Vector Concept Reference

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.
typedef unspecified_type	iterator
	the iterator type for accessing components.
typedef unspecified_type	const_iterator
	the const iterator type for accessing components.

Creation
	Vector ()
	creates an instance v of type Vector.
	Vector (int d)
	creates an instance v of type Vector.
	Vector (int d, NT x)
	creates an instance v of type Vector.
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).

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

Constructor & Destructor Documentation

Vector() [1/3]

Vector::Vector

(

int

d

)

creates an instance v of type Vector.

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

Vector() [2/3]

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() [3/3]

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

operator*()

NT Vector::operator*

(

const Vector &

v1

)

Inner Product.

Precondition

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

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-()

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[]()

NT & Vector::operator[]

(

int

i

)

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

Precondition

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