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<a name="Rearranging-Matrices"></a>
Next: <a rel="next" accesskey="n" href="Applying-a-Function-to-an-Array.html#Applying-a-Function-to-an-Array">Applying a Function to an Array</a>,
Previous: <a rel="previous" accesskey="p" href="Finding-Elements-and-Checking-Conditions.html#Finding-Elements-and-Checking-Conditions">Finding Elements and Checking Conditions</a>,
Up: <a rel="up" accesskey="u" href="Matrix-Manipulation.html#Matrix-Manipulation">Matrix Manipulation</a>
<hr>
</div>
<h3 class="section">16.2 Rearranging Matrices</h3>
<!-- ./general/fliplr.m -->
<p><a name="doc_002dfliplr"></a>
<div class="defun">
— Function File: <b>fliplr</b> (<var>x</var>)<var><a name="index-fliplr-1272"></a></var><br>
<blockquote><p>Return a copy of <var>x</var> with the order of the columns reversed. For
example,
<pre class="example"> fliplr ([1, 2; 3, 4])
2 1
4 3
</pre>
<p>Note that <code>fliplr</code> only work with 2-D arrays. To flip N-d arrays
use <code>flipdim</code> instead.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dflipud.html#doc_002dflipud">flipud</a>, <a href="doc_002dflipdim.html#doc_002dflipdim">flipdim</a>, <a href="doc_002drot90.html#doc_002drot90">rot90</a>, <a href="doc_002drotdim.html#doc_002drotdim">rotdim</a>.
</p></blockquote></div>
<!-- ./general/flipud.m -->
<p><a name="doc_002dflipud"></a>
<div class="defun">
— Function File: <b>flipud</b> (<var>x</var>)<var><a name="index-flipud-1273"></a></var><br>
<blockquote><p>Return a copy of <var>x</var> with the order of the rows reversed. For
example,
<pre class="example"> flipud ([1, 2; 3, 4])
3 4
1 2
</pre>
<p>Due to the difficulty of defining which axis about which to flip the
matrix <code>flipud</code> only work with 2-d arrays. To flip N-d arrays
use <code>flipdim</code> instead.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dfliplr.html#doc_002dfliplr">fliplr</a>, <a href="doc_002dflipdim.html#doc_002dflipdim">flipdim</a>, <a href="doc_002drot90.html#doc_002drot90">rot90</a>, <a href="doc_002drotdim.html#doc_002drotdim">rotdim</a>.
</p></blockquote></div>
<!-- ./general/flipdim.m -->
<p><a name="doc_002dflipdim"></a>
<div class="defun">
— Function File: <b>flipdim</b> (<var>x, dim</var>)<var><a name="index-flipdim-1274"></a></var><br>
<blockquote><p>Return a copy of <var>x</var> flipped about the dimension <var>dim</var>.
For example
<pre class="example"> flipdim ([1, 2; 3, 4], 2)
2 1
4 3
</pre>
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<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dfliplr.html#doc_002dfliplr">fliplr</a>, <a href="doc_002dflipud.html#doc_002dflipud">flipud</a>, <a href="doc_002drot90.html#doc_002drot90">rot90</a>, <a href="doc_002drotdim.html#doc_002drotdim">rotdim</a>.
</p></blockquote></div>
<!-- ./general/rot90.m -->
<p><a name="doc_002drot90"></a>
<div class="defun">
— Function File: <b>rot90</b> (<var>x, n</var>)<var><a name="index-rot90-1275"></a></var><br>
<blockquote><p>Return a copy of <var>x</var> with the elements rotated counterclockwise in
90-degree increments. The second argument is optional, and specifies
how many 90-degree rotations are to be applied (the default value is 1).
Negative values of <var>n</var> rotate the matrix in a clockwise direction.
For example,
<pre class="example"> rot90 ([1, 2; 3, 4], -1)
3 1
4 2
</pre>
<p class="noindent">rotates the given matrix clockwise by 90 degrees. The following are all
equivalent statements:
<pre class="example"> rot90 ([1, 2; 3, 4], -1)
rot90 ([1, 2; 3, 4], 3)
rot90 ([1, 2; 3, 4], 7)
</pre>
<p>Due to the difficulty of defining an axis about which to rotate the
matrix <code>rot90</code> only work with 2-D arrays. To rotate N-d arrays
use <code>rotdim</code> instead.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drotdim.html#doc_002drotdim">rotdim</a>, <a href="doc_002dflipud.html#doc_002dflipud">flipud</a>, <a href="doc_002dfliplr.html#doc_002dfliplr">fliplr</a>, <a href="doc_002dflipdim.html#doc_002dflipdim">flipdim</a>.
</p></blockquote></div>
<!-- ./general/rotdim.m -->
<p><a name="doc_002drotdim"></a>
<div class="defun">
— Function File: <b>rotdim</b> (<var>x, n, plane</var>)<var><a name="index-rotdim-1276"></a></var><br>
<blockquote><p>Return a copy of <var>x</var> with the elements rotated counterclockwise in
90-degree increments. The second argument is optional, and specifies
how many 90-degree rotations are to be applied (the default value is 1).
The third argument is also optional and defines the plane of the
rotation. As such <var>plane</var> is a two element vector containing two
different valid dimensions of the matrix. If <var>plane</var> is not given
Then the first two non-singleton dimensions are used.
<p>Negative values of <var>n</var> rotate the matrix in a clockwise direction.
For example,
<pre class="example"> rotdim ([1, 2; 3, 4], -1, [1, 2])
3 1
4 2
</pre>
<p class="noindent">rotates the given matrix clockwise by 90 degrees. The following are all
equivalent statements:
<pre class="example"> rotdim ([1, 2; 3, 4], -1, [1, 2])
rotdim ([1, 2; 3, 4], 3, [1, 2])
rotdim ([1, 2; 3, 4], 7, [1, 2])
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drot90.html#doc_002drot90">rot90</a>, <a href="doc_002dflipud.html#doc_002dflipud">flipud</a>, <a href="doc_002dfliplr.html#doc_002dfliplr">fliplr</a>, <a href="doc_002dflipdim.html#doc_002dflipdim">flipdim</a>.
</p></blockquote></div>
<!-- data.cc -->
<p><a name="doc_002dcat"></a>
<div class="defun">
— Built-in Function: <b>cat</b> (<var>dim, array1, array2, <small class="dots">...</small>, arrayN</var>)<var><a name="index-cat-1277"></a></var><br>
<blockquote><p>Return the concatenation of N-d array objects, <var>array1</var>,
<var>array2</var>, <small class="dots">...</small>, <var>arrayN</var> along dimension <var>dim</var>.
<pre class="example"> A = ones (2, 2);
B = zeros (2, 2);
cat (2, A, B)
ans =
1 1 0 0
1 1 0 0
</pre>
<p>Alternatively, we can concatenate <var>A</var> and <var>B</var> along the
second dimension the following way:
<pre class="example"> [A, B].
</pre>
<p><var>dim</var> can be larger than the dimensions of the N-d array objects
and the result will thus have <var>dim</var> dimensions as the
following example shows:
<pre class="example"> cat (4, ones(2, 2), zeros (2, 2))
ans =
ans(:,:,1,1) =
1 1
1 1
ans(:,:,1,2) =
0 0
0 0
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dhorzcat.html#doc_002dhorzcat">horzcat</a>, <a href="doc_002dvertcat.html#doc_002dvertcat">vertcat</a>.
</p></blockquote></div>
<!-- data.cc -->
<p><a name="doc_002dhorzcat"></a>
<div class="defun">
— Built-in Function: <b>horzcat</b> (<var>array1, array2, <small class="dots">...</small>, arrayN</var>)<var><a name="index-horzcat-1278"></a></var><br>
<blockquote><p>Return the horizontal concatenation of N-d array objects, <var>array1</var>,
<var>array2</var>, <small class="dots">...</small>, <var>arrayN</var> along dimension 2.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dcat.html#doc_002dcat">cat</a>, <a href="doc_002dvertcat.html#doc_002dvertcat">vertcat</a>.
</p></blockquote></div>
<!-- data.cc -->
<p><a name="doc_002dvertcat"></a>
<div class="defun">
— Built-in Function: <b>vertcat</b> (<var>array1, array2, <small class="dots">...</small>, arrayN</var>)<var><a name="index-vertcat-1279"></a></var><br>
<blockquote><p>Return the vertical concatenation of N-d array objects, <var>array1</var>,
<var>array2</var>, <small class="dots">...</small>, <var>arrayN</var> along dimension 1.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dcat.html#doc_002dcat">cat</a>, <a href="doc_002dhorzcat.html#doc_002dhorzcat">horzcat</a>.
</p></blockquote></div>
<!-- data.cc -->
<p><a name="doc_002dpermute"></a>
<div class="defun">
— Built-in Function: <b>permute</b> (<var>a, perm</var>)<var><a name="index-permute-1280"></a></var><br>
<blockquote><p>Return the generalized transpose for an N-d array object <var>a</var>.
The permutation vector <var>perm</var> must contain the elements
<code>1:ndims(a)</code> (in any order, but each element must appear just once).
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dipermute.html#doc_002dipermute">ipermute</a>.
</p></blockquote></div>
<!-- data.cc -->
<p><a name="doc_002dipermute"></a>
<div class="defun">
— Built-in Function: <b>ipermute</b> (<var>a, iperm</var>)<var><a name="index-ipermute-1281"></a></var><br>
<blockquote><p>The inverse of the <code>permute</code> function. The expression
<pre class="example"> ipermute (permute (a, perm), perm)
</pre>
<p>returns the original array <var>a</var>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dpermute.html#doc_002dpermute">permute</a>.
</p></blockquote></div>
<!-- data.cc -->
<p><a name="doc_002dreshape"></a>
<div class="defun">
— Built-in Function: <b>reshape</b> (<var>a, m, n, <small class="dots">...</small></var>)<var><a name="index-reshape-1282"></a></var><br>
— Built-in Function: <b>reshape</b> (<var>a, size</var>)<var><a name="index-reshape-1283"></a></var><br>
<blockquote><p>Return a matrix with the given dimensions whose elements are taken
from the matrix <var>a</var>. The elements of the matrix are accessed in
column-major order (like Fortran arrays are stored).
<p>For example,
<pre class="example"> reshape ([1, 2, 3, 4], 2, 2)
1 3
2 4
</pre>
<p class="noindent">Note that the total number of elements in the original
matrix must match the total number of elements in the new matrix.
<p>A single dimension of the return matrix can be unknown and is flagged
by an empty argument.
</p></blockquote></div>
<!-- data.cc -->
<p><a name="doc_002dresize"></a>
<div class="defun">
— Built-in Function: <b>resize</b> (<var>x, m</var>)<var><a name="index-resize-1284"></a></var><br>
— Built-in Function: <b>resize</b> (<var>x, m, n</var>)<var><a name="index-resize-1285"></a></var><br>
— Built-in Function: <b>resize</b> (<var>x, m, n, <small class="dots">...</small></var>)<var><a name="index-resize-1286"></a></var><br>
<blockquote><p>Resize <var>x</var> cutting off elements as necessary.
<p>In the result, element with certain indices is equal to the corresponding
element of <var>x</var> if the indices are within the bounds of <var>x</var>;
otherwise, the element is set to zero.
<p>In other words, the statement
<pre class="example"> y = resize (x, dv);
</pre>
<p class="noindent">is equivalent to the following code:
<pre class="example"> y = zeros (dv, class (x));
sz = min (dv, size (x));
for i = 1:length (sz), idx{i} = 1:sz(i); endfor
y(idx{:}) = x(idx{:});
</pre>
<p class="noindent">but is performed more efficiently.
<p>If only <var>m</var> is supplied and it is a scalar, the dimension of the
result is <var>m</var>-by-<var>m</var>. If <var>m</var> is a vector, then the
dimensions of the result are given by the elements of <var>m</var>.
If both <var>m</var> and <var>n</var> are scalars, then the dimensions of
the result are <var>m</var>-by-<var>n</var>.
<p>An object can be resized to more dimensions than it has;
in such case the missing dimensions are assumed to be 1.
Resizing an object to fewer dimensions is not possible.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dreshape.html#doc_002dreshape">reshape</a>, <a href="doc_002dpostpad.html#doc_002dpostpad">postpad</a>.
</p></blockquote></div>
<!-- ./general/circshift.m -->
<p><a name="doc_002dcircshift"></a>
<div class="defun">
— Function File: <var>y</var> = <b>circshift</b> (<var>x, n</var>)<var><a name="index-circshift-1287"></a></var><br>
<blockquote><p>Circularly shifts the values of the array <var>x</var>. <var>n</var> must be
a vector of integers no longer than the number of dimensions in
<var>x</var>. The values of <var>n</var> can be either positive or negative,
which determines the direction in which the values or <var>x</var> are
shifted. If an element of <var>n</var> is zero, then the corresponding
dimension of <var>x</var> will not be shifted. For example
<pre class="example"> x = [1, 2, 3; 4, 5, 6; 7, 8, 9];
circshift (x, 1)
7, 8, 9
1, 2, 3
4, 5, 6
circshift (x, -2)
7, 8, 9
1, 2, 3
4, 5, 6
circshift (x, [0,1])
3, 1, 2
6, 4, 5
9, 7, 8
</pre>
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<p class="noindent"><strong>See also:</strong> permute, ipermute, shiftdim.
</p></blockquote></div>
<!-- ./general/shiftdim.m -->
<p><a name="doc_002dshiftdim"></a>
<div class="defun">
— Function File: <var>y</var> = <b>shiftdim</b> (<var>x, n</var>)<var><a name="index-shiftdim-1288"></a></var><br>
— Function File: [<var>y</var>, <var>ns</var>] = <b>shiftdim</b> (<var>x</var>)<var><a name="index-shiftdim-1289"></a></var><br>
<blockquote><p>Shifts the dimension of <var>x</var> by <var>n</var>, where <var>n</var> must be
an integer scalar. When <var>n</var> is positive, the dimensions of
<var>x</var> are shifted to the left, with the leading dimensions
circulated to the end. If <var>n</var> is negative, then the dimensions
of <var>x</var> are shifted to the right, with <var>n</var> leading singleton
dimensions added.
<p>Called with a single argument, <code>shiftdim</code>, removes the leading
singleton dimensions, returning the number of dimensions removed
in the second output argument <var>ns</var>.
<p>For example
<pre class="example"> x = ones (1, 2, 3);
size (shiftdim (x, -1))
[1, 1, 2, 3]
size (shiftdim (x, 1))
[2, 3]
[b, ns] = shiftdim (x);
b = [1, 1, 1; 1, 1, 1]
ns = 1
</pre>
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<p class="noindent"><strong>See also:</strong> reshape, permute, ipermute, circshift, squeeze.
</p></blockquote></div>
<!-- ./general/shift.m -->
<p><a name="doc_002dshift"></a>
<div class="defun">
— Function File: <b>shift</b> (<var>x, b</var>)<var><a name="index-shift-1290"></a></var><br>
— Function File: <b>shift</b> (<var>x, b, dim</var>)<var><a name="index-shift-1291"></a></var><br>
<blockquote><p>If <var>x</var> is a vector, perform a circular shift of length <var>b</var> of
the elements of <var>x</var>.
<p>If <var>x</var> is a matrix, do the same for each column of <var>x</var>.
If the optional <var>dim</var> argument is given, operate along this
dimension
</p></blockquote></div>
<!-- data.cc -->
<p><a name="doc_002dsort"></a>
<div class="defun">
— Loadable Function: [<var>s</var>, <var>i</var>] = <b>sort</b> (<var>x</var>)<var><a name="index-sort-1292"></a></var><br>
— Loadable Function: [<var>s</var>, <var>i</var>] = <b>sort</b> (<var>x, dim</var>)<var><a name="index-sort-1293"></a></var><br>
— Loadable Function: [<var>s</var>, <var>i</var>] = <b>sort</b> (<var>x, mode</var>)<var><a name="index-sort-1294"></a></var><br>
— Loadable Function: [<var>s</var>, <var>i</var>] = <b>sort</b> (<var>x, dim, mode</var>)<var><a name="index-sort-1295"></a></var><br>
<blockquote><p>Return a copy of <var>x</var> with the elements arranged in increasing
order. For matrices, <code>sort</code> orders the elements in each column.
<p>For example,
<pre class="example"> sort ([1, 2; 2, 3; 3, 1])
1 1
2 2
3 3
</pre>
<p>The <code>sort</code> function may also be used to produce a matrix
containing the original row indices of the elements in the sorted
matrix. For example,
<pre class="example"> [s, i] = sort ([1, 2; 2, 3; 3, 1])
s = 1 1
2 2
3 3
i = 1 3
2 1
3 2
</pre>
<p>If the optional argument <var>dim</var> is given, then the matrix is sorted
along the dimension defined by <var>dim</var>. The optional argument <code>mode</code>
defines the order in which the values will be sorted. Valid values of
<code>mode</code> are `ascend' or `descend'.
<p>For equal elements, the indices are such that the equal elements are listed
in the order that appeared in the original list.
<p>The <code>sort</code> function may also be used to sort strings and cell arrays
of strings, in which case the dictionary order of the strings is used.
<p>The algorithm used in <code>sort</code> is optimized for the sorting of partially
ordered lists.
</p></blockquote></div>
<!-- ./general/sortrows.m -->
<p><a name="doc_002dsortrows"></a>
<div class="defun">
— Function File: <b>sortrows</b> (<var>a, c</var>)<var><a name="index-sortrows-1296"></a></var><br>
<blockquote><p>Sort the rows of the matrix <var>a</var> according to the order of the
columns specified in <var>c</var>. If <var>c</var> is omitted, a
lexicographical sort is used. By default ascending order is used
however if elements of <var>c</var> are negative then the corresponding
column is sorted in descending order.
</p></blockquote></div>
<!-- data.cc -->
<p><a name="doc_002dissorted"></a>
<div class="defun">
— Built-in Function: <b>issorted</b> (<var>a, rows</var>)<var><a name="index-issorted-1297"></a></var><br>
<blockquote><p>Returns true if the array is sorted, ascending or descending.
NaNs are treated as by <code>sort</code>. If <var>rows</var> is supplied and
has the value "rows", checks whether the array is sorted by rows
as if output by <code>sortrows</code> (with no options).
<p>This function does not yet support sparse matrices.
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dsortrows.html#doc_002dsortrows">sortrows</a>, <a href="doc_002dsort.html#doc_002dsort">sort</a>.
</p></blockquote></div>
<p>Since the <code>sort</code> function does not allow sort keys to be specified,
it can't be used to order the rows of a matrix according to the values
of the elements in various columns<a rel="footnote" href="#fn-1" name="fnd-1"><sup>1</sup></a>
in a single call. Using the second output, however, it is possible to
sort all rows based on the values in a given column. Here's an example
that sorts the rows of a matrix based on the values in the second
column.
<pre class="example"> a = [1, 2; 2, 3; 3, 1];
[s, i] = sort (a (:, 2));
a (i, :)
3 1
1 2
2 3
</pre>
<p><a name="doc_002dtriu"></a><!-- ./general/tril.m -->
<a name="doc_002dtril"></a>
<div class="defun">
— Function File: <b>tril</b> (<var>a, k</var>)<var><a name="index-tril-1298"></a></var><br>
— Function File: <b>triu</b> (<var>a, k</var>)<var><a name="index-triu-1299"></a></var><br>
<blockquote><p>Return a new matrix formed by extracting the lower (<code>tril</code>)
or upper (<code>triu</code>) triangular part of the matrix <var>a</var>, and
setting all other elements to zero. The second argument is optional,
and specifies how many diagonals above or below the main diagonal should
also be set to zero.
<p>The default value of <var>k</var> is zero, so that <code>triu</code> and
<code>tril</code> normally include the main diagonal as part of the result
matrix.
<p>If the value of <var>k</var> is negative, additional elements above (for
<code>tril</code>) or below (for <code>triu</code>) the main diagonal are also
selected.
<p>The absolute value of <var>k</var> must not be greater than the number of
sub- or super-diagonals.
<p>For example,
<pre class="example"> tril (ones (3), -1)
0 0 0
1 0 0
1 1 0
</pre>
<p class="noindent">and
<pre class="example"> tril (ones (3), 1)
1 1 0
1 1 1
1 1 1
</pre>
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<!-- A simple blank line produces the correct behavior. -->
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dtriu.html#doc_002dtriu">triu</a>, <a href="doc_002ddiag.html#doc_002ddiag">diag</a>.
</p></blockquote></div>
<!-- ./linear-algebra/vec.m -->
<p><a name="doc_002dvec"></a>
<div class="defun">
— Function File: <b>vec</b> (<var>x</var>)<var><a name="index-vec-1300"></a></var><br>
<blockquote><p>Return the vector obtained by stacking the columns of the matrix <var>x</var>
one above the other.
</p></blockquote></div>
<!-- ./linear-algebra/vech.m -->
<p><a name="doc_002dvech"></a>
<div class="defun">
— Function File: <b>vech</b> (<var>x</var>)<var><a name="index-vech-1301"></a></var><br>
<blockquote><p>Return the vector obtained by eliminating all supradiagonal elements of
the square matrix <var>x</var> and stacking the result one column above the
other.
</p></blockquote></div>
<p><a name="doc_002dpostpad"></a><!-- ./general/prepad.m -->
<a name="doc_002dprepad"></a>
<div class="defun">
— Function File: <b>prepad</b> (<var>x, l, c</var>)<var><a name="index-prepad-1302"></a></var><br>
— Function File: <b>prepad</b> (<var>x, l, c, dim</var>)<var><a name="index-prepad-1303"></a></var><br>
<blockquote><p>Prepend (append) the scalar value <var>c</var> to the vector <var>x</var>
until it is of length <var>l</var>. If the third argument is not
supplied, a value of 0 is used.
<p>If <code>length (</code><var>x</var><code>) > </code><var>l</var>, elements from the beginning (end) of
<var>x</var> are removed until a vector of length <var>l</var> is obtained.
<p>If <var>x</var> is a matrix, elements are prepended or removed from each row.
<p>If the optional <var>dim</var> argument is given, then operate along this
dimension.
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dpostpad.html#doc_002dpostpad">postpad</a>.
</p></blockquote></div>
<!-- data.cc -->
<p><a name="doc_002ddiag"></a>
<div class="defun">
— Built-in Function: <b>diag</b> (<var>v, k</var>)<var><a name="index-diag-1304"></a></var><br>
<blockquote><p>Return a diagonal matrix with vector <var>v</var> on diagonal <var>k</var>. The
second argument is optional. If it is positive, the vector is placed on
the <var>k</var>-th super-diagonal. If it is negative, it is placed on the
<var>-k</var>-th sub-diagonal. The default value of <var>k</var> is 0, and the
vector is placed on the main diagonal. For example,
<pre class="example"> diag ([1, 2, 3], 1)
0 1 0 0
0 0 2 0
0 0 0 3
0 0 0 0
</pre>
<p class="noindent">Given a matrix argument, instead of a vector, <code>diag</code> extracts the
<var>k</var>-th diagonal of the matrix.
</p></blockquote></div>
<!-- ./general/blkdiag.m -->
<p><a name="doc_002dblkdiag"></a>
<div class="defun">
— Function File: <b>blkdiag</b> (<var>a, b, c, <small class="dots">...</small></var>)<var><a name="index-blkdiag-1305"></a></var><br>
<blockquote><p>Build a block diagonal matrix from <var>a</var>, <var>b</var>, <var>c</var>, <small class="dots">...</small>.
All the arguments must be numeric and are two-dimensional matrices or
scalars.
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002ddiag.html#doc_002ddiag">diag</a>, <a href="doc_002dhorzcat.html#doc_002dhorzcat">horzcat</a>, <a href="doc_002dvertcat.html#doc_002dvertcat">vertcat</a>.
</p></blockquote></div>
<div class="footnote">
<hr>
<h4>Footnotes</h4><p class="footnote"><small>[<a name="fn-1" href="#fnd-1">1</a>]</small> For example, to first sort
based on the values in column 1, and then, for any values that are
repeated in column 1, sort based on the values found in column 2, etc.</p>
<hr></div>
</body></html>
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