Vector Class Reference

#include <Concepts/Vector.h>

Definition

An instance of data type Vector is a vector of variables of number type NT. Together with the type Matrix it realizes the basic operations of linear algebra.

Types
typedef unspecified_type	NT
	the ring type of the components. More...
typedef unspecified_type	iterator
	the iterator type for accessing components. More...
typedef unspecified_type	const_iterator
	the const iterator type for accessing components. More...

Creation
	Vector ()
	creates an instance v of type Vector. More...
	Vector (int d)
	creates an instance v of type Vector. More...
	Vector (int d, NT x)
	creates an instance v of type Vector. More...
template<class Forward_iterator >
	Vector (Forward_iterator first, Forward_iterator last)
	creates an instance v of type Vector; v is initialized to the vector with entries set [first,last). More...

Operations
int	dimension ()
	returns the dimension of v. More...
bool	is_zero ()
	returns true iff v is the zero vector. More...
NT &	operator[] (int i)
	returns the \( i\)-th component of v. More...
iterator	begin ()
	iterator to the first component. More...
iterator	end ()
	iterator beyond the last component. More...
const_iterator	begin () const
	iterator to the first component. More...
const_iterator	end () const
	iterator beyond the last component. More...
Vector	operator+ (const Vector &v1)
	Addition. More...
Vector	operator- (const Vector &v1)
	Subtraction. More...
NT	operator* (const Vector &v1)
	Inner Product. More...
Vector	operator- ()
	Negation. More...
Vector &	operator+= (const Vector &v1)
	Addition plus assignment. More...
Vector &	operator-= (const Vector &v1)
	Subtraction plus assignment. More...
Vector &	operator*= (const NT &s)
	Scalar multiplication plus assignment. More...
Vector &	operator/= (const NT &s)
	Scalar division plus assignment. More...
Vector	operator* (const NT &r, const Vector &v)
	Component-wise multiplication with number \( r\). More...
Vector	operator* (const Vector &v, const NT &r)
	Component-wise multiplication with number \( r\). More...

Member Typedef Documentation

const_iterator

typedef unspecified_type Vector::const_iterator

the const iterator type for accessing components.

iterator

typedef unspecified_type Vector::iterator

the iterator type for accessing components.

NT

typedef unspecified_type Vector::NT

the ring type of the components.

Constructor & Destructor Documentation

Vector() [1/4]

Vector::Vector

(

)

creates an instance v of type Vector.

Vector() [2/4]

Vector::Vector

(

int

d

)

creates an instance v of type Vector.

v is initialized to a vector of dimension \( d\).

Vector() [3/4]

Vector::Vector	(	int	d,
		NT	x
	)

creates an instance v of type Vector.

v is initialized to a vector of dimension \( d\) with entries x.

Vector() [4/4]

template<class Forward_iterator >

Vector::Vector	(	Forward_iterator	first,
		Forward_iterator	last
	)

creates an instance v of type Vector; v is initialized to the vector with entries set [first,last).

Template Parameters

ForwardIterator

has NT as value type.

Member Function Documentation

begin() [1/2]

iterator Vector::begin

(

)

iterator to the first component.

begin() [2/2]

const_iterator Vector::begin

(

)

const

iterator to the first component.

dimension()

int Vector::dimension

(

)

returns the dimension of v.

end() [1/2]

iterator Vector::end

(

)

iterator beyond the last component.

end() [2/2]

const_iterator Vector::end

(

)

const

iterator beyond the last component.

is_zero()

bool Vector::is_zero

(

)

returns true iff v is the zero vector.

operator*() [1/3]

Vector Vector::operator*	(	const NT &	r,
		const Vector &	v
	)

Component-wise multiplication with number \( r\).

operator*() [2/3]

Vector Vector::operator*	(	const Vector &	v,
		const NT &	r
	)

Component-wise multiplication with number \( r\).

operator*() [3/3]

NT Vector::operator*

(

const Vector &

v1

)

Inner Product.

Precondition

v.dimension() = v1.dimension().

operator*=()

Vector& Vector::operator*=

(

const NT &

s

)

Scalar multiplication plus assignment.

operator+()

Vector Vector::operator+

(

const Vector &

v1

)

Addition.

Precondition

v.dimension() == v1.dimension().

operator+=()

Vector& Vector::operator+=

(

const Vector &

v1

)

Addition plus assignment.

Precondition

v.dimension() == v1.dimension().

operator-() [1/2]

Vector Vector::operator-

(

)

Negation.

operator-() [2/2]

Vector Vector::operator-

(

const Vector &

v1

)

Subtraction.

Precondition

v.dimension() = v1.dimension().

operator-=()

Vector& Vector::operator-=

(

const Vector &

v1

)

Subtraction plus assignment.

Precondition

v.dimension() == v1.dimension().

operator/=()

Vector& Vector::operator/=

(

const NT &

s

)

Scalar division plus assignment.

operator[]()

NT& Vector::operator[]

(

int

i

)

returns the \( i\)-th component of v.

Precondition

\( 0\le i \le v.dimension()-1\).