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<a name="Function-Application"></a>
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<hr>
<a name="Function-Application-1"></a>
<h3 class="section">19.3 Function Application</h3>
<a name="index-map"></a>
<a name="index-apply"></a>
<a name="index-function-application"></a>

<p>As a general rule, functions should already be written with matrix
arguments in mind and should consider whole matrix operations in a
vectorized manner.  Sometimes, writing functions in this way appears
difficult or impossible for various reasons.  For those situations,
Octave provides facilities for applying a function to each element of an
array, cell, or struct.
</p>
<a name="XREFarrayfun"></a><dl>
<dt><a name="index-arrayfun"></a>: <em></em> <strong>arrayfun</strong> <em>(<var>func</var>, <var>A</var>)</em></dt>
<dt><a name="index-arrayfun-1"></a>: <em><var>x</var> =</em> <strong>arrayfun</strong> <em>(<var>func</var>, <var>A</var>)</em></dt>
<dt><a name="index-arrayfun-2"></a>: <em><var>x</var> =</em> <strong>arrayfun</strong> <em>(<var>func</var>, <var>A</var>, <var>b</var>, &hellip;)</em></dt>
<dt><a name="index-arrayfun-3"></a>: <em>[<var>x</var>, <var>y</var>, &hellip;] =</em> <strong>arrayfun</strong> <em>(<var>func</var>, <var>A</var>, &hellip;)</em></dt>
<dt><a name="index-arrayfun-4"></a>: <em></em> <strong>arrayfun</strong> <em>(&hellip;, &quot;UniformOutput&quot;, <var>val</var>)</em></dt>
<dt><a name="index-arrayfun-5"></a>: <em></em> <strong>arrayfun</strong> <em>(&hellip;, &quot;ErrorHandler&quot;, <var>errfunc</var>)</em></dt>
<dd>
<p>Execute a function on each element of an array.
</p>
<p>This is useful for functions that do not accept array arguments.  If the
function does accept array arguments it is better to call the function
directly.
</p>
<p>The first input argument <var>func</var> can be a string, a function
handle, an inline function, or an anonymous function.  The input
argument <var>A</var> can be a logic array, a numeric array, a string
array, a structure array, or a cell array.  By a call of the function
<code>arrayfun</code> all elements of <var>A</var> are passed on to the named
function <var>func</var> individually.
</p>
<p>The named function can also take more than two input arguments, with
the input arguments given as third input argument <var>b</var>, fourth
input argument <var>c</var>, &hellip;  If given more than one array input
argument then all input arguments must have the same sizes, for
example:
</p>
<div class="example">
<pre class="example">arrayfun (@atan2, [1, 0], [0, 1])
     &rArr; [ 1.57080   0.00000 ]
</pre></div>

<p>If the parameter <var>val</var> after a further string input argument
<code>&quot;UniformOutput&quot;</code> is set <code>true</code> (the default), then the named
function <var>func</var> must return a single element which then will be
concatenated into the return value and is of type matrix.  Otherwise,
if that parameter is set to <code>false</code>, then the outputs are
concatenated in a cell array.  For example:
</p>
<div class="example">
<pre class="example">arrayfun (@(x,y) x:y, &quot;abc&quot;, &quot;def&quot;, &quot;UniformOutput&quot;, false)
&rArr;
   {
     [1,1] = abcd
     [1,2] = bcde
     [1,3] = cdef
   }
</pre></div>

<p>If more than one output arguments are given then the named function
must return the number of return values that also are expected, for
example:
</p>
<div class="example">
<pre class="example">[A, B, C] = arrayfun (@find, [10; 0], &quot;UniformOutput&quot;, false)
&rArr;
A =
{
   [1,1] =  1
   [2,1] = [](0x0)
}
B =
{
   [1,1] =  1
   [2,1] = [](0x0)
}
C =
{
   [1,1] =  10
   [2,1] = [](0x0)
}
</pre></div>

<p>If the parameter <var>errfunc</var> after a further string input argument
<code>&quot;ErrorHandler&quot;</code> is another string, a function handle, an inline
function, or an anonymous function, then <var>errfunc</var> defines a
function to call in the case that <var>func</var> generates an error.
The definition of the function must be of the form
</p>
<div class="example">
<pre class="example">function [&hellip;] = errfunc (<var>s</var>, &hellip;)
</pre></div>

<p>where there is an additional input argument to <var>errfunc</var>
relative to <var>func</var>, given by <var>s</var>.  This is a structure with
the elements <code>&quot;identifier&quot;</code>, <code>&quot;message&quot;</code>, and
<code>&quot;index&quot;</code> giving, respectively, the error identifier, the error
message, and the index of the array elements that caused the error.  The
size of the output argument of <var>errfunc</var> must have the same size as the
output argument of <var>func</var>, otherwise a real error is thrown.  For
example:
</p>
<div class="example">
<pre class="example">function y = ferr (s, x), y = &quot;MyString&quot;; endfunction
arrayfun (@str2num, [1234],
          &quot;UniformOutput&quot;, false, &quot;ErrorHandler&quot;, @ferr)
&rArr;
   {
     [1,1] = MyString
   }
</pre></div>


<p><strong>See also:</strong> <a href="#XREFspfun">spfun</a>, <a href="#XREFcellfun">cellfun</a>, <a href="#XREFstructfun">structfun</a>.
</p></dd></dl>


<a name="XREFspfun"></a><dl>
<dt><a name="index-spfun"></a>: <em><var>y</var> =</em> <strong>spfun</strong> <em>(<var>f</var>, <var>S</var>)</em></dt>
<dd><p>Compute <code>f(<var>S</var>)</code> for the nonzero values of <var>S</var>.
</p>
<p>This results in a sparse matrix with the same structure as <var>S</var>.  The
function <var>f</var> can be passed as a string, a function handle, or an
inline function.
</p>
<p><strong>See also:</strong> <a href="#XREFarrayfun">arrayfun</a>, <a href="#XREFcellfun">cellfun</a>, <a href="#XREFstructfun">structfun</a>.
</p></dd></dl>


<a name="XREFcellfun"></a><dl>
<dt><a name="index-cellfun"></a>: <em></em> <strong>cellfun</strong> <em>(<var>name</var>, <var>C</var>)</em></dt>
<dt><a name="index-cellfun-1"></a>: <em></em> <strong>cellfun</strong> <em>(&quot;size&quot;, <var>C</var>, <var>k</var>)</em></dt>
<dt><a name="index-cellfun-2"></a>: <em></em> <strong>cellfun</strong> <em>(&quot;isclass&quot;, <var>C</var>, <var>class</var>)</em></dt>
<dt><a name="index-cellfun-3"></a>: <em></em> <strong>cellfun</strong> <em>(<var>func</var>, <var>C</var>)</em></dt>
<dt><a name="index-cellfun-4"></a>: <em></em> <strong>cellfun</strong> <em>(<var>func</var>, <var>C</var>, <var>D</var>)</em></dt>
<dt><a name="index-cellfun-5"></a>: <em>[<var>a</var>, &hellip;] =</em> <strong>cellfun</strong> <em>(&hellip;)</em></dt>
<dt><a name="index-cellfun-6"></a>: <em></em> <strong>cellfun</strong> <em>(&hellip;, &quot;ErrorHandler&quot;, <var>errfunc</var>)</em></dt>
<dt><a name="index-cellfun-7"></a>: <em></em> <strong>cellfun</strong> <em>(&hellip;, &quot;UniformOutput&quot;, <var>val</var>)</em></dt>
<dd>
<p>Evaluate the function named <var>name</var> on the elements of the cell array
<var>C</var>.
</p>
<p>Elements in <var>C</var> are passed on to the named function individually.  The
function <var>name</var> can be one of the functions
</p>
<dl compact="compact">
<dt><code>isempty</code></dt>
<dd><p>Return 1 for empty elements.
</p>
</dd>
<dt><code>islogical</code></dt>
<dd><p>Return 1 for logical elements.
</p>
</dd>
<dt><code>isnumeric</code></dt>
<dd><p>Return 1 for numeric elements.
</p>
</dd>
<dt><code>isreal</code></dt>
<dd><p>Return 1 for real elements.
</p>
</dd>
<dt><code>length</code></dt>
<dd><p>Return a vector of the lengths of cell elements.
</p>
</dd>
<dt><code>ndims</code></dt>
<dd><p>Return the number of dimensions of each element.
</p>
</dd>
<dt><code>numel</code></dt>
<dt><code>prodofsize</code></dt>
<dd><p>Return the number of elements contained within each cell element.  The
number is the product of the dimensions of the object at each cell element.
</p>
</dd>
<dt><code>size</code></dt>
<dd><p>Return the size along the <var>k</var>-th dimension.
</p>
</dd>
<dt><code>isclass</code></dt>
<dd><p>Return 1 for elements of <var>class</var>.
</p></dd>
</dl>

<p>Additionally, <code>cellfun</code> accepts an arbitrary function <var>func</var>
in the form of an inline function, function handle, or the name of a
function (in a character string).  The function can take one or more
arguments, with the inputs arguments given by <var>C</var>, <var>D</var>, etc.
Equally the function can return one or more output arguments.  For example:
</p>
<div class="example">
<pre class="example">cellfun (&quot;atan2&quot;, {1, 0}, {0, 1})
     &rArr; [ 1.57080   0.00000 ]
</pre></div>

<p>The number of output arguments of <code>cellfun</code> matches the number of
output arguments of the function.  The outputs of the function will be
collected into the output arguments of <code>cellfun</code> like this:
</p>
<div class="example">
<pre class="example">function [a, b] = twoouts (x)
  a = x;
  b = x*x;
endfunction
[aa, bb] = cellfun (@twoouts, {1, 2, 3})
     &rArr;
        aa =
           1 2 3
        bb =
           1 4 9
</pre></div>

<p>Note that per default the output argument(s) are arrays of the same size as
the input arguments.  Input arguments that are singleton (1x1) cells will be
automatically expanded to the size of the other arguments.
</p>
<p>If the parameter <code>&quot;UniformOutput&quot;</code> is set to true (the default),
then the function must return scalars which will be concatenated into the
return array(s).  If <code>&quot;UniformOutput&quot;</code> is false, the outputs are
concatenated into a cell array (or cell arrays).  For example:
</p>
<div class="example">
<pre class="example">cellfun (&quot;tolower&quot;, {&quot;Foo&quot;, &quot;Bar&quot;, &quot;FooBar&quot;},
         &quot;UniformOutput&quot;, false)
&rArr; {&quot;foo&quot;, &quot;bar&quot;, &quot;foobar&quot;}
</pre></div>

<p>Given the parameter <code>&quot;ErrorHandler&quot;</code>, then <var>errfunc</var> defines a
function to call in case <var>func</var> generates an error.  The form of the
function is
</p>
<div class="example">
<pre class="example">function [&hellip;] = errfunc (<var>s</var>, &hellip;)
</pre></div>

<p>where there is an additional input argument to <var>errfunc</var> relative to
<var>func</var>, given by <var>s</var>.  This is a structure with the elements
<code>&quot;identifier&quot;</code>, <code>&quot;message&quot;</code>, and <code>&quot;index&quot;</code> giving
respectively the error identifier, the error message, and the index into the
input arguments of the element that caused the error.  For example:
</p>
<div class="example">
<pre class="example">function y = foo (s, x), y = NaN; endfunction
cellfun (&quot;factorial&quot;, {-1,2}, &quot;ErrorHandler&quot;, @foo)
&rArr; [NaN 2]
</pre></div>

<p>Use <code>cellfun</code> intelligently.  The <code>cellfun</code> function is a
useful tool for avoiding loops.  It is often used with anonymous
function handles; however, calling an anonymous function involves an
overhead quite comparable to the overhead of an m-file function.
Passing a handle to a built-in function is faster, because the
interpreter is not involved in the internal loop.  For example:
</p>
<div class="example">
<pre class="example">a = {&hellip;}
v = cellfun (@(x) det (x), a); # compute determinants
v = cellfun (@det, a); # faster
</pre></div>


<p><strong>See also:</strong> <a href="#XREFarrayfun">arrayfun</a>, <a href="#XREFstructfun">structfun</a>, <a href="#XREFspfun">spfun</a>.
</p></dd></dl>


<a name="XREFstructfun"></a><dl>
<dt><a name="index-structfun"></a>: <em></em> <strong>structfun</strong> <em>(<var>func</var>, <var>S</var>)</em></dt>
<dt><a name="index-structfun-1"></a>: <em>[<var>A</var>, &hellip;] =</em> <strong>structfun</strong> <em>(&hellip;)</em></dt>
<dt><a name="index-structfun-2"></a>: <em></em> <strong>structfun</strong> <em>(&hellip;, &quot;ErrorHandler&quot;, <var>errfunc</var>)</em></dt>
<dt><a name="index-structfun-3"></a>: <em></em> <strong>structfun</strong> <em>(&hellip;, &quot;UniformOutput&quot;, <var>val</var>)</em></dt>
<dd>
<p>Evaluate the function named <var>name</var> on the fields of the structure
<var>S</var>.  The fields of <var>S</var> are passed to the function <var>func</var>
individually.
</p>
<p><code>structfun</code> accepts an arbitrary function <var>func</var> in the form of an
inline function, function handle, or the name of a function (in a character
string).  In the case of a character string argument, the function must
accept a single argument named <var>x</var>, and it must return a string value.
If the function returns more than one argument, they are returned as
separate output variables.
</p>
<p>If the parameter <code>&quot;UniformOutput&quot;</code> is set to true (the default), then
the function must return a single element which will be concatenated into
the return value.  If <code>&quot;UniformOutput&quot;</code> is false, the outputs are
placed into a structure with the same fieldnames as the input structure.
</p>
<div class="example">
<pre class="example">s.name1 = &quot;John Smith&quot;;
s.name2 = &quot;Jill Jones&quot;;
structfun (@(x) regexp (x, '(\w+)$', &quot;matches&quot;){1}, s,
           &quot;UniformOutput&quot;, false)
&rArr;
   {
     name1 = Smith
     name2 = Jones
   }
</pre></div>

<p>Given the parameter <code>&quot;ErrorHandler&quot;</code>, <var>errfunc</var> defines a function
to call in case <var>func</var> generates an error.  The form of the function is
</p>
<div class="example">
<pre class="example">function [&hellip;] = errfunc (<var>se</var>, &hellip;)
</pre></div>

<p>where there is an additional input argument to <var>errfunc</var> relative to
<var>func</var>, given by <var>se</var>.  This is a structure with the
elements <code>&quot;identifier&quot;</code>, <code>&quot;message&quot;</code> and <code>&quot;index&quot;</code>,
giving respectively the error identifier, the error message, and the index
into the input arguments of the element that caused the error.  For an
example on how to use an error handler, see <a href="#XREFcellfun">cellfun</a>.
</p>

<p><strong>See also:</strong> <a href="#XREFcellfun">cellfun</a>, <a href="#XREFarrayfun">arrayfun</a>, <a href="#XREFspfun">spfun</a>.
</p></dd></dl>


<p>Consistent with earlier advice, seek to use Octave built-in functions whenever
possible for the best performance.  This advice applies especially to the four
functions above.  For example, when adding two arrays together
element-by-element one could use a handle to the built-in addition function
<code>@plus</code> or define an anonymous function <code>@(x,y) x + y</code>.  But, the
anonymous function is 60% slower than the first method.
See <a href="Operator-Overloading.html#Operator-Overloading">Operator Overloading</a>, for a list of basic functions which might be used
in place of anonymous ones.
</p>
<hr>
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