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<h3 class="section">17.4 Sums and Products</h3>
<!-- sum src/data.cc -->
<p><a name="doc_002dsum"></a>
<div class="defun">
— Built-in Function: <b>sum</b> (<var>x</var>)<var><a name="index-sum-1837"></a></var><br>
— Built-in Function: <b>sum</b> (<var>x, dim</var>)<var><a name="index-sum-1838"></a></var><br>
— Built-in Function: <b>sum</b> (<var><small class="dots">...</small>, 'native'</var>)<var><a name="index-sum-1839"></a></var><br>
— Built-in Function: <b>sum</b> (<var><small class="dots">...</small>, 'double'</var>)<var><a name="index-sum-1840"></a></var><br>
— Built-in Function: <b>sum</b> (<var><small class="dots">...</small>, 'extra'</var>)<var><a name="index-sum-1841"></a></var><br>
<blockquote><p>Sum of elements along dimension <var>dim</var>. If <var>dim</var> is
omitted, it defaults to the first non-singleton dimension.
<p>If the optional argument 'native' is given, then the sum is performed
in the same type as the original argument, rather than in the default
double type. For example:
<pre class="example"> sum ([true, true])
⇒ 2
sum ([true, true], 'native')
⇒ true
</pre>
<p>On the contrary, if 'double' is given, the sum is performed in double
precision even for single precision inputs.
<p>For double precision inputs, 'extra' indicates that a more accurate algorithm
than straightforward summation is to be used. For single precision inputs,
'extra' is the same as 'double'. Otherwise, 'extra' has no effect.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dcumsum.html#doc_002dcumsum">cumsum</a>, <a href="doc_002dsumsq.html#doc_002dsumsq">sumsq</a>, <a href="doc_002dprod.html#doc_002dprod">prod</a>.
</p></blockquote></div>
<!-- prod src/data.cc -->
<p><a name="doc_002dprod"></a>
<div class="defun">
— Built-in Function: <b>prod</b> (<var>x</var>)<var><a name="index-prod-1842"></a></var><br>
— Built-in Function: <b>prod</b> (<var>x, dim</var>)<var><a name="index-prod-1843"></a></var><br>
<blockquote><p>Product of elements along dimension <var>dim</var>. If <var>dim</var> is
omitted, it defaults to the first non-singleton dimension.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dcumprod.html#doc_002dcumprod">cumprod</a>, <a href="doc_002dsum.html#doc_002dsum">sum</a>.
</p></blockquote></div>
<!-- cumsum src/data.cc -->
<p><a name="doc_002dcumsum"></a>
<div class="defun">
— Built-in Function: <b>cumsum</b> (<var>x</var>)<var><a name="index-cumsum-1844"></a></var><br>
— Built-in Function: <b>cumsum</b> (<var>x, dim</var>)<var><a name="index-cumsum-1845"></a></var><br>
— Built-in Function: <b>cumsum</b> (<var><small class="dots">...</small>, 'native'</var>)<var><a name="index-cumsum-1846"></a></var><br>
— Built-in Function: <b>cumsum</b> (<var><small class="dots">...</small>, 'double'</var>)<var><a name="index-cumsum-1847"></a></var><br>
— Built-in Function: <b>cumsum</b> (<var><small class="dots">...</small>, 'extra'</var>)<var><a name="index-cumsum-1848"></a></var><br>
<blockquote><p>Cumulative sum of elements along dimension <var>dim</var>. If <var>dim</var>
is omitted, it defaults to the first non-singleton dimension.
<p>See <code>sum</code> for an explanation of the optional parameters 'native',
'double', and 'extra'.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dsum.html#doc_002dsum">sum</a>, <a href="doc_002dcumprod.html#doc_002dcumprod">cumprod</a>.
</p></blockquote></div>
<!-- cumprod src/data.cc -->
<p><a name="doc_002dcumprod"></a>
<div class="defun">
— Built-in Function: <b>cumprod</b> (<var>x</var>)<var><a name="index-cumprod-1849"></a></var><br>
— Built-in Function: <b>cumprod</b> (<var>x, dim</var>)<var><a name="index-cumprod-1850"></a></var><br>
<blockquote><p>Cumulative product of elements along dimension <var>dim</var>. If
<var>dim</var> is omitted, it defaults to the first non-singleton dimension.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dprod.html#doc_002dprod">prod</a>, <a href="doc_002dcumsum.html#doc_002dcumsum">cumsum</a>.
</p></blockquote></div>
<!-- sumsq src/data.cc -->
<p><a name="doc_002dsumsq"></a>
<div class="defun">
— Built-in Function: <b>sumsq</b> (<var>x</var>)<var><a name="index-sumsq-1851"></a></var><br>
— Built-in Function: <b>sumsq</b> (<var>x, dim</var>)<var><a name="index-sumsq-1852"></a></var><br>
<blockquote><p>Sum of squares of elements along dimension <var>dim</var>. If <var>dim</var>
is omitted, it defaults to the first non-singleton dimension.
<p>This function is conceptually equivalent to computing
<pre class="example"> sum (x .* conj (x), dim)
</pre>
<p class="noindent">but it uses less memory and avoids calling <code>conj</code> if <var>x</var> is real.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dsum.html#doc_002dsum">sum</a>.
</p></blockquote></div>
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