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# 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.

#include < LEDA/numbers/integer_vector.h >

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(const integer& a, const integer& b) creates an instance v of type integer_vector. v is initialized to the two-dimensional vector (a, b). integer_vector v(const integer& a, const integer& b, const integer& c) creates an instance v of type integer_vector. v is initialized to the three-dimensional vector (a, b, c). integer_vector v(const integer& a, const integer& b, const integer& c, const 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 += const integer_vector& v1 Addition plus assignment. Precondition v.dim() == v1.dim(). integer_vector& v -= const integer_vector& v1 Subtraction plus assignment. Precondition v.dim() == v1.dim(). integer_vector v + const integer_vector& v1 Addition. Precondition v.dim() == v1.dim(). integer_vector v - const integer_vector& v1 Subtraction. Precondition v.dim() == v1.dim(). integer v * const integer_vector& v1 Inner Product. Precondition v.dim() == v1.dim(). integer_vector const integer& r * const integer_vector& v Componentwise multiplication with number r. integer_vector const integer_vector& v * const integer& r Componentwise multiplication with number r. ostream& ostream& O « const integer_vector& 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()).     Next: Matrices with Integer Entries Up: Number Types and Linear Previous: Double-Valued Matrices ( matrix   Contents   Index