Set operations

Elementary set operations

It's possible to perform elementary set operations with Matlab. Let's assume we have given two vectors or arrays

A = randi([0 10],1,5);
B = randi([-1 9], 1,5);

and we want to find all elements which are in A and in B. For this we can use

C = intersect(A,B);

C will include all numbers which are part of A and part of B. If we also want to find the position of these elements we call

[C,pos] = intersect(A,B);

pos is the position of these elements such that C == A(pos).

Another basic operation is the union of two sets

D = union(A,B);

Herby contains D all elements of A and B.

Note that A and B are hereby treated as sets which means that it does not matter how often an element is part of A or B. To clarify this one can check D == union(D,C).

If we want to obtain the data that is in 'A' but not in 'B' we can use the following function

E = setdiff(A,B);

We want to note again that this are sets such that following statement holds D == union(E,B).

Suppose we want to check if

x = randi([-10 10],1,1);

is an element of either A or B we can execute the command

a = ismember(A,x);
b = ismember(B,x);

If a==1 then x is element of A and x is no element is a==0. The same goes for B. If a==1 && b==1 x is also an element of C. If a == 1 || b == 1 x is element of D and if a == 1 || b == 0 it's also element of E.

Syntax

1. C = union(A,B);
2. C = intersect(A,B);
3. C = setdiff(A,B);
4. a = ismember(A,x);

Parameters

Parameter	Details
A,B	sets, possibly matrices or vectors
x	possible element of a set