Vector

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

Vector::NT
	the ring type of the components.
Vector::iterator
	the iterator type for accessing components.
Vector::const_iterator
	the const iterator type for accessing components.

Creation

Vector v;
	creates an instance v of type Vector.
Vector v ( int d);
	creates an instance v of type Vector. v is initialized to a vector of dimension $$d.
Vector v ( int d, NT x);
	creates an instance v of type Vector. v is initialized to a vector of dimension $$d with entries x.
template <class Forward_iterator>
Vector v ( Forward_iterator first, Forward_iterator last);
	creates an instance v of type Vector; v is initialized to the vector with entries set [first,last). Requirement: Forward_iterator has value type NT.

Operations

int	v.dimension ()	returns the dimension of v.
bool	v.is_zero ()	returns true iff v is the zero vector.
NT&	v [ int i]	returns the $$i-th component of v. Precondition: $$0 i v.dimension()-1.
iterator	v.begin ()	iterator to the first component.
iterator	v.end ()	iterator beyond the last component.

The same operations begin(), end() exist for const_iterator.

Vector	v + v1	Addition. Precondition: v.dimension() == v1.dimension().
Vector	v - v1	Subtraction. Precondition: v.dimension() = v1.dimension().
NT	v * v1	Inner Product. Precondition: v.dimension() = v1.dimension().
Vector	- v	Negation.
Vector&	v += v1	Addition plus assignment. Precondition: v.dimension() == v1.dimension().
Vector&	v -= v1	Subtraction plus assignment. Precondition: v.dimension() == v1.dimension().
Vector&	v *= NT s	Scalar multiplication plus assignment.
Vector&	v /= NT s	Scalar division plus assignment.
Vector	NT r * v	Componentwise multiplication with number $$r.
Vector	v * NT r	Componentwise multiplication with number $$r.