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<h3 class="section">17.4 Sums and Products</h3>
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<p><a name="doc_002dsum"></a>
<div class="defun">
— Built-in Function: <b>sum</b> (<var>x</var>)<var><a name="index-sum-1422"></a></var><br>
— Built-in Function: <b>sum</b> (<var>x, dim</var>)<var><a name="index-sum-1423"></a></var><br>
— Built-in Function: <b>sum</b> (<var><small class="dots">...</small>, 'native'</var>)<var><a name="index-sum-1424"></a></var><br>
<blockquote><p>Sum of elements along dimension <var>dim</var>. If <var>dim</var> is
omitted, it defaults to 1 (column-wise sum).
<p>As a special case, if <var>x</var> is a vector and <var>dim</var> is omitted,
return the sum of the elements.
<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>
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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>
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<p><a name="doc_002dprod"></a>
<div class="defun">
— Built-in Function: <b>prod</b> (<var>x</var>)<var><a name="index-prod-1425"></a></var><br>
— Built-in Function: <b>prod</b> (<var>x, dim</var>)<var><a name="index-prod-1426"></a></var><br>
<blockquote><p>Product of elements along dimension <var>dim</var>. If <var>dim</var> is
omitted, it defaults to 1 (column-wise products).
<p>As a special case, if <var>x</var> is a vector and <var>dim</var> is omitted,
return the product of the elements.
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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>
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<p><a name="doc_002dcumsum"></a>
<div class="defun">
— Built-in Function: <b>cumsum</b> (<var>x</var>)<var><a name="index-cumsum-1427"></a></var><br>
— Built-in Function: <b>cumsum</b> (<var>x, dim</var>)<var><a name="index-cumsum-1428"></a></var><br>
— Built-in Function: <b>cumsum</b> (<var><small class="dots">...</small>, 'native'</var>)<var><a name="index-cumsum-1429"></a></var><br>
<blockquote><p>Cumulative sum of elements along dimension <var>dim</var>. If <var>dim</var>
is omitted, it defaults to 1 (column-wise cumulative sums).
<p>As a special case, if <var>x</var> is a vector and <var>dim</var> is omitted,
return the cumulative sum of the elements as a vector with the
same orientation as <var>x</var>.
<p>The "native" argument implies the summation is performed in native type.
See <code>sum</code> for a complete description and example of the use of
"native".
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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>
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<p><a name="doc_002dcumprod"></a>
<div class="defun">
— Built-in Function: <b>cumprod</b> (<var>x</var>)<var><a name="index-cumprod-1430"></a></var><br>
— Built-in Function: <b>cumprod</b> (<var>x, dim</var>)<var><a name="index-cumprod-1431"></a></var><br>
<blockquote><p>Cumulative product of elements along dimension <var>dim</var>. If
<var>dim</var> is omitted, it defaults to 1 (column-wise cumulative
products).
<p>As a special case, if <var>x</var> is a vector and <var>dim</var> is omitted,
return the cumulative product of the elements as a vector with the
same orientation as <var>x</var>.
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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>
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<p><a name="doc_002dsumsq"></a>
<div class="defun">
— Built-in Function: <b>sumsq</b> (<var>x</var>)<var><a name="index-sumsq-1432"></a></var><br>
— Built-in Function: <b>sumsq</b> (<var>x, dim</var>)<var><a name="index-sumsq-1433"></a></var><br>
<blockquote><p>Sum of squares of elements along dimension <var>dim</var>. If <var>dim</var>
is omitted, it defaults to 1 (column-wise sum of squares).
<p>As a special case, if <var>x</var> is a vector and <var>dim</var> is omitted,
return the sum of squares of the elements.
<p>This function is conceptually equivalent to computing
<pre class="example"> sum (x .* conj (x), dim)
</pre>
<p>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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<p><a name="doc_002daccumarray"></a>
<div class="defun">
— Function File: <b>accumarray</b> (<var>subs, vals, sz, func, fillval, issparse</var>)<var><a name="index-accumarray-1434"></a></var><br>
— Function File: <b>accumarray</b> (<var>csubs, vals, <small class="dots">...</small></var>)<var><a name="index-accumarray-1435"></a></var><br>
<blockquote>
<p>Create an array by accumulating the elements of a vector into the
positions defined by their subscripts. The subscripts are defined by
the rows of the matrix <var>subs</var> and the values by <var>vals</var>. Each row
of <var>subs</var> corresponds to one of the values in <var>vals</var>.
<p>The size of the matrix will be determined by the subscripts themselves.
However, if <var>sz</var> is defined it determines the matrix size. The length
of <var>sz</var> must correspond to the number of columns in <var>subs</var>.
<p>The default action of <code>accumarray</code> is to sum the elements with the
same subscripts. This behavior can be modified by defining the <var>func</var>
function. This should be a function or function handle that accepts a
column vector and returns a scalar. The result of the function should not
depend on the order of the subscripts.
<p>The elements of the returned array that have no subscripts associated with
them are set to zero. Defining <var>fillval</var> to some other value allows
these values to be defined.
<p>By default <code>accumarray</code> returns a full matrix. If <var>issparse</var> is
logically true, then a sparse matrix is returned instead.
<p>An example of the use of <code>accumarray</code> is:
<pre class="example"> accumarray ([1,1,1;2,1,2;2,3,2;2,1,2;2,3,2], 101:105)
⇒ ans(:,:,1) = [101, 0, 0; 0, 0, 0]
ans(:,:,2) = [0, 0, 0; 206, 0, 208]
</pre>
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