/usr/share/doc/octave/octave.html/Demonstration-Functions.html

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<p>
Previous: <a href="Test-Functions.html#Test-Functions" accesskey="p" rel="prev">Test Functions</a>, Up: <a href="Test-and-Demo-Functions.html#Test-and-Demo-Functions" accesskey="u" rel="up">Test and Demo Functions</a> &nbsp; [<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="Demonstration-Functions-1"></a>
<h3 class="section">B.2 Demonstration Functions</h3>

<a name="XREFdemo"></a><dl>
<dt><a name="index-demo"></a>: <em></em> <strong>demo</strong> <em><var>name</var></em></dt>
<dt><a name="index-demo-1"></a>: <em></em> <strong>demo</strong> <em><var>name</var> <var>n</var></em></dt>
<dt><a name="index-demo-2"></a>: <em></em> <strong>demo</strong> <em>(&quot;<var>name</var>&quot;)</em></dt>
<dt><a name="index-demo-3"></a>: <em></em> <strong>demo</strong> <em>(&quot;<var>name</var>&quot;, <var>n</var>)</em></dt>
<dd>
<p>Run example code block <var>n</var> associated with the function <var>name</var>.
</p>
<p>If <var>n</var> is not specified, all examples are run.
</p>
<p>The preferred location for example code blocks is embedded within the script
m-file immediately following the code that it exercises.  Alternatively,
the examples may be stored in a file with the same name but no extension
located on Octave&rsquo;s load path.  To separate examples from regular script
code all lines are prefixed by <code>%!</code>.  Each example must also be
introduced by the keyword <code>&quot;demo&quot;</code> flush left to the prefix with no
intervening spaces.  The remainder of the example can contain arbitrary
Octave code.  For example:
</p>
<div class="example">
<pre class="example">%!demo
%! t = 0:0.01:2*pi;
%! x = sin (t);
%! plot (t, x);
%! title (&quot;one cycle of a sine wave&quot;);
%! #-------------------------------------------------
%! # the figure window shows one cycle of a sine wave
</pre></div>

<p>Note that the code is displayed before it is executed so that a simple
comment at the end suffices for labeling what is being shown.  For plots,
labeling can also be done with <code>title</code> or <code>text</code>.  It is generally
<strong>not</strong> necessary to use <code>disp</code> or <code>printf</code> within the demo.
</p>
<p>Demos are run in a stand-alone function environment with no access to
external variables.  This means that every demo must have separate
initialization code.  Alternatively, all demos can be combined into a single
large demo with the code
</p>
<div class="example">
<pre class="example">%! input (&quot;Press &lt;enter&gt; to continue: &quot;, &quot;s&quot;);
</pre></div>

<p>between the sections, but this usage is discouraged.  Other techniques to
avoid multiple initialization blocks include using multiple plots with a new
<code>figure</code> command between each plot, or using <code>subplot</code> to put
multiple plots in the same window.
</p>
<p>Finally, because <code>demo</code> evaluates within a function context it is not
possible to define new functions within the code.  Anonymous functions make
a good substitute in most instances.  If function blocks <strong>must</strong> be
used then the code <code>eval (example (&quot;function&quot;, n))</code> will allow Octave
to see them.  This has its own problems, however, as <code>eval</code> only
evaluates one line or statement at a time.  In this case the function
declaration must be wrapped with <code>&quot;if 1 &lt;demo stuff&gt; endif&quot;</code> where
<code>&quot;if&quot;</code> is on the same line as <code>&quot;demo&quot;</code>.  For example:
</p>
<div class="example">
<pre class="example">%!demo if 1
%!  function y = f(x)
%!    y = x;
%!  endfunction
%!  f(3)
%! endif
</pre></div>


<p><strong>See also:</strong> <a href="#XREFrundemos">rundemos</a>, <a href="#XREFexample">example</a>, <a href="Test-Functions.html#XREFtest">test</a>.
</p></dd></dl>


<a name="XREFexample"></a><dl>
<dt><a name="index-example"></a>: <em></em> <strong>example</strong> <em><var>name</var></em></dt>
<dt><a name="index-example-1"></a>: <em></em> <strong>example</strong> <em><var>name</var> <var>n</var></em></dt>
<dt><a name="index-example-2"></a>: <em></em> <strong>example</strong> <em>(&quot;<var>name</var>&quot;)</em></dt>
<dt><a name="index-example-3"></a>: <em></em> <strong>example</strong> <em>(&quot;<var>name</var>&quot;, <var>n</var>)</em></dt>
<dt><a name="index-example-4"></a>: <em>[<var>s</var>, <var>idx</var>] =</em> <strong>example</strong> <em>(&hellip;)</em></dt>
<dd>
<p>Display the code for example <var>n</var> associated with the function
<var>name</var>, but do not run it.
</p>
<p>If <var>n</var> is not specified, all examples are displayed.
</p>
<p>When called with output arguments, the examples are returned in the form of
a string <var>s</var>, with <var>idx</var> indicating the ending position of the
various examples.
</p>
<p>See <code>demo</code> for a complete explanation.
</p>
<p><strong>See also:</strong> <a href="#XREFdemo">demo</a>, <a href="Test-Functions.html#XREFtest">test</a>.
</p></dd></dl>


<a name="XREFrundemos"></a><dl>
<dt><a name="index-rundemos"></a>: <em></em> <strong>rundemos</strong> <em>()</em></dt>
<dt><a name="index-rundemos-1"></a>: <em></em> <strong>rundemos</strong> <em>(<var>directory</var>)</em></dt>
<dd><p>Execute built-in demos for all m-files in the specified <var>directory</var>.
</p>
<p>Demo blocks in any C++ source files (<samp>*.cc</samp>) will also be executed
for use with dynamically linked oct-file functions.
</p>
<p>If no directory is specified, operate on all directories in Octave&rsquo;s search
path for functions.
</p>
<p><strong>See also:</strong> <a href="#XREFdemo">demo</a>, <a href="#XREFruntests">runtests</a>, <a href="Manipulating-the-Load-Path.html#XREFpath">path</a>.
</p></dd></dl>


<a name="XREFruntests"></a><dl>
<dt><a name="index-runtests"></a>: <em></em> <strong>runtests</strong> <em>()</em></dt>
<dt><a name="index-runtests-1"></a>: <em></em> <strong>runtests</strong> <em>(<var>directory</var>)</em></dt>
<dd><p>Execute built-in tests for all m-files in the specified <var>directory</var>.
</p>
<p>Test blocks in any C++ source files (<samp>*.cc</samp>) will also be executed
for use with dynamically linked oct-file functions.
</p>
<p>If no directory is specified, operate on all directories in Octave&rsquo;s search
path for functions.
</p>
<p><strong>See also:</strong> <a href="#XREFrundemos">rundemos</a>, <a href="Test-Functions.html#XREFtest">test</a>, <a href="Manipulating-the-Load-Path.html#XREFpath">path</a>.
</p></dd></dl>


<a name="XREFspeed"></a><dl>
<dt><a name="index-speed"></a>: <em></em> <strong>speed</strong> <em>(<var>f</var>, <var>init</var>, <var>max_n</var>, <var>f2</var>, <var>tol</var>)</em></dt>
<dt><a name="index-speed-1"></a>: <em>[<var>order</var>, <var>n</var>, <var>T_f</var>, <var>T_f2</var>] =</em> <strong>speed</strong> <em>(&hellip;)</em></dt>
<dd>
<p>Determine the execution time of an expression (<var>f</var>) for various input
values (<var>n</var>).
</p>
<p>The <var>n</var> are log-spaced from 1 to <var>max_n</var>.  For each <var>n</var>, an
initialization expression (<var>init</var>) is computed to create any data needed
for the test.  If a second expression (<var>f2</var>) is given then the
execution times of the two expressions are compared.  When called without
output arguments the results are printed to stdout and displayed
graphically.
</p>
<dl compact="compact">
<dt><code><var>f</var></code></dt>
<dd><p>The code expression to evaluate.
</p>
</dd>
<dt><code><var>max_n</var></code></dt>
<dd><p>The maximum test length to run.  The default value is 100.  Alternatively,
use <code>[min_n, max_n]</code> or specify the <var>n</var> exactly with
<code>[n1, n2, &hellip;, nk]</code>.
</p>
</dd>
<dt><code><var>init</var></code></dt>
<dd><p>Initialization expression for function argument values.  Use <var>k</var> for
the test number and <var>n</var> for the size of the test.  This should compute
values for all variables used by <var>f</var>.  Note that <var>init</var> will be
evaluated first for <em>k = 0</em>, so things which are constant throughout
the test series can be computed once.  The default value is
<code><var>x</var> = randn (<var>n</var>, 1)</code>.
</p>
</dd>
<dt><code><var>f2</var></code></dt>
<dd><p>An alternative expression to evaluate, so that the speed of two
expressions can be directly compared.  The default is <code>[]</code>.
</p>
</dd>
<dt><code><var>tol</var></code></dt>
<dd><p>Tolerance used to compare the results of expression <var>f</var> and expression
<var>f2</var>.  If <var>tol</var> is positive, the tolerance is an absolute one.
If <var>tol</var> is negative, the tolerance is a relative one.  The default is
<code>eps</code>.  If <var>tol</var> is <code>Inf</code>, then no comparison will be made.
</p>
</dd>
<dt><code><var>order</var></code></dt>
<dd><p>The time complexity of the expression <em>O(a*n^p)</em>.  This is a
structure with fields <code>a</code> and <code>p</code>.
</p>
</dd>
<dt><code><var>n</var></code></dt>
<dd><p>The values <var>n</var> for which the expression was calculated <strong>AND</strong>
the execution time was greater than zero.
</p>
</dd>
<dt><code><var>T_f</var></code></dt>
<dd><p>The nonzero execution times recorded for the expression <var>f</var> in seconds.
</p>
</dd>
<dt><code><var>T_f2</var></code></dt>
<dd><p>The nonzero execution times recorded for the expression <var>f2</var> in seconds.
If required, the mean time ratio is simply <code>mean (T_f ./ T_f2)</code>.
</p>
</dd>
</dl>

<p>The slope of the execution time graph shows the approximate power of the
asymptotic running time <em>O(n^p)</em>.  This power is plotted for the
region over which it is approximated (the latter half of the graph).  The
estimated power is not very accurate, but should be sufficient to
determine the general order of an algorithm.  It should indicate if, for
example, the implementation is unexpectedly <em>O(n^2)</em> rather than
<em>O(n)</em> because it extends a vector each time through the loop rather
than pre-allocating storage.  In the current version of Octave, the
following is not the expected <em>O(n)</em>.
</p>
<div class="example">
<pre class="example">speed (&quot;for i = 1:n, y{i} = x(i); endfor&quot;, &quot;&quot;, [1000, 10000])
</pre></div>

<p>But it is if you preallocate the cell array <code>y</code>:
</p>
<div class="example">
<pre class="example">speed (&quot;for i = 1:n, y{i} = x(i); endfor&quot;, ...
       &quot;x = rand (n, 1); y = cell (size (x));&quot;, [1000, 10000])
</pre></div>

<p>An attempt is made to approximate the cost of individual operations, but
it is wildly inaccurate.  You can improve the stability somewhat by doing
more work for each <code>n</code>.  For example:
</p>
<div class="example">
<pre class="example">speed (&quot;airy(x)&quot;, &quot;x = rand (n, 10)&quot;, [10000, 100000])
</pre></div>

<p>When comparing two different expressions (<var>f</var>, <var>f2</var>), the slope of
the line on the speedup ratio graph should be larger than 1 if the new
expression is faster.  Better algorithms have a shallow slope.  Generally,
vectorizing an algorithm will not change the slope of the execution time
graph, but will shift it relative to the original.  For example:
</p>
<div class="example">
<pre class="example">speed (&quot;sum (x)&quot;, &quot;&quot;, [10000, 100000], ...
       &quot;v = 0; for i = 1:length (x), v += x(i); endfor&quot;)
</pre></div>

<p>The following is a more complex example.  If there was an original version
of <code>xcorr</code> using for loops and a second version using an FFT, then
one could compare the run speed for various lags as follows, or for a fixed
lag with varying vector lengths as follows:
</p>
<div class="example">
<pre class="example">speed (&quot;xcorr (x, n)&quot;, &quot;x = rand (128, 1);&quot;, 100,
       &quot;xcorr_orig (x, n)&quot;, -100*eps)
speed (&quot;xcorr (x, 15)&quot;, &quot;x = rand (20+n, 1);&quot;, 100,
       &quot;xcorr_orig (x, n)&quot;, -100*eps)
</pre></div>

<p>Assuming one of the two versions is in xcorr_orig, this would compare their
speed and their output values.  Note that the FFT version is not exact, so
one must specify an acceptable tolerance on the comparison <code>100*eps</code>.
In this case, the comparison should be computed relatively, as
<code>abs ((<var>x</var> - <var>y</var>) ./ <var>y</var>)</code> rather than absolutely as
<code>abs (<var>x</var> - <var>y</var>)</code>.
</p>
<p>Type <kbd>example (&quot;speed&quot;)</kbd> to see some real examples or
<kbd>demo (&quot;speed&quot;)</kbd> to run them.
</p></dd></dl>




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Previous: <a href="Test-Functions.html#Test-Functions" accesskey="p" rel="prev">Test Functions</a>, Up: <a href="Test-and-Demo-Functions.html#Test-and-Demo-Functions" accesskey="u" rel="up">Test and Demo Functions</a> &nbsp; [<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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