From AIMSWiki

Table of contents

1 Creating a set 2 Manipulating sets

Octave implements some 'very' basic set operations. Sets are implemented as ordered vectors and, for this reason, the set functions may also be useful for

• sorting and
• finding unique elements in

a vector.

Creating a set

You can create an empty set by using an empty vector:

octave:1> A = [];

This is often a good place to start and you can use the functions for manipulating sets (see the next section) to add elements to this.

You can also create a set from a vector using

octave:2> A = create_set(x);

Here, x is a vector or matrix and the result, stored in A contains unique values from x sorted in ascending order. For example,

octave:3> create_set([1, 2; 3, 4; 4, 2])
ans =

  1  2  3  4

Manipulating sets

The three set operations union, , intersection, and complement, are implemented in Octave and behaves in the normal way. The commands for these functions are

• union(a, b) returns a set of elements that are in at least one of a and b
• intersection(a, b) returns the elements that are in both a and b
• complement(a, b) returns the elements from b that are not in a (this is actually the set difference, B / A, but can be thought of as the complement of A if B is the universe of elements)

The following examples illustrate the functions.

octave:4> u = create_set([1, 10, 5, 2, 4])
u =

   1   2   4   5  10

octave:5> v = create_set([3, 4, 5, 6])
v =

  3  4  5  6

octave:6> union(u, v)
ans =

   1   2   3   4   5   6  10

octave:7> intersection(u, v)
ans =

  4  5

octave:8> complement(u, [1:10])
ans =

  3  6  7  8  9