	J	s,
		VectorTyped< T, n >	v )

constexpr

◆ operator*() [4/5]

template<typename T>

Matrix< T > PLMD::operator*	(	T &	v,
		const Matrix< T > &	m )

Multiply matrix by scalar.

◆ operator*() [5/5]

template<typename T, typename J, unsigned n>

VectorTyped< T, n > PLMD::operator*	(	VectorTyped< T, n >	v,
		J	s )

constexpr

◆ operator+() [1/2]

template<typename T, unsigned n, unsigned m>

TensorTyped< T, n, m > PLMD::operator+	(	const TensorTyped< T, n, m > &	t1,
		const TensorTyped< T, n, m > &	t2 )

constexpr

◆ operator+() [2/2]

template<typename T, unsigned n>

VectorTyped< T, n > PLMD::operator+	(	const VectorTyped< T, n > &	v1,
		const VectorTyped< T, n > &	v2 )

constexpr

◆ operator-() [1/2]

template<typename T, unsigned n, unsigned m>

TensorTyped< T, n, m > PLMD::operator-	(	const TensorTyped< T, n, m > &	t1,
		const TensorTyped< T, n, m > &	t2 )

constexpr

◆ operator-() [2/2]

template<typename T, unsigned n>

VectorTyped< T, n > PLMD::operator-	(	VectorTyped< T, n >	v1,
		const VectorTyped< T, n > &	v2 )

constexpr

◆ operator/() [1/2]

template<typename T, typename J, unsigned n, unsigned m>

TensorTyped< T, n, m > PLMD::operator/	(	const TensorTyped< T, n, m > &	t1,
		J	s )

constexpr

◆ operator/() [2/2]

template<typename T, typename J, unsigned n>

VectorTyped< T, n > PLMD::operator/	(	const VectorTyped< T, n > &	v,
		J	s )

constexpr

◆ operator<()

bool PLMD::operator<	(	const AtomNumber &	a,
		const AtomNumber &	b )

inline

◆ operator<<() [1/9]

template<typename T>

Log & PLMD::operator<<	(	Log &	ostr,
		const Matrix< T > &	mat )

◆ operator<<() [2/9]

Log & PLMD::operator<<	(	Log &	ostr,
		const PDB &	pdb )

◆ operator<<() [3/9]

template<class T>

OFile & PLMD::operator<<	(	OFile &	of,
		const T &	t )

Write using << syntax.

Formatted output with << operator.

◆ operator<<() [4/9]

std::ostream & PLMD::operator<<	(	std::ostream &	log,
		const Citations &	cit )

It writes on the ostream the list of all the bibliographic items prefixed with their reference number

◆ operator<<() [5/9]

std::ostream & PLMD::operator<<	(	std::ostream &	log,
		const Register &	reg )

◆ operator<<() [6/9]

std::ostream & PLMD::operator<<	(	std::ostream &	os,
		const Stopwatch &	sw )

◆ operator<<() [7/9]

template<typename T, unsigned n, unsigned m>

std::ostream & PLMD::operator<<	(	std::ostream &	os,
		const TensorTyped< T, n, m > &	t )

Allows printing tensor t with std::cout<<t;

◆ operator<<() [8/9]

template<typename T, unsigned n>

std::ostream & PLMD::operator<<	(	std::ostream &	os,
		const VectorTyped< T, n > &	v )

Allows printing vector v with std::cout<<v;

◆ operator<<() [9/9]

template<class T>

Subprocess & PLMD::operator<<	(	Subprocess &	ep,
		const T &	t )

◆ operator<=()

bool PLMD::operator<=	(	const AtomNumber &	a,
		const AtomNumber &	b )

inline

◆ operator==()

bool PLMD::operator==	(	const AtomNumber &	a,
		const AtomNumber &	b )

inline

◆ operator>()

bool PLMD::operator>	(	const AtomNumber &	a,
		const AtomNumber &	b )

inline

◆ operator>=()

bool PLMD::operator>=	(	const AtomNumber &	a,
		const AtomNumber &	b )

inline

◆ operator|()

template<typename enumtype>

std::enable_if_t< enum_traits::BitmaskEnum< enumtype >::has_bit_or, enumtype > PLMD::operator\|	(	enumtype	a,
		enumtype	b )

constexpr

Perform a bitwise OR between two enum values.

Parameters

a	The first enum value.
b	The second enum value.

Returns: The result of performing a bitwise OR between the two values.

This operator is only available for enum types that have a specialization of enum_traits::BitmaskEnum with the has_bit_or trait enabled.

The principal use is to compose named enum values into masks or combined options.

See also: valid(enumtype) for a complete example; operator&(enumtype, enumtype)

◆ pseudoInvert()

template<typename T>

int PLMD::pseudoInvert	(	const Matrix< T > &	A,
		Matrix< T > &	pseudoinverse )

◆ render()

auto PLMD::render ( const TokenizedLine::line & l )

inline

◆ stoat()

Keywords::argType PLMD::stoat ( std::string_view str )

Converts a string to the corresponding Keywords::argType.

Parameters

str	The string to convert.

Returns: The Keywords::argType corresponding to the string.

Exceptions

std::invalid_argument If the string does not match any enum value.

◆ stoct()

Keywords::componentType PLMD::stoct ( std::string_view str )

inline

Converts a string to the corresponding Keywords::componentType.

Parameters

str	The string to convert.

Returns: The Keywords::componentType corresponding to the string.

Exceptions

std::invalid_argument if the string does not match any enum value.

◆ StopwatchEmptyString()

static const std::string & PLMD::StopwatchEmptyString ( )

inlinestaticnoexcept

Return an empty string.

Inline static so that it can store a static variable (for quicker access) without adding a unique global symbol to a library including this header file.

◆ SubprocessPidGetenvSignals()

static bool PLMD::SubprocessPidGetenvSignals ( )

inlinestaticnoexcept

Retrieve PLUMED_ENABLE_SIGNALS.

Inline static so that it can store a static variable (for quicker access) without adding a unique global symbol to a library including this header file.

◆ sumT()

template<typename T, typename TT, unsigned n>

VectorTyped< T, n > PLMD::sumT	(	const VectorTyped< T, n > &	v1,
		const VectorTyped< TT, n > &	v2 )

constexpr

◆ testThrow()

static void PLMD::testThrow ( const char * what )

static

Small utility just used in this file to throw arbitrary exceptions.

◆ toString() [1/2]

std::string PLMD::toString ( Keywords::argType at )

◆ toString() [2/2]

std::string PLMD::toString ( Keywords::componentType at )

◆ transpose() [1/2]

template<typename T>

void PLMD::transpose	(	const Matrix< T > &	A,
		Matrix< T > &	AT )

◆ transpose() [2/2]

template<typename T, unsigned n, unsigned m>

TensorTyped< T, n, m > PLMD::transpose ( const TensorTyped< T, m, n > & t )

constexpr

returns the transpose of a tensor (same as TensorGeneric::transpose())

◆ typesafePtrSizeof()

template<class T>

std::size_t PLMD::typesafePtrSizeof ( )

◆ typesafePtrSizeof< const void >()

template<>

std::size_t PLMD::typesafePtrSizeof< const void > ( )

inline

◆ typesafePtrSizeof< void >()

template<>

std::size_t PLMD::typesafePtrSizeof< void > ( )

inline

◆ typesafePtrSkipCheck()

static bool PLMD::typesafePtrSkipCheck ( )

inlinestatic

◆ valid()

template<typename enumtype>

std::enable_if_t< enum_traits::BitmaskEnum< enumtype >::has_valid, bool > PLMD::valid ( enumtype a )

constexpr

Test if an enum value is valid.

Parameters

a	The enum value to test.

Returns: true if the enum value is not equal to zero, false otherwise.

This operator is only available for enum types that have a specialization of enum_traits::BitmaskEnum with the has_valid trait enabled.

// Note: explicit declarations of the values, and
enum class myenum { A=1,B=1<<1,C=1<<2 };
//then activate the functions `&`, `|` and `valid`
template<>
struct BitmaskEnum< myenum > {
 static constexpr bool has_valid   = true;
 static constexpr bool has_bit_or  = true;
 static constexpr bool has_bit_and = true;
};
//...code...
myenum val = myenum::A | myenum::C;
std::cout <<"val is "<< int(val) << "\n";
if(PLMD::valid( val & myenum::A)) {
  std::cout << "val has A\n";
}
if(PLMD::valid(val & myenum::B)) {
  std::cout << "val has B\n";
}
if(PLMD::valid(val & myenum::C)) {
  std::cout << "val has C\n";
}
if(PLMD::valid(val & (myenum::A | myenum::C))) {
  std::cout << "val has C and A\n";
}
//will produce:
///>val is 5
///>val has A
///>val has C
///>val has C and A

See also: operator|(enumtype, enumtype); operator&(enumtype, enumtype)

◆ VcrossTensor() [1/2]

template<typename T>

TensorTyped< T, 3, 3 > PLMD::VcrossTensor	(	const TensorTyped< T, 3, 3 > &	v2,
		const VectorTyped< T, 3 > &	v1 )

inline

◆ VcrossTensor() [2/2]

template<typename T>

TensorTyped< T, 3, 3 > PLMD::VcrossTensor	(	const VectorTyped< T, 3 > &	v1,
		const TensorTyped< T, 3, 3 > &	v2 )

inline

◆ wholeLineReplicas()

TokenizedLine::line PLMD::wholeLineReplicas ( const std::string & myLine )

Variable Documentation

◆ doi_map

const Tools::FastStringUnorderedMap<std::string> PLMD::doi_map

static

Initial value:

= {
{"10.1021/acs.jctc.6b01073","G. A. Tribello, F. Giberti, G. C. Sosso, M. Salvalaglio, M. Parrinello, Analyzing and Driving Cluster Formation in Atomistic Simulations. Journal of Chemical Theory and Computation. 13, 1317–1327 (2017)"}# 30 "/home/runner/work/plumed2/plumed2/src/tools/Citations.cpp" 2
}

◆ DP2CUTOFF

double PLMD::DP2CUTOFF =6.25

constexpr

◆ dp2cutoffA

double PLMD::dp2cutoffA =1.00193418799744762399

constexpr

◆ dp2cutoffB

double PLMD::dp2cutoffB =-.00193418799744762399

constexpr

◆ epsilon

const double PLMD::epsilon =1e-14

◆ isActionType

template<typename T>

bool PLMD::isActionType = std::is_base_of<Action, T>::value

inlineconstexpr

Namespaces

Classes

Typedefs

Functions

Variables

Typedef Documentation

◆ mdMemoryView

◆ MemoryView

◆ TensorGeneric

◆ unique_FILE

◆ VectorGeneric

◆ VectorView

Function Documentation

◆ actionRegister() [1/2]

◆ chol_elsolve()

◆ cholesky()

◆ cltoolRegister() [1/2]

◆ crossProduct()

◆ dcrossDv1()

◆ dcrossDv2()

◆ delta() [1/2]

◆ delta() [2/2]

◆ deriNorm()

◆ determinant()

◆ diagMat()

◆ diagMatSym() [1/2]

◆ diagMatSym() [2/2]

◆ dotProduct() [1/2]

◆ dotProduct() [2/2]

◆ dp2cutoff()

◆ dp2cutoffNoStretch()

◆ extProduct()

◆ frobeniusNorm()

◆ getModuleMap()

◆ getPointer()

◆ getWords_replicas()

◆ indexed_lt()

◆ inverse()

◆ Invert()

◆ isZero()

◆ logdet()

◆ lowestEigenpairSym()

◆ make_const_view()

◆ make_view() [1/2]

◆ make_view() [2/2]

◆ mapCreator()

◆ matmul() [1/8]

◆ matmul() [2/8]

◆ matmul() [3/8]

◆ matmul() [4/8]

◆ matmul() [5/8]

◆ matmul() [6/8]

◆ matmul() [7/8]

◆ matmul() [8/8]

◆ matrixOut()

◆ max_cell()

◆ min_cell()

◆ modulo()

◆ modulo2()

◆ mult() [1/3]

◆ mult() [2/3]

◆ mult() [3/3]

◆ norm()

◆ operator!=()

◆ operator&()

◆ operator*() [1/5]

◆ operator*() [2/5]

◆ operator*() [3/5]

◆ operator*() [4/5]

◆ operator*() [5/5]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator<()

◆ operator<<() [1/9]

◆ operator<<() [2/9]

◆ operator<<() [3/9]