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<a name="Sums-and-Products"></a>
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<p>
Next: <a href="Utility-Functions.html#Utility-Functions" accesskey="n" rel="next">Utility Functions</a>, Previous: <a href="Trigonometry.html#Trigonometry" accesskey="p" rel="prev">Trigonometry</a>, Up: <a href="Arithmetic.html#Arithmetic" accesskey="u" rel="up">Arithmetic</a> [<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>
</div>
<hr>
<a name="Sums-and-Products-1"></a>
<h3 class="section">17.4 Sums and Products</h3>
<a name="XREFsum"></a><dl>
<dt><a name="index-sum"></a>Built-in Function: <em></em> <strong>sum</strong> <em>(<var>x</var>)</em></dt>
<dt><a name="index-sum-1"></a>Built-in Function: <em></em> <strong>sum</strong> <em>(<var>x</var>, <var>dim</var>)</em></dt>
<dt><a name="index-sum-2"></a>Built-in Function: <em></em> <strong>sum</strong> <em>(…, "native")</em></dt>
<dt><a name="index-sum-3"></a>Built-in Function: <em></em> <strong>sum</strong> <em>(…, "double")</em></dt>
<dt><a name="index-sum-4"></a>Built-in Function: <em></em> <strong>sum</strong> <em>(…, "extra")</em></dt>
<dd><p>Sum of elements along dimension <var>dim</var>.
</p>
<p>If <var>dim</var> is omitted, it defaults to the first non-singleton dimension.
</p>
<p>The optional <code>"type"</code> input determines the class of the variable
used for calculations. If the argument <code>"native"</code> is given, then
the operation is performed in the same type as the original argument, rather
than the default double type.
</p>
<p>For example:
</p>
<div class="example">
<pre class="example">sum ([true, true])
⇒ 2
sum ([true, true], "native")
⇒ true
</pre></div>
<p>On the contrary, if <code>"double"</code> is given, the sum is performed in
double precision even for single precision inputs.
</p>
<p>For double precision inputs, the <code>"extra"</code> option will use a more
accurate algorithm than straightforward summation. For single precision
inputs, <code>"extra"</code> is the same as <code>"double"</code>. Otherwise,
<code>"extra"</code> has no effect.
</p>
<p><strong>See also:</strong> <a href="#XREFcumsum">cumsum</a>, <a href="#XREFsumsq">sumsq</a>, <a href="#XREFprod">prod</a>.
</p></dd></dl>
<a name="XREFprod"></a><dl>
<dt><a name="index-prod"></a>Built-in Function: <em></em> <strong>prod</strong> <em>(<var>x</var>)</em></dt>
<dt><a name="index-prod-1"></a>Built-in Function: <em></em> <strong>prod</strong> <em>(<var>x</var>, <var>dim</var>)</em></dt>
<dt><a name="index-prod-2"></a>Built-in Function: <em></em> <strong>prod</strong> <em>(…, "native")</em></dt>
<dt><a name="index-prod-3"></a>Built-in Function: <em></em> <strong>prod</strong> <em>(…, "double")</em></dt>
<dd><p>Product of elements along dimension <var>dim</var>.
</p>
<p>If <var>dim</var> is omitted, it defaults to the first non-singleton dimension.
</p>
<p>The optional <code>"type"</code> input determines the class of the variable
used for calculations. If the argument <code>"native"</code> is given, then
the operation is performed in the same type as the original argument, rather
than the default double type.
</p>
<p>For example:
</p>
<div class="example">
<pre class="example">prod ([true, true])
⇒ 1
prod ([true, true], "native")
⇒ true
</pre></div>
<p>On the contrary, if <code>"double"</code> is given, the operation is performed
in double precision even for single precision inputs.
</p>
<p><strong>See also:</strong> <a href="#XREFcumprod">cumprod</a>, <a href="#XREFsum">sum</a>.
</p></dd></dl>
<a name="XREFcumsum"></a><dl>
<dt><a name="index-cumsum"></a>Built-in Function: <em></em> <strong>cumsum</strong> <em>(<var>x</var>)</em></dt>
<dt><a name="index-cumsum-1"></a>Built-in Function: <em></em> <strong>cumsum</strong> <em>(<var>x</var>, <var>dim</var>)</em></dt>
<dt><a name="index-cumsum-2"></a>Built-in Function: <em></em> <strong>cumsum</strong> <em>(…, "native")</em></dt>
<dt><a name="index-cumsum-3"></a>Built-in Function: <em></em> <strong>cumsum</strong> <em>(…, "double")</em></dt>
<dt><a name="index-cumsum-4"></a>Built-in Function: <em></em> <strong>cumsum</strong> <em>(…, "extra")</em></dt>
<dd><p>Cumulative sum of elements along dimension <var>dim</var>.
</p>
<p>If <var>dim</var> is omitted, it defaults to the first non-singleton dimension.
</p>
<p>See <code>sum</code> for an explanation of the optional parameters
<code>"native"</code>, <code>"double"</code>, and <code>"extra"</code>.
</p>
<p><strong>See also:</strong> <a href="#XREFsum">sum</a>, <a href="#XREFcumprod">cumprod</a>.
</p></dd></dl>
<a name="XREFcumprod"></a><dl>
<dt><a name="index-cumprod"></a>Built-in Function: <em></em> <strong>cumprod</strong> <em>(<var>x</var>)</em></dt>
<dt><a name="index-cumprod-1"></a>Built-in Function: <em></em> <strong>cumprod</strong> <em>(<var>x</var>, <var>dim</var>)</em></dt>
<dd><p>Cumulative product of elements along dimension <var>dim</var>.
</p>
<p>If <var>dim</var> is omitted, it defaults to the first non-singleton dimension.
</p>
<p><strong>See also:</strong> <a href="#XREFprod">prod</a>, <a href="#XREFcumsum">cumsum</a>.
</p></dd></dl>
<a name="XREFsumsq"></a><dl>
<dt><a name="index-sumsq"></a>Built-in Function: <em></em> <strong>sumsq</strong> <em>(<var>x</var>)</em></dt>
<dt><a name="index-sumsq-1"></a>Built-in Function: <em></em> <strong>sumsq</strong> <em>(<var>x</var>, <var>dim</var>)</em></dt>
<dd><p>Sum of squares of elements along dimension <var>dim</var>.
</p>
<p>If <var>dim</var> is omitted, it defaults to the first non-singleton dimension.
</p>
<p>This function is conceptually equivalent to computing
</p>
<div class="example">
<pre class="example">sum (x .* conj (x), dim)
</pre></div>
<p>but it uses less memory and avoids calling <code>conj</code> if <var>x</var> is real.
</p>
<p><strong>See also:</strong> <a href="#XREFsum">sum</a>, <a href="#XREFprod">prod</a>.
</p></dd></dl>
<hr>
<div class="header">
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Next: <a href="Utility-Functions.html#Utility-Functions" accesskey="n" rel="next">Utility Functions</a>, Previous: <a href="Trigonometry.html#Trigonometry" accesskey="p" rel="prev">Trigonometry</a>, Up: <a href="Arithmetic.html#Arithmetic" accesskey="u" rel="up">Arithmetic</a> [<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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