A lightweight class describing a Vector object. Vectors are array with size n (>0) of doubles. More...

#include <vector.h>

Public Member Functions
	Vector ()
	Construct a new Vector object. Default constructor. Return an empty vector of 0 dimension. More...

	Vector (uint16_t)
	Construct a new Vector object. Return a Vector with dimension \(n\) filled with zeros. More...

	Vector (double *, uint16_t)
	Construct a new Vector object. Construct a vector object from an array of double. More...

	Vector (const Vector &)
	Construct a new Vector object. Copy constructor. More...

	~Vector ()
	Destroy the Vector object. More...

uint16_t	get_dim () const
	Get the dimension of a Vector object. More...

double &	operator[] (uint16_t) const
	Access the n-th value of a Vector object. More...

double &	operator() (uint16_t) const
	Access the n-th value of a Vector object. Same as operator []. More...

Vector &	operator= (const Vector &)
	Overload the assignement operator. Acts like a copy constructor. More...

Vector &	operator+= (const Vector &)
	Overload operator += for vectors objects. More...

Vector &	operator-= (const Vector &)
	Overload operator -= for vectors objects. More...

Vector	operator- () const
	Operator to get the opposite vector. More...

double	norm (uint8_t)
	A general method to compute the norm of a Vector object. More...

double	norm1 ()
	Compute the \(L^1\) norm of a Vector object. More...

double	norm2 ()
	Compute the Euclidean norm of a Vector object. More...

double	normp (uint8_t)
	Compute the \(L^p\) norm of a Vector object. More...

double	normInf ()
	Compute the \(L^{\infty}\) norm of a Vector object. More...

void	sort ()
	Sort the vector with the quickSort algorithm. More...

std::vector< double >	to_std_vector ()
	Conversion to a standard library vector object. More...

Static Public Member Functions
static Vector	basis (uint16_t, uint16_t)
	Construct vector of the canonical basis of \(\mathbb{R}^n\). More...

static Vector	zeros (uint16_t)
	Construct a Vector object of length n filled with zeros. More...

static Vector	ones (uint16_t)
	Construct a Vector object of length n filled with ones. More...

static Vector	rand (uint16_t)
	Construct a Vector object of length \(n\) filled with random values sampled from 0. to 1. More...

static Vector	randn (uint16_t)
	Construct a Vector object of length \(n\) filled with random values sampled from the Gaussian random number distribution: mean is 0. and standart deviation is 1. More...

static Vector	randn (uint16_t, double, double)
	Construct a Vector object of length \(n\) filled with random values sampled from a Gaussian random number distribution. More...

static Vector	linspace (double, double, uint16_t)
	Construct a Vector object of length n filled with equally points spaced between t0 and t1 included. More...

Friends
bool	operator== (const Vector &, const Vector &)
	Overload of the equality operator for Vector objects. Two vectors are said to be equal if and only if they have the same dimension and they have exactly the same values. More...

double	operator* (const Vector &, const Vector &)
	Dot product between vectors. More...

Vector	operator* (const double, const Vector &)
	Operator of multiplication of a Vector object by a scalar. More...

Vector	operator* (const Vector &, const double)
	Operator of multiplication of a Vector object by a scalar. More...

Vector	operator+ (const Vector &, const Vector &)
	Addition of two vector objects. More...

Vector	operator+ (const double, const Vector &)
	Operator of addition of a Vector object with a scalar. More...

Vector	operator+ (const Vector &, const double)
	Operator of addition of a Vector object with a scalar. More...

Vector	operator- (const Vector &, const Vector &)
	Substract two vector objects. More...

Vector	operator- (const double, const Vector &)
	Operator of remove a scalar to a Vector. More...

Vector	operator- (const Vector &, const double)
	Operator of remove a scalar to a Vector. More...

Vector	operator/ (const Vector &, const double)
	Operator to divide a Vector by a scalar. More...

std::ostream &	operator<< (std::ostream &, const Vector &)
	Overload output stream operator for Vector object. More...

Vector	abs (const Vector &)
	Elementwise absolute value of a vector. More...

Vector	pow2 (const Vector &)
	Elementwise square of a vector. More...

double	prod (const Vector &)
	Compute the product of the element of a vector. More...

Vector	prod (const Vector &, const Vector &)
	Compute the elementwise product of two vectors. More...

Vector	sqrt (const Vector &)
	Elementwise square root of a vector. More...

double	sum (const Vector &)
	Compute the sum of the element of a vector. More...

Detailed Description

A lightweight class describing a Vector object. Vectors are array with size n (>0) of doubles.

Warning: Maximum dimension of a Vector is 65 535; Indices are 0-based. Math formulae must be adapted consequently.

Todo:

Template this class to use different data types (double, float, complex)

Parallelize the class

Interface with eigen or other lib if exists

Constructor & Destructor Documentation

◆ Vector() [1/4]

Vector::Vector ( )

Construct a new Vector object. Default constructor. Return an empty vector of 0 dimension.

◆ Vector() [2/4]

Vector::Vector ( uint16_t n )

Construct a new Vector object. Return a Vector with dimension \(n\) filled with zeros.

Parameters

n	Dimension of the desired vector (must be greater or equal than \(1\))

◆ Vector() [3/4]

Vector::Vector	(	double *	dat,
		uint16_t	n
	)

Construct a new Vector object. Construct a vector object from an array of double.

Parameters

dat	Array of double of size n
n	Size of the input array

◆ Vector() [4/4]

Vector::Vector ( const Vector & v )

Construct a new Vector object. Copy constructor.

Parameters

v	Vector oject to be copied.

◆ ~Vector()

Vector::~Vector ( )

Destroy the Vector object.

Member Function Documentation

◆ basis()

Vector Vector::basis	(	uint16_t	n,
		uint16_t	k
	)

static

Construct vector of the canonical basis of \(\mathbb{R}^n\).

Parameters

n	Dimension of the vector space (must be greater or equal than 1)
k	Number of the basis vector (must be between 0 and n-1).

Returns: Vector k-th vector of the canonical basis of \(\mathbb{R}^n\).

Warning: Indices are 0-based.

◆ get_dim()

uint16_t Vector::get_dim ( ) const

Get the dimension of a Vector object.

Returns: uint16_t Dimension of the Vector.

◆ linspace()

Vector Vector::linspace	(	double	t0,
		double	t1,
		uint16_t	n
	)

static

Construct a Vector object of length n filled with equally points spaced between t0 and t1 included.

Parameters

t0	Starting value
t1	Final value (must be greater than t0)
n	Number of timestep including t0 and t1 (must be greater or equal than 2)

Returns: Vector of size n of equally spaced timestep between t0 and t1

◆ norm()

double Vector::norm ( uint8_t type )

A general method to compute the norm of a Vector object.

Parameters

type	Unisgned integer to decide the norm to choose: type = 0 compute the \(L^{\infty}\) norm type >= 1 Compute the \(L^p\) norm

Returns: double \(L^p\) norm of the Vector.

◆ norm1()

double Vector::norm1 ( )

Compute the \(L^1\) norm of a Vector object.

Returns: double \(L^1\) norm of the Vector.

◆ norm2()

double Vector::norm2 ( )

Compute the Euclidean norm of a Vector object.

Returns: double Euclidean of the Vector.

◆ normInf()

double Vector::normInf ( )

Compute the \(L^{\infty}\) norm of a Vector object.

Returns: double \(L^{\infty}\) norm of the Vector.

◆ normp()

double Vector::normp ( uint8_t p )

Compute the \(L^p\) norm of a Vector object.

Parameters

p	Order of the norm

Returns: double \(L^p\) norm of the Vector.

◆ ones()

Vector Vector::ones ( uint16_t n )

static

Construct a Vector object of length n filled with ones.

Parameters

n	Dimension of the vector (must be greater or equal than 1).

Returns: Vector A Vector object of size n filled with ones

◆ operator()()

double & Vector::operator() ( uint16_t n ) const

Access the n-th value of a Vector object. Same as operator [].

Parameters

n	index of the required value (must be between 0 and dim-1)

Returns: double & address of the n-th element of the Vector object.

Warning: indices are 0-based.

◆ operator+=()

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

Overload operator += for vectors objects.

Parameters

v RHS

Returns: Vector& Addition of current object with rhs

Warning: Both vector must be of the same dimension

◆ operator-()

Vector Vector::operator- ( ) const

Operator to get the opposite vector.

Parameters

v	a Vector object

Returns: Vector the opposite of v, i.e. -v

◆ operator-=()

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

Overload operator -= for vectors objects.

Parameters

v RHS

Returns: Vector& Difference of current object with rhs

Warning: Both vector must be of the same dimension

◆ operator=()

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

Overload the assignement operator. Acts like a copy constructor.

Parameters

v	The vector to be copied.

Returns: Vector& A copy of vector v.

◆ operator[]()

double & Vector::operator[] ( uint16_t n ) const

Access the n-th value of a Vector object.

Parameters

n	index of the required value (must be between 0 and dim-1)

Returns: double & address of the n-th element of the Vector object.

Warning: indices are 0-based.

◆ rand()

Vector Vector::rand ( uint16_t n )

static

Construct a Vector object of length \(n\) filled with random values sampled from 0. to 1.

Parameters

n	Dimension of the vector (must be greater or equal than 1).

Returns: Vector A Vector object of size n filled with random values

◆ randn() [1/2]

Vector Vector::randn ( uint16_t n )

static

Construct a Vector object of length \(n\) filled with random values sampled from the Gaussian random number distribution: mean is 0. and standart deviation is 1.

Parameters

n	Dimension of the vector (must be greater or equal than 1).

Returns: Vector A Vector object of size \(n\) filled with random values picked following a \(\mathcal{N}(0,1)\) law.

◆ randn() [2/2]

Vector Vector::randn	(	uint16_t	n,
		double	m,
		double	s
	)

static

Construct a Vector object of length \(n\) filled with random values sampled from a Gaussian random number distribution.

Parameters

n	Dimension of the vector (must be greater or equal than 1).
m	Mean of the Gaussian distribution.
s	Standart deviation of the Gaussian distribution

Returns: Vector A Vector object of size \(n\) filled with random values picked following a \(\mathcal{N}(m,s)\) law.

◆ sort()

void Vector::sort ( )

Sort the vector with the quickSort algorithm.

◆ to_std_vector()

std::vector< double > Vector::to_std_vector ( )

Conversion to a standard library vector object.

Returns: std::vector<double> a standard vector object with the same data as the current object

◆ zeros()

Vector Vector::zeros ( uint16_t n )

static

Construct a Vector object of length n filled with zeros.

Parameters

n	Dimension of the Mector (must be greater or equal than 1).

Returns: Vector A Vector object of size n filled with zeros

Friends And Related Function Documentation

◆ abs

Vector abs ( const Vector & v )

friend

Elementwise absolute value of a vector.

Parameters

v a vector

Returns: Vector a vector whose components are the absolute value of the components of v

◆ operator* [1/3]

Vector operator*	(	const double	d,
		const Vector &	v
	)

friend

Operator of multiplication of a Vector object by a scalar.

Parameters

d	Double value to multiply v with
v	Vector to be multiplied

Returns: Vector whose components are v[i]*d

◆ operator* [2/3]

Vector operator*	(	const Vector &	v,
		const double	d
	)

friend

Operator of multiplication of a Vector object by a scalar.

Parameters

v	Vector to be multiplied
d	Double value to multiply v with

Returns: Vector whose components are v[i]*d

◆ operator* [3/3]

double operator*	(	const Vector &	lhs,
		const Vector &	rhs
	)

friend

Dot product between vectors.

Parameters

lhs	Left Hand Side
rhs	Right Hand Side

Returns: double Dot product between vetcor object and v

Warning: Both vectors must be of the same dimension.

◆ operator+ [1/3]

Vector operator+	(	const double	d,
		const Vector &	v
	)

friend

Operator of addition of a Vector object with a scalar.

Parameters

d	Double value added to v
v	Vector to be additioned

Returns: Vector whose components are v[i] + d

◆ operator+ [2/3]

Vector operator+	(	const Vector &	v,
		const double	d
	)

friend

Operator of addition of a Vector object with a scalar.

Parameters

v	Vector to be additioned
d	Double value added to v

Returns: Vector whose components are v[i] + d

◆ operator+ [3/3]

Vector operator+	(	const Vector &	lhs,
		const Vector &	rhs
	)

friend

Addition of two vector objects.

Parameters

lhs	A vector of dimension \(n\),
rhs	A vector of dimension \(n\)

Warning: lhs and rhs must be of the same dimension.

Returns: Vector Sum of lhs and rhs.

◆ operator- [1/3]

Vector operator-	(	const double	d,
		const Vector &	v
	)

friend

Operator of remove a scalar to a Vector.

Parameters

d	Double value to remove fro v
v	Right Hand Side

Returns: Vector whose components are d - v[i]

◆ operator- [2/3]

Vector operator-	(	const Vector &	v,
		const double	d
	)

friend

Operator of remove a scalar to a Vector.

Parameters

v	Left Hand Side
d	Double value to remove from v

Returns: Vector whose components are v[i] - d

◆ operator- [3/3]

Vector operator-	(	const Vector &	lhs,
		const Vector &	rhs
	)

friend

Substract two vector objects.

Parameters

lhs	A vector of dimension \(n\),
rhs	A vector of dimension \(n\)

Warning: lhs and rhs must be of the same dimension.

Returns: Vector Difference of lhs and rhs.

◆ operator/

Vector operator/	(	const Vector &	v,
		const double	d
	)

friend

Operator to divide a Vector by a scalar.

Parameters

v	Vector v
d	Double value to divide v (must be non-zero)

Returns: Vector whose components are v[i] / d

Warning: d must me non-zero

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const Vector &	v
	)

friend

Overload output stream operator for Vector object.

Parameters

os	Output stream.
v	Vector object.

Returns: std::ostream & updated output stream

◆ operator==

bool operator==	(	const Vector &	lhs,
		const Vector &	rhs
	)

friend

Overload of the equality operator for Vector objects. Two vectors are said to be equal if and only if they have the same dimension and they have exactly the same values.

Parameters

lhs	Left hand side
rhs	Right hand side

Returns: true If all values of both vectors coincide.; false If at least of the value of the two vectors differ.

◆ pow2

Vector pow2 ( const Vector & v )

friend

Elementwise square of a vector.

Parameters

v a vector

Returns: Vector a vector whose components are the square of the components of v

◆ prod [1/2]

double prod ( const Vector & v )

friend

Compute the product of the element of a vector.

Parameters

v	a vector object

Returns: double product of the components of \(v\)

Warning: If v has zero length then we return 1

◆ prod [2/2]

Vector prod	(	const Vector &	v1,
		const Vector &	v2
	)

friend

Compute the elementwise product of two vectors.

Parameters

v1	a vector
v2	a vector

Returns: Vector a vector whose elements are the product of the corresponding elements of v1 and v2

Warning: v1 and v2 must have the same dimension

◆ sqrt

Vector sqrt ( const Vector & v )

friend

Elementwise square root of a vector.

Parameters

v a vector

Returns: Vector a vector whose components are the square root of the components of v

Warning: the components must be non negative

◆ sum

double sum ( const Vector & v )

friend

Compute the sum of the element of a vector.

Parameters

v	a vector object

Returns: double sum of the components of \(v\)

Warning: If v has zero length then we return 0

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

include/header/vector.h
src/vector.cpp

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Vector() [1/4]

◆ Vector() [2/4]

◆ Vector() [3/4]

◆ Vector() [4/4]

◆ ~Vector()

Member Function Documentation

◆ basis()

◆ get_dim()

◆ linspace()

◆ norm()

◆ norm1()

◆ norm2()

◆ normInf()

◆ normp()

◆ ones()

◆ operator()()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator=()

◆ operator[]()

◆ rand()

◆ randn() [1/2]

◆ randn() [2/2]

◆ sort()

◆ to_std_vector()

◆ zeros()

Friends And Related Function Documentation

◆ abs

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

◆ operator+ [1/3]

◆ operator+ [2/3]

◆ operator+ [3/3]

◆ operator- [1/3]

◆ operator- [2/3]

◆ operator- [3/3]

◆ operator/

◆ operator<<

◆ operator==

◆ pow2

◆ prod [1/2]

◆ prod [2/2]

◆ sqrt

◆ sum