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@c Copyright (C) 1996-2025 The Octave Project Developers
@c
@c This file is part of Octave.
@c
@c Octave is free software: you can redistribute it and/or modify it
@c under the terms of the GNU General Public License as published by
@c the Free Software Foundation, either version 3 of the License, or
@c (at your option) any later version.
@c
@c Octave is distributed in the hope that it will be useful, but
@c WITHOUT ANY WARRANTY; without even the implied warranty of
@c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
@c GNU General Public License for more details.
@c
@c You should have received a copy of the GNU General Public License
@c along with Octave; see the file COPYING. If not, see
@c <https://www.gnu.org/licenses/>.
@node Sets
@chapter Sets
Octave has a number of functions for managing sets of data. A set is defined
as a collection of unique elements and is typically represented by a vector of
numbers sorted in ascending order. Any vector or matrix can be converted to a
set by removing duplicates through the use of the @code{unique} function.
However, it isn't necessary to explicitly create a set as all of the functions
which operate on sets will convert their input to a set before proceeding.
@DOCSTRING(unique)
@DOCSTRING(uniquetol)
@menu
* Set Operations::
@end menu
@node Set Operations
@section Set Operations
Octave supports several basic set operations. Octave can compute the union,
intersection, and difference of two sets. Octave also supports the
@emph{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 @code{a} and
@code{b} contains two sets, then
@example
union (a, b)
@end example
@noindent
computes the union of the two sets.
Finally, determining whether elements belong to a set can be done with the
@code{ismember} function. Because sets are ordered this operation is very
efficient and is of order O(log2(n)) which is preferable to the @code{find}
function which is of order O(n).
@DOCSTRING(intersect)
@DOCSTRING(union)
@DOCSTRING(setdiff)
@DOCSTRING(setxor)
@DOCSTRING(ismember)
@DOCSTRING(ismembertol)
@DOCSTRING(powerset)
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