A Vector is a Cartesian vector. More...

#include <Vector.h>

Public Member Functions
Constructors
	Vector ()
	Default constructor. More...

	Vector (const Vector &v)
	Copy constructor. More...

	Vector (double scalar)
	Constructor, initialize all elements to a scalar value. More...

	Vector (const double *v)
	Construct Vector from C double[3] array. More...

	Vector (double x, double y, double z=0.0)
	Construct Vector from its coordinates. More...

Vector &	zero ()
	Set all elements of a 3D vector to zero. More...

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)
	Serialize to/from an archive. More...

Assignment
Vector &	operator= (const Vector &v)
	Copy assignment. More...

Vector &	operator= (const double *v)
	Assignment from C double[3] array. More...

Arithmetic Assignment
void	operator+= (const Vector &dv)
	Add vector dv to this vector. More...

void	operator-= (const Vector &dv)
	Subtract vector dv from this vector. More...

void	operator*= (double s)
	Multiply this vector by scalar s. More...

void	operator/= (double s)
	Divide this vector by scalar s. More...

Array Subscript
const double &	operator[] (int i) const
	Return one Cartesian element by value. More...

double &	operator[] (int i)
	Return one element of the vector by references. More...

Scalar-valued functions
double	square () const
	Return square magnitude of this vector. More...

double	abs () const
	Return absolute magnitude of this vector. More...

double	dot (const Vector &v) const
	Return dot product of this vector and vector v. More...

double	projection (const Vector &p) const
	Return projection of this vector along vector p. More...

Vector valued functions (result assigned to invoking object)
Vector &	add (const Vector &v1, const Vector &v2)
	Add vectors v1 and v2. More...

Vector &	subtract (const Vector &v1, const Vector &v2)
	Subtract vector v2 from v1. More...

Vector &	multiply (const Vector &v, double s)
	Multiply a vector v by a scalar s. More...

Vector &	divide (const Vector &v, double s)
	Divide vector v by scalar s. More...

Vector &	cross (const Vector &v1, const Vector &v2)
	Calculate cross product of vectors v1 and v2. More...

Vector &	versor (const Vector &v)
	Calculate unit vector parallel to input vector v. More...

Vector &	parallel (const Vector &v, const Vector &p)
	Calculate component of vector v parallel to vector p. More...

Vector &	transverse (const Vector &v, const Vector &p)
	Calculate component of vector v transverse to vector p. More...

int	minId (const Vector &v)
	Computes the index corresponding to minimum element in a vector. More...

int	maxId (const Vector &v)
	Computes the index corresponding to maximum element in a vector. More...

Static Members
static const Vector	Zero = Vector(0.0)
	Zero Vector = {0.0, 0.0, 0.0}. More...

static void	initStatic ()
	Initialize Zero Vector. More...

static void	commitMpiType ()
	Commit MPI datatype MpiTraits<Vector>::type. More...

bool	operator== (const Vector &v1, const Vector &v2)
	Equality for Vectors. More...

bool	operator== (const Vector &v1, const double *v2)
	Equality of Vector and C array. More...

std::istream &	operator>> (std::istream &in, Vector &vector)
	istream extractor for a Vector. More...

std::ostream &	operator<< (std::ostream &out, const Vector &vector)
	ostream inserter for a Vector. More...

Detailed Description

A Vector is a Cartesian vector.

The Cartesian elements of a Vector can be accessed using array notation: The elements of a three dimensional Vector v are v[0], v[1], and v[2]. The subscript operator [] returns elements as references, which can be used on either the left or right side of an assignment operator.

The arithmetic assignment operators +=, -=, *=, and /= are overloaded. The operators += and -= represent increment or decrement by a vector, while *= and /= represent multiplication or division by a scalar.

All other unary and binary mathematical operations are implemented as methods. Operations that yield a scalar result, such as a dot product, are implemented as methods that return the resulting value. Operations that yield a Vector, such as vector addition, are implemented by methods that assign the result to the invoking vector, and return a reference to the invoking vector. For example,

Vector a, b, c;
double s;
 
a[0] = 0.0
a[1] = 1.0
a[2] = 2.0
 
b[0] =  0.5
b[1] = -0.5
b[2] = -1.5
 
// Set s = a.b
s = a.dot(b)
 
// Set c = a + b
c.add(a, b)
 
// Set a = a + b
a += b
 
// Set b = b*2
b *= 2

This syntax for Vector valued operations avoids dynamic allocation of temporary Vector objects, by requiring that the invoking function provide an object to hold the result.

For efficiency, all methods in this class are declared inline.

Definition at line 75 of file Vector.h.

Constructor & Destructor Documentation

◆ Vector() [1/5]

Util::Vector::Vector ( )

inline

Default constructor.

Definition at line 463 of file Vector.h.

◆ Vector() [2/5]

Util::Vector::Vector ( const Vector & v )

inline

Copy constructor.

Parameters

v	Vector to be copied

Definition at line 470 of file Vector.h.

◆ Vector() [3/5]

Util::Vector::Vector ( double scalar )

inlineexplicit

Constructor, initialize all elements to a scalar value.

Parameters

scalar initial value for all elements.

Definition at line 481 of file Vector.h.

◆ Vector() [4/5]

Util::Vector::Vector ( const double * v )

inlineexplicit

Construct Vector from C double[3] array.

Parameters

v	array of 3 coordinates

Definition at line 492 of file Vector.h.

◆ Vector() [5/5]

Util::Vector::Vector	(	double	x,
		double	y,
		double	z = `0.0`
	)

inline

Construct Vector from its coordinates.

Parameters

x	x-axis coordinate, v[0]
y	y-axis coordinate, v[1]
z	z-axis coordinate, v[2]

Definition at line 503 of file Vector.h.

Member Function Documentation

◆ zero()

Vector & Util::Vector::zero ( )

inline

Set all elements of a 3D vector to zero.

Definition at line 514 of file Vector.h.

Referenced by Util::setToZero().

◆ serialize()

template<class Archive >

void Util::Vector::serialize	(	Archive &	ar,
		const unsigned int	version
	)

inline

Serialize to/from an archive.

Parameters

ar	archive
version	archive version id

Definition at line 818 of file Vector.h.

◆ operator=() [1/2]

Vector & Util::Vector::operator= ( const Vector & v )

inline

Copy assignment.

Parameters

v	Vector to assign.

Definition at line 526 of file Vector.h.

◆ operator=() [2/2]

Vector & Util::Vector::operator= ( const double * v )

inline

Assignment from C double[3] array.

Parameters

v	C-array of components

Definition at line 538 of file Vector.h.

◆ operator+=()

void Util::Vector::operator+= ( const Vector & dv )

inline

Add vector dv to this vector.

Upon return, *this = this + dv.

Parameters

dv	vector increment (input)

Definition at line 550 of file Vector.h.

◆ operator-=()

void Util::Vector::operator-= ( const Vector & dv )

inline

Subtract vector dv from this vector.

Upon return, *this = this + dv.

Parameters

dv	vector increment (input)

Definition at line 561 of file Vector.h.

◆ operator*=()

void Util::Vector::operator*= ( double s )

inline

Multiply this vector by scalar s.

Upon return, *this = (*this)*s.

Parameters

s	scalar multiplier

Definition at line 572 of file Vector.h.

◆ operator/=()

void Util::Vector::operator/= ( double s )

inline

Divide this vector by scalar s.

Upon return, *this = (*this)/s.

Parameters

s	scalar divisor (input)

Definition at line 583 of file Vector.h.

◆ operator[]() [1/2]

const double & Util::Vector::operator[] ( int i ) const

inline

Return one Cartesian element by value.

Parameters

i	element index

Returns: element i of the vector

Definition at line 594 of file Vector.h.

References Util::Dimension.

◆ operator[]() [2/2]

double & Util::Vector::operator[] ( int i )

inline

Return one element of the vector by references.

Parameters

i	element index

Returns: element i of this vector

Definition at line 605 of file Vector.h.

References Util::Dimension.

◆ square()

double Util::Vector::square ( ) const

inline

Return square magnitude of this vector.

Returns: square magnitude of this vector

Definition at line 616 of file Vector.h.

Referenced by abs(), parallel(), and transverse().

◆ abs()

double Util::Vector::abs ( ) const

inline

Return absolute magnitude of this vector.

Returns: absolute magnitude (norm) of this vector.

Definition at line 625 of file Vector.h.

References square().

Referenced by projection(), and versor().

◆ dot()

double Util::Vector::dot ( const Vector & v ) const

inline

Return dot product of this vector and vector v.

Parameters

v	input vector

Returns: dot product of this vector and vector v

Definition at line 632 of file Vector.h.

Referenced by parallel(), Util::product(), projection(), and transverse().

◆ projection()

double Util::Vector::projection ( const Vector & p ) const

inline

Return projection of this vector along vector p.

Parameters

p	vector parallel to direction along which to project

Returns: scalar projection this->dot(p)/p.abs()

Definition at line 641 of file Vector.h.

References abs(), and dot().

◆ add()

Vector & Util::Vector::add	(	const Vector &	v1,
		const Vector &	v2
	)

inline

Add vectors v1 and v2.

Upon return, *this = v1 + v2.

Parameters

v1	vector (input)
v2	vector (input)

Returns: modified invoking vector

Definition at line 657 of file Vector.h.

◆ subtract()

Vector & Util::Vector::subtract	(	const Vector &	v1,
		const Vector &	v2
	)

inline

Subtract vector v2 from v1.

Upon return, *this = v1 - v2.

Parameters

v1	vector (input)
v2	vector (input)

Returns: modified invoking vector

Definition at line 672 of file Vector.h.

◆ multiply()

Vector & Util::Vector::multiply	(	const Vector &	v,
		double	s
	)

inline

Multiply a vector v by a scalar s.

Upon return, *this = v*s.

Parameters

v	vector input
s	scalar input

Returns: modified invoking vector

Definition at line 686 of file Vector.h.

◆ divide()

Vector & Util::Vector::divide	(	const Vector &	v,
		double	s
	)

inline

Divide vector v by scalar s.

Upon return, *this = v/s;

Parameters

v	vector input
s	scalar input

Returns: modified invoking vector

Definition at line 700 of file Vector.h.

◆ cross()

Vector & Util::Vector::cross	(	const Vector &	v1,
		const Vector &	v2
	)

inline

Calculate cross product of vectors v1 and v2.

Upon return, *this = v1 x v2.

Parameters

v1	input vector
v2	input vector

Returns: modified invoking vector

Definition at line 714 of file Vector.h.

◆ versor()

Vector & Util::Vector::versor ( const Vector & v )

inline

Calculate unit vector parallel to input vector v.

Upon return *this = unit vector.

Parameters

v	input vector

Returns: modified invoking Vector

Definition at line 726 of file Vector.h.

References abs().

◆ parallel()

Vector & Util::Vector::parallel	(	const Vector &	v,
		const Vector &	p
	)

inline

Calculate component of vector v parallel to vector p.

Upon return, the invoking vector is equal to the vector projection of vector v along a direction parallel to vector p.

The vector projection of v along p is parallel to p and has an absolute magnitude equal to the scalar projection of v along p.

Parameters

v	vector to project
p	vector along which to project

Returns: modified invoking Vector

Definition at line 749 of file Vector.h.

References dot(), and square().

◆ transverse()

Vector & Util::Vector::transverse	(	const Vector &	v,
		const Vector &	p
	)

inline

Calculate component of vector v transverse to vector p.

Upon return, the invoking vector is equal to the vector projection of vector v perpendicular to vector p.

Parameters

v	input vector
p	vector perpendicular to which to project.

Returns: modified invoking Vector

Definition at line 771 of file Vector.h.

References dot(), and square().

◆ minId()

int Util::Vector::minId ( const Vector & v )

Computes the index corresponding to minimum element in a vector.

Parameters

v	input vector

Returns: index of the minimum element.

◆ maxId()

int Util::Vector::maxId ( const Vector & v )

Computes the index corresponding to maximum element in a vector.

Parameters

v	input vector

Returns: index of the maximum element.

◆ initStatic()

void Util::Vector::initStatic ( )

static

Initialize Zero Vector.

Definition at line 119 of file Vector.cpp.

Referenced by Util::initStatic().

◆ commitMpiType()

void Util::Vector::commitMpiType ( )

static

Commit MPI datatype MpiTraits<Vector>::type.

Commit MPI Datatype.

Definition at line 97 of file Vector.cpp.

References Util::MpiStructBuilder::addMember(), Util::MpiStructBuilder::commit(), and Util::MpiStructBuilder::setBase().

Friends And Related Function Documentation

◆ operator== [1/2]

bool operator==	(	const Vector &	v1,
		const Vector &	v2
	)

friend

Equality for Vectors.

Definition at line 26 of file Vector.cpp.

◆ operator== [2/2]

bool operator==	(	const Vector &	v1,
		const double *	v2
	)

friend

Equality of Vector and C array.

Definition at line 36 of file Vector.cpp.

◆ operator>>

std::istream & operator>>	(	std::istream &	in,
		Vector &	vector
	)

friend

istream extractor for a Vector.

Input elements of a vector from stream, without line breaks.

Parameters

in	input stream
vector	Vector to be read from stream

Returns: modified input stream

Definition at line 65 of file Vector.cpp.

◆ operator<<

std::ostream & operator<<	(	std::ostream &	out,
		const Vector &	vector
	)

friend

ostream inserter for a Vector.

Output elements of a vector to stream, without line breaks.

Parameters

out	output stream
vector	Vector to be written to stream

Returns: modified output stream

Definition at line 76 of file Vector.cpp.

Member Data Documentation

◆ Zero

const Vector Util::Vector::Zero = Vector(0.0)

static

Zero Vector = {0.0, 0.0, 0.0}.

Definition at line 369 of file Vector.h.

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

Public Member Functions

Static Members

Detailed Description

Constructor & Destructor Documentation

◆ Vector() [1/5]

◆ Vector() [2/5]

◆ Vector() [3/5]

◆ Vector() [4/5]

◆ Vector() [5/5]

Member Function Documentation

◆ zero()

◆ serialize()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator+=()

◆ operator-=()

◆ operator*=()

◆ operator/=()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ square()

◆ abs()

◆ dot()

◆ projection()

◆ add()

◆ subtract()

◆ multiply()

◆ divide()

◆ cross()

◆ versor()

◆ parallel()

◆ transverse()

◆ minId()

◆ maxId()

◆ initStatic()

◆ commitMpiType()

Friends And Related Function Documentation

◆ operator== [1/2]

◆ operator== [2/2]

◆ operator>>

◆ operator<<

Member Data Documentation

◆ Zero