Vectors with Integer Entries (integer_vector)

Definition

An instance of data type integer_vector is a vector of variables of type integer, the so called ring type. Together with the type integer_matrix it realizes the basic operations of linear algebra. Internal correctness tests are executed if compiled with the flag LA_SELFTEST.

Creation

integer_vector	v;	creates an instance v of type integer_vector. v is initialized to the zero-dimensional vector.
integer_vector	v(int d);	creates an instance v of type integer_vector. v is initialized to a vector of dimension d.
integer_vector	v(integer a, integer b);	creates an instance v of type integer_vector. v is initialized to the two-dimensional vector (a,b).
integer_vector	v(integer a, integer b, integer c);
		creates an instance v of type integer_vector. v is initialized to the three-dimensional vector (a,b,c).
integer_vector	v(integer a, integer b, integer c, integer d);
		creates an instance v of type integer_vector; v is initialized to the four-dimensional vector (a,b,c,d).

Operations

int	v.dim()	returns the dimension of v.
integer&	v[int i]	returns i-th component of v. Precondition: 0<= i <= v.dim()-1.
integer_vector&	v += v1	Addition plus assignment. Precondition: v.dim() == v1.dim().
integer_vector&	v -= v1	Subtraction plus assignment. Precondition: v.dim() == v1.dim().
integer_vector	v + v1	Addition. Precondition: v.dim() == v1.dim().
integer_vector	v - v1	Subtraction. Precondition: v.dim() == v1.dim().
integer	v * v1	Inner Product. Precondition: v.dim() == v1.dim().
integer_vector	integer r * v	Componentwise multiplication with number r.
integer_vector	v * integer r	Componentwise multiplication with number r.
ostream&	ostream& O << v	writes v componentwise to the output stream O.
istream&	istream& I >> integer_vector& v
		reads v componentwise from the input stream I.

Implementation

Vectors are implemented by arrays of type integer. All operations on a vector v take time O(v.dim()), except for dimension and [ ] which take constant time. The space requirement is O(v.dim()).