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## 26.1 Set Operations

Octave supports the basic set operations. That is, Octave can compute the union, intersection, complement, and difference of two sets. Octave also supports the Exclusive Or set operation, and membership determination. The functions for set operations all work in pretty much the same way. As an example, assume that `x` and `y` contains two sets, then

 ```union(x, y) ```

computes the union of the two sets.

Function File: [tf = ismember (A, S)
Function File: [tf, S_idx] = ismember (A, S)
Function File: [tf, S_idx] = ismember (A, S, "rows")

Return a matrix tf with the same shape as A which has a 1 if `A(i,j)` is in S and 0 if it is not. If a second output argument is requested, the index into S of each of the matching elements is also returned.

 ```a = [3, 10, 1]; s = [0:9]; [tf, s_idx] = ismember (a, s); ⇒ tf = [1, 0, 1] ⇒ s_idx = [4, 0, 2] ```

The inputs, A and S, may also be cell arrays.

 ```a = {'abc'}; s = {'abc', 'def'}; [tf, s_idx] = ismember (a, s); ⇒ tf = [1, 0] ⇒ s_idx = [1, 0] ```

With the optional third argument `"rows"`, and matrices A and S with the same number of columns, compare rows in A with the rows in S.

 ```a = [1:3; 5:7; 4:6]; s = [0:2; 1:3; 2:4; 3:5; 4:6]; [tf, s_idx] = ismember(a, s, 'rows'); ⇒ tf = logical ([1; 0; 1]) ⇒ s_idx = [2; 0; 5]; ```

Function File: union (a, b)
Function File: union (a, b, "rows")

Return the set of elements that are in either of the sets a and b. For example,

 ```union ([1, 2, 4], [2, 3, 5]) ⇒ [1, 2, 3, 4, 5] ```

If the optional third input argument is the string "rows" each row of the matrices a and b will be considered an element of sets. For example,

 ```union([1, 2; 2, 3], [1, 2; 3, 4], "rows") ⇒ 1 2 2 3 3 4 ```
Function File: [c, ia, ib] = union (a, b)

Return index vectors ia and ib such that `a == c(ia)` and `b == c(ib)`.

Function File: intersect (a, b)
Function File: [c, ia, ib] = intersect (a, b)

Return the elements in both a and b, sorted in ascending order. If a and b are both column vectors return a column vector, otherwise return a row vector.

Return index vectors ia and ib such that `a(ia)==c` and `b(ib)==c`.

Function File: complement (x, y)

Return the elements of set y that are not in set x. For example,

 ```complement ([ 1, 2, 3 ], [ 2, 3, 5 ]) ⇒ 5 ```

Function File: setdiff (a, b)
Function File: setdiff (a, b, "rows")
Function File: [c, i] = setdiff (a, b)

Return the elements in a that are not in b, sorted in ascending order. If a and b are both column vectors return a column vector, otherwise return a row vector.

Given the optional third argument ‘"rows"’, return the rows in a that are not in b, sorted in ascending order by rows.

If requested, return i such that `c = a(i)`.

Function File: setxor (a, b)
Function File: setxor (a, b, 'rows')

Return the elements exclusive to a or b, sorted in ascending order. If a and b are both column vectors return a column vector, otherwise return a row vector.

Function File: [c, ia, ib] = setxor (a, b)

Return index vectors ia and ib such that `a == c(ia)` and `b == c(ib)`.

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