A NVector<T> object represents the coordinates of a finite dimension dense vector \( x \). More...

Inheritance diagram for NVector< T >:

Public Member Functions
	NVector (const std::vector< T > &data)
	Construct a vector using a `std::vector`. \( x_k \) represents `data[k]`. More...

	NVector (std::initializer_list< T > list)
	Construct a vector using an initializer list `{}`. More...

	NVector (size_t dim=0)
	Construct a vector of a given size. More...

	NVector (const NVector< T > &u)
	Construct a vector by using `copy()` method. More...

virtual	~NVector ()=default

virtual std::string	str () const
	Creates a string representing the vector. More...

size_t	dim () const
	Dimension of the vector. More...

std::vector< T >	array () const
	Creates an array with `this` vector. More...

NVector< T > &	operator+= (const NVector< T > &u)

NVector< T > &	operator-= (const NVector< T > &u)

virtual NVector< T > &	operator*= (T s)

virtual NVector< T > &	operator/= (T s)

NVector< T > &	operator= (const NVector< T > &u)
	Copy source object on this object using `copy()`. More...

Extremums
Methods related to maximum minimum value research. They all use `std::max` or `std::min`.
T	max () const
	Maximum of the coordinates of the vector \( (x_0, x_1, .. x_{(n-1)}) \). More...

T	min () const
	Minimum of the coordinates of the vector \( (x_0, x_1, .. x_{(n-1)}) \). More...

size_t	maxIndex () const
	Index of maximum of the coordinates of vector \( (x_0, x_1, ..., x_{(n-1)}) \). More...

size_t	minIndex () const
	Index of minimum of the coordinates of vector \( (x_0, x_1, ..., x_{(n-1)}) \). More...

T	maxAbs () const
	Maximum of the coordinates of the vector \( (\|x_0\|, \|x_1\|, ..., \|x_{(n-1)}\|) \). More...

T	minAbs () const
	Minimum of the coordinates of the vector \( (\|x_0\|, \|x_1\|, ..., \|x_{(n-1)}\|) \). More...

size_t	maxAbsIndex () const
	Index of maximum of the coordinates of vector \( (\|x_0\|, \|x_1\|, ..., \|x_{(n-1)}\|) \). More...

size_t	minAbsIndex () const
	Index of minimum of the coordinates of vector \( (\|x_0\|, \|x_1\|, ..., \|x_{(n-1)}\|) \). More...

Manipulators
Manipulators such as swap, shift... All the manipulator return a reference to `*this` in order to allow cascade calls eg `swap().shift()`.
NVector< T > &	swap (size_t k1, size_t k2)
	Permutation of two elements. More...

NVector< T > &	shift (long iterations)
	Shifts `this` vector `iterations` times. More...

NVector< T > &	fill (T s)
	Fill vector with a scalar. For example `fill(3)` will set \( (3, 3, 3, ..., 3) \). More...

Function Operator
Access to components and sub-matrix C++ function operator are here used to give intuitive access to the vector. It behaves like numpy `[:]`.
T &	operator() (long k)
	Simple access operator. More...

T	operator() (long k) const

NVector< T >	operator() (size_t k1, size_t k2) const
	Manipulate sub-vector. More...

NVector< T > &	operator() (size_t k1, size_t k2)
	Manipulate sub-vector. More...

Iterators
Similar iterators as `std::vector` except that they allow use of `operator()()`.
iterator	begin ()

const_iterator	begin () const

iterator	end ()

const_iterator	end () const

Static Public Member Functions
static NVector< T >	zeros (size_t dim)

static NVector< T >	ones (size_t dim)

static NVector< T >	scalar (T s, size_t dim)

static NVector< T >	cano (size_t k, size_t dim)

static NVector< T >	sum (const std::vector< NVector > &vectors)
	Sum of multiples vectors. More...

static NVector< T >	sumProd (const std::vector< T > &scalars, const std::vector< NVector > &vectors)
	Linear combination of `scalars` and `vectors`. More...

Protected Member Functions
	NVector (const std::vector< T > &data, size_t k1, size_t k2)
	Vector with regularly spaced components. More...

NVector< T > &	add (const NVector< T > &u)

NVector< T > &	sub (const NVector< T > &u)

virtual NVector< T > &	opp ()

virtual NVector< T > &	prod (T s)

virtual NVector< T > &	div (T s)

T	dotProduct (const NVector< T > &u) const

T	norm () const

T	distance (const NVector< T > &u) const

bool	isValidIndex (size_t k) const

bool	isBetweenK12 (size_t k) const

bool	isNull () const

bool	isEqual (const NVector< T > &u) const

bool	hasSameSize (const NVector< T > &u) const

virtual bool	hasDefaultBrowseIndices () const

virtual void	setDefaultBrowseIndices () const

NVector< T > &	forEach (const NVector< T > &u, const std::function< void(T &, const T &)> &binary_op)

virtual NVector< T > &	forEach (T s, const std::function< void(T &, T)> &binary_op)

NVector< T > &	copy (const NVector< T > &u)

NVector< T >	subVector (size_t k1, size_t k2) const

void	setSubVector (const NVector< T > &u)

Protected Attributes
size_t	_k1 {}

size_t	_k2 {}

Friends
std::ostream &	operator<< (std::ostream &os, const NVector< T > &u)
	Usual stream insertion of vector. More...

Algebra
Vector algebraical operations. Represent euclidean vector space operations such as sum, inner product, distance...
NVector< T >	operator+ (NVector< T > u, const NVector< T > &v)
	Add two vectors. More...

NVector< T >	operator- (NVector< T > u, const NVector< T > &v)
	Substract two vectors. More...

NVector< T >	operator- (NVector< T > u)
	Opposite of vector. More...

NVector< T >	operator* (T s, NVector< T > u)
	Multiply vector by scalar. More...

NVector< T >	operator* (const NVector< T > &u, T s)

NVector< T >	operator/ (NVector< T > u, T s)
	Divide vector by scalar. More...

T	operator\| (const NVector< T > &u, const NVector< T > &v)
	Dot product of two vectors. More...

T	operator! (const NVector< T > &u)
	Norm of the vector. More...

T	operator/ (const NVector< T > &u, const NVector< T > &v)
	Distance between two vectors. More...

Comparaison
Norm based comparaison between two vectors.
bool	operator== (const NVector< T > &u, const NVector< T > &v)
	Equality of two vectors. More...

bool	operator== (const NVector< T > &u, T s)
	Equality to zero. More...

bool	operator== (T s, const NVector< T > &u)

bool	operator!= (const NVector< T > &u, const NVector< T > &v)
	Non equality of two vector. More...

bool	operator!= (const NVector< T > &u, T s)

bool	operator!= (T s, const NVector< T > &u)

Detailed Description

template<typename T>
class NVector< T >

A NVector<T> object represents the coordinates of a finite dimension dense vector \( x \).

Copyright: Dahoux Sami 2018 All rights reserved.

Date: 03/05/2018

Author: samiBendou

Coordinates are stored in the form [ \( x_0, x_1, ..., x_{(n-1)} \) ]. where [...] is a std::vector<T>, \( n \) is the dimension and \( (x_0, x_1, ..., x_{(n-1)}) \) are the coordinates.

    This object inherits from `std::vector<T>`, it is a STL container, iterators and STL library functions can be
    used.

Features

     Featuring algebraical operations \form#72, swaps, shifts and
     classic vectors generator such as ones, zeros...

Sub-range operators

     The `NVector` class provides a function operator which behaves like a classic array subscript operator
     of `std::vector` except that it comes on two version detailed further in the documentation.
     It allows operations on sub-ranges.

Definitions

We will often refer to the following variables in this page :

x/u/v : An arbitrary given NVector. By default, \( x \) denotes this vector
n/dim : Size of this vector, can be seen as the dimension of the underlying vector space
s : a scalar of type T
k : index of vector \( u_k \)
\( |.| \) : Absolute value, if meaningfull with scalar type T

Constructor & Destructor Documentation

template<typename T>

NVector< T >::NVector ( const std::vector< T > & data )

inline

Construct a vector using a std::vector. \( x_k \) represents data[k].

Parameters

data	`std::vector` source.

template<typename T>

NVector< T >::NVector ( std::initializer_list< T > list )

inline

Construct a vector using an initializer list {}.

Parameters

list	`std::initializer_list` source.

Convert list and uses array constructor.

template<typename T>

NVector< T >::NVector ( size_t dim = 0 )

inlineexplicit

Construct a vector of a given size.

Parameters

dim	vector size

template<typename T>

NVector< T >::NVector ( const NVector< T > & u )

inline

Construct a vector by using copy() method.

Parameters

u	`NVector` source.

template<typename T>

virtual NVector< T >::~NVector ( )

virtualdefault

template<typename T>

NVector< T >::NVector	(	const std::vector< T > &	data,
		size_t	k1,
		size_t	k2
	)

explicitprotected

Vector with regularly spaced components.

Parameters

x	start value of the range
y	end value of the range
h	step between elements

Returns: Returns \( ( x, x + h, x + 2h, ..., y) \)

Member Function Documentation

template<typename T >

string NVector< T >::str ( ) const

virtual

Creates a string representing the vector.

The returned string has the following form :

```commandline "(x(0), x(1), ..., x((n-1)))" `` Eachx(k)is formatted using the default<<operator of the typeT`.

Returns: Returns a string representing the vector.

Reimplemented in NPMatrix< T >, and NPMatrix< double_t >.

template<typename T >

size_t NVector< T >::dim ( ) const

Dimension of the vector.

Returns: \( dim \)

template<typename T >

std::vector< T > NVector< T >::array ( ) const

Creates an array with this vector.

Returns: a std::vector representing this.

template<typename T >

T NVector< T >::max ( ) const

Maximum of the coordinates of the vector \( (x_0, x_1, .. x_{(n-1)}) \).

Returns: value of maximum

template<typename T >

T NVector< T >::min ( ) const

Minimum of the coordinates of the vector \( (x_0, x_1, .. x_{(n-1)}) \).

Returns: value of minimum

template<typename T >

size_t NVector< T >::maxIndex ( ) const

Index of maximum of the coordinates of vector \( (x_0, x_1, ..., x_{(n-1)}) \).

Returns: index of maximum

template<typename T >

size_t NVector< T >::minIndex ( ) const

Index of minimum of the coordinates of vector \( (x_0, x_1, ..., x_{(n-1)}) \).

Returns: index of minimum

template<typename T >

T NVector< T >::maxAbs ( ) const

Maximum of the coordinates of the vector \( (|x_0|, |x_1|, ..., |x_{(n-1)}|) \).

Returns: absolute value of absolute maximum

template<typename T >

T NVector< T >::minAbs ( ) const

Minimum of the coordinates of the vector \( (|x_0|, |x_1|, ..., |x_{(n-1)}|) \).

Returns: absolute value of absolute minimum

template<typename T >

size_t NVector< T >::maxAbsIndex ( ) const

Index of maximum of the coordinates of vector \( (|x_0|, |x_1|, ..., |x_{(n-1)}|) \).

Returns: index of absolute maximum

template<typename T >

size_t NVector< T >::minAbsIndex ( ) const

Index of minimum of the coordinates of vector \( (|x_0|, |x_1|, ..., |x_{(n-1)}|) \).

Returns: index of absolute minimum

template<typename T >

NVector< T > & NVector< T >::swap	(	size_t	k1,
		size_t	k2
	)

Permutation of two elements.

Parameters

k1	First index to swap
k2	Second index to swap

The vector is set to \( (x_0, ..., x_{(k_1 - 1)}, x_{k_2}, ..., x_{(k_2 - 1)}, x_{k_1}, ..., x_{(n-1)}) \). \( x_{k_1} \) and \( x_{k_2} \) have been swaped used std::swap.

template<typename T >

NVector< T > & NVector< T >::shift ( long iterations )

Shifts this vector iterations times.

Parameters

iterations number of times to shift.

If iterations is positive, shift is powered to the left, else to the right. For example shift(2) will set \( (x_2, x_3, ..., x_{(n-1)}, x_0, x_1) \).

template<typename T>

NVector< T > & NVector< T >::fill ( T s )

Fill vector with a scalar. For example fill(3) will set \( (3, 3, 3, ..., 3) \).

Parameters

s	value to fill the vector with

template<typename T>

NVector<T>& NVector< T >::operator+= ( const NVector< T > & u )

inline

template<typename T>

NVector<T>& NVector< T >::operator-= ( const NVector< T > & u )

inline

template<typename T>

virtual NVector<T>& NVector< T >::operator*= ( T s )

inlinevirtual

Reimplemented in NPMatrix< T >, and NPMatrix< double_t >.

template<typename T>

virtual NVector<T>& NVector< T >::operator/= ( T s )

inlinevirtual

Reimplemented in NPMatrix< T >, and NPMatrix< double_t >.

template<typename T >

T & NVector< T >::operator() ( long k )

Simple access operator.

Access operator equivalent to [k] on std::vector. Operator can be used to read or write values. const version returns const reference to the element. For example, x(-1) returns the last element, x(0) returns the first element.

Returns: component \( x_{k} \) of the vector.

template<typename T >

T NVector< T >::operator() ( long k ) const

template<typename T>

NVector<T> NVector< T >::operator()	(	size_t	k1,
		size_t	k2
	)		const

inline

Manipulate sub-vector.

Parameters

k1	first element to take
k2	last element to take \( n \gt k_2 \geq k_1 \geq 0 \)

Allows operations on a restricted range of the vector \( (x_{k_1}, x_{(k_1+1)}, ...,x_{k_2}) \) . The two arguments function operator has the following behavior :

It can be used to read/write values.
It Allows chaining operations : u(0, 1) + v(1, 2), x(1, 4).max(), ...

Most of methods or operators can be chained. It will be explicitly specified if it's not the case. For example x(1, 3) will return the value of \( (x_1, x_2, x_3) \).

Returns: value of the sub-vector.

template<typename T >

NVector< T > & NVector< T >::operator()	(	size_t	k1,
		size_t	k2
	)

Manipulate sub-vector.

This operator is similar to previous operator()(size_t, size_t) const "operator" except that it sets browse indices _k1 and _k2 in order to modify efficiently non const reference.

Returns: reference to *this.

template<typename T>

NVector<T>& NVector< T >::operator= ( const NVector< T > & u )

inline

Copy source object on this object using copy().

Parameters

u	source `NVector<T>` object

Returns: reference to this.

template<typename T>

iterator NVector< T >::begin ( )

inline

template<typename T>

const_iterator NVector< T >::begin ( ) const

inline

template<typename T>

iterator NVector< T >::end ( )

inline

template<typename T>

const_iterator NVector< T >::end ( ) const

inline

template<typename T>

static NVector<T> NVector< T >::zeros ( size_t dim )

inlinestatic

Parameters

dim	dimension of the vector

Returns: a 0 vector \( (0, 0, ..., 0) \).

template<typename T>

static NVector<T> NVector< T >::ones ( size_t dim )

inlinestatic

Parameters

dim	dimension of the vector

Returns: Returns vector filled with 1 \( (1, 1, ..., 1) \).

template<typename T>

NVector< T > NVector< T >::scalar	(	T	s,
		size_t	dim
	)

static

Parameters

s	value of the scalar vector
dim	dimension of the scalar vector

Returns: a vector filled with s \( (s, s, ..., s) \).

template<typename T >

NVector< T > NVector< T >::cano	(	size_t	k,
		size_t	dim
	)

static

Parameters

k	index of vector in base
dim	dimension of vector space represented by the base.

Returns: return the kth vector of canonical base. ie \( (e_{0}, e_{1}, ..., e_{(n-1)}) \) where :

\[ \begin{align*} & e_{0} &=& (1, 0, 0, ..., 0) \\ & e_{1} &=& (0, 1, 0, ..., 0) \\ & &\vdots & \\ &e_{(n - 1)} &=& (0, 0, 0, ..., 1) \\ \end{align*} \]

template<typename T >

NVector< T > NVector< T >::sum ( const std::vector< NVector< T > > & vectors )

static

Sum of multiples vectors.

Parameters

vectors an array of vectors \( (u, v, ..., x) \).

Sum of the vectors contained in vectors array.

Returns: \( u + v + ... + x \).

template<typename T>

NVector< T > NVector< T >::sumProd	(	const std::vector< T > &	scalars,
		const std::vector< NVector< T > > &	vectors
	)

static

Linear combination of scalars and vectors.

Parameters

scalars	coefficients of linear combination `[` \( \alpha, \beta, ..., \lambda \)`]`.
vectors	vectors of linear combination \( (u, v, ..., x) \)

Returns: \( \alpha u + \beta v + ... + \lambda x \).

template<typename T>

NVector<T>& NVector< T >::add ( const NVector< T > & u )

inlineprotected

template<typename T>

NVector<T>& NVector< T >::sub ( const NVector< T > & u )

inlineprotected

template<typename T>

virtual NVector<T>& NVector< T >::opp ( )

inlineprotectedvirtual

Reimplemented in NPMatrix< T >, and NPMatrix< double_t >.

template<typename T>

virtual NVector<T>& NVector< T >::prod ( T s )

inlineprotectedvirtual

Reimplemented in NPMatrix< T >, and NPMatrix< double_t >.

template<typename T>

virtual NVector<T>& NVector< T >::div ( T s )

inlineprotectedvirtual

Reimplemented in NPMatrix< T >, and NPMatrix< double_t >.

template<typename T>

T NVector< T >::dotProduct ( const NVector< T > & u ) const

protected

template<typename T>

T NVector< T >::norm ( ) const

inlineprotected

template<typename T>

T NVector< T >::distance ( const NVector< T > & u ) const

inlineprotected

template<typename T>

bool NVector< T >::isValidIndex ( size_t k ) const

inlineprotected

template<typename T>

bool NVector< T >::isBetweenK12 ( size_t k ) const

inlineprotected

template<typename T>

bool NVector< T >::isNull ( ) const

inlineprotected

template<typename T>

bool NVector< T >::isEqual ( const NVector< T > & u ) const

protected

template<typename T>

bool NVector< T >::hasSameSize ( const NVector< T > & u ) const

inlineprotected

template<typename T>

virtual bool NVector< T >::hasDefaultBrowseIndices ( ) const

inlineprotectedvirtual

Reimplemented in NPMatrix< T >, and NPMatrix< double_t >.

template<typename T>

virtual void NVector< T >::setDefaultBrowseIndices ( ) const

inlineprotectedvirtual

Reimplemented in NPMatrix< T >, and NPMatrix< double_t >.

template<typename T>

NVector< T > & NVector< T >::forEach	(	const NVector< T > &	u,
		const std::function< void(T &, const T &)> &	binary_op
	)

protected

template<typename T>

NVector< T > & NVector< T >::forEach	(	T	s,
		const std::function< void(T &, T)> &	binary_op
	)

protectedvirtual

template<typename T>

NVector< T > & NVector< T >::copy ( const NVector< T > & u )

protected

template<typename T >

NVector< T > NVector< T >::subVector	(	size_t	k1,
		size_t	k2
	)		const

protected

template<typename T>

void NVector< T >::setSubVector ( const NVector< T > & u )

protected

Friends And Related Function Documentation

template<typename T>

NVector<T> operator+	(	NVector< T >	u,
		const NVector< T > &	v
	)

friend

Add two vectors.

Using usual addition \( (u_0 + v_0, u_1 + v_1, ...) \).

Returns: value of \( u + v \)

template<typename T>

NVector<T> operator-	(	NVector< T >	u,
		const NVector< T > &	v
	)

friend

Substract two vectors.

Using usual difference \( (u_0 - v_0, u_1 - v_1, ...) \).

Returns: value of \( u - v \)

template<typename T>

NVector<T> operator- ( NVector< T > u )

friend

Opposite of vector.

Returns: value of \( (-u_0, -u_1, ...). \)

template<typename T>

NVector<T> operator*	(	T	s,
		NVector< T >	u
	)

friend

Multiply vector by scalar.

Using usual scalar multiplication difference \( (s \cdot u_0, s \cdot u_1, ...) \).

Returns: value of \( s \cdot u \)

template<typename T>

NVector<T> operator*	(	const NVector< T > &	u,
		T	s
	)

friend

template<typename T>

NVector<T> operator/	(	NVector< T >	u,
		T	s
	)

friend

Divide vector by scalar.

Usual scalar division based on multiplication.

Returns: value of \( s^{-1} \cdot u \)

template<typename T>

T operator\|	(	const NVector< T > &	u,
		const NVector< T > &	v
	)

friend

Dot product of two vectors.

Usual inner product \( u_0 \cdot v_0 + u_1 \cdot v_1 + ... + u_{(n-1)} \cdot v_{(n-1)} \).

Returns: value of \( u \cdot v \)

template<typename T>

T operator! ( const NVector< T > & u )

friend

Norm of the vector.

The norm of vector \( ||u|| = \sqrt{u \cdot u} \) derived from dot product.

Returns: value of \( ||u|| \).

template<typename T>

T operator/	(	const NVector< T > &	u,
		const NVector< T > &	v
	)

friend

Distance between two vectors.

Returns: value of \( ||u - v|| \).

template<typename T>

std::ostream& operator<<	(	std::ostream &	os,
		const NVector< T > &	u
	)

friend

Usual stream insertion of vector.

Parameters

os	output stream
u	vector source

Inserts u.str() into os stream.

Returns: reference to os.

template<typename T>

bool operator==	(	const NVector< T > &	u,
		const NVector< T > &	v
	)

friend

Equality of two vectors.

Returns: return true if \( ||u - v|| < \epsilon \).

template<typename T>

bool operator==	(	const NVector< T > &	u,
		T	s
	)

friend

Equality to zero.

Returns: true if s is 0 and \( u \lt \epsilon \).

template<typename T>

bool operator==	(	T	s,
		const NVector< T > &	u
	)

friend

template<typename T>

bool operator!=	(	const NVector< T > &	u,
		const NVector< T > &	v
	)

friend

Non equality of two vector.

Returns: return true if \( ||u - v|| \geq \epsilon \).

template<typename T>

bool operator!=	(	const NVector< T > &	u,
		T	s
	)

friend

template<typename T>

bool operator!=	(	T	s,
		const NVector< T > &	u
	)

friend

Member Data Documentation

template<typename T>

size_t NVector< T >::_k1 {}

mutableprotected

template<typename T>

size_t NVector< T >::_k2 {}

mutableprotected

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

template<typename T> class NVector< T >

Features

Sub-range operators

Definitions

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<typename T>
class NVector< T >