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<a name="Index-Expressions-1"></a>
<h3 class="section">8.1 Index Expressions</h3>

<a name="index-_0028"></a>
<a name="index-_0029"></a>
<a name="index-_003a-1"></a>

<p>An <em>index expression</em> allows you to reference or extract selected
elements of a matrix or vector.
</p>
<p>Indices may be scalars, vectors, ranges, or the special operator
&lsquo;<samp>:</samp>&rsquo;, which may be used to select entire rows or columns.
</p>
<p>Vectors are indexed using a single index expression.  Matrices (2-D)
and higher multi-dimensional arrays are indexed using either one index
or <em>N</em> indices where <em>N</em> is the dimension of the array.
When using a single index expression to index 2-D or higher data the
elements of the array are taken in column-first order (like Fortran).
</p>
<p>The output from indexing assumes the dimensions of the index
expression.  For example:
</p>
<div class="example">
<pre class="example">a(2)       # result is a scalar
a(1:2)     # result is a row vector
a([1; 2])  # result is a column vector
</pre></div>

<p>As a special case, when a colon is used as a single index, the output
is a column vector containing all the elements of the vector or
matrix.  For example:
</p>
<div class="example">
<pre class="example">a(:)       # result is a column vector
a(:)'      # result is a row vector
</pre></div>

<p>The above two code idioms are often used in place of <code>reshape</code>
when a simple vector, rather than an arbitrarily sized array, is
needed.
</p>
<p>Given the matrix
</p>
<div class="example">
<pre class="example">a = [1, 2; 3, 4]
</pre></div>

<p>all of the following expressions are equivalent and select the first
row of the matrix.
</p>
<div class="example">
<pre class="example">a(1, [1, 2])  # row 1, columns 1 and 2
a(1, 1:2)     # row 1, columns in range 1-2
a(1, :)       # row 1, all columns
</pre></div>

<a name="index-end_002c-indexing"></a>
<a name="index-_003aend"></a>

<p>In index expressions the keyword <code>end</code> automatically refers to
the last entry for a particular dimension.  This magic index can also
be used in ranges and typically eliminates the needs to call
<code>size</code> or <code>length</code> to gather array bounds before indexing.
For example:
</p>
<div class="example">
<pre class="example">a = [1, 2, 3, 4];

a(1:end/2)        # first half of a =&gt; [1, 2]
a(end + 1) = 5;   # append element 
a(end) = [];      # delete element 
a(1:2:end)        # odd elements of a =&gt; [1, 3]
a(2:2:end)        # even elements of a =&gt; [2, 4]
a(end:-1:1)       # reversal of a =&gt; [4, 3, 2 , 1]
</pre></div>

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