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Next: <a href="Polynomial-Manipulations.html" accesskey="n" rel="next">Polynomial Manipulations</a>, Previous: <a href="Statistics.html" accesskey="p" rel="prev">Statistics</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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<hr>
<h2 class="chapter" id="Sets-1"><span>27 Sets<a class="copiable-link" href="#Sets-1"> ¶</a></span></h2>
<p>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 class="code">unique</code> 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.
</p>
<a class="anchor" id="XREFunique"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-unique"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">unique</strong> <code class="def-code-arguments">(<var class="var">x</var>)</code><a class="copiable-link" href="#index-unique"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-unique-1"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">unique</strong> <code class="def-code-arguments">(<var class="var">x</var>, "rows")</code><a class="copiable-link" href="#index-unique-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-unique-2"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">unique</strong> <code class="def-code-arguments">(…, "sorted")</code><a class="copiable-link" href="#index-unique-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-unique-3"><span><code class="def-type"><var class="var">y</var> =</code> <strong class="def-name">unique</strong> <code class="def-code-arguments">(…, "stable")</code><a class="copiable-link" href="#index-unique-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-unique-4"><span><code class="def-type">[<var class="var">y</var>, <var class="var">i</var>, <var class="var">j</var>] =</code> <strong class="def-name">unique</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-unique-4"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-unique-5"><span><code class="def-type">[<var class="var">y</var>, <var class="var">i</var>, <var class="var">j</var>] =</code> <strong class="def-name">unique</strong> <code class="def-code-arguments">(…, "first")</code><a class="copiable-link" href="#index-unique-5"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-unique-6"><span><code class="def-type">[<var class="var">y</var>, <var class="var">i</var>, <var class="var">j</var>] =</code> <strong class="def-name">unique</strong> <code class="def-code-arguments">(…, "last")</code><a class="copiable-link" href="#index-unique-6"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-unique-7"><span><code class="def-type">[<var class="var">y</var>, <var class="var">i</var>, <var class="var">j</var>] =</code> <strong class="def-name">unique</strong> <code class="def-code-arguments">(…, "legacy")</code><a class="copiable-link" href="#index-unique-7"> ¶</a></span></dt>
<dd><p>Return the unique elements of <var class="var">x</var>.
</p>
<p>If the input <var class="var">x</var> is a column vector then return a column vector;
Otherwise, return a row vector. <var class="var">x</var> may also be a cell array of
strings.
</p>
<p>If the optional argument <code class="code">"rows"</code> is given then return the unique
rows of <var class="var">x</var>. The input must be a 2-D numeric matrix to use this option.
</p>
<p>The optional argument <code class="code">"sorted"</code>/<code class="code">"stable"</code> controls the order
in which unique values appear in the output. The default is
<code class="code">"sorted"</code> and values in the output are placed in ascending order.
The alternative <code class="code">"stable"</code> preserves the order found in the input
<var class="var">x</var>.
</p>
<p>If requested, return column index vectors <var class="var">i</var> and <var class="var">j</var> such that
<code class="code"><var class="var">y</var> = <var class="var">x</var>(<var class="var">i</var>)</code> and <code class="code"><var class="var">x</var> = <var class="var">y</var>(<var class="var">j</var>)</code>.
</p>
<p>Additionally, if <var class="var">i</var> is a requested output then one of the flags
<code class="code">"first"</code> or <code class="code">"last"</code> may be given. If <code class="code">"last"</code> is
specified, return the highest possible indices in <var class="var">i</var>, otherwise, if
<code class="code">"first"</code> is specified, return the lowest. The default is
<code class="code">"first"</code>.
</p>
<p>Example 1 : sort order
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">unique ([3, 1, 1, 2])
⇒ [1, 2, 3]
unique ([3, 1, 1, 2], "stable")
⇒ [3, 1, 2]
</pre></div></div>
<p>Example 2 : index selection
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">[~, <var class="var">i</var>] = unique ([3, 1, 1, 2], "first")
⇒ <var class="var">i</var> = [2; 4; 1]
[~, <var class="var">i</var>] = unique ([3, 1, 1, 2], "last")
⇒ <var class="var">i</var> = [3; 4; 1]
</pre></div></div>
<p>Programming Notes: The input flag <code class="code">"legacy"</code> changes the algorithm
to be compatible with <small class="sc">MATLAB</small> releases prior to R2012b. Specifically,
The index ordering flag is changed to <code class="code">"last"</code>, and the shape of the
outputs <var class="var">i</var>, <var class="var">j</var> will follow the shape of the input <var class="var">x</var> rather
than always being column vectors.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFuniquetol">uniquetol</a>, <a class="ref" href="Set-Operations.html#XREFunion">union</a>, <a class="ref" href="Set-Operations.html#XREFintersect">intersect</a>, <a class="ref" href="Set-Operations.html#XREFsetdiff">setdiff</a>, <a class="ref" href="Set-Operations.html#XREFsetxor">setxor</a>, <a class="ref" href="Set-Operations.html#XREFismember">ismember</a>.
</p></dd></dl>
<a class="anchor" id="XREFuniquetol"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-uniquetol"><span><code class="def-type"><var class="var">c</var> =</code> <strong class="def-name">uniquetol</strong> <code class="def-code-arguments">(<var class="var">A</var>)</code><a class="copiable-link" href="#index-uniquetol"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-uniquetol-1"><span><code class="def-type"><var class="var">c</var> =</code> <strong class="def-name">uniquetol</strong> <code class="def-code-arguments">(<var class="var">A</var>, <var class="var">tol</var>)</code><a class="copiable-link" href="#index-uniquetol-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-uniquetol-2"><span><code class="def-type"><var class="var">c</var> =</code> <strong class="def-name">uniquetol</strong> <code class="def-code-arguments">(…, <var class="var">property</var>, <var class="var">value</var>)</code><a class="copiable-link" href="#index-uniquetol-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-uniquetol-3"><span><code class="def-type">[<var class="var">c</var>, <var class="var">ia</var>, <var class="var">ic</var>] =</code> <strong class="def-name">uniquetol</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-uniquetol-3"> ¶</a></span></dt>
<dd><p>Return the unique elements of <var class="var">A</var> within tolerance <var class="var">tol</var>.
</p>
<p>Two values, <var class="var">x</var> and <var class="var">y</var>, are within relative tolerance if
<code class="code">abs (<var class="var">x</var> - <var class="var">y</var>) <= <var class="var">tol</var> * max (abs (<var class="var">A</var>(:)))</code>.
</p>
<p>The input <var class="var">A</var> must be a real (non-complex) floating point type (double
or single).
</p>
<p>If <var class="var">tol</var> is unspecified, the default tolerance is 1e-12 for double
precision input or 1e-6 for single precision input.
</p>
<p>The function may also be called with the following optional property/value
pairs. Property/value pairs must be passed after other input arguments:
</p>
<dl class="table">
<dt><code class="code">"ByRows"</code> (default: <code class="code">false</code>)</dt>
<dd><p>When true, return the unique rows of <var class="var">A</var>. <var class="var">A</var> must be a 2-D array
to use this option. For rows, the criteria for uniqueness is changed to
<code class="code">all (abs (<var class="var">x</var> - <var class="var">y</var>) <= <var class="var">tol</var>*max (abs (<var class="var">A</var>),[],1))</code>
which compares each column component of a row against a column-specific
tolerance.
</p>
</dd>
<dt><code class="code">"DataScale"</code></dt>
<dd><p>The tolerance test is changed to
<code class="code">abs (<var class="var">x</var> - <var class="var">y</var>) <= <var class="var">tol</var>*<var class="var">DS</var></code> where <var class="var">DS</var> is a
scalar unless the property <code class="code">"ByRows"</code> is true. In that case, <var class="var">DS</var>
can either be a scalar or a vector with a length equal to the number of
columns in <var class="var">A</var>. Using a value of <code class="code">1.0</code> for <var class="var">DS</var> will change
the tolerance from a relative one to an absolute tolerance. Using a value
of <code class="code">Inf</code> will disable testing.
</p>
</dd>
<dt><code class="code">"OutputAllIndices"</code> (default: <code class="code">false</code>)</dt>
<dd><p>When true, <var class="var">ia</var> is a cell array (not a vector) that contains the indices
for <em class="emph">all</em> elements in <var class="var">A</var> that are within tolerance of a value in
<var class="var">C</var>. That is, each cell in <var class="var">ia</var> corresponds to a single unique
value in <var class="var">C</var>, and the values in each cell correspond to locations in
<var class="var">A</var>.
</p></dd>
</dl>
<p>The output <var class="var">c</var> is a row vector if the input <var class="var">A</var> is a row vector.
For all other cases, a column vector is returned.
</p>
<p>The optional output <var class="var">ia</var> is a column index vector such that
<code class="code"><var class="var">c</var> = <var class="var">A</var>(<var class="var">ia</var>)</code>. If the <code class="code">"ByRows"</code> property is
true, the condition is <code class="code"><var class="var">c</var> = <var class="var">A</var>(<var class="var">ia</var>, :)</code>. If the
<code class="code">"OutputAllIndices"</code> property is true, then the values
<code class="code"><var class="var">A</var>(<var class="var">ia</var>{<var class="var">i</var>})</code> are all within tolerance of the unique
value <code class="code"><var class="var">c</var>(<var class="var">i</var>)</code>.
</p>
<p>The optional output <var class="var">ic</var> is a column index vector such that
<code class="code"><var class="var">A</var> = <var class="var">c</var>(<var class="var">ic</var>)</code> when <var class="var">A</var> is a vector. When <var class="var">A</var>
is a matrix, <code class="code"><var class="var">A</var>(:) = <var class="var">c</var>(<var class="var">ic</var>)</code>. If the <code class="code">"ByRows"</code>
property is true then <code class="code"><var class="var">A</var> = <var class="var">c</var>(<var class="var">ic</var>,:)</code>.
</p>
<p>Example: small round-off errors require <code class="code">uniquetol</code>, not <code class="code">unique</code>
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">x = [1:5];
## Inverse_Function (Function (x)) should return exactly x
y = exp (log (x));
D = unique ([x, y])
⇒ [1 2 3 3 4 5 5]
C = uniquetol ([x, y])
⇒ [1 2 3 4 5]
</pre></div></div>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFunique">unique</a>, <a class="ref" href="Set-Operations.html#XREFunion">union</a>, <a class="ref" href="Set-Operations.html#XREFintersect">intersect</a>, <a class="ref" href="Set-Operations.html#XREFsetdiff">setdiff</a>, <a class="ref" href="Set-Operations.html#XREFsetxor">setxor</a>, <a class="ref" href="Set-Operations.html#XREFismember">ismember</a>.
</p></dd></dl>
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