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<h3 class="section">8.1 Index Expressions</h3>
<p><a name="index-g_t_0028-513"></a><a name="index-g_t_0029-514"></a><a name="index-g_t_003a-515"></a>
An <dfn>index expression</dfn> allows you to reference or extract selected
elements of a matrix or vector.
<p>Indices may be scalars, vectors, ranges, or the special operator
‘<samp><span class="samp">:</span></samp>’, which may be used to select entire rows or columns.
<p>Vectors are indexed using a single index expression. Matrices (2-D)
and higher multi-dimensional arrays are indexed using either one index
or N indices where N 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>The output from indexing assumes the dimensions of the index
expression. For 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>
<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:
<pre class="example"> a(:) # result is a column vector
a(:)' # result is a row vector
</pre>
<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>Given the matrix
<pre class="example"> a = [1, 2; 3, 4]
</pre>
<p class="noindent">all of the following expressions are equivalent and select the first
row of the matrix.
<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>
<p><a name="index-g_t_0040code_007bend_007d_002c-indexing-516"></a><a name="index-g_t_003aend-517"></a>
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:
<pre class="example"> a = [1, 2, 3, 4];
a(1:end/2) # first half of a => [1, 2]
a(end + 1) = 5; # append element
a(end) = []; # delete element
a(1:2:end) # odd elements of a => [1, 3]
a(2:2:end) # even elements of a => [2, 4]
a(end:-1:1) # reversal of a => [4, 3, 2 , 1]
</pre>
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