Octave supports several basic set operations. Octave can compute the union,
intersection, and difference of two sets. Octave also supports the
*Exclusive Or* set operation.

The functions for set operations all work in the same way by accepting two
input sets and returning a third set. As an example, assume that `a`

and
`b`

contains two sets, then

union (a, b)

computes the union of the two sets.

Finally, determining whether elements belong to a set can be done with the
`ismember`

function. Because sets are ordered this operation is very
efficient and is of order O(log2(n)) which is preferable to the `find`

function which is of order O(n).

- :
`c`=**intersect***(*¶`a`,`b`) - :
`c`=**intersect***(*¶`a`,`b`, "rows") - :
`c`=**intersect***(…, "sorted")*¶ - :
`c`=**intersect***(…, "stable")*¶ - :
`c`=**intersect***(…, "legacy")*¶ - :
*[*`c`,`ia`,`ib`] =**intersect***(…)*¶ -
Return the unique elements common to both

`a`and`b`.If

`a`and`b`are both row vectors then return a row vector; Otherwise, return a column vector. The inputs may also be cell arrays of strings.If the optional input

`"rows"`

is given then return the common rows of`a`and`b`. The inputs must be 2-D numeric matrices to use this option.The optional argument

`"sorted"`

/`"stable"`

controls the order in which unique values appear in the output. The default is`"sorted"`

and values in the output are placed in ascending order. The alternative`"stable"`

preserves the order found in the input.If requested, return column index vectors

`ia`and`ib`such that

and`c`=`a`(`ia`)

.`c`=`b`(`ib`)Programming Note: The input flag

`"legacy"`

changes the algorithm to be compatible with MATLAB releases prior to R2012b.

- :
`c`=**union***(*¶`a`,`b`) - :
`c`=**union***(*¶`a`,`b`, "rows") - :
`c`=**union***(…, "sorted")*¶ - :
`c`=**union***(…, "stable")*¶ - :
`c`=**union***(…, "legacy")*¶ - :
*[*`c`,`ia`,`ib`] =**union***(…)*¶ -
Return the unique elements that are in either

`a`or`b`.If

`a`and`b`are both row vectors then return a row vector; Otherwise, return a column vector. The inputs may also be cell arrays of strings.If the optional input

`"rows"`

is given then return rows that are in either`a`or`b`. The inputs must be 2-D numeric matrices to use this option.The optional argument

`"sorted"`

/`"stable"`

controls the order in which unique values appear in the output. The default is`"sorted"`

and values in the output are placed in ascending order. The alternative`"stable"`

preserves the order found in the input.The optional outputs

`ia`and`ib`are column index vectors such that

and`a`(`ia`)

are disjoint sets whose union is`b`(`ib`)`c`.Programming Note: The input flag

`"legacy"`

changes the algorithm to be compatible with MATLAB releases prior to R2012b.

- :
`c`=**setdiff***(*¶`a`,`b`) - :
`c`=**setdiff***(*¶`a`,`b`, "rows") - :
`c`=**setdiff***(…, "sorted")*¶ - :
`c`=**setdiff***(…, "stable")*¶ - :
`c`=**setdiff***(…, "legacy")*¶ - :
*[*`c`,`ia`] =**setdiff***(…)*¶ Return the unique elements in

`a`that are not in`b`.If

`a`is a row vector return a row vector; Otherwise, return a column vector. The inputs may also be cell arrays of strings.If the optional input

`"rows"`

is given then return the rows in`a`that are not in`b`. The inputs must be 2-D numeric matrices to use this option.The optional argument

`"sorted"`

/`"stable"`

controls the order in which unique values appear in the output. The default is`"sorted"`

and values in the output are placed in ascending order. The alternative`"stable"`

preserves the order found in the input.If requested, return the index vector

`ia`such that

.`c`=`a`(`ia`)Programming Note: The input flag

`"legacy"`

changes the algorithm to be compatible with MATLAB releases prior to R2012b.

- :
`c`=**setxor***(*¶`a`,`b`) - :
`c`=**setxor***(*¶`a`,`b`, "rows") - :
`c`=**setxor***(…, "sorted")*¶ - :
`c`=**setxor***(…, "stable")*¶ - :
`c`=**setxor***(…, "legacy")*¶ - :
*[*`c`,`ia`,`ib`] =**setxor***(…)*¶ -
Return the unique elements exclusive to sets

`a`or`b`.If

`a`and`b`are both row vectors then return a row vector; Otherwise, return a column vector. The inputs may also be cell arrays of strings.If the optional input

`"rows"`

is given then return the rows exclusive to sets`a`and`b`. The inputs must be 2-D numeric matrices to use this option.`"sorted"`

/`"stable"`

controls the order in which unique values appear in the output. The default is`"sorted"`

and values in the output are placed in ascending order. The alternative`"stable"`

preserves the order found in the input.The optional outputs

`ia`and`ib`are column index vectors such that

and`a`(`ia`)

are disjoint sets whose union is`b`(`ib`)`c`.`"legacy"`

changes the algorithm to be compatible with MATLAB releases prior to R2012b.

- :
`tf`=**ismember***(*¶`a`,`s`) - :
`tf`=**ismember***(*¶`a`,`s`, "rows") - :
*[*`tf`,`s_idx`] =**ismember***(…)*¶ -
Return a logical matrix

`tf`with the same shape as`a`which is true (1) if the element in`a`is found in`s`and false (0) if it is not.If a second output argument is requested then the index into

`s`of each matching element 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 ⇒ s_idx = 1

If the optional third argument

`"rows"`

is given then compare rows in`a`with rows in`s`. The inputs must be 2-D matrices with the same number of columns to use this option.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];

**See also:**lookup, unique, union, intersect, setdiff, setxor.

- :
`p`=**powerset***(*¶`a`) - :
`p`=**powerset***(*¶`a`, "rows") Compute the powerset (all subsets) of the set

`a`.The set

`a`must be a numerical matrix or a cell array of strings. The output will always be a cell array of either vectors or strings.With the optional argument

`"rows"`

, each row of the set`a`is considered one element of the set. The input must be a 2-D numeric matrix to use this argument.**See also:**unique, union, intersect, setdiff, setxor, ismember.