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<a name="Advanced-Indexing"></a>
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Up: <a href="Index-Expressions.html#Index-Expressions" accesskey="u" rel="up">Index Expressions</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Advanced-Indexing-1"></a>
<h4 class="subsection">8.1.1 Advanced Indexing</h4>

<p>An array with &lsquo;<samp>nd</samp>&rsquo; dimensions can be indexed by a vector <var>idx</var> which
has from 1 to &lsquo;<samp>nd</samp>&rsquo; elements.  If any element of <var>idx</var> is not a
scalar then the complete set of index tuples will be generated from the
Cartesian product of the index elements.
</p>
<p>For the ordinary and most common case, the number of indices
(<code>nidx = numel (<var>idx</var>)</code>) matches the number of dimensions &lsquo;<samp>nd</samp>&rsquo;.
In this case, each element of <var>idx</var> corresponds to its respective dimension,
i.e., <code><var>idx</var>(1)</code> refers to dimension 1, <code><var>idx</var>(2)</code> refers to
dimension 2, etc.  If <code>nidx&nbsp;&lt;&nbsp;nd</code><!-- /@w -->, and every index is less than the
size of the array in the <em>i^{th}</em> dimension
(<code><var>idx</var>(i) &lt; size (<var>array</var>, i)</code>), then the index expression is
padded with <code>nd&nbsp;<span class="nolinebreak">-</span>&nbsp;nidx</code><!-- /@w --> trailing singleton dimensions.  If
<code>nidx&nbsp;&lt;&nbsp;nd</code><!-- /@w --> but one of the indices <code><var>idx</var>(i)</code> is outside the
size of the current array, then the last <code>nd&nbsp;<span class="nolinebreak">-</span>&nbsp;nidx&nbsp;+&nbsp;1</code><!-- /@w --> dimensions
are folded into a single dimension with an extent equal to the product of
extents of the original dimensions.  This is easiest to understand with an
example.  
</p>
<div class="example">
<pre class="example">A = reshape (1:8, 2, 2, 2)  # Create 3-D array
A =

ans(:,:,1) =

   1   3
   2   4

ans(:,:,2) =

   5   7
   6   8

A(2,1,2);   # Case (nidx == nd): ans = 6
A(2,1);     # Case (nidx &lt; nd), idx within array:
            # equivalent to A(2,1,1), ans = 2
A(2,4);     # Case (nidx &lt; nd), idx outside array:
            # Dimension 2 &amp; 3 folded into new dimension of size 2x2 = 4
            # Select 2nd row, 4th element of [2, 4, 6, 8], ans = 8
</pre></div>

<p>One advanced use of indexing is to create arrays filled with a single
value.  This can be done by using an index of ones on a scalar value.
The result is an object with the dimensions of the index expression
and every element equal to the original scalar.  For example, the
following statements
</p>
<div class="example">
<pre class="example">a = 13;
a(ones (1, 4))
</pre></div>

<p>produce a vector whose four elements are all equal to 13.
</p>
<p>Similarly, by indexing a scalar with two vectors of ones it is
possible to create a matrix.  The following statements
</p>
<div class="example">
<pre class="example">a = 13;
a(ones (1, 2), ones (1, 3))
</pre></div>

<p>create a 2x3 matrix with all elements equal to 13.
</p>
<p>The last example could also be written as
</p>
<div class="example">
<pre class="example">13(ones (2, 3))
</pre></div>

<p>It is more efficient to use indexing rather than the code construction
<code>scalar * ones (N, M, &hellip;)</code> because it avoids the unnecessary
multiplication operation.  Moreover, multiplication may not be
defined for the object to be replicated whereas indexing an array is
always defined.  The following code shows how to create a 2x3 cell
array from a base unit which is not itself a scalar.
</p>
<div class="example">
<pre class="example">{&quot;Hello&quot;}(ones (2, 3))
</pre></div>

<p>It should be, noted that <code>ones (1, n)</code> (a row vector of ones)
results in a range (with zero increment).  A range is stored
internally as a starting value, increment, end value, and total number
of values; hence, it is more efficient for storage than a vector or
matrix of ones whenever the number of elements is greater than 4.  In
particular, when &lsquo;<samp>r</samp>&rsquo; is a row vector, the expressions
</p>
<div class="example">
<pre class="example">  r(ones (1, n), :)
</pre></div>

<div class="example">
<pre class="example">  r(ones (n, 1), :)
</pre></div>

<p>will produce identical results, but the first one will be
significantly faster, at least for &lsquo;<samp>r</samp>&rsquo; and &lsquo;<samp>n</samp>&rsquo; large enough.
In the first case the index is held in compressed form as a range
which allows Octave to choose a more efficient algorithm to handle the
expression.
</p>
<p>A general recommendation, for a user unaware of these subtleties, is
to use the function <code>repmat</code> for replicating smaller arrays into
bigger ones.
</p>
<p>A second use of indexing is to speed up code.  Indexing is a fast
operation and judicious use of it can reduce the requirement for
looping over individual array elements which is a slow operation.
</p>
<p>Consider the following example which creates a 10-element row vector
<em>a</em> containing the values
a(i) = sqrt (i).
</p>
<div class="example">
<pre class="example">for i = 1:10
  a(i) = sqrt (i);
endfor
</pre></div>

<p>It is quite inefficient to create a vector using a loop like this.  In
this case, it would have been much more efficient to use the
expression
</p>
<div class="example">
<pre class="example">a = sqrt (1:10);
</pre></div>

<p>which avoids the loop entirely.
</p>
<p>In cases where a loop cannot be avoided, or a number of values must be
combined to form a larger matrix, it is generally faster to set the
size of the matrix first (pre-allocate storage), and then insert
elements using indexing commands.  For example, given a matrix
<code>a</code>,
</p>
<div class="example">
<pre class="example">[nr, nc] = size (a);
x = zeros (nr, n * nc);
for i = 1:n
  x(:,(i-1)*nc+1:i*nc) = a;
endfor
</pre></div>

<p>is considerably faster than
</p>
<div class="example">
<pre class="example">x = a;
for i = 1:n-1
  x = [x, a];
endfor
</pre></div>

<p>because Octave does not have to repeatedly resize the intermediate
result.
</p>
<a name="XREFsub2ind"></a><dl>
<dt><a name="index-sub2ind"></a>: <em><var>ind</var> =</em> <strong>sub2ind</strong> <em>(<var>dims</var>, <var>i</var>, <var>j</var>)</em></dt>
<dt><a name="index-sub2ind-1"></a>: <em><var>ind</var> =</em> <strong>sub2ind</strong> <em>(<var>dims</var>, <var>s1</var>, <var>s2</var>, &hellip;, <var>sN</var>)</em></dt>
<dd><p>Convert subscripts to linear indices.
</p>
<p>The input <var>dims</var> is a dimension vector where each element is the size of
the array in the respective dimension (see <a href="Object-Sizes.html#XREFsize">size</a>).  The remaining
inputs are scalars or vectors of subscripts to be converted.
</p>
<p>The output vector <var>ind</var> contains the converted linear indices.
</p>
<p>Background: Array elements can be specified either by a linear index which
starts at 1 and runs through the number of elements in the array, or they may
be specified with subscripts for the row, column, page, etc.  The functions
<code>ind2sub</code> and <code>sub2ind</code> interconvert between the two forms.
</p>
<p>The linear index traverses dimension 1 (rows), then dimension 2 (columns), then
dimension 3 (pages), etc. until it has numbered all of the elements.  Consider
the following 3-by-3 matrices:
</p>
<div class="example">
<pre class="example">[(1,1), (1,2), (1,3)]     [1, 4, 7]
[(2,1), (2,2), (2,3)] ==&gt; [2, 5, 8]
[(3,1), (3,2), (3,3)]     [3, 6, 9]
</pre></div>

<p>The left matrix contains the subscript tuples for each matrix element.  The
right matrix shows the linear indices for the same matrix.
</p>
<p>The following example shows how to convert the two-dimensional indices
<code>(2,1)</code> and <code>(2,3)</code> of a 3-by-3 matrix to linear indices with a
single call to <code>sub2ind</code>.
</p>
<div class="example">
<pre class="example">s1 = [2, 2];
s2 = [1, 3];
ind = sub2ind ([3, 3], s1, s2)
    &rArr; ind =  2   8
</pre></div>

<p><strong>See also:</strong> <a href="#XREFind2sub">ind2sub</a>, <a href="Object-Sizes.html#XREFsize">size</a>.
</p></dd></dl>


<a name="XREFind2sub"></a><dl>
<dt><a name="index-ind2sub"></a>: <em>[<var>s1</var>, <var>s2</var>, &hellip;, <var>sN</var>] =</em> <strong>ind2sub</strong> <em>(<var>dims</var>, <var>ind</var>)</em></dt>
<dd><p>Convert linear indices to subscripts.
</p>
<p>The input <var>dims</var> is a dimension vector where each element is the size of
the array in the respective dimension (see <a href="Object-Sizes.html#XREFsize">size</a>).  The second
input <var>ind</var> contains linear indies to be converted.
</p>
<p>The outputs <var>s1</var>, &hellip;, <var>sN</var> contain the converted subscripts.
</p>
<p>Background: Array elements can be specified either by a linear index which
starts at 1 and runs through the number of elements in the array, or they may
be specified with subscripts for the row, column, page, etc.  The functions
<code>ind2sub</code> and <code>sub2ind</code> interconvert between the two forms.
</p>
<p>The linear index traverses dimension 1 (rows), then dimension 2 (columns), then
dimension 3 (pages), etc. until it has numbered all of the elements.  Consider
the following 3-by-3 matrices:
</p>
<div class="example">
<pre class="example">[1, 4, 7]     [(1,1), (1,2), (1,3)]
[2, 5, 8] ==&gt; [(2,1), (2,2), (2,3)]
[3, 6, 9]     [(3,1), (3,2), (3,3)]
</pre></div>

<p>The left matrix contains the linear indices for each matrix element.  The right
matrix shows the subscript tuples for the same matrix.
</p>
<p>The following example shows how to convert the two-dimensional indices
<code>(2,1)</code> and <code>(2,3)</code> of a 3-by-3 matrix to linear indices with a
single call to <code>sub2ind</code>.
</p>
<p>The following example shows how to convert the linear indices <code>2</code> and
<code>8</code> in a 3-by-3 matrix into subscripts.
</p>
<div class="example">
<pre class="example">ind = [2, 8];
[r, c] = ind2sub ([3, 3], ind)
    &rArr; r =  2   2
    &rArr; c =  1   3
</pre></div>

<p>If the number of output subscripts exceeds the number of dimensions, the
exceeded dimensions are set to <code>1</code>.  On the other hand, if fewer
subscripts than dimensions are provided, the exceeding dimensions are merged
into the final requested dimension.  For clarity, consider the following
examples:
</p>
<div class="example">
<pre class="example">ind  = [2, 8];
dims = [3, 3];
## same as dims = [3, 3, 1]
[r, c, s] = ind2sub (dims, ind)
    &rArr; r =  2   2
    &rArr; c =  1   3
    &rArr; s =  1   1
## same as dims = [9]
r = ind2sub (dims, ind)
    &rArr; r =  2   8
</pre></div>

<p><strong>See also:</strong> <a href="#XREFind2sub">ind2sub</a>, <a href="Object-Sizes.html#XREFsize">size</a>.
</p></dd></dl>


<a name="XREFisindex"></a><dl>
<dt><a name="index-isindex"></a>: <em></em> <strong>isindex</strong> <em>(<var>ind</var>)</em></dt>
<dt><a name="index-isindex-1"></a>: <em></em> <strong>isindex</strong> <em>(<var>ind</var>, <var>n</var>)</em></dt>
<dd><p>Return true if <var>ind</var> is a valid index.
</p>
<p>Valid indices are either positive integers (although possibly of real data
type), or logical arrays.
</p>
<p>If present, <var>n</var> specifies the maximum extent of the dimension to be
indexed.  When possible the internal result is cached so that subsequent
indexing using <var>ind</var> will not perform the check again.
</p>
<p>Implementation Note: Strings are first converted to double values before the
checks for valid indices are made.  Unless a string contains the NULL
character &quot;\0&quot;, it will always be a valid index.
</p></dd></dl>


<a name="XREFallow_005fnoninteger_005frange_005fas_005findex"></a><dl>
<dt><a name="index-allow_005fnoninteger_005frange_005fas_005findex"></a>: <em><var>val</var> =</em> <strong>allow_noninteger_range_as_index</strong> <em>()</em></dt>
<dt><a name="index-allow_005fnoninteger_005frange_005fas_005findex-1"></a>: <em><var>old_val</var> =</em> <strong>allow_noninteger_range_as_index</strong> <em>(<var>new_val</var>)</em></dt>
<dt><a name="index-allow_005fnoninteger_005frange_005fas_005findex-2"></a>: <em></em> <strong>allow_noninteger_range_as_index</strong> <em>(<var>new_val</var>, &quot;local&quot;)</em></dt>
<dd><p>Query or set the internal variable that controls whether non-integer
ranges are allowed as indices.
</p>
<p>This might be useful for <small>MATLAB</small> compatibility; however, it is still not
entirely compatible because <small>MATLAB</small> treats the range expression
differently in different contexts.
</p>
<p>When called from inside a function with the <code>&quot;local&quot;</code> option, the
variable is changed locally for the function and any subroutines it calls.
The original variable value is restored when exiting the function.
</p></dd></dl>


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